uk: Математика, природничі науки

description: The atmosphere and ocean of the North Atlantic have undergone significant changes in the past century. To understand these changes, their mechanisms, and their regional implications requires a quantitative understanding of processes in the coupled ocean and atmosphere system. Central to this understanding is the role played by the dominant patterns of ocean and atmospheric variability which define coherent variations in physical characteristics over large areas. Four dominant subseasonal weather regimes are defined using Bayesian Gaussian mixture models. All correlation patterns of the Sea Level Pressure (SLP) anomalies with the membership probability timeseries for the weather regimes show similarities with the dipole structure typical for the North Atlantic Oscillation (NAO). The SLP patterns of two of the regimes represent the opposite phases NAO+ and NAO-. The two other weather regimes, the Atlantic Ridge (AR) and Scandinavian-Greenland dipole (SG), have dipole spatial structures with the northern and southern centres of action shifted with respect to the NAO pattern. These two patterns define blocking structures over Scandinavia and near the southern tip of Greenland, respectively. The storm tracks typical for the four regimes resemble the well known paths for positive/negative phases of NAO for the NAO+/NAO- weather regimes, and paths influenced by blocking off the south Greenland tip for AR and over Scandinavia for SG. The correlation patterns of momentum and heat fluxes to the ocean for the four regimes have tripole structures with positive (warm) downward heat flux anomalies over the Subpolar North Atlantic (SPNA) for the NAO- and the AR and negative heat flux anomalies over the SPNA for the NAO+. The downward heat flux anomalies associated with the SG are negative over the Labrador Sea and positive over the eastern SPNA. The long-term impact of the weather regimes on the regional climate is characterized by their distribution; i.e. the frequency of occurrence and persistence in time of each of them. Four typical distributions of the weather regimes are identified in this study which are associated with four dominant spatial interannual patterns representing the phases of two asymmetrical ``modes''. The first two patterns have the spatial structures of positive and negative phases of the North Atlantic Oscillation (NAO). The third and fourth patterns, here referred to as G+ and G-, define the opposite phases of a mode, that has a spatial structure defined by three centers found over Florida, south of Greenland and over Scandinavia. The NAO+ interannual patterns are associated with negative anomalies of the surface downward heat flux and ocean heat content over the SPNA. The NAO- and G+ are associated with positive anomalies of heat flux and ocean heat content. In the 1960s the dominant NAO- and G+ interannual patterns favored warmer than normal atmospheric and ocean temperatures over the SPNA. The winters in the late 1980s and early 1990s over the SPNA were colder than normal. This decadal shift in the atmospheric state between the 1970s and 1980s was associated with a change in the dominant interannual patterns towards NAO+~and~G- in the late 1980s and early 1990s. The recent warming of the SPNA since the mid-1990s was related to the dominance of the G+/G- interannual patterns in the distribution of interannual patterns probability membership. Our analysis suggests that this decadal variability was associated with a long-term shifts in atmospheric behavior over the SPNA that can be described by a change in the 1980s of the distribution of membership probabilities for interannual patterns. In the phase space of the interannual patterns, this transition is characterized with a shift from the NAO-/G+/G- subspace subspace in the 1950 and 1960s, towards NAO+/G+/G- since the mid 1980s.. Based on this analysis we developed a a computationally efficient stochastic weather generator for analysis and prediction of the Subpolar North Atlantic amospheric decadal variability. The method is tested by the stochastic simulation of sea level pressure over the sub-polar North Atlantic. The weather generator includes a hidden Markov model, which propagates regional circulation patterns identified by a self organising map analysis, conditioned on the state of large-scale interannual patterns. The remaining residual effects are propagated by a regression model with added noise components. The regression step is performed by one of two methods, a linear model or artificial neural networks and the performance of these two methods is assessed and compared.

uk: вхід без авторизації

name: North Atlantic atmospheric and ocean variability over the past fifty years: dominant patterns and abrupt climate shifts


Shaoqing Zhang

type: Person

cs: Matematika

de: Mathematik

fi: matematiikka

uk: Математика

en: Mathematics

fr: Mathématiques

da: Matematik

es: Matemáticas

nl: Wiskunde

de: Mathematik, Naturwissenschaften

uk: Математика, природничі науки

en: Mathematics, Natural Sciences

TIB AV-Portal

type: Service

type: WebContent

type: MediaObject

@language: en

cs: přihlášení není vyžadováno

de: keine Anmeldung erforderlich

uk: вхід без авторизації

en: no login required

nl: geen login vereist

name: A high efficiency approximation of EnKF for coupled model data assimilation

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

type: Organization

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


uk: Математика, природничі науки

description: We introduce a conditional Gaussian framework for data assimilation and prediction of nonlinear turbulent dynamical systems. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows a practical information barrier that requires an exponential increase of the number of tracers. A suite of reduced filters are designed and compared in filtering different dynamical features, where an information-theoretic framework is adopted to assess the model error. In the last part of the talk, a brief discussion of applying conditional Gaussian filters to solve high-dimensional Fokker-Planck equation will be included. This method is able to beat the curse of dimensions in traditional particle methods. It has a potential in understanding parameterization and causality in turbulent flows.

uk: вхід без авторизації

name: A conditional Gaussian framework for data assimilation and prediction of nonlinear turbulent dynamical systems


uk: Математика, природничі науки

description: In weather and climate prediction, data assimilation combines data with dynamical models to make prediction, using ensemble of solutions to represent the uncertainty. Due to limited computational resources, reduced models are needed and coarse-grid models are often used, and the effects of the subgrid scales are left to be taken into account. A major challenge is to account for the memory effects due to coarse graining while capturing the key statistical-dynamical properties. We propose a stochastic parametrization method which accounts for the memory effects by nonlinear autoregression moving average (NARMA) type models, and demonstrate by examples that the resulting NARMA type stochastic reduced models can capture the key statistical and dynamical properties and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the Kuramoto-Sivashinsky equation of spatiotemporally chaotic dynamics.

uk: вхід без авторизації

name: Data assimilation with stochastic model reduction


uk: Математика, природничі науки

description: In this talk, we will present some progresses in improving seasonal climate predictions by using more advanced mathematical methods. The first example is to rely on the basic properties of stochastic theory to develop an efficient technique for the extraction of climatically relevant singular vectors (CSV) in the presence of weather noise. Emphasis is placed on the applications of the CSV in seasonal climate predictions and to construct optimal ensemble climate predictions. The results indicates that the CSVs can well characterize the optimal error growth of the climate predictions and lead to better ensemble predictions than traditional time lag (TLE) method. The second example is about our recent progress in the state estimate of state-space models with applications of Bayesian-based algorithms. A simplified algorithm of Sigma-point Kalman filter is develop to deal with the state estimation of high-dimensional systems like atmospheric and oceanic general circulation models.

uk: вхід без авторизації

name: Progress towards improving seasonal climate prediction by mathematical methods


uk: Математика, природничі науки

description: Designing an efficient seasonal forecasting system is ensuring that the uncertainty in the initial conditions is sampled optimally. Perturbation in the initial condition and the methodology used for sampling perturbation optimally plays a key role in the improvement of the current seasonal climate forecast. In this study the error growth properties of initial perturbation are investigated using climatically relevant singular vectors (CSVs). The Community Climate System Model version 4 (CCSM4) is used as a simulation tool to examine the growth of optimal perturbations with different lead times over the South Asian Monsoon region. It is found that reliable set of CSVs can be estimated by running an ensemble of model forecasts. Amplification of the optimal perturbations occurs for more than 1 month and possibly up to 6 months. The results show the growth rates of the singular vectors are very sensitive to the variable of perturbation, number of perturbations and the error norm. When the SV is used as an initial perturbation, the forecast skill of key atmospheric variables over South Asian Monsoon region is significantly improved. Further, it is demonstrated that the predictions with the singular vector have a more reliable ensemble spread, suggesting a potential merit for a probabilistic forecast. The promising results reported here should hopefully encourage further investigation of the methodology at different timescales.

uk: вхід без авторизації

name: Optimum initialization of South Asian seasonal forecast using climatological relevant singular vectors


uk: Математика, природничі науки

description: In this joint work with Ming-Cheng Shiue, a semi-discretized Euler scheme to solve three dimensional primitive equations is studied. With suitable assumptions on the initial data, the long time stability of the proposed scheme is shown by proving that the H1 norm (in space variables) is bounded.

uk: вхід без авторизації

name: On the long time stability of a temporal discretization scheme for the three dimensional primitive equations


uk: Математика, природничі науки

uk: вхід без авторизації

name: Target observations for improving initializations for two types of El Nino events predictions


uk: Математика, природничі науки

description: How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño–Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism. Moreover, reasonable considerations of the model-error perturbations during the ensemble forecast process can alleviate the barrier caused by initial uncertainties through coordinately simulating the seasonal variations of the forecast uncertainty in order to significantly improve the probabilistic prediction skills and then to disorder the seasonal predictability related to the spring prediction barrier.

uk: вхід без авторизації

name: Effects of stochastic model error on improving ENSO prediction skills


uk: Математика, природничі науки

description: Stochastic schemes to represent model uncertainty in the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system has helped improve its probabilistic forecast skill over the past decade by both improving its reliability and reducing the ensemble mean error. The largest uncertainties in the model arise from the model physics parameterizations. In the tropics, the parameterization of moist convection presents a major challenge for the accurate prediction of weather and climate. Super-parameterisation is a promising recent alternative strategy for including the effects of moist convection through explicit turbulent fluxes calculated from a cloud-resolving model (CRM) embedded within a global climate model (GCM). These two approaches (stochastic and super-parameterization) in convection parameterization have emerged as new paths forward and complement the conventional approaches rather than replace them. We study the impact of these two approaches and a combination of the two on forecasts from weather to sub-seasonal and climate timescales. Results from the evaluation of model forecast skill and fidelity in the Tropics and for organized convective systems such as the MJO will be presented. We show that the combination of the two approaches helps improve the reliability of forecasts of certain tropical phenomena, especially in regions that are affected by deep convective systems. This has implications for improving conventional convection parameterization using hybrid approaches for probabilistic earth system forecasting as we await the exascale computing systems of the future to resolve convective processes in climate models.

uk: вхід без авторизації

name: Exploring stochastic and multi-scale modeling approaches for a seamless prediction system


uk: Математика, природничі науки

description: Nonlinear local Lyapunov vectors (NLLVs), theoretically inherited from the linear Lyapunov vectors (LVs) in a nonlinear framework, are developed to indicate orthogonal directions in phase space with different perturbation growth rates. Practically NLLVs generates flow dependent perturbations with full nonlinear models as in the breeding method, but regularly conducts the Gram–Schmidt reorthonormalization processes on the perturbations. The advantages of the sampling of the unstable subspace with the mutually orthogonal NLLVs instead of the most unstable direction with the dependent bred vectors (BVs) are clarified by using their respective unstable mode to predict the structure of forecast error growth. Additionally, the NLLVs have overall higher but correlated local dimensions compared to the BVs which may be beneficial for the former to increase the ensemble spread and capture the instabilities as well. The NLLV method is used to generate initial perturbations and implement ensemble forecasts in nonlinear models (the Lorenz63 model, Lorenz96 model, a barotropic quasi-geostrophic model and the Zebiak-Cane model) to explore the validity of the NLLV method. The performance of the NLLV method is compared comprehensively and systematically with other methods such as the ensemble transform Kalman filter (ETKF) method, the BV and the random perturbation (Monte Carlo) methods. Overall, the ensemble spread of NLLVs is more consistent with the errors of the ensemble mean, which indicates the better performance of NLLVs in simulating the evolution of analysis errors. In addition, the NLLVs perform significantly better than the BVs in terms of reliability and the random perturbations in resolution. The NLLV scheme has slightly higher ensemble forecast skill than the ETKF scheme. The NLLV scheme has significantly simpler algorithm and less computation time than the ETKF.

uk: вхід без авторизації

name: Nonlinear local lyapunov vectors and their applications to ensemble predictions


keywords:
Mathematics
Mechanics of deformable solids
Partial differential equations
Material science

uk: Математика, природничі науки

uk: вхід без авторизації

name: Chemical patterning and actuation of nematic elastomers


uk: Математика, природничі науки

uk: вхід без авторизації

name: Statics and Hydrodynamics of Biaxial Nematics


uk: Математика, природничі науки

uk: вхід без авторизації

name: Onsager-theory-based tensor model for nematic phases of bent-core molecules


uk: Математика, природничі науки

uk: вхід без авторизації

name: Numerical simulation for wormlike chains in two-dimensional confinement


uk: Математика, природничі науки

uk: вхід без авторизації

name: The Well Order Reconstruction Solution for nematic liquid crystals in square


uk: Математика, природничі науки

uk: вхід без авторизації

name: Multiscale modelling of mesoscopic polymer dynamics


uk: Математика, природничі науки

uk: вхід без авторизації

name: Multistability for Liquid Crystal Systems


uk: Математика, природничі науки

uk: вхід без авторизації

name: Global well-posedness for dynamical models of nematic liquid crystals

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: An exterior problem in the Oseen-Frank theory


uk: Математика, природничі науки

uk: вхід без авторизації

name: Calderón-Zygmund theory for nonlinear partial differential equations


uk: Математика, природничі науки

uk: вхід без авторизації

name: Some Study on the Molecular and Multiscale Modelling of Liquid Crystals


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bayesian inference about smooth functions on grahps


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bayesian nonparametric models for networks


uk: Математика, природничі науки

uk: вхід без авторизації

name: Mixture modeling with psi-sticking breaking and kernel perturbation


Symmetry and Convergence

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Asymptotic for the number of groups in a sample from the geometric stick-breaking process


uk: Математика, природничі науки

uk: вхід без авторизації

name: α-Variational Bayes and its statistical properties


uk: Математика, природничі науки

uk: вхід без авторизації

name: Automated, Scalable Bayesian Inference with Theoretical Guarantees


uk: Математика, природничі науки

uk: вхід без авторизації

name: On the frequentist validity of Bayesian limits


uk: Математика, природничі науки

uk: вхід без авторизації

name: Dependent nonparametric modelling through compound random measures


Joint Estimation of Quantile Planes

uk: Математика, природничі науки

uk: вхід без авторизації


Some Polya trees properties

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bayesian subspace approximation via mixtures of spherelets


uk: Математика, природничі науки

uk: вхід без авторизації

name: On vectors of random probability measures


uk: Математика, природничі науки

uk: вхід без авторизації

name: Exact Sampling and Unbiased Estimation in the Hierarchical Pitman-Yor Process


uk: Математика, природничі науки

uk: вхід без авторизації

name: Sensitivity of Portfolio Allocation Strategies: A Bayesian ES Perspective in Reinsurance


uk: Математика, природничі науки

uk: вхід без авторизації

name: Dependent processes with local drift for functional forecasting in virtual gas markets


uk: Математика, природничі науки

description: Non-Gaussian spatial data arise in a number of disciplines. Examples include spatial data on disease incidences (counts), and satellite images of ice sheets (presence-absence). Spatial generalized linear mixed models (SGLMMs), which build on latent Gaussian processes or Gaussian Markov random fields, are convenient and flexible models for such data and are used widely in mainstream statistics and other disciplines. For high-dimensional data, SGLMMs present significant computational challenges due to the large number of dependent spatial random effects. Furthermore, spatial confounding makes the regression coefficients challenging to interpret. I will discuss projection-based approaches that reparameterize and reduce the number of random effects in SGLMMs, thereby improving the efficiency of Markov chain Monte Carlo (MCMC) algorithms for inference. Our approach also addresses spatial confounding issues. This talk is based on joint work with Yawen Guan (SAMSI) and John Hughes (U of Colorado-Denver).

uk: вхід без авторизації

name: A Projection-based Approach for Spatial Generalized Linear Mixed Models

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: In order to adapt to a changing climate, policymakers need information about what to expect for the climate system. Typically local information about certain aspects of the climate system comes from regional climate models as well as from observational records. A regional climate model is a downscaled global circulation model, a mathematical model that describes, using partial differential equations, the temporal evolution of climate, oceans, atmosphere, ice, and land-use processes over a gridded spatial domain of interest. An important problem is understand how well regional models can reproduce observed climate variables. Using two motivating analyses based on data from the Swedish Meteorological and Hydrological Institute, I will discuss different spatio-temporal modeling strategies that can be used to assess regional climate models using observational data. I will also outline the associated statistical and computational challenges in building hierarchical models using data sources with varying spatial and temporal support. My intention is to motivate a dialogue about the broader challenges underlying spatio-temporal climate model assessment. This talk is based on joint research with Peter Guttorp and Veronica Berrocal.

uk: вхід без авторизації

name: Regional climate model assessment via spatio-temporal modeling


uk: Математика, природничі науки

description: Many people living in low- and middle-income countries are not covered by civil registration and vital statistics systems. Consequently, household sample surveys with complex designs are often used to estimate health and population indicators. In this talk I will describe both discrete and continuous spatial models with time modeled discretely. Topics that will be touched upon include: how to account for the sampling design; the simultaneous use of both point- and area-level data; how to make adjustments for HIV epidemics; the inclusion of so-called indirect data; and covariate modeling. The modeling of under-5 mortality in Kenya is used to motivate and illustrate the issues raised. Data come from a variety of sources including Demographic and Health Surveys conducted over the period 1991–2010.

uk: вхід без авторизації

name: Space-Time Modeling of Complex Survey Data in a Developing World Setting


uk: Математика, природничі науки

description: The EUSTACE project will give publicly available daily estimates of surface air temperature since 1850 across the globe for the first time by combining surface and satellite data using novel statistical techniques." To fulfil this ambitious mission, a spatio-temporal multiscale statistical Gaussian random field model is constructed, with a hierarchy of spatio-temporal dependence structures, ranging from weather on a daily timescale to climate on a multidecadal timescale. Data from weather stations, ships, and satellites are combined in a hierarchical structure with individual measurement error models, and transformations of the latent random fields to allow joint estimation of current and past temperature fields across the globe. Connections between SPDEs and Markov random fields are used to obtain sparse matrices for the practical computation of point estimates, uncertainty estimates, and posterior samples. The extreme size of the problem necessitates the use of iterative solvers, which requires using the multiscale structure of the model to design an effective preconditioner, leveraging domain specific knowledge, traditional statistical techniques, and modern numerical methods.

uk: вхід без авторизації

name: A case study in hierarchical space-time modelling


keywords:
Mathematics
Statistics
Applied statistics

uk: Математика, природничі науки

uk: вхід без авторизації

name: Quipus and Questions: Tying it all together


uk: Математика, природничі науки

description: 1. Air Pollution, Spatial statistics, and Mortality in India: Where we area and where to next, 2. Model Checking in Regression Analyses with Spatio-Temporal Observations (48:46 min without the end)

uk: вхід без авторизації

name: Air Pollution, Spatial statistics, and Mortality in India: Where we area and where to next, Model Checking in Regression Analyses with Spatio-Temporal Observations


uk: Математика, природничі науки

uk: вхід без авторизації

name: ...you might like to give a talk about how priors are seful for modelling spatial data but we certainly would not hold you to that


uk: Математика, природничі науки

uk: вхід без авторизації

name: Functional peaks-over-threshold analysis with an application to extreme European winter storms


uk: Математика, природничі науки

uk: вхід без авторизації

name: Analysis of multi-species point patterns using multivariate log Gaussian Cox processes


On Fire Challenges

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

description: This was the year that we celebrated the centennial of the seminal work by D'Arcy Thompson, “On Growth and Form”. D'Arcy Thompson and his work has often been criticised for ignoring genetics, or at least considering genetics hardly more than a distraction. Here I will argue that what he instead wanted to offer us are different perspectives on the development of plants and animals. It is through broadening our perspectives that D'Arcy Thompson is able to keep inspiring us in our current work, 100 years after his book, and its illustrations, started to influence scientists and artists alike.

uk: вхід без авторизації

name: Some perspectives on growth and form: The continuing inspiration of D'Arcy Thompson


uk: Математика, природничі науки

description:
The reaction-diffusion model presented by Alan Turing has recently been supported by experimental data and accepted by most biologists. However, scientists have recognized shortcomings when the model is used as the working hypothesis in biological experiments, particularly in studies in which the underlying molecular network is not fully understood. Temporal models mainly utilize the diffusion of the ligand molecules as the basis of nonlocal interaction. However, recent studies have shown that the nonlocal signals are often transfered by other cellular behavior. Therefore, the mathemtaical model need to be flexible. To address some such problems, I would like to proposes a new simpler version of the Turing model.

 This simpler model is not represented by partial differential equations, but rather by the shape of an activation-inhibition kernel. Therefore, it is named the kernel-based Turing model (KT model). Simulation of the KT model with kernels of various shapes showed that it can generate all standard variations of the stable 2D patterns (spot, stripes and network), as well as some complex patterns that are difficult to generate with conventional mathematical models. The KT model can be used even when the detailed mechanism is poorly known, as the interaction kernel can often be detected by a simple experiment and the KT model simulation can be performed based on that experimental data. These properties of the KT model complement the shortcomings of conventional models and will contribute to the understanding of biological pattern formation.

uk: вхід без авторизації

name: A simpler version of Turing model for experimental biology


uk: Математика, природничі науки

description: The mechanisms by which domains of gene activity lead to the generation of tissues with intricate three dimensional shapes are poorly understood. We have been using a combination of genetic, morphological, computational and imaging approaches to address this problem in plants. Our findings suggest that spatiotemporal patterns of gene activity control shape by introducing conflicts at the subcellular, cellular and tissue levels. Resolution and interactions between these different levels of conflicts may underlie the enormous diversity of forms that have evolved in plants and animals.

uk: вхід без авторизації

name: Resolving conflicts: The genetic control of plant morphogenesis, Modelling growth and form of the sea anemone Nematostella vectensis (7 min)


uk: Математика, природничі науки

description: A growing leaf is a thin sheet of active solid, which expands while obeying the laws of mechanics. The effective rheology of this active solid is nontrivial, allowing the leaf to increase its area by orders of magnitude, keeping its "proper" geometry. The questions of what the characteristics of the leaf growth field are and how it is regulated without any central "headquarter" are still open. I will present measurements of natural leaf growth with high time and space resolution. These show that the growth is a highly fluctuating process in both time and space. We suggest that the entire statistics of the growth field, not just its averages contain information important for the understanding of growth regulation. In another set of experiments we measure the effect of mechanical stress on deformation and growth. The measured effective rheology is viscoelastic with time varying parameters, indicating remodeling of the tissue in response to extended application of mechanical stress.

uk: вхід без авторизації

name: A growing leaf as a sheet of active solid


Shapes and growth motions of leaves

uk: Математика, природничі науки

description: Leaf shapes are very variable but restricted to some stereotyped families. Among one family of lobed leaves, this shape can be related to its folded growth within the bud. In general, this open the question of how much the final shape can be constrained by steric constrains during its development. Similarly, since most of the leaves do not first expand flat and straight, but commonly folded or rolled in different ways, there needs to be some regulations to reach the usually rather flat and straight state. This growth, from the primordial to the final leaf, presents several striking motions. On some examples we propose that these motions precisely help the regulation.

uk: вхід без авторизації


uk: Математика, природничі науки

description:
Leaves of eudicots show tremendous morphological diversity. Remarkably different leaf morphologies may occur between closely-related species, as within-species variants, or even in the same plant. Diverse leaf shapes also emerge in molecular-level studies of reference plants including Arabidopsis thaliana, Cardamine hirsuta and tomato, where small genetic or hormonal changes yield significantly different forms. This lability of shapes, juxtaposed with similar molecular mechanisms underlying leaf development in reference plants, suggests that the striking diversity of eudicot leaves results from variations of a common generative program. Notably, this mechanism acts jointly on leaf shape and vasculature, patterning both marginal protrusions and corresponding veins in the blade.

 Inspired by this perspective, we propose a geometric model of leaf development and diversity. It simulates development as a feedback between two processes: the dynamic patterning of growth centers at the leaf margin, and control of growth directions by veins associated with these points. Our models show that the spatial separation of the processes patterning and directing growth facilitates the generation of a wide range of leaf forms, from simple to lobed and compound. Additionally, transitions between different forms can be controlled in a continuous manner. These transitions reproduce frequently observed, and often drastic, changes in leaf form within the same plant or between closely related species. Our results highlight the flexible and self-organizing nature of leaf development, and provide a path towards an integrated understanding of their development and diversity.

uk: вхід без авторизації

name: Towards an integrated understanding of leaf form development and diversity


50 years of L-systems

uk: Математика, природничі науки

description: L-systems were introduced in 1968 as a formalism for reasoning about plant development. Soon afterwards, they became a tool for computational modeling of plants at the architectural level. In my talk, I will review the key conceptual contributions of the original formalism, the objectives of subsequent extensions, the resulting range of applications, and the current research problems spawned by L-systems.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Despite the significance of cellular morphology as a functional phenotype, it remains challenging to quantitatively relate morphological phenotype to the behavior of subcellular molecules. Molecular studies have identified many components controlling cell morphogenesis, but it is unclear how this information is translated into the physical world. In plant cells, growth requires synthesis of cytoplasmic components as well as expansion of the cell wall. The cell wall is a stiff yet flexible polymeric network that encapsulates cells and counterbalances stress created by turgor pressure inside the cell, thereby controlling cell shape. It is now well established that the cytoskeleton plays a key role in the biogenesis and morphogenesis of the cell wall. While the microtubules guide cellulose synthase complex movement (Paredez et al. 2006), the actin network is responsible for global distribution of cellulose synthase complexes (Gutierrez et al. 2009; Sampathkumar et al. 2013). It is also suggested that mechanical stresses orient the microtubules along their principal direction (Hamant et al. 2008; Sampathkumar, Krupinski, et al. 2014; Sampathkumar, Yan, et al. 2014). Nevertheless, to fully understand how plant cells are shaped and how external mechanical stresses influence this process, a quantitative approach to evaluate the mechano-response in single cells needs to be established. Here we present a technique (Chang et al. 2014) to confine single plant protoplasts into molds of defined shapes. The principle is to confine a plant protoplast expressing fluorescent cytoskeletal reporters into micro-wells of different shapes with sizes of 10 to 30 μm. The protoplasts are then monitored with a confocal microscope to evaluate changes in cytoskeletal organization and dynamics during the process of symmetry breaking. These experiments are the basis of assessing quantitatively how different shapes control cytoskeleton organization behavior by regulating the distribution of physical stresses.

uk: вхід без авторизації

name: Quantitative evaluation of feedback mechanisms between cell shape and cytoskeleton organization


keywords:
Mathematics
Biology and other natural sciences
Mathematical biology

uk: Математика, природничі науки

description: Stem cells in the plant shoot are maintained via a gene regulatory feedback network, and perturbations to these genes lead to changes in the size and shape of the stem cell niche. Growth itself is highly dependent on cell wall properties where heterogeneous and anisotropic mechanical properties need to be regulated to generate correct size and shape of the tissue. We use a Computational Morphodynamics approach, combining live imaging and mathematical models of cell wall mechanics and gene networks, to understand how growth and differentiation is coordinated in the plant shoot. I will discuss how mechanical patterning can overlap with gene expression patterns, and how cell size and tissue size are regulated and influence the maintenance of the stem cell niche.

uk: вхід без авторизації

name: Growth, form and organization of plant meristems - a computational morphodynamics approach


Why plants make puzzle-shaped cells

uk: Математика, природничі науки

description: The shape and function of plant cells are thought to be closely related. The puzzle-shaped epidermal cells that appear in the epidermis of many plants are a striking example of a complex cell shape, however their functional benefit has remained elusive. We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall. When tissue-level growth is isotropic, we hypothesize that lobes emerge at the cellular level to prevent formation of large isodiametric cells that would bulge under the stress produced by turgor pressure. Data from various plant organs and species support the relationship between lobes and growth isotropy, which we test directly with mutants where growth direction is perturbed. Using simulation models we show that a mechanism actively regulating cellular stress plausibly reproduces the development of epidermal cell shape. Together, our results suggest that mechanical stress is a key driver of cell-shape morphogenesis.

uk: вхід без авторизації


uk: Математика, природничі науки

description: How do organs and organisms grow to elongated forms? I will show how the coupling between biochemical polarity and tissue mechanics enables elongated growth forms, by considering three model systems: fission yeast, fruit fly, and Arabidopsis.

uk: вхід без авторизації

name: Symmetry breaking and axis maintenance in morphogenesis


uk: Математика, природничі науки

description: We are interested in how cell size and organ size are developmentally determined in Arabidopsis flowers, particularly the sepals. I will discuss two collaborative projects in which modeling both helped us direct our experiments and interpret our experimental results. In examining the robust control of organ size, there was a eureka moment when we realized that our initially separate modeling and biological projects were converging on the same idea: variable cellular growth undergoes spatiotemporal averaging to create reproducibly sized and shaped organs. In this case, the modeling directed us to analyze the cellular variability and explained why reducing cellular variability increased organ shape variability. Second, in examining cell size control, model development coincided with biological experiments and the two informed each other to reveal that fluctuations of a transcription factor determine whether a cell becomes a giant or a small cell.

uk: вхід без авторизації

name: The interface between modeling and plant development experiments from a biologist’s perspective

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: The modeling and simulation of morphogenetic phenomena require to take into account the coupling between the processes that take place in a space and the modification of that space due to those processes, leading to a chicken-and-egg problem. To address this issue, we proposed to consider a growing structure as the byproduct of a multitude of interactions between its constitutive elements. An interaction-based model of computation relying on spatial relationships has then been developed leading to an original style of programming implemented in the MGS programming language. Contributions of MGS include a generic programming mechanism that captures most of the unconventional computing models by simply varying the underlying structure of interactions. I will introduce the interaction-based way of programming and review some current works taking roots in the fertile ground of MGS.

uk: вхід без авторизації

name: Interaction-based programming: A review of MGS


uk: Математика, природничі науки

description: A wide variety of modeling problems can be approached by dividing the problem into a spatial arrangement of discrete components which communicate with one another. Modeling multicellular development fits this framework well; a tissue is composed of discrete cells which communicate by methods such as hormonal signaling or mechanosensing. One of the chief challenges in modeling development is that the number and arrangement of components changes, as cells grow and divide. By choosing the right underlying structural representation, however, the task of the modeler can be made easier. Representing a growing tissue with the mathematical formalism of the cell complex lets the modeler consider interactions locally and assign properties to entities of the right dimension. I describe a framework for developmental plant modeling based on cell complexes, and demonstrate models of development in one, two, and three dimensions.

uk: вхід без авторизації

name: Modelling development with cell complexes in one, two, and three dimensions


uk: Математика, природничі науки

description:
During embryonic development, the behavior of individual cells must be coordinated to create the large scale patterns and tissue movements that shape the whole embryo. Apart from chemical signaling, it has recently become clear that mechanical cell-cell communication is equally important in the coordination of such collective cell behavior. To get a better understanding of mechanical cell-cell communication, we are developing computational models of cells and the extracellular matrix (ECM) - the hard or jelly materials (e.g. collagens, fibronectin) that form the micro-environment of many cells. The models are detailed enough for explaining the response of individual cells to the mechanical properties of the ECM, and sufficiently coarse-grained so as to allow for efficient computational upscaling to the tissue level and beyond. Our model is based on a novel, hybrid Cellular Potts and finite element computational framework. It describes the contractile forces that cells exert on the ECM, the resulting strain fields in the ECM, and the cellular response to local strains. The model simulations reproduce the behavior of individual endothelial cells on compliant matrices, and show that local cell-ECM interactions suffice for explaining interactions of endothelial cell pairs and collective cell behavior, including the formation of cellular networks and sprouting from spheroids [1]. If an external strain is exerted on the ECM, the cells rapidly align with the strain fields, even in response to very subtle strain cues [2]. These initial models relied on phenomenological descriptions of the interactions between cellular protrusions and the ECM. Recently, detailed measurements and new mathematical models of the kinetics of individual focal adhesions (the macromolecular assemblies responsible for mechanical cell-ECM interactions) have become available. In our ongoing work we have include kinetic descriptions of focal adhesions in our models. We will sketch how this approach will allow us to mechanistically predict changes in cell shape and in collective cell behavior from changes in focal adhesion kinetics. Altogether, our models suggest simple mechanisms by which local, mechanical cell-ECM interactions can assist in integrating morphological information in embryos across organizational levels.
 [1] R. F. M. van Oers, E. G. Rens, D. J. LaValley, C. A. Reinhart-King, and R. M. H. Merks, “Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro,” PLoS Comput. Biol., vol. 10, no. 8, p. e1003774, Aug. 2014.
 [2] E. G. Rens and R. M. H. Merks, “Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch,” Biophysical Journal, vol. 112, no. 4, pp. 755–766, Feb. 2017.

uk: вхід без авторизації

name: Cell-based modeling of mechanical cell-matrix interactions during embryonic development


Inference of Lindenmayer Systems

uk: Математика, природничі науки

description: Lindenmayer systems (L systems) provide a concise mathematical formulation for creating simulations of plants that are descriptively accurate, while also taking into account various molecular-level controls. At present, most plant models are created manually by experts from measured data and scientific knowledge. However, manual creation does not scale to the creation of thousands of models needed to correspond to plants developed by plant breeders. In this talk, we discuss existing and new approaches to the automatic inference of Lindenmayer systems from data, with a focus on inductive inference. This includes exact approaches, approaches using evolutionary algorithms, and other heuristics.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In developmental biology we find modeling problems that stretch the boundaries of traditional computational science: complex local information-processing, regulation of dynamically changing neighborhood relations, reticulated geometric structures of multiple dimensionalities, highly heterogeneous laws of motion, and a rich multiscale structure. It may be advantageous to enlist automation in the form of mathematical AI (artificial intelligence, both symbolic and machine learning) to help manage this essential model complexity. Machine learning (ML) naturally applies to the problem of finding scale changes in mathematical models, as we will show. But a new kind of mathematical AI/ML may be required overall, in order to create such an “intelligent” architecture for multiscale scientific modeling. To that end I suggest desiderata, consider useful new and existing mathematical ingredients, and propose an overall structure for such an architecture.

uk: вхід без авторизації

name: Towards a mathematical architecture for more flexible scientific modeling


uk: Математика, природничі науки

description: Within the narrowly defined context of a strictly continuum-mechanical formulation, a body is a differentiable manifold and its material properties are described by one or more functions of its deformations. It is shown that the corresponding differential-geometric object is given precisely by a groupoid, whose variation in time characterizes the various phenomena of material evolution. In this context, one can identify and distinguish between pure remodeling and other evolutive phenomena, which can be further classified according to whether or not material symmetries are preserved.

uk: вхід без авторизації

name: Growth, remodeling, aging and morphogenesis within the continuum mechanics context


uk: Математика, природничі науки

description: We discuss a general method for discretizing and simulating numerically thin structures based on the ideas of discrete differential geometry and on variational formulations. The method is successively first applied to elastic rods and viscous jets, and then to active viscous axisymmetric membranes, a model relevant to cytokinesis. We shortly discuss how contact and an enclosed incompressible fluids can be taken into account.

uk: вхід без авторизації

name: Numerical models for thin biological structures: From thin viscous threads to visco-active shells


uk: Математика, природничі науки

description: Simulating the mechanics of biological tissues entails a number of challenging requirements, including non-linear, anisotropic and nearly-incompressible materials, organic shapes with flat and thin structures, and large changes in shape such as bending twisting, bulging and stretching. To address these challenges, we are developing an open source dynamics simulator, ArtiSynth, that combines rigid body models with large-deformation finite-element models together with contact and constraints. In this talk, I will describe ArtiSynth’s mathematical framework within the context of the biological problem of simulating the muscle tissue structures found in tongues, tentacles and trunks.

uk: вхід без авторизації

name: Non-linear finite-element analysis of biological tissue deformation


uk: Математика, природничі науки

description: Cotyledons (embryonic leaves) in conifer trees form in a single ring, or whorl. The number of cotyledons is quite variable, commonly from 3 to 10, unlike flowering plants, which are classified as to whether they have one or two cotyledons. Our data indicate that cotyledon positioning has a radial component, for the ring position, and a circumferential component, for the between-cotyledon positioning within the ring, and that these have different dependences on polar transport of the growth regulator auxin. We present a two-stage reaction-diffusion mechanism as a framework for understanding these observations and early cotyledon morphogenesis.

uk: вхід без авторизації

name: Two-stage patterning dynamics in conifer cotyledon whorl morphogenesis


uk: Математика, природничі науки

description: The first phyllotaxis pattern formation model was proposed in 1868 by Schwendener, and consists of stacking one disk at a time on the surface of a cylinder. As simple as it is, this model exhibits plenty of geometric and dynamical richness, which are best revealed by systematic computer simulations. It helps explain the predominance of Fibonacci phyllotaxis, where the number of helixes (parastichies) in the two transverse families are successive Fibonacci numbers. It also helped us the mechanisms of formation of a type of pattern never mentioned in the literature, that we called Quasi Symmetric. In these patterns, often characterized by rapid parameter changes, the two parastichies numbers tend to be close to one another. Now go and count parastichies on a strawberry….

uk: вхід без авторизації

name: Fibonacci and quasi-symmetric phyllotaxis


uk: Математика, природничі науки

description: We have developed several models of branching morphogenesis in the lung, considering a variety of factors, including transport and mechanics. How reasonable a model appears initially is not necessarily correlated with its explanatory power. In this talk, we will present a variety of models of branching morphogenesis, and compare their implications.

uk: вхід без авторизації

name: Surprises from modeling lung development


uk: Математика, природничі науки

description: Tree-forms are ubiquitous in nature and recent observation technologies make it increasingly easy to capture their details, as well as the dynamics of their development, in 3 dimensions with unprecedented accuracy. These massive and complex structural data raise new conceptual and computational issues related to their analysis and to the quantification of their variability. Mathematical and computational techniques that usually successfully apply to traditional scalar or vectorial datasets fail to apply to such structural objects: How to define the average form of a set of tree-forms? How to compare and classify tree-forms? Can we solve efficiently optimization problems in tree-form spaces? How to approximate tree-forms? Can their intrinsic exponential computational curse be circumvented? In this talk, I will present a recent work that I have made with my colleague Romain Azais to approach these questions from a new perspective, in which tree-forms show properties similar to that of numbers or real functions: they can be decomposed, approximated, averaged, and transformed in dual spaces where specific computations can be carried out more efficiently. I will discuss how these first results can be applied to the analysis and simulation of tree-forms in developmental biology.

uk: вхід без авторизації

name: Can we manipulate tree forms like numbers?


uk: Математика, природничі науки

description: L-systems are widely used for modelling the growth and development of plants. However, until now L-systems did not simulate mechanical collisions between plant parts and entire plants. We show that L-systems can be combined with the position-based collision detection and resolution method, originally devised in computer graphics and subsequently extended to plant modelling. To this end, we extend turtle interpretation by creating a persistent geometric representation of a plant and updating it after each simulated growth step while resolving collisions. We also augment the method to simulate propagation of mechanical collisions between terminal organs represented as surfaces and their supporting branches represented as rods. We illustrate the methods using models of individual plants and fields of plants with all collisions resolved automatically. The presented work is the starting point for faithfully representing different phenotypes in virtual plant breeding trials, and visualizing plants in the field.

uk: вхід без авторизації

name: Modelling collisions with and between plants


uk: Математика, природничі науки

description: The Hippo pathway, which is a central pathway in the control of cell proliferation and apoptosis in Drosophila and mammalian cells, contains a core kinase mechanism that affects control of the cell cycle and growth. Studies involving over- and under-expression of components in the morphogen and Hippo pathways in Drosophila reveal conditions that lead to over- or undergrowth. In this talk we discuss a mathematical model that incorporates the current understanding of the Hippo signal transduction network in Drosophila and which can explain qualitatively both the observations on whole-disc manipulations and the results arising from mutant clones. We find that a number of non-intuitive experimental results can be explained by subtle changes in the balances between inputs to the Hippo pathway. Since signal transduction and growth control pathways are highly conserved across species and directly involved in tumor growth, much of what is learned about Drosophila may have relevance to tumor dynamics in mammalian systems.

uk: вхід без авторизації

name: The role of the Hippo pathway in patterning and growth control


uk: Математика, природничі науки

description: In multicellular organisms, ranging from cellular amoebae to the human body, it is essential for cells to communicate with each other. One common mechanism to initiate communication between cells that are not in close contact is for cells to secrete diffusible signaling molecules into the extracellular space between the spatially segregated units to initiate some collective response. We formulate and analyze a class of coupled cell-bulk ODE-PDE models in a two-dimensional domain. For this coupled system, the method of matched asymptotic expansions is used to construct steady-state solutions and to formulate a spectral problem that characterizes the linear stability properties of the steady-state solutions, with the aim of predicting whether temporal oscillations can be triggered by the cell-bulk coupling. Different ranges of diffusion coefficient are considered and conditions for which the release of this signaling molecule leads to the triggering of some collective synchronous oscillatory behavior among the localized cells are characterized.

uk: вхід без авторизації

name: A 2-D Model of Dynamically Active Cells Coupled by Bulk Diffusion: Triggered Synchronous Oscillations and Quorum-Sensing


uk: Математика, природничі науки

description: I will present two programs that facilitate computational exploration of reaction-diffusion patterns. The first program operates on a flat 2D grid and employs a graphical processing unit to simulate such patterns at interactive rates. The second program allows for simulation of reaction-diffusion processes on arbitrary triangulated surfaces. Parameter values and initial distributions of morphogens can be interactively “painted” on the domain to simulate non-homogeneous environments and different starting conditions. Experimentation with the models is facilitated by the use of a software versioning system, adapted to organize computational experiments and the models.

uk: вхід без авторизації

name: Interactive exploration of reaction-diffusion patterns


uk: Математика, природничі науки

description:
Interactive simulations put the "human in the loop", i.e. they make it possible for the human modeller or analyst to change parameters and immediately see the effects, to explore the model's dynamics in novel directions, to quickly gain an intuition about the most beneficial questions to ask next. Due to the field's importance and the need communicated to us by experts in the field, we are committed to realising according interactive simulations in the domain of developmental biology.

 In this joint presentation, we first summarise the challenges developmental biologists laid out for us in terms of data integration, model building, simulation and optimisation. Second, we present our efforts addressing them. In particular, we elaborate on various computational approaches that we have integrated to meet the specified requirements -- from visual programming over importing and editing annotated volumetric data to efficient, GPU-based simulation and effective methods of visualisation and interaction. For honing these aspects, we have devised a virtual cell model that runs at realtime speeds and realises some of the basic morphogenetic interactions, including morphogen-based signalling, adhesion, proliferation, and growth. We present an according prototype that serves as a basis to gain feedback from developmental biologists and experts in developmental models.

uk: вхід без авторизації

name: Interactive simulation of developmental biological models (joint presentation with Andreas Knote)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Angiogenesis and somite splitting: An ultra-short presentation

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: Mesoscopic Modeling of Branching Structures


uk: Математика, природничі науки

description: The cytoskeleton drives many essential processes in the cell, such as division, the specification of the division axis, movements, polarization and changes in cell shape. These fundamental processes are naturally essential in the development of any organism, and are on their own already complicated to model or understand. What is the correct level of description of intracellular state if one wants to model the development of multiple cells It is possible to capture the dynamics of the cytoskeleton in some simplified way Alternatively, should we carry the full complexity of these cellular processes in a multicellular model Is this desirable

uk: вхід без авторизації

name: How to account for intracellular dynamics [the cytoskeleton] in developmental processes


Moonshine – old and new

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: On the Malle-Robinson conjecture for groups of Lie type


uk: Математика, природничі науки

description: Semidefinite programming (SDP) has important applications in optimization problems that involve moment cones or, by duality, cones of nonnegative polynomials. Examples can be found in statistics, signal processing, control, and non-convex polynomial optimization. The talk will give an introduction to the connections between moment theory and SDP, and discuss SDP algorithms in this context. The focus will be on applications in experiment design.

uk: вхід без авторизації

name: Semidefinite programming and experiment design


uk: Математика, природничі науки

description: In this talk, we will discuss model reduction techniques that can be used to construct fast approximation algorithms for shape optimization problems. The goal is to obtain approximate solutions at run times that are independent of the resolution of the discrete shapes to be optimized. As applications we will discuss methods for real-time elasticity-based shape interpolation and the processing of curves in shape spaces in which a shape is a single point. Finally, I will outline the concept of compressed vibration modes of elastic bodies, which in contrast to the natural vibration modes, are localized ("sparse") deformations.

uk: вхід без авторизації

name: Model Reduction for Elasticity-Based Shape Processing


uk: Математика, природничі науки

description: Blender2SOFA is a software bridge that semi-automates the scene-generation cycle, a key bottleneck in authoring, modeling and developing VR units for surgery simulation.

uk: вхід без авторизації

name: Blender2SOFA: Towards surgeon-authored VR training: the scene-development cycle


uk: Математика, природничі науки

description:
Networks of interacting spin-1/2 particles form the basis for a wide range of quantum technologies including quantum communication, simulation and computation devices. Optimal control provides methods to steer their dynamics to implement specific quantum operations. It is usually implemented to find optimal time-dependent control fields to implement quantum gates or transformations of quantum states or observables in the context of open-loop quantum control. We recently proposed an alternative approach of static controls, based on shaping the energy landscape of quantum systems. For coupled spin systems this type of control could be realized in terms of spatially distributed gates that introduce energy level shifts using quasi-static local electric or magnetic fields. Although there are insufficient control degrees of freedom for the system to be completely controllable, many practically interesting operations can be implemented using these controls, including efficient transfer of excitations in spin networks. Furthermore, the resulting controllers combine high fidelity and strong robustness properties under device uncertainties, surpassing traditional limits in classical control. In particular, we observe positive correlations between the logarithmic sensitivity and the control error in many cases, i.e., the highest fidelity controllers are also the most robust. Structured singular value analysis shows the same trend for large structured variation using $\mu$-analysis tools.
 One way to understand the surprising robustness of the controllers is in terms of feedback control laws. The energy biases create direct feedback loops. Similar to feedback loops in electronic circuits such as operational amplifiers, this feedback is highly effective and does not require measurements.
 I will discuss results on energy landscape control for quantum spin devices with a focus on robustness at high fidelities of the operations and the interpretation of the controllers in terms of feedback control laws. References: [1] Emergence of Classicality under decoherence in robust quantum transport, S. Schirmer, E. Jonckheere, S. Oâ Neil, and F. Langbein, in preparation. [2] Design of Feedback Control Laws for Information Transfer in Spintronics Networks, S Schirmer, E Jonckheere, F Langbein, arXiv:1607.05294, 2016. [3] Time optimal information transfer in spintronics networks, FC Langbein, S Schirmer, E Jonckheere, 2015 IEEE 54th Annual Conference on Decision and Control (CDC), 6454-58, 5, 2015. [4] Structured singular value analysis for spintronics network information transfer control, E Jonckheere, S Schirmer, F Langbein, IEEE Transactions on Automatic Control, DOI: 10.109/TAC.2017.2714623, arXiv:1706.03247, in press, 2017.[5] Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers, E Jonckheere, S Schirmer, F Langbein, arXiv:1612.02784, 2016. [6] Information transfer fidelity in spin networks and ring-based quantum routers, E Jonckheere, F Langbein, S Schirmer, Quantum Information Processing 14 (12), 4751-4785. [7] Multi-fractal Geometry of Finite Networks of Spins, P Bogdan, E Jonckheere, S Schirmer, arXiv:1608.08192, 2016.

uk: вхід без авторизації

name: Control of Quantum Spin Devices, feedback control laws and hidden feedback


uk: Математика, природничі науки

description: We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a time-dependent superposition of Lewis-dot resonance structures. Coupled with the initial state solution to obtain such dynamics with TDDFT, this chemical picture facilitates interpretation of electron.

uk: вхід без авторизації

name: Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well Defined Initial State


uk: Математика, природничі науки

uk: вхід без авторизації

name: Block systems on the facets of toroidal hypertopes


Small regular hypertopes of rank 3

uk: Математика, природничі науки

description: We describe the smallest C-groups with complete diagram whose rank 3 residues are hypermaps of type (n,n,n). It turns out that these C-groups are not hypertopes, indeed all rank 3 residues fail to be thin. We then focus on rank 3 regular hypertopes. A characterization of thiness will be given and some infinite families of ``small'' rank 3 regular hypertopes of type (n,n,n) will arise.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Generalized polygons are Bruhat-Tits buildings of rank two. They can also be defined in terms of their bipartite incidence graph, which has the property that the girth is twice the diameter. By the Feit-Higman Theorem (1964), the only finite generalized polygons are thin (two points on each line or two lines on each point) or the diameter is 3, 4, 6 or 8, corresponding to the finite projective planes, the generalized quadrangles, the generalized hexagons and the generalized octagons, respectively. In particular there are no generalized pentagons. An alternative way to generalize the pentagon was introduced by Simeon Ball et al. in [1]. In this talk I will discuss what we know about these incidence geometries. [1] S. Ball, J. Bamberg, A. Devillers and K. Stokes. An alternative way to generalize the pentagon. J. Combin. Des., 21:163â 179, 2013. [2] T. S. Griggs and K. Stokes. On pentagonal geometries with block size 3, 4 or 5. Springer Proc. in Math. & Stat., 159:147â 157, 2016.

uk: вхід без авторизації

name: Pentagonal geometries with connected deficiency graph


keywords: Calculus of variations and optimal control

uk: Математика, природничі науки

uk: вхід без авторизації

name: Dissipative PDE systems for plasticity and micro-structure phase transitions


uk: Математика, природничі науки

uk: вхід без авторизації

name: Variational models for dislocations at grain boundaries


Ripples in graphene

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Necessary and sufficient conditions for strong local minimizers on a class of non-smooth domains


uk: Математика, природничі науки

uk: вхід без авторизації

name: Equilibrium measure for a nonlocal dislocation energy


uk: Математика, природничі науки

description: We describe two matrix-free methods for solving large-scale affine inclusion problems on the product (or intersection) of convex sets. The first approach is a novel iterative re-weighting algorithm (IRWA) that iteratively minimizes quadratic models of relaxed subproblems while automatically updating a relaxation vector. The second approach is based on alternating direction augmented Lagrangian (ADAL) technology. The main computational costs of each algorithm are the repeated minimizations of convex quadratic functions which can be performed matrix-free. Both algorithms are globally convergent under loose assumptions, and each requires at most O(1/ε2) iterations to reach ε-optimality of the objective function. Numerical experiments show that both algorithms efficiently find inexact solutions. However, in certain cases, these experiments indicate that IRWA can be significantly more efficient than ADAL.

uk: вхід без авторизації

name: Iteratively re-weighted least squares for Sums of Convex Functions


uk: Математика, природничі науки

description: In this talk, we present a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. The pointwise iteration-complexity of the new variant is better than the corresponding one for the standard ADMM method and, up to a logarithmic term, is identical to the ergodic iteration-complexity of the latter method. We discuss how this regularized ADMM can be seen as an instance of a regularized hybrid proximal extragradient framework whose error condition at each iteration includes both a relative error and a summable error.

uk: вхід без авторизації

name: Improved pointwise iteration-complexity of a regularized ADMM


uk: Математика, природничі науки

description: Spectral stability captures behavior of a solution perturbed by an infinitesimal perturbation. It often determines nonlinear stability but it is limited to the exact form of the dynamics of the system. However, governing equations are often only an approximation of a larger system that models real world situation. We show how are the spectral stability of a solution in the reduced and full (extended) system related, particularly for ODEs in the case of frequently used quasi-steady-state reduction but also in a general case of reduced/extended system. A connection is also drawn with the geometric Krein signature that is shown to naturally characterize spectral properties under such extensions.

uk: вхід без авторизації

name: Spectral stability in reduced and extended systems

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: The Maslov index is a powerful and well known tool in the study of Hamiltonian systems, providing a generalization of Sturm-Liouville theory to systems of equations. For non-Hamiltonian systems, one no longer has the symplectic structure needed to define the Maslov index. In this talk I will describe a recent construction of a "generalized Maslov index" for a very broad class of differential equations. The key observation is that the manifold of Lagrangian planes can be enlarged considerably without altering its topological structure, and in particular its fundamental group. This is joint work with Paul Cornwell, Chris Jones and Robert Marangell.

uk: вхід без авторизації

name: Constructing a generalized Maslov index for non-Hamiltonian systems


uk: Математика, природничі науки

description: One of the main features of micro magnetic materias is the formation of magnetic domain separated by the so called magnetic walls. These walls are transition layers that move upon the application of external magnetic fields. In bulk material the main type of walls is the Bloch wall. There are two models for micro magnetic precession dynamics with damping. One based in Landau-Lifshitz-Gilbert (LLG) equation and other based on eddy current damping. In this talk we prove some stability results for the Bloch wall under the eddy current damping model and the LLG model.

uk: вхід без авторизації

name: On the stability of Bloch walls in a dynamical model with eddy currents


keywords:
Mathematics
Numerical analysis
Approximations and expansions
Control/optimization/operation research

uk: Математика, природничі науки

description: The goal in cryo-electron microscopy is to recover the three-dimensional structure of a molecule from many of its two-dimensional tomographic projection images. A key challenge in this imaging setup is that the two-dimensional images are extremely noisy. Thus, the process of reconstructing a three-dimensional model form the two-dimensional images typically requires some form of denoising, to improve the quality (signal-to-noise ratio) of the two-dimensional images. Such denoising is often implemented by one of the existing class averaging algorithms, or by other forms of statistical analysis, such as principal components analysis and its variants. We present an algorithm for denoising the entire set of two-dimensional images at once, by exploiting the geometrical property that all (unknown) clean images corresponding to the same underlying structure lie on a manifold of intrinsic dimension three. Thus, each image can be denoised by projecting it onto this (unknown) low-dimensional manifold of clean images. We show that all the quantities required to compute this projection can be estimated using only the two-dimensional projection images. In particular, no prior assumptions on the images nor the three-dimensional volume are required.

uk: вхід без авторизації

name: Manifold methods for cryo-EM image denoising


uk: Математика, природничі науки

uk: вхід без авторизації

name: Mathematical aspects of compressive sensing


uk: Математика, природничі науки

description: A new generation of beam monochromators has recently pushed the energy resolution of (scanning) transmission electron microscopes (S)TEMs deep into the sub 20meV range [1]. In addition to the obvious increase in resolution, the flexibility of these instruments is allowing the energy resolution, beam current and optics can be adjusted seamlessly within a greatly increased range, thus enabling tantalising new modes of operations. This contribution will illustrate some of the new possibilities offered by these instruments through a number of examples, putting a specific emphasis on the need for advanced theoretical calculations to rationalise the experimental results. The increase in resolution has made it possible to explore the phonon region of the electron energy loss spectrum (EELS). Although the physical origin of vibrational signals in the STEM is very similar to that giving rise to low-energy phonon vibrations in neutron or inelastic X-ray scattering, differences in experimental geometries and selection rules, among other factors, have made their interpretation challenging. A better understanding of this phonon response can be achieved by observing the dependence of the phonon peaks under different optical conditions and mapping their energy in momentum space. A theoretical formalism based on that used by inelastic X-ray and neutron scattering [2] can be applied to obtain a good agreement with experimental data, e.g. from two polymorphs of boron nitride, across different directions in the Brillouin zone [3]. However, while this approach is successful, more complex and computationally demanding models taking into account finite momentum resolution and final sample size are shown to be necessary if a truly quantitative match between experiment and theory is to be achieved [3]. Furthermore, the effect of atomic scale defects on the bonding of materials can now be fingerprinted through core and low loss spectroscopy with a greater precision and sensitivity than ever before. Here, 2-dimensional materials have provided an ideal â sandboxâ : low energy excitons can be clearly distinguished in MoS2, while the introduction of a single B or N atom in graphene results in subtle localised modifications of its electronic structure [5,6]. However, for a reliable prediction of the loss function of these materials, at finite momentum transfer within density functional theory (DFT), it is necessary to invoke corrections for local field effects, in addition to any excitonic modification to the optical absorption. Thus for a comprehensive understanding of the experimental results a theoretical treatment beyond classical dielectric theory is imperative. In conclusion, this contribution will aim to illustrate that while modern electron microscopes are now sufficiently advanced to push the validity of the approximations used in theoretical electronic structure calculations, there is evidently a growing need to increase the efficiency of more advanced computational schemes using the GW and BSE formalisms, among others, and to tackle increasingly large atomic models to provide realistic and quantitative simulations to validate the experiments. [1] O.L. Krivanek, T.C. Lovejoy, N. Dellby et al., Nature 514 (2014), pp. 209-212. [2] E. Burkel, J.Phys.: Cond. Mat. 13 (2001), 7627. [3] F.S. Hage, R. Nicholls, J. Yates et al., Submitted (2017). [4] H.C. Nerl, K.T. Winther, F.S. Hage et al., NPJ 2D Mat. Appl. 1 (2017), pp. 1-11. [5] T.P. Hardcastle, C.R. Seabourne, D.M. Kepaptsoglou et al., J.Phys.: Cond. Mat. 29 (2017), 225303. [6] F.S. Hage, T.P. Hardcastle, M.N. Gjerding et al., Submitted (2017).

uk: вхід без авторизації

name: From phonons to core losses in real and momentum space: recent applications of sub 100meV STEM-EELS


Remarks on Constrained Minimum Problems

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bayesian Nonparamteric Modelling of Recurrent Event Processes


uk: Математика, природничі науки

description: Several important issues of El Niño-Southern Oscillation (ENSO) predictability were studied using the latest version of the Zebiak-Cane model. A fully physically-based tangent linear model was constructed for the Zebiak-Cane model and a singular vector (SV) analysis for the 161 year (1856-2016) was performed. It was found that the leading SVs are less sensitive to initial conditions while singular values and final perturbation patterns exhibit a strong sensitivity to initial conditions. The dynamical diagnosis shows that the total linear and nonlinear heating terms play opposite roles in controlling the optimal perturbation growth. At decadal/interdecadal time scales, an inverse relationship exists between the leading singular value (S1) and correlation-based skill measures whereas an in-phase relationship exists between the S1 and MSE-based skill measures. However, S1 is not a good predictor of prediction skill at shorter time scales and for individual predictions. An offsetting effect was found between linear and nonlinear perturbation growth rates, which have opposite contributions to the S1. Ensemble and probabilistic ENSO predictions were performed for the 161 yrs. Results suggest that “reliability” is more sensitive to choice of ensemble construction strategy than “resolution”. The strategy produces the most reliable and skillful ENSO probabilistic prediction, benefiting from the contribution of the stochastic optimal winds and singular vector of SSTA.

uk: вхід без авторизації

name: ENSO ensemble prediction for the past 161 years from 1856-2016


uk: Математика, природничі науки

description: The second eigenfunction of the Laplace-Beltrami operator (often called Fiedler vector in discrete settings) follows the pattern of the overall shape of an object. This geometric property is well known and used for various applications including mesh processing, feature extraction, manifold learning, spectral embedding and the minimum linear arrangement problem. Surprisingly, this geometric property has not been precisely formulated yet. This problem is directly related to the somewhat obscure hot spots conjecture in differential geometry that postulates the behavior of heat diffusion near boundary. The aim of the talk is to discuss and raise the awareness of the problem. As an application of the hot spots conjecture, we show how the second eigenfunction alone can be used for shape modeling of elongated anatomical structures such as hippocampus and mandible, and determining the diameter of large-scale brain networks.Â This talk is based on Chung et al. 2015 Medical Image Analysis 22:63076.

uk: вхід без авторизації

name: Heat kernel smoothing, hot spots conjecture and Fiedler vector


uk: Математика, природничі науки

description: There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation depth, for functional data. As a measure of depth, its properties are studied theoretically, and the associated outlier detection performance is investigated through simulations. Compared to magnitude outliers, shape outliers are often masked among the rest of samples and harder to identify. We show that the proposed total variation depth has many desirable features and is well suited for outlier detection. In particular, we propose to decompose the total variation depth into two components that are associated with shape and magnitude outlyingness, respectively. This decomposition allows us to develop an effective procedure for outlier detection and useful visualization tools, while naturally accounting for the correlation in functional data. Finally, the proposed methodology is demonstrated using real datasets of curves, images, and video frames.

uk: вхід без авторизації

name: Total Variation Depth for Functional Data


Sparse Functional Additive Models

uk: Математика, природничі науки

description: We propose a new, more flexible model to tackle the issue of lack of t for conventional functional linear regression. This new model, called the sparse functional additive model, is used to characterize the relationship between a functional predictor and a scalar response of interest. The effect of the functional predictor is represented in a nonparametric additive form, where the arguments are the scaled functional principal component scores. Component selection and smoothing are considered when fitting the model to reduce the variability and enhance the prediction accuracy, while providing an adequate t. To achieve these goals, we propose using the adaptive group LASSO method to select relevant components and smoothing splines to obtain a smoother estimate of those relevant components. Simulation studies show that the proposed estimation method compares favorably with various conventional methods in terms of prediction accuracy and component selection. The advantage of our proposed model and the estimation method is further demonstrated in two real data examples.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Bayesian phylogenetics, which approximates a posterior distribution of phylogenetic trees, has become more and more popular with the development of Monte Carlo methods. Standard Bayesian estimation of phylogenetic trees can handle rich evolutionary models but requires expensive Markov chain Monte Carlo (MCMC) simulations, which may suffer from two difficulties, the curse of dimensionality and the local-trap problem. Our previous work [1] has shown that the combinatorial sequential Monte Carlo (CSMC) method can serve as a good alternative to MCMC in posterior inference over phylogenetic trees. However, the simple proposal distribution used in CSMC is inefficient to combine with MCMC in the framework of the particle Gibbs sampler. Moreover, CSMC is inapplicable to the particle Gibbs with ancestor sampling [2]. In this talk, we will present a more efficient CSMC method, called CSMC-BF, with a more flexible proposal. The proposed CSMC-BF can improve the performance of the particle Gibbs sampler compared with the original CSMC, and can be used in the particle Gibbs with ancestor sampling. We will demonstrate the advantages of the proposed CSMC-BF using simulation studies and real data analysis. References [1] Liangliang Wang, Alexandre Bouchard-CÃ´tÃ©, and Arnaud Doucet. Bayesian phylogenetic inference using a combinatorial sequential Monte Carlo method. Journal of the American Statistical Association, 110(512):13621374, 2015. [2] Fredrik Lindsten, Michael I. Jordan, and Thomas B. SchÃ¶n. Particle Gibbs with ancestor sampling. Journal of Machine Learning Research, 15(1):21452184, 2014.urvival models.

uk: вхід без авторизації

name: Particle Gibbs with Ancestor Sampling for Bayesian Phylogenetics


uk: Математика, природничі науки

description: We present an algorithm for the approximation of high-dimensional functions using tree-based low-rank approximation formats (tree tensor networks). A multivariate function is here considered as an element of a Hilbert tensor space of functions defined on a product set equipped with a probability measure. The algorithm only requires evaluations of functions on a structured set of points which is constructed adaptively. The algorithm is a variant of higher-order singular value decomposition which constructs a hierarchy of subspaces associated with the different nodes of a dimension partition tree and a corresponding hierarchy of interpolation operators. Optimal subspaces are estimated using empirical principal component analysis of interpolations of partial random evaluations of the function. The algorithm is able to provide an approximation in any tree-based format with either a prescribed rank or a prescribed relative error, with a number of evaluations of the order of the storage complexity of the approximation format. Reference : A. Nouy. Higher-order principal component analysis for the approximation of tensors in tree-based low rank formats. arxiv preprint, 2017.

uk: вхід без авторизації

name: Principal component analysis for the approximation of high-dimensional functions in tree-based tensor formats


uk: Математика, природничі науки

description: The present work concerns the approximation of the solution map S associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution of the Helmholtz equation. We introduce a least squares rational PadÃ©-type approximation technique applicable to any meromorphic Hilbert space-valued univariate map, and we prove the uniform convergence of the PadÃ© approximation error on any compact subset of the interval of interest that excludes any pole. This general result is then applied to the Helmholtz solution map S, which is proven to be meromorphic in â , with a pole of order one in every (single or multiple) eigenvalue of the Laplace operator with the considered boundary conditions. Numerical tests are provided that confirm the theoretical upper bound on the PadÃ© approximation error for the Helmholtz solution map. The PadÃ©-type approximation can then be used to compute the probability distribution of quantities of interest associated to the Helmholtz problem with random wavenumber.

uk: вхід без авторизації

name: Convergence analysis of PadÃ© approximations for Helmholtz problems with parametric/ stochastic wavenumber


uk: Математика, природничі науки

description: Integration against an intractable probability measure is among the fundamental challenges of statistical inference, particularly in the Bayesian setting. A principled approach to this problem seeks a deterministic coupling of the measure of interest with a tractable "reference" measure (e.g., a standard Gaussian). This coupling is induced by a transport map, and enables direct simulation from the desired measure simply by evaluating the transport map at samples from the reference. Yet characterizing such a map---e.g., representing, constructing, and evaluating it---grows challenging in high dimensions. We use the conditional independence structure of the target measure to establish the existence of certain low-dimensional couplings, induced by transport maps that are sparse or decomposable. We also describe conditions, common in Bayesian inverse problems, under which transport maps have a particular low-rank structure. Our analysis not only facilitates the construction of couplings in high-dimensional settings, but also suggests new inference methodologies. For instance, in the context of nonlinear and non-Gaussian state space models, we will describe new variational algorithms for nonlinear smoothing and sequential parameter estimation. We will also outline a new class of nonlinear filters induced by local couplings, for inference in high-dimensional spatiotemporal processes with chaotic dynamics.

uk: вхід без авторизації

name: A class of nonlinear filters induced by local couplings


uk: Математика, природничі науки

description: In this talk, firstly I would like to survey some arithmetic properties of Henon maps. Then I would like to talk about joint work in progress with Liang-Chung Hsia on some arithmetic properties of a certain family of Henon maps.

uk: вхід без авторизації

name: Arithmetic properties of a certain family of Henon maps


uk: Математика, природничі науки

description: Using results on the structure of the topological full groups of minimal subshifts, we prove that the isomorphism relation on the space of finitely generated complete groups is not smooth.

uk: вхід без авторизації

name: Topological full groups and the classification problem forÂ finitely generated complete groups


uk: Математика, природничі науки

description: We will discuss a recent approach to non amenability based on studying Liouville actions. We give a reformulation of Liouville property, which in its turn implies that this approach can not be used for strongly transitive actions. This is a joint work with Tianyi Zheng.

uk: вхід без авторизації

name: Liouville actions of finitely generated groups


uk: Математика, природничі науки

description: Variational integrators for Lagrangian systems have the advantage of conserving the momenta up to machine precision, independent of the time step. While the theory of variational integrators for mechanical systems is well developed, there applications of these integrators to systems involving fluid-structure interactions have proven difficult. In this talk, we derive a variational integrator for a particular type of fluid-structure interactions, namely, simulating the dynamics of a bendable tube conveying ideal fluid that can change its cross-section (collapsible tube). First, we derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. Based on this theory, we derive a variational discretization of the dynamics based on the appropriate discretization of the fluidâ s back-to-labels map, coupled with a variational discretization of elastic part of the Lagrangian. We also show the results of simulations of the system with the spatial discretization using a very small number of points demonstrating a non-trivial and interesting behavior.

uk: вхід без авторизації

name: Variational integrator methods for fluid-structure interactions

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: Suspensions of rigid particles can be found in a wide range of natural and industrial settings. Detailed models of the movement of individual particles can be a useful tool to predict and understand macroscopic properties of these suspensions. Boundary integral equations have been shown to be an efficient method to do this, however for dense suspensions avoiding particle overlaps requires excessively small time steps. By applying a constraint requiring no contact at each time step to the variational Stokes equations we are able to maintain separation of all the particles without requiring a small time step. This enables long time horizon simulations of dense suspensions of rigid particles. After presenting the method and demonstrating its robustness we demonstrate its applicability to modeling physical phenomena such as effective viscosity and particle alignment angles.

uk: вхід без авторизації

name: Contact-Free Rigid Body Motion Using Boundary Integral Equations


uk: Математика, природничі науки

description: While the field of fast direct solvers solvers for boundary integral equations has been growing, the development of these methods for fluid applications is limited. Since most fluid application involve evolving geometries, it is not possible to amortize the high computational cost of building a direct solver over many solves out of the box. In this talk, we will present extensions of the standard fast direct solver framework to fluid applications.

uk: вхід без авторизації

name: Fast direct integral equation solvers for fluid applications


uk: Математика, природничі науки

uk: вхід без авторизації

name: Matrix Estimation via Collaborative Filtering


uk: Математика, природничі науки

description: For years, I have been torn by a constant pressure to add more â detailâ to our cellular models of plant development while also being driven to capture the essence of a phenomenon. I hope to illustrate this conundrum by a case-study on plant development and nutrient uptake. Through modelling and mathematical analysis and combined with experimental verifications, I will show how 1) very fast temporal cellular responses are critical for maintaining steady-state tissue-level behaviour, even in the absence of external variation; and 2) how sub-cellular spatial compartments, such as the cell wall, enable tissue-scale patterns to arise that are fundamentally distinct from what is possible without these sub-cellular features. We were only able to achieve these insights by capturing certain â detailsâ within multilevel cellular models, only later realising their true significance. Nevertheless, the mechanisms, relying on detailed spatial and temporal structures in a multi-level setting, yielded parsimonious explanations.

uk: вхід без авторизації

name: As simple as possible, but no simpler: coming to (mathematical) terms with the impact of fine temporal and spatial scales in plant developmental homeostasis


uk: Математика, природничі науки

description: I shall introduce a noncommutative version of the notion of a CohFT, where the role of Deligne-Mumford compactifications of moduli spaces is played by toric varieries of Loday's realisations of associahedra. The corresponding noncommutative analogues of Gerstenhaber and Batalin-Vilkovisky algebras will also be discussed. This is a joint work with S.Shadrin and B.Vallette.

uk: вхід без авторизації

name: Noncommutative cohomological field theories


Matricial quantum field theory

uk: Математика, природничі науки

description: This subject combines ideas from quantum field theory on noncommutative spaces with technologies developed for matrix models to rigorously compute all renormalised correlation functions of these toy models. There is a natural projection of matricial correlation functions to Schwinger functions of an ordinary Euclidean quantum field theory. The main question we are working on is whether or not these functions satisfy Osterwalder-Schrader reflection positivity. If so the model would define a true relativistic (but very simple) quantum field theory in four dimensions. We have partial results that this could be the case.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In work with David Ben-Zvi and Adrien Brochier, we introduced a (would-be) 4-D topological field theory which relates to N=4 d=4 SYM in the same way that the Reshetikhin-Turaev 3-D theory relates to Chern-Simons theory. On surfaces it assigns certain explicit categories quantizing quasi-coherent sheaves on the character variety of the surface (along the Atiyah-Bott/ Goldman/Fock-Rosly Poisson bracket), and these in turn relate to many well-known constructions in quantum algebra. The parenthetical "would be" above means that, while the theory had an a priori definition on *surfaces* via factorization homology -- due to work of Ayala-Francis, Lurie, and Scheimbauer, these techniques do not apply to 3- and 4-manifolds. In this talk I'll explain work with Adrien Brochier and Noah Snyder, which constructs the 3-manifold invariants following the prescription of the cobordism hypothesis. This is in the spirit of Douglas-Schommer-Pries-Snyder's work on finite tensor categories -- but in the infinite setting -- and also echoes early ideas of Lurie and Walker. The resulting 3-manifold invariants quantize Lagrangians in the character variety of the boundary. They are not at all well-understood or computed explicitly in general, but they appear phenomenologically to relate to many emerging structures, such as quantum A-polyonomials, DAHA-Jones polynomials, and Khovanov-Rozansky knot homologies.

uk: вхід без авторизації

name: Braided tensor categories and the cobordism hypothesis