uk: Математика, природничі науки

description: The classical theorem of Fary states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generalizations of Fary's theorem to surfaces equipped with Riemannian metrics. In this setting, we require that every edge is drawn as a shortest path between its two endpoints and we call an embedding with this property a shortest path embedding. The main question considered in the talk is whether given a closed surface \(S\), there exists a Riemannian metric for which every topologically embeddable graph admits a shortest path embedding. This question is also motivated by various problems regarding crossing numbers on surfaces. It is easy to observe that the round metrics on the sphere and the projective plane have this property. We provide flat metrics on the torus and the Klein bottle which also have this property. On the other hand the unit square flat metric on the Klein bottle there exists a graph without shortest path embeddings. For large \(g\), there exist graphs \(G\) embeddable into the orientable surface of genus \(g\), such that with large probability a random hyperbolic metric does not admit a shortest path embedding of \(G\) (w.r.t. the Weil-Petersson volume on moduli space). On the other hand, it is possible to construct a hyperbolic metric on every orientable surface \(S\) of genus \(g\), such that every graph embeddable into \(S\) can be embedded so that every edge is a concatenation of at most \(O(g)\) shortest paths. Joint with A. Hubard, V. Kaluza, A. de Mesmay.

uk: вхід без авторизації

name: Shortest path embeddings of graphs on surfaces


Maria Chudnovsky

type: Person

keywords:
Mathematics
Combinatorics
Computer science
Discrete mathematics

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

description: The problem of testing if a graph can be colored with a given number $k$ of colors is NP-complete for every $k>2$. But what if we have more information about the input graph, namely that some fixed graph $H$ is not present in it as an induced subgraph? It is known that the problem remains NP-complete even for $k=3$, unless $H$ is the disjoint union of paths. We consider the following two questions: 1. For which graphs $H$ is there a polynomial time algorithm to 3-color (or in general $k$-color) an $H$-free graph? 2. For which graphs $H$ are there finitely many 4-critical $H$-free graphs? This talk will survey recent progress on these questions, and in particular give a complete answer to the second one.

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: Coloring graphs with forbidden induced subgraphs

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: When $F$ is a set of four-vertex graphs the complexity of the vertex coloring problem in the class of $F$-free graphs is known, with three exceptions: $F = \{\text{claw}, 4K_1\}$, $F = \{\text{claw}, 4K_1, \text{co-diamond}\}$, and $F = \{C_4, 4K_1\}$. We study the coloring problem for $\{\text{claw},4K_1\}$-free graphs. We solve the vertex coloring problem for a subclass of this class which contains the class of $4K_1$-free line graphs. Our result implies that the chromatic index of a graph with no matching of size four can be computed in polynomial time.

uk: вхід без авторизації

name: A coloring algorithm for 4K 1-free line graphs


Detecting an induced subdivision of K 4

uk: Математика, природничі науки

description: We propose a polynomial-time algorithm to test whether a given graph contains a subdivision of \(K_4\) as an induced subgraph. This continues the study of detecting an induced subdivision of \(H\) for some fixed graph \(H\), which is still far from being complete. Our result answers a question posed by Chudnovsky et al. and Lévêque et al.

uk: вхід без авторизації


uk: Математика, природничі науки

description: I will talk about an explicit construction for triangle-free graphs that do not contain a six-vertex path as an induced subgraph. Examples include the 16-vertex Clebsch graph, and the graph that arises from a complete bipartite graph by subdividing every edge of a perfect matching exactly once. We show that every connected triangle-free graph with no six-vertex induced path can be obtained from an induced subgraph of one of these two by restricted homogeneous set and homogeneous pair operations.

uk: вхід без авторизації

name: Triangle-free graphs with no six-vertex induced path


(Theta, wheel)-free graphs

uk: Математика, природничі науки

description: A theta is a subdivision of $K_{2,3}$, and a wheel is a graph that consist of a chorldless cycle of length at least 4 and a vertex that has at least 3 neighbors on the cycle. In recently completed joint work with Trotignon and Radovanovic we obtained a structure theorem for graphs that do not contain thetas and wheels as induced subgraphs (i.e. (theta, wheel)-free graphs) and several of its algorithmic consequences. We decompose (theta, wheel)-free graphs using clique cutsets and 2-joins into graphs that are essentially formed of a line graph of a triangle-free chordless graph plus a (possibly empty) clique (that attaches to the rest of the graph in a particular way). A 2-join is an edge cutset that appears in decomposition theorems for several complex hereditary classes, such as perfect graphs, even-hole-free graphs and others. In these decomposition theorems 2-joins are used together with vertex cutsets that are stronger than clique cutsets, such as star cutsets and their generalizations (which are much harder to use in algorithms). This is a first example of a decomposition theorem that uses just the combination of clique cutsets and 2-joins. This has several consequences. First, we can easily transform our decomposition theorem into a complete structure theorem for (theta, wheel)-free graphs, i.e. we show how every graph in the class can be built starting from basic graphs that can be explicitly constructed, and gluing them together by prescribed composition operations, and all graphs built this way are in the class. Such structure theorems are rare for hereditary graph classes, only a few examples are known. Next, we construct a polynomial-time decomposition-based recognition algorithm. Recognizing classes of graphs defined by excluding different combinations of Truemper configurations (i.e. wheels, thetas, prisms and pyramids) is a much studied problem. For some combinations the problem is known to be polynomial (e.g. recognizing pyramids and thetas), whereas for others it is NP-complete (e.g. recognizing prisms and wheels). The class of (theta, wheel)-free graphs was the last of these types of recognition problems that was open, and we now resolve. We then use the decomposition theorem to obtain polynomial-time algorithms for weighted stable set, weighted clique and vertex coloring problems. For the weighted stable set problem, it was essential to decompose the graph using a sequence of non-crossing 2-joins. The weighted clique problem we solve by first showing the existence of a bisimplicial vertex (a vertex whose neighborhood partitions into 2 cliques). This is done elegantly by using the existence of an extreme 2-join (a 2-join whose one block of decomposition does not have a 2-join). We also prove that every (theta, wheel)-free graph with maximum clique size $\omega$ admits a coloring with at most max$\{\omega ,3\}$ colors. Finally, we obtain a polynomial-time algorithm for the induced version of the $k$-linkage problem (for fixed $k$): given $k$ distinct pairs of vertices $(s_i,t_i)$ of a graph $G$, decide whether there are $k$ vertex-disjoint paths $P_i=s_i \ldots t_i$, $i=1, \ldots ,k$, such that there are no edges between the vertices of these paths.

uk: вхід без авторизації


On a local version of Reed's conjecture

uk: Математика, природничі науки

description: In 1998, Reed conjectured that the chromatic number of a graph is at most the average of its maximum degree plus one and its clique number (rounded up). As evidence for his conjecture, he proved that it is at most some non-trivial convex combination of the two. Recently, Michelle Delcourt and I proved the same is true for list chromatic number. Tom Kelly and I meanwhile conjectured that a `local' version of Reed's conjecture wherein the parameters are replaced by local parameters (list size, degree and clique number of neighborhood) and proved a non-trivial convex combination under some mild assumptions.

uk: вхід без авторизації


Polynomial chi-boundedness

uk: Математика, природничі науки

description: A graph $G$ is $\chi$-bounded by the function $f$ if every induced subgraph $H$ of $G$ satisfied $\chi(H) \le f(\omega(H))$. A class of graphs is $\chi$-bounded if there exists a function $f$ such that every graph in the class is $\chi$-bounded by $f$. It is polynomially $\chi$-bounded if there is such a function $f$ that is a polynomial. Some classes of graphs are $\chi$-bounded, some are not. It is not known whether there exists a hereditary class of graph that is $\chi$-bounded but not polynomially $\chi$-bounded. The goal of this talk is to survey several results, proof techniques, and open questions around the notion of polynomial $\chi$-boundedness.

uk: вхід без авторизації


Complex flows of soft particles

uk: Математика, природничі науки

description: Soft particles such as drops, vesicles, and red blood cells, display rich dynamics in externally applied flow and electric fields. For example, vesicles have multiple dynamical states in shear flow (tank-treading, tumbling); drops in uniform electric field undergo various symmetry-breaking instabilities. I will overview the complex flow behavior of these inertialess systems and discuss how it arises from the nonlinear interaction of a deformable microstructure and external forcing.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Rigid or flexible particles suspended in viscoelastic fluids are ubiquitous in the food industry (e.g. pastes), industrial molding applications (all composites and 3-D printed parts), the energy industry (e.g. fracking fluids), and biological fluids (i.e. swimming of bacteria in mucous). The mathematics of the description of these suspensions is in its infancy. However, while the mathematics of this subject is subtle a major breakthrough in this area has been the development of computational simulations of such viscoelastic suspensions, with particle level resolution, such that predictions can be made and tested at all volume fraction loadings. I describe the use of an Immersed Boundary methodology that allows the simulation of hundreds of particles in elastic fluids, with particle level flow and stress field resolution. This simulation capability is unique and overcomes the major hurdle in understanding the physics of these suspensions – which in many cases are simply qualitatively different than that of Newtonian suspensions. The simplest flows of such suspensions are not understood at a fundamental level, primarily because the collective behavior of particles in an elastic liquid has no foundation – this will change dramatically in the next few years. I will describe three foundational problems that have now been analyzed using this new computational method – including fracking fluid design and swimming in mucous.

uk: вхід без авторизації

name: Computing the Dynamics of Suspended Particles in Complex Fluids: From Fracking Fluids to Swimming Worms


uk: Математика, природничі науки

description: Boundary integral methods are among the most popular methods for computing interfacial fluid flow, and have the advantage that they can be made high-order accurate. Thus, they are useful for investigating phenomena that require high accuracy to resolve features, such as "pinching" or topological singularities that can occur on the interface. However, standard BI methods lose accuracy when two parts of an interface are near touching. In this talk, we present a new algorithm based on the QBX method of Klockner et al. for the accurate computation of boundary integrals with singular or nearly singular kernels in 3D. The QBX method is typically based on a spherical harmonics expansion which when truncated at $\mathcal{O}(p)$ has $\mathcal{O}(p^2)$ terms. This expansion can equivalently be written with $\mathcal{O}(p)$ terms, but paying the price that the expansion coefficients will depend on the target point. Based on this observation, we develop a target specific QBX method. We give error estimates for our method, and illustrate its performance in several examples.

uk: вхід без авторизації

name: A target specific QBX method for the accurate computation of boundary integrals with nearly touching interfaces


uk: Математика, природничі науки

description: The level of complexity in blood flow simulation depends on the application. The focus here is on cellular blood where major cells and proteins must be included in the analysis. The progress in cellular blood flow simulation based on lattice-Boltzmann method (LBM) will be discussed. Advantages of this method in terms of scalability, accuracy and flexibility for multiscale analysis critical to many applications will be presented.

uk: вхід без авторизації

name: LBM-based method for simulation of cellular blood flow with nanoscale proteins


uk: Математика, природничі науки

description: A central part of integral equation methods are the quadrature methods used to evaluate boundary integrals that are singular or have nearby singularities. A relatively new such method is quadrature by expansion (QBX), which evaluates the solution using local expansions formed at points inside the domain. I will in this talk discuss how QBX can be used for Stokes flow simulations in both two and three dimensions. In particular, I will discuss techniques for accelerating the method such that it can be combined with existing fast methods, and also how parameter selection can be simplified through accurate estimation of quadrature errors.

uk: вхід без авторизації

name: Quadrature by expansion in integral equation methods for Stokes flow


Granular Erosion in Stokes Flow

uk: Математика, природничі науки

description: Fluid-mechanical erosion of solid material occurs across many scales, from massive geological structures down to tiny granular constituents. Here we examine the erosion of a granular medium in Stokes flow - the typical flow regime of groundwater - using numerical simulations. We combine a highly-accurate boundary-integral formulation (for the Stokes flow) with stable interface-evolution methods (to treat the eroding bodies). A single eroding body tends toward a slender, for-aft-symmetric morphology which can be described analytical. Supplementing the Stokes solver with the Fast Multiple Method allows us to simulate 10-100 bodies. We find that the erosion of many bodies naturally leads to the formation of channels, as well as anisotropy in the medium conductivity. This latter feature we connect to the single-body limiting morphology.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The electrohydrodynamics (EHD) of vesicle suspensions is characterized by studying their pairwise interactions in applied DC electric fields in two dimensions. A boundary integral equation (BIE) based formulation for vesicle EHD is introduced, followed by a solution scheme based on Stokes and Laplace potential theory. In the dilute limit, the rheology of the suspension is shown to vary nonlinearly with the electric conductivity ratio of the interior and exterior fluids. We demonstrate our capability of simulating EHD phenomena including one vesicle deformation, pairwise interaction, and multiple vesicle interactions.

uk: вхід без авторизації

name: A Boundary Integral Equation Formulation for Vesicle Electrohydrodynamics


uk: Математика, природничі науки

description: We will discuss a parallel boundary integral method for simulating highly concentrated vesicle suspensions in a Stokesian fluid. The simulation of high volume fraction vesicle suspensions which are representative of real biological systems (such as blood with 35% - 50% volume fraction for RBCs) presents several challenges. It requires computing accurate vesicle-vesicle interactions at length scales where standard quadratures are too expensive. The inter-vesicle separation can become arbitrarily small leading to vesicle collisions. Numerical errors can accumulate over time, making long-timescale simulations inaccurate. We tackle these challenges by developing state-of-the-art parallel algorithms for efficient computation of boundary integrals and an adaptive time-stepping scheme. We will also discuss algorithms for handling vesicle collisions and re-meshing of vesicle surfaces.

uk: вхід без авторизації

name: Parallel Simulation of Concentrated Vesicle Suspensions in 3D


uk: Математика, природничі науки

description: Blood is a suspension of objects of various shapes, sizes and mechanical properties, whose distribution during flow is important in many contexts. Red blood cells tend to migrate toward the center of a blood vessel, leaving a cell-free layer at the vessel wall, while white blood cells and platelets are preferentially found near the walls, a phenomenon called margination that is critical for the physiological responses of inflammation and hemostasis. Additionally, drug delivery particles in the bloodstream also undergo margination – the influence of these phenomena on the efficacy of such particles is unknown. In this talk a mechanistic theory is developed to describe segregation in blood and other confined multicomponent suspensions. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and wall-induced migration. The theory predicts that the cell-free layer thickness follows a master curve relating it in a specific way to confinement ratio and volume fraction. Results from experiments and detailed simulations with different parameters (flexibility of different components in the suspension, viscosity ratio, confinement, among others) collapse onto the same curve. In simple shear flow, several regimes of segregation arise, depending on the value of a "margination parameter" M. Most importantly, there is a critical value of M below which a sharp "drainage transition" occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes. Results are presented for both Couette and plane Poiseuille flow. Experiments performed in the laboratory of Wilbur Lam indicate the physiological and clinical importance of these observations.

uk: вхід без авторизації

name: Theory of margination in blood and other multicomponent suspensions


uk: Математика, природничі науки

description: The three-dimensional spatiotemporal organization of genetic material inside the cell nucleus remains an open question in cellular biology. During the time between two cell divisions, the functional form of DNA in cells, known as chromatin, fills the cell nucleus in its uncondensed polymeric form, which allows the transcriptional machinery to access DNA. Recent in vivo imaging experiments have cast light on the existence of coherent chromatin motions inside the nucleus, in the form of large-scale correlated displacements on the scale of microns and lasting for seconds. To elucidate the mechanisms for such motions, we have developed a coarse-grained active polymer model where chromatin is represented as a confined flexible chain acted upon by active molecular motors, which perform work and thus exert dipolar forces on the system. Numerical simulations of this model that account for steric and hydrodynamic interactions as well as internal chain mechanics demonstrate the emergence of coherent motions in systems involving extensile dipoles, which are accompanied by large-scale chain reconfigurations and local nematic ordering. Comparisons with experiments show good qualitative agreement and support the hypothesis that long-ranged hydrodynamic couplings between chromatin-associated active motors are responsible for the observed coherent dynamics.

uk: вхід без авторизації

name: Active hydrodynamics of interphase chromatin: coarse-grained modeling and simulations


uk: Математика, природничі науки

description: Microfluidic cell separation techniques are of great interest since they help rapid medical diagnoses and tests. Deterministic lateral displacement (DLD) is one of them. A DLD device consists of arrays of pillars. Main flow and alignment of the pillars define two different directions. Size-based separation of rigid spherical particles is possible as they follow one of these directions depending on their sizes. However, the separation of non- spherical deformable particles such as red blood cells (RBCs) is more complicated than that due to their intricate dynamics. We study the separation of RBCs in DLD using an in-house integral equation solver. We systematically investigate the effects of the interior fluid viscosity and the membrane elasticity of an RBC on its behavior. These mechanical properties of a cell determine its deformability, which can be altered by several diseases. We particularly consider deep devices in which an RBC can show rich dynamics such as tank-treading and tumbling. It turns out that strong hydrodynamic lift force moves the tank-treading cells along the pillars and weak or negative lift force leads the tumbling ones to move with the flow. Thereby, deformability-based separation of RBCs is possible. We also assess the efficiency of the technique for dense suspensions.

uk: вхід без авторизації

name: Deformability-based red blood cell separation using a microfluidic device


uk: Математика, природничі науки

description: Recent work has demonstrated the interesting dynamics possible when considering multicomponent vesicles. Up to now, the dynamics of two dimensional vesicles have been studied. In this work, the dynamics of fully three dimensional, multicomponent vesicles will be investigated. Building upon a volume and surface area conserving Navier-Stokes projection method, the appropriate forcing terms are derived from the energy of a multicomponent membrane. The evolution of the surface components is done via a conserving, surface Cahn-Hilliard model. Time permitting, further extensions to the vesicle model will also be discussed.

uk: вхід без авторизації

name: Three-Dimensional Multicomponent Vesicles - Modeling, Results, and Extensions


uk: Математика, природничі науки

description: We present a fluctuating boundary integral method (FBIM) for Brownian Dynamics (BD) of suspensions of rigid particles of complex shape immersed in a Stokes fluid. Our approach relies on a first-kind boundary integral formulation of a Stochastic Stokes Boundary Value Problem (SSBVP) in which a random surface velocity is prescribed on the particle surface. This random surface velocity has zero mean and covariance proportional to the Green’s function for the Stokes flow (Stokeslet). Furthermore, we demonstrate that discretizing the first-kind formulation using standard boundary integral techniques leads to an efficient numerical method that strictly preserves discrete fluctuation-dissipation balance (DFDB). We develop fast linear-scaling algorithms for performing matrix-vector products and for rapidly generating the random surface velocity by employing the Hasimoto splitting of the Stokeslet, which guarantees that the near-field (short-ranged) and far-field (long-ranged) contributions of the Stokeslet are independently symmetric and positive-definite. This ensures that the computaitonal cost of Brownian simulation is only marginally larger than the cost of deterministic simulations, in stark contrast to traditional BD approaches. To handle the inherent ill-conditioning of the linear system due to the first-kind formulation, we employ an effective block-diagonal preconditioner that ignores all the hydrodynamic interactions between distinct particles. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator. We numerically demonstrate the linear scaling of FBIM and discuss the computational cost of the various components of the algorithm.

uk: вхід без авторизації

name: A Fluctuating Boundary Integral Method for Brownian Suspensions


uk: Математика, природничі науки

description: A common challenge in simulating dense suspension of rigid particles in Stokes flow is the numerical inaccuracies and instabilities that arises due to particle collisions. To overcome this problem, a strong repulsive potential between particles is often prescribed. This in turn leads to numerical stiffness and dramatic reduction in stable time-step sizes. In this work, we eliminate such stiffness by introducing contact constraints explicitly and solving the hydrodynamic equations in tandem with a linear complementarity problem with inequality constraints. Satisfaction of Newtons third law for the collision force is explicitly guaranteed, allowing the consistent calculation of collision stresses. Efficient parallelization for shared-memory and distributed-memory architectures is also implemented. This method can be coupled to any Stokes hydrodynamics solver for particles with various shapes and allows us to simulate $10^4-10^7$ spheres on a laptop, depending on the cost of the Stokes hydrodynamics solver. We demonstrate its performance on a range of applications of rigid suspensions.

uk: вхід без авторизації

name: Resolving collisions in Stokes suspensions with an efficient and stable potential-free constrained optimization algorithm


uk: Математика, природничі науки

description: When discretizing the Navier-Stokes equations with an IMEX scheme in time, the modified Stokes equation must be solved to advance the solution from one time step to the next. The Green's function for the modified Stokes equation is given in terms of the difference of the Green's functions for the Laplace and modified Helmholtz equations. Unfortunately, it is unstable, particularly on fine grids or at low Reynolds number, to evaluate the Green's function by first evaluating the Laplace and modified Helmholtz Green's functions and then taking the difference. As an alternative, we present a fast multipole method for the modified Stokes kernel itself, which leverages new special functions to stably evaluate the interactions.

uk: вхід без авторизації

name: A stabilized fast multipole method for fluid flow


Regular Maps - an overview

uk: Математика, природничі науки

description: Introduction (by Marston Conder and Tom Tucker) to regular maps and edge-transitive maps, including some important open questions in this theme area.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Introduction (by Ernesto Girondo and Gabino González-Diez) to Belyi theory and the absolute Galois group, including some important open questions in this theme area.

uk: вхід без авторизації

name: A quick introduction to dessins d'enfants, Belyi's theorem and Galois action


uk: Математика, природничі науки

description: Introduction (by Allen Broughton and Aaron Wootton) to defining equations for a Riemann surface, including some important open questions in this theme area.

uk: вхід без авторизації

name: Defining equations for a Riemann surface

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


A database of group actions

uk: Математика, природничі науки

description: In the late 1990s, Thomas Breuer created an algorithm, and wrote corresponding computer code, which determines all groups acting on Riemann surfaces of a fixed genus. His code also determined generating vectors for the actions, but he did not record that data. The results of his program up to genus 15, along with additional information such as if the Riemann surface is hyperelliptic or cyclic trigonal, the decomposition of the corresponding Jacobian Variety, and the dimension of the corresponding Shimura variety, can now be found online at: http://www.lmfdb.org/HigherGenus/C/Aut/. We’ll briefly introduce these pages, discuss features of them, and mention future planned additions.

uk: вхід без авторизації


uk: Математика, природничі науки

description: I will present a number of relevant results which may be not known in the ribbon graph or dessins communities.

uk: вхід без авторизації

name: Some topics on dessins and ribbon graphs


Almost simple groups and polytopes

uk: Математика, природничі науки

description: In this talk we will briefly summarise what is known about almost simple groups acting regularly/chirally on abstract polytopes, and state some open questions.

uk: вхід без авторизації


uk: Математика, природничі науки

description: During numerous talks and conferences, a question was often raised: How to find a complete set of combinatorial and/or group-theoretic invariants of the Galois action on dessins. We will show that this is impossible. Indeed, sometimes combinatorial orbits of dessins split into several Galois orbits because of some subtle Diophantine relations between degrees of of vertices and faces.

uk: вхід без авторизації

name: Diophantine invariants of dessins d'enfants


Endotrivial modules via homotopy theory

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Equivariant cohomology and fixed points of smooth Calogero-Moser spaces


keywords:
Mathematics
Group theory and generalizations

uk: Математика, природничі науки

uk: вхід без авторизації

name: Restriction of characters to Sylow p-subgroups


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

uk: Математика, природничі науки

uk: вхід без авторизації

name: Chromatic Aberration Corrected TEM: State of the Art and Future Challenges in Data Acquisition and Analysis


uk: Математика, природничі науки

description: From the minute 19:42 of video does not have audio. Molecules imaged using cryo-electron microscopy (cryo-EM) often exhibit a significant amount of variability, be it in conformation or composition. The molecules are typically represented as 3D volume maps of the electric potential as a function of space. In order to characterize the variability of these maps, the authors propose a method for fast and accurate estimation of the 3D covariance matrix. The estimator is given by the least-squares solution to a linear inverse problem and is efficiently calculated by exploiting its 6D convolutional structure. Combining this with a circulant preconditioner, the solution is obtained using the conjugate gradient method. For $n$ images of size $N$-by-$N$, the computational complexity of the algorithm is $O(n N^4 + \sqrt{\kappa} N^6 \log N)$, where $\kappa$ is a condition number typically of the order $200$. The method is evaluated on simulated and experimental datasets, achieving results comparable to the state of the art at very short runtimes.

uk: вхід без авторизації

name: Structural Heterogeneity from 3D Covariance Estimation in Cryo-EM


uk: Математика, природничі науки

description: The talk of Tamir Bendory will focus on invariants for the multireference alignment (MRA) and cryo-EM problems. MRA is a simplification and abstraction of the cryo-EM problem. In MRA, we aim to estimate a signal from its circularly-translated copies in high noise regimes. It will be shown that the optimal estimation rate for MRA can be achieved by exploiting features of the signal that are invariant under translation. In a similar manner, these invariant features are used for the heterogeneous MRA problem in which one aims to estimate multiple signals simultaneously. Then, the invariants of the cryo-EM problem will be discussed using the framework of Kam's method. We will show how an ab initio model of the molecule can be estimated directly from the data, without estimating the viewing direction. Finally, we will discuss extensions of Kam's method.

uk: вхід без авторизації

name: Invariants for multireference alignment and cryo-EM


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bright and Dark-Field Imaging of Complex Oxides


uk: Математика, природничі науки

description: A general problem is to understand all (injective) homomorphisms between (finite index subgroups of) mapping class groups of surfaces. Birman and Hilden proved that if $S\rightarrow X$ is a regular branched covering space of surfaces, there is an embedding of the subgroup of the mapping class group of $X$ consisting of mapping classes that have representatives that lift to $S$ in the mapping class group of $S$ modulo the group of deck transformations. This relationship does not always hold for irregular branched covers. We give a necessary condition and a sufficient condition for when such an embedding exists. We also give new explicit examples that satisfy the necessary condition and examples that do not satisfy the sufficient condition.

uk: вхід без авторизації

name: Homomorphisms between mapping class groups of surfaces


uk: Математика, природничі науки

description: In this talk we introduce a surprising correspondence between $(m,n)$-complete regular dessins and admissible pairs of skew-morphisms of the cyclic groups of orders $m$ and $n$. A skew-morphism $\varphi$ of a finite group $A$ is a permutation on $A$ such that $\varphi(1)=1$ and $\varphi(xy)=\varphi(x)\varphi^{\pi(x)}(y)$ for all $x,y\in A$ where $\pi:A\to\mathbb{Z}_{|\varphi|}$ is an integer function. We determine the pairs $(m,n)$ for which there exists exactly one dual pair of $(m,n)$-complete regular dessins, thus generalising an earlier result by Jones, Nedela and \v Skoviera (2008). This is joint work with Y.Q.Feng, Kan Hu and M. {\v S}koviera.

uk: вхід без авторизації

name: Skew morphisms of cyclic groups and complete regular dessins


uk: Математика, природничі науки

description: Define QC$(n)$ to be the number of isomorphisms classes of quasiplatonic cyclic $n$-gonal surfaces. We use formulas of R.\ Benim and A.\ Wootton to describe a method for computing QC$(n)$. We also relate QC$(n)$ to the number of regular dessins d'enfants having a cyclic group of automorphisms of order $n$.

uk: вхід без авторизації

name: Counting quasiplatonic cyclic group Actions of Order n


uk: Математика, природничі науки

uk: вхід без авторизації

name: Morita equivalence and normal subgroups of index $p$


uk: Математика, природничі науки

uk: вхід без авторизації

name: On the inductive blockwise Alperin weight condition


uk: Математика, природничі науки

uk: вхід без авторизації

name: Some refinements of Dade's projective conjecture


uk: Математика, природничі науки

uk: вхід без авторизації

name: The Alperin weight conjecture for symmetric and general linear groups revisited


uk: Математика, природничі науки

uk: вхід без авторизації

name: On Galois automorphisms acting on characters and the Sylow 2-normalizer conjectures


uk: Математика, природничі науки

uk: вхід без авторизації

name: Structure of root data and smooth regular embeddings

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


uk: Математика, природничі науки

uk: вхід без авторизації

name: Does (co-)sparsity characterize the success (or failure) of l1-analysis recovery in compressed sensing?


uk: Математика, природничі науки

uk: вхід без авторизації

name: Structure Optimization for Complex Materials Incorporating Microscopy (and Other) Data


uk: Математика, природничі науки

description: A (face-)primer hypermap is a regular oriented hypermap whose orientation-preserving automorphism group $G$ acts faithfully on the hyperfaces. In this paper, we investigate the primer hypermaps for which $G$ is nilpotent and the hypervertex-valency is a prime $p$. (We call these PNp-hypermaps.) We prove that for any PNp-hypermap, the group $G$ must be a finite $p$-group, and the number of hyperfaces is bounded above by a function of the nilpotency class of $G$. Moreover, we show that for any positive integer $c$, there is a unique PNp hypermap $H_c$ of class $c$ attaining the given bound, and every other PNp hypermap of class at most $c$ is a quotient of H_c.

uk: вхід без авторизації

name: Nilpotent primer hypermaps with hypervertices of valency a prime


Dessins d’enfants and a curve of Wiman

keywords:
Mathematics
Manifolds and cell complexes
Group theory and generalizations
Discrete mathematics

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Generic modular representations and Hilbert schemes of surfaces


uk: Математика, природничі науки

description: 2D materials such as graphene and transition metal dichalcogenides (TMDCs) have demonstrated new properties underpinned by exotic charge carriers with enhanced conductivity and novel light-matter interactions. These properties can be harnessed by ‘stacking’ 2D crystals on top of one another to form a van der Waals heterostructure: a series of atomically thin sheets glued together by weak forces[1]. Heterostructures made in this way allow the new properties of 2D materials to be characterised and applied as transistors[2], optical modulators[3] and light emitting diodes[4]. We demonstrate cross-sectional STEM images of these heterostructures, showing how each 2D crystal interfaces its neighbour at high resolution. Cross sections are fabricated in a dual-beam FIB-SEM instrument using the in situ lift-out method and polished with low energy ions to achieve electron transparency.[5] Cross sections were imaged in high resolution HAADF STEM using a probe-side aberration corrected FEI Titan G2 80-200 kV with an X-FEG electron source. The nature of these van der Waals interfaces not only determines the carrier injection between components, but also affects the bandstructure of the device and its ultimate functionality. However, measurements at these buried interfaces are only possible by cross-sectional STEM. Image processing and principle component analysis were used to determine the width of the interfaces, demonstrating that some 2D materials have cleaner interfaces than others and that fabrication in inert atmosphere produces better interfaces than in air.[6] This analysis is extended to bends and folds which underpin the structure of kink-bands in graphite and other bulk ‘van der Waals’ materials such as hexagonal boron nitride and MoSe2. Extensive image processing allows the bent basal planes to be fitted by functions to reveal their radius of curvature, angle and distance to the nearest neighbour plane. Three broad classes of bend emerge which depend on the bend angle and crystal thickness. [1] A. K. Geim and I. V. Grigorieva, ‘Van der Waals heterostructures’, Nature, vol. 499, no. 7459, pp. 419–425, Jul. 2013. [2] L. Britnell et al., ‘Field-Effect Tunneling Transistor Based on Vertical Graphene Heterostructures’, Science, vol. 335, no. 6071, pp. 947–950, Feb. 2012. [3] P. A. Thomas et al., ‘Nanomechanical electro-optical modulator based on atomic heterostructures’, Nat. Commun., vol. 7, p. ncomms13590, Nov. 2016. [4] F. Withers et al., ‘Light-emitting diodes by band-structure engineering in van der Waals heterostructures’, Nat Mater, vol. 14, no. 3, pp. 301–306, 2015. [5] M. Schaffer, B. Schaffer, and Q. Ramasse, ‘Sample preparation for atomic-resolution STEM at low voltages by FIB’, Ultramicroscopy, vol. 114, no. 0, pp. 62–71, 2012. [6] A. P. Rooney et al., ‘Observing Imperfection in Atomic Interfaces for van der Waals Heterostructures’, Nano Lett., Jul. 2017.

uk: вхід без авторизації

name: Image processing to characterise 2D material heterostructures and graphitic folds


uk: Математика, природничі науки

description: Electron tomography is a technique to obtain 3D nanoscale image reconstructions from 2D electron microscopy projection images, i.e. a tomographic tilt series. Due to the nature of imaging at the nanoscale, the data processing procedures leading from data acquisition to accurate approximation of the 3D scene are far from automated and rarely streamline. These challenges include accurate alignment of the sinogram data and accurate reconstruction from a limited number angles in the tilt series. This talk addresses some of the most recent advances to resolving these issues and the concerns that still remain. We consider two new methods for accurate alignment of the sinogram data, which can be characterized by center-of-mass methods and phase based autofocusing [1,2]. Next, we consider accurate 3D reconstruction techniques based on higher order total variation L1 regularization and multiscale generalizations [3]. [1] Sanders, Toby, et al. "Physically motivated global alignment method for electron tomography." Advanced Structural and Chemical Imaging 1.1 (2015): 4. [2] Sanders, Toby, Ilke Arslan. “Improved 3D resolution of electron tomograms using robust mathematical data processing techniques.” Microscopy and Microanalysis. (accepted, 2017). [3] Sanders, Toby, et al. "Recovering fine details from under-resolved electron tomography data using higher order total variation L1 regularization." Ultramicroscopy 174 (2017): 97-105.

uk: вхід без авторизації

name: Techniques for Data Alignment and Image Reconstruction for Electron Tomography


uk: Математика, природничі науки

description: Image simulation for scanning transmission electron microscopy at atomic resolution for samples with realistic dimensions can require very large computation times using existing simulation algorithms. We present a new algorithm named PRISM that combines features of the two most commonly used algorithms, namely the Bloch wave and multislice methods. PRISM uses a Fourier interpolation factor f that has typical values of 4–20 for atomic resolution simulations. We show that in many cases PRISM can provide a speedup that scales with f^4 compared to multislice simulations, with a negligible loss of accuracy. We demonstrate the usefulness of this method with large-scale scanning transmission electron microscopy image simulations of a crystalline nanoparticle on an amorphous carbon substrate. We also present a software package called Prismatic for parallelized simulation of image formation in STEM using both the PRISM and multislice methods. By distributing the workload between multiple CUDA-enabled GPUs and multicore processors, accelerations as high as 1000x for PRISM and 15x for multislice are achieved relative to traditional multislice implementations using a single 4-GPU machine.Prismatic is freely available both as an open-source CUDA/C++ package with a graphical user interface for Windows and OSX, and as a Python package.

uk: вхід без авторизації

name: PRISM and Prismatic - a new algorithm and code for very fast scanning transmission electron microscopy (STEM) simulations


uk: Математика, природничі науки

uk: вхід без авторизації

name: Phase measurement beyond the shot-noise limit


uk: Математика, природничі науки

description: Teichmüller curves are totally geodesic complex curves inside the moduli space of Riemann surfaces. Under a Prym-Torelli map, one can see them as curves in some Hilbert modular variety, which parametrises abelian varieties with real multiplication. We give an overview of how to cut out these curves as the vanishing locus of Hilbert modular forms and the invariants that can be computed from this viewpoint.

uk: вхід без авторизації

name: Teichmüller curves and Hilbert modular surfaces


uk: Математика, природничі науки

uk: вхід без авторизації

name: Introduction to incidence geometry with an emphasis on polytopes, hypertopes, maps and maniplexes


External symmetries of regular maps

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Overview on n-gonal automorphism of Riemann surfaces


Cayley Maps and Skew Morphisms

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: On the blockwise modular isomorphism problem


uk: Математика, природничі науки

uk: вхід без авторизації

name: Puig equivalence conjecture for 2-blocks


uk: Математика, природничі науки

uk: вхід без авторизації

name: Fields of character values in finite groups


On the average degree of characters

uk: Математика, природничі науки

uk: вхід без авторизації


Perfect isometries and basic sets

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

description: In his talk, J. LeBeau presented his work improving both the accuracy and precision of STEM imaging. While electron microscopy has been revolutionized by the aberration corrector, which dramatically improved spatial resolution, real-space distance measurements have remained semi-quantitative. In particular, accuracy and precision for scanning transmission electron microscopy (STEM) was significantly hampered by the presence of sample drift and scan distortion. Until recently, this limitation has obscured the capabilities to characterize minute changes to the atomic structure that can ultimately define material properties. He discussed his approach to resolve this problem, called revolving scanning transmission electron microscopy (RevSTEM). The method uses a series of fast-acquisition STEM images, but with the scan coordinates rotated between successive frames, which encodes drift rate and direction to the resulting image distortion. Multiple case studies were presented to highlight the power of this new technique to characterize materials. For example, picometer precise measurements were shown to enable the direct quantification of static atomic displacements within a complex oxide solid solution due to local chemistry. He also discussed recent work implementing deep convolutional neural networks to autonomously quantify electron diffraction data. The networks were shown to first calibrate the zero-order disk size, center position, and rotation without the need for pretreating the data for sample thickness and tilt measurements. The performance of the network was explored as a function of a variety of variables including thickness, tilt, and dose. The processing speed was also shown to far outpace a least squares approach by orders of magnitude. He also discussed the generality of the method to other materials/orientations as well as a hybrid approach that combines the features of the neural network with least squares fitting for even more robust analysis.

uk: вхід без авторизації

name: Quantifying local structure and chemistry with the scanning transmission electron microscope


Processing of EDX tomography data

uk: Математика, природничі науки

description: The procedure consists of several steps: analysis of the combined spectrum of all the data; identification and extraction of the concentration of the main elements for each of the frames; aligning of the frames; and tomographic reconstruction of each of the main elements. The analysis includes calculation of local centre of mass displacements, decomposition of the combined spectrum into a sum of gaussians, and discrete filtering for extraction of elements concentration. The alignment procedure estimates the frame displacements using the centres of mass of several element maps. The tomography reconstruction uses a generalization of TV regularization employing total variation term of order two. This is a joint work with Kelsey Larkin (University of South Carolina), Zineb Saghi (CEA-LETI, Grenoble), and Toby Sanders (Arizona State University).

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bad primes and character degrees in finite groups of Lie type


On Pyber's base size conjecture

uk: Математика, природничі науки

uk: вхід без авторизації

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


uk: Математика, природничі науки

uk: вхід без авторизації

name: Morita equivalences with endopermutation source


uk: Математика, природничі науки

description: Deep learning introduces the potential for autonomous S/TEM characterization, a step towards unsupervised data acquisition and analysis through machine learning. Whole image classification is the first step towards the long-term goal of autonomous image data acquisition and analysis. We have successfully retrained AlexNet, b-FCN, and U-Net, pre-existing deep learning Convolutional Neural Networks(CNNs), for autonomous, whole image classification and analysis, on TEM image datasets.

uk: вхід без авторизації

name: 4D Holography of Beam/topological Defect Interaction and Big, Smart, and Deep Data


uk: Математика, природничі науки

uk: вхід без авторизації

name: Optimization challenges from robust statistics


uk: Математика, природничі науки

uk: вхід без авторизації

name: Role of Optimization Algorithms in Deep Learning


Conformal Field Theory Correlators

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Anthropic Estimates for Many Parameters of Physics and Astronomy


(Augmented) Phase-Space Quantization

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Loops of gauge fields, gravitons, and strings


uk: Математика, природничі науки

uk: вхід без авторизації

name: Superconducting Dirac fermions and mirror symmetry


uk: Математика, природничі науки

uk: вхід без авторизації

name: More than 100 years of superconductivity?: Do we need a paradigm shift


uk: Математика, природничі науки

uk: вхід без авторизації

name: A (thorough) introduction to mathematics and physics


uk: Математика, природничі науки

uk: вхід без авторизації

name: Contemporary tools for stellar interactions: where at least on star is a "normal" star


Connectivity of the Cosmic Web

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Measures of Statistical Complexity and Dynamical System Applications


uk: Математика, природничі науки

uk: вхід без авторизації

name: Spacetime Entanglement Entropy: From Continuum Geometries to Discrete Causal Sets


What is mirror symmetry?

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: A New Type of Many-Body Majorana Zero Modes in Fermionic Flux Ladder Model


uk: Математика, природничі науки

uk: вхід без авторизації

name: Maximum Likelihood Estimation under Total Positivity


uk: Математика, природничі науки

uk: вхід без авторизації

name: Learning Developmental Landscapes from Single Cell Gene Expression with Optimal Transport


uk: Математика, природничі науки

uk: вхід без авторизації

name: Dissipativity Theory for Algorithm Analysis


Sketchy Decisions

uk: Математика, природничі науки

uk: вхід без авторизації

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


uk: Математика, природничі науки

description: There is an increasing focus on geo-spatial linking of the large data sets related to both health and the environment at the urban level. For the last several years, I have been leading a team to build the Kinder Institute for Urban Research Urban Data Platform (UDP) to study the greater Houston area. Similar to many open government data platforms, the UDP hosts a large amount of data across many categories for the Houston area. The objective is to build up a system that helps to understand how residents live, work, learn and play in the area. In this discussion, I will demonstrate the use of the UDP resources coupled with advanced space-time statistical modeling to further our understanding of the link between air quality and health. This knowledge has led to improved management of childhood asthma faced by over 6000 students in the Houston Independent School District. I will close with how the UDP system is facilitating environmental sampling in the post-Hurricane Harvey recovery period and offer insights on developing a space-time cumulative environmental map for the area.

uk: вхід без авторизації

name: Furthering Our Understanding of the Link between Health and Environment in an Urban Setting


uk: Математика, природничі науки

description: In a world with rapid climactic change and intensifying extremes, it becomes increasingly important to improve predictive modeling. The Sustainability and Data Sciences Laboratory (SDS Lab) at Northeastern University in Boston, MA has taken an interdisciplinary approach to understanding interconnected complex systems using a combination of mathematical, scientific, engineering, and computational tools. Through the use of machine learning, statistics, physics, and nonlinear dynamical methods—such as chaos and complex networks—we have developed enhanced quantitative understandings of extremes and change in a way that can be translated so as to inform policy and create more resilient social systems. The focus of our research centers around risk and adaptation, resilience of critical infrastructure and lifeline networks, and sustainability of ecosystems and resources. This presentation provides an overview of the research done at the SDS Lab, including methodologies, the use of interdisciplinary approaches, and important trends and outputs being observed in our results.

uk: вхід без авторизації

name: Big Data, Downscaling, and Interdisciplinary Approaches to Understanding Extreme Events


uk: Математика, природничі науки

description: We present an approach to assess the accuracy of climate models based on multi-objective optimization and an infrastructure to support analyzing massive amounts of the model data. Many previous studies have demonstrated that multi-model ensembles generally show better skill than each ensemble member. When generating weighted multi-model ensembles, the first step is measuring the performance of individual model simulations using observations. There is a consensus on the assignment of weighting factors based on a single evaluation metric. When considering only one evaluation metric, the weighting factor for each model is proportional to a performance score or inversely proportional to an error for the model. While this conventional approach can provide appropriate combinations of multiple models, the approach confronts a big challenge when there are multiple metrics under consideration. When considering multiple evaluation metrics, it is obvious that a simple averaging of multiple performance scores or model ranks does not address the trade-off problem between conflicting metrics. So far, there seems to be no best method to generate weighted multi-model ensembles based on multiple performance metrics. The current study applies the multi-objective optimization, a mathematical process that provides a set of optimal trade-off solutions based on a range of evaluation metrics, to combining multiple performance metrics for the global chemistry climate models and generating a weighted multi-model ensemble. In general, both observational and model data required for this optimization effort are scattered across the network. As a result, the optimization can be hampered by increasing costs of computation and communication between data servers where NASA satellite data and climate model simulations are archived. To address this Big Data challenge, we outline a plan to apply the Virtual Information Fabric Infrastructure (VIFI) to the multi-objective optimization of climate model simulations with large ensembles. VIFI enables executing scalable analytics optimized for distributed data systems. Our proof-of-concept implementation shows the considerable variability across the climate simulations. We conclude that the optimally weighted multi-model ensemble always shows better performance than an arithmetic ensemble average and may provide reliable future projections. The VIFI architecture, including resource management and scheduling, is critical to achieve processing of massive Earth Science datasets from observations and climate models.

uk: вхід без авторизації

name: Multi-objective optimization for generating a weighted multi-model ensemble: application of the Virtual Information Fabric Infrastructure (VIFI) distributed analytics framework


uk: Математика, природничі науки

description: We will present a technique for studying the geometry of data-clouds, using multivariate quantiles and extremes. Using multivariate quantiles one can construct data-depth functions, which are rank-like functions that may be used for center-to-tails ordering of observations. Several robust inferential procedure can be based on data-depth functions and multivariate quantiles, and we will first discuss a few such techniques. Then, we present a method of using resampling coupled with data-depth functions, that can be used for consistently estimating the joint distribution of all parameter estimators under all candidate models, while simultaneously assigning a score to each candidate model. The model-score may be used for model evaluation and selection. The candidate models do not need to be nested within each other, and the number of parameters in each model as well as in the data generating process can grow with sample size. An illustrative example of prediction and obtaining the true physical forces driving Indian summer monsoon rainfall will be presented. This talk includes joint work with Lindsey Dietz, Megan Heyman, and Subho Majumdar.

uk: вхід без авторизації

name: Data-geometry and resampling-based inference for selecting predictors for monsoon precipitation


uk: Математика, природничі науки

description: Globalization has created complex problems that can no longer be adequately forecasted and mitigated using traditional data analysis techniques and data sources. Disease spread is a major health concern around the world and is compounded by the increasing globalization of our society. As such, epidemiological modeling approaches need to account for rapid changes in human behavior and community perceptions. Social media has recently played a crucial role in informing and changing the response of people to the spread of infectious diseases. Recent events, such as the 2014-2015 Ebola epidemic and the 2015-2016 Zika virus epidemic, have highlighted the importance of reliable disease forecasting for decision support. This talk will discuss: 1) an operational analytic that provides global context during an unfolding outbreak and 2) a framework that combines clinical surveillance data with social Internet data and mathematical models to provide probabilistic forecasts of disease incidence and will demonstrate the value of Internet data and the real-time utility of our approach.

uk: вхід без авторизації

name: Real-time Social Internet Data to Guide Desease Forecasting Models


uk: Математика, природничі науки

description: In this presentation we will define Synthetic populations and illustrate the value it provides to modelers and policy makers. Accuracy of models optimizing response to disease, natural disasters, or distributions of various resources among people depends on the accuracy of the knowledge about the population. This knowledge is not limited to demographics, but has to consider geography, ethnography, social connectivity, and many other factors. Synthetic populations are computational representations of every person in a country. They provide an opportunity to probabilistically link multiple datasets into an accurate database that could be then used by modelers to simulate outcomes of interest, such as evacuation routes, distributions of vaccines, optimal location of first responders, etc. With large amounts of information that is publicly available linking multiple databases poses a threat to privacy. Synthetic populations are natural means to provide census-like accuracy without violating anyone’s privacy. Finally, Synthetic populations could be projected into the future so that the forecasts of 2020 epidemics would be based on 2020 projection and not on 2010 data. This is critical for forecasting the consequences of climate change, population aging and depletion of natural resources.

uk: вхід без авторизації

name: Agent-Based (and other) Modeling with Synthetic Populations


uk: Математика, природничі науки

description: Modeling spatio-temporal flows is a challenging problem, as dynamic spatio-temporal data possess underlying complex interactions and nonlinearities. Traditional statistical modeling approaches use a data generating process, generally motivated by physical laws or constraints. Deep learning (DL) is a form of machine learning for nonlinear high dimensional data reduction and prediction. It applies layers of hierarchical hidden variables to capture these interactions and nonlinearities without using a data generating process. This talk uses a Bayesian perspective of DL to explain its application to the prediction and uncertainty quantification of spatio-temporal flows from big data. Using examples in traffic flow and high frequency trading, we demonstrate why DL is able to predict sharp discontinuities in spatio-temporal flows. We proceed to discussing the far reaching practical implications of embedding deep spatio-temporal flow predictors into novel actuarial climate models.

uk: вхід без авторизації

name: Uncertainty Quantification of Spatio-Temporal Flows with Deep Learning


uk: Математика, природничі науки

description: The ranges of plants and animals are moving in response to change in climate. In particular, if temperatures rise, some species will have to move their range. On a fine spatial scale, this may mean moving up in elevation; on a larger spatial scale, this may result in a latitudinal change. In this regard, the notion of velocity of climate change has been introduced to reflect change in location corresponding to change in temperature. If location is viewed as one dimensional, say x and time is denoted by t, the velocity becomes dx/dt. In the crudest form, given a relationship between temperature (Temp) and time as well as a relationship between Temp and location, we would have dxdt=dTempdt/Tempdx. The contribution here is to extend this simple definition to more realistic models, models incorporating more sophisticated explanations of temperature, models introducing spatial locations, and, most importantly, models that are stochastic over space and time. With such model components, we can learn about directional velocities, with uncertainty. We can capture spatial structure in velocities. We can assess whether velocities tend to be positive or negative, and in fact, whether and where they tend to be significantly different from 0. Extension of the model development can be envisioned to the species level, i.e., to species- specific velocities. Here, we replace a temperature model as the driver with presence-only or presence/absence models. We can make attractive connections to customary advection and diffusion specifications through partial differential equations. We illustrate with 118 years of data at 10 km resolution (resulting in more than 21,000 cells) for the eastern United States. We adopt a Bayesian framework and can obtain posterior distributions of directional velocities at arbitrary spatial locations and times.

uk: вхід без авторизації

name: Stochastic Modeling for Climate Change Velocities


uk: Математика, природничі науки

description: This talk presents methods to estimate the number of changepoint time(s) and their locations in time-ordered data sequences when prior information is known about some of the changepoint times. A Bayesian version of a penalized likelihood objective function is developed from minimum description length (MDL) information theory principles. Optimizing the objective function yields estimates of the changepoint number(s) and location time(s). Our MDL penalty depends on where the changepoint(s) lie, but not solely on the total number of changepoints (such as classical AIC and BIC penalties). Specifically, configurations with changepoints that occur relatively closely to one and other are penalized more heavily than sparsely arranged changepoints. The techniques allow for autocorrelation in the observations and mean shifts at each changepoint time. This scenario arises in climate time series where a "metadata" record exists documenting some, but not necessarily all, of station move times and instrumentation changes. Applications to climate time series are presented throughout.

uk: вхід без авторизації

name: Bayesian Multiple Breakpoint Detection: Mixing Documented and Undocumented Changepoints


Deep Learning: A Bayesian Perspective

uk: Математика, природничі науки

description: Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. We present a Bayesian probabilistic perspective, and provide a number of insights, for example, more efficient algorithms for optimization and hyper-parameter tuning, and an explanation of finding good predictors. Traditional high-dimensional data reduction techniques, such as principal component analysis (PCA), partial least squares (PLS), reduced rank regression (RRR), projection pursuit regression (PPR) are all shown to be shallow learners. Their deep learning counterparts exploit multiple deep layers of data reduction which provide performance gains. We discuss stochastic gradient descent (SGD) training optimisation, and Dropout (DO) that provide estimation and variable selection, as well as Bayesian regularization, which is central to finding weights and connections in networks to optimize the bias-variance trade-off. To illustrate our methodology, we provide an analysis of spatio-temporal data. Finally, we conclude with directions for future research.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Drought is a spatio-temporal phenomenon; however, due to limitations of traditional statistical techniques it is often analyzed solely temporally—for instance, by taking the hydroclimate average over a spatial area to produce a timeseries. Herein, we use machine learning based Markov Random Field methods that identify drought in three-dimensional space-time. Critically, the joint space-time character of this technique allows both the temporal and spatial characteristics of drought to be analyzed. We apply these methods to climate model output from the Coupled Model Intercomparison Project phase 5 and tree-ring based reconstructions of hydroclimate over the full Northern Hemisphere for the past 1000 years. Analyzing reconstructed and simulated drought in this context provides a paleoclimate constraint on the spatio-temporal character of past and future droughts, with some surprising and important insights into future drought projections. Climate models, for instance, suggest large increases in the severity and length of future droughts but little change in their width (latitudinal and longitudinal extent). These models, however, exhibit biases in the mean width of drought over large parts of the Northern Hemisphere, which may undermine their usefulness for future projections. Despite these limitations, and in contrast to previous high-profile claims, there are no fundamental differences in the spatio-temporal character of simulated and reconstructed drought during the historical interval (1850-present), with critical implications for our confidence in future projections derived from climate models.

uk: вхід без авторизації

name: Paleoclimate constraints on the spatio-temporal character of past and future drought in climate models


uk: Математика, природничі науки

description: The oceans plays a pivotal role in the global climate system, and to develop our understanding there is a need to connect physical models of ocean dynamics with vast arrays of data collected from modern sensors. In this talk, I will present a stochastic spatiotemporal model that describes the motion of freely drifting satellite-tracked instruments, commonly known as “drifters”. The trajectories of drifters provide useful measurements about currents, turbulence and dispersion across our oceans. The challenge is that the data moves in both time and space, sometimes referred to a “Lagrangian” perspective, and these types of data require new data science methodology. Our spatiotemporal model captures effects that are oscillatory, spatially anisotropic, and have varying degrees of small-scale roughness or fractal dimension. We use our model to analyse the entire Global Drifter Program database of observations since 1979, constituting over 70 million data points from over 20,000 drifters. Our findings uncover interesting spatial patterns and develop general understanding of ocean circulation and ocean surface dynamics. This is a joint work with Sofia Olhede (UCL) and Jonathan Lilly and Jeffrey Early (NWRA, Seattle).

uk: вхід без авторизації

name: Spatiotemporal modelling of ocean surface drifter trajectories


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. 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


uk: Математика, природничі науки

description: Agriculture is one of the sectors most likely to be impacted by climate change. Agricultural producers have always operated under high levels of production and price risk, but there are concerns that climate change will further exacerbate these risks while making recent historical experience less predictive of future conditions. The impacts are generally expected to increase over time as temperatures become more likely to exceed thresholds that negatively impact crop growth and the distribution of precipitation is increasingly altered. However, there is considerable variation in future climate projections both temporally and spatially as well as differences in responsiveness to climate change across different crops and production practices. Agriculture is a very heterogeneous sector, making it important to incorporate disaggregated biophysical data within economic models used to assess the potential impacts of alternative climate and policy scenarios. To assess potential long-term implications of climate change on landowner decisions regarding land use, crop mix, and production practices, we combine the outputs of global circulation models (GCMs) with the Environmental Policy Integrated Climate (EPIC) crop process model and the Forest and Agricultural Sector Optimization Model (FASOM) economic model. GCMs use assumptions regarding future emissions and atmospheric concentrations of GHGs as model inputs to simulate impacts on the future spatial distribution of temperature and precipitation across the globe. The outputs of the GCMs were then incorporated into EPIC to simulate the impacts of alternative climate scenarios on crop yields over time. Crop growth is simulated by calculating the potential daily photosynthetic production of biomass. Daily potential growth is decreased by stresses caused by shortages of solar radiation, water, and nutrients, by temperature extremes and by inadequate soil aeration. Thus, EPIC can account for the effects of climate-induced changes in temperature, precipitation, and other variables, including episodic events affecting agriculture, on potential yields. The model also includes a nonlinear equation accounting for plant response to CO2 concentration and has been applied in several previous studies of climate change impacts. In this application, we simulated yields for barley, corn, cotton, hay, potatoes, rice, sorghum, soybeans, and wheat under each climate scenario considered. These crop yields were then used as inputs into a stochastic version of FASOM to assess market outcomes given climate-induced shifts in yields that vary by crop and region. The stochastic version of the model is used to model crop allocation decisions by crop and management categories based on the relative returns and risk associated with alternative cropping patterns under each of the modeled scenarios. This enables exploration of potential shifts in cropping patterns within and across regions in response to changing yield distributions as well as the associated price effects. In addition to implications for landowner decisions regarding land use, crop mix, and production practices, changing agricultural risks could potentially affect the performance of risk management strategies such as crop insurance programs. Thus, we also explore the potential implications of changes in yield and price distributions for these insurance markets.

uk: вхід без авторизації

name: Modeling Climate Change Impacts on Agricultural Production and Implications for Risk Management


uk: Математика, природничі науки

description: Genetic diversity is the engine of evolution. Thanks to it species can adapt to different environmental conditions and we humans are able to domesticate wild species, modifying them to fit our needs. When climate changes, species either move with it, become extinct or adapt to the new conditions. The domesticated species upon which our food systems are based are also affected by environmental conditions, so adapting them to the current human induced climate change is of special concern. Mexico is a mega-diverse country where the domestication of important cultivates occurred, such as maize, beans and pumpkins. As a consequence, here there are crop wild relatives that have been evolving for million of years; and traditional crop varieties that have been grown in a wide range of environmental conditions for thousands of years, and that currently continue evolving. The genetic diversity enclosed within these crop wild relatives and traditional varieties is enormous, and likely holds the needed diversity to adapt our cultivate to climate change. Here, I will discuss the need to appreciate Mexican crops genetic diversity in terms of the evolutionary service it provides; and then I will discuss the outcomes and challenges of characterizing, modeling, conserving and using such genetic diversity at a national scale.

uk: вхід без авторизації

name: Genetic diversity in space and time, an insurance vs climate change


uk: Математика, природничі науки

description: In general, reliable trend estimates for temperature data may be challenging to obtain, mainly due to data scarcity. Short data series represent an intrinsic problem, whereas spatial sparsity may, in the case of spatially correlated data, be managed by adding appropriate spatial structure to the model. In this study, we analyse European temperature data over a period of 65 years. We search for trends in seasonal means and investigate the effect of varying the data grid resolution on the significance of the trend estimates obtained. We consider a set of models with different temporal and spatial structures and compare the resulting spatial trends along axes of model complexity and data grid resolution. This is ongoing work and the presentation will sketch the idea and give some preliminary results.

uk: вхід без авторизації

name: Spatial trend analysis of gridded temperature data sets at varying spatial scales


uk: Математика, природничі науки

uk: вхід без авторизації

name: First Order Methods Beyond Smoothness and Convexity


uk: Математика, природничі науки

uk: вхід без авторизації

name: "New Sh*t Has Come To Light": Perspectives on Integer Programming for Sparse Optimization

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


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Framework for Globally Convergent Methods in Nonsmooth and Nonconvex Optimization


uk: Математика, природничі науки

uk: вхід без авторизації

name: Complexity analysis of second-order algorithms based on line search for smooth nonconvex optimization


uk: Математика, природничі науки

uk: вхід без авторизації

name: Worst-Case Complexity Guarantees and Nonconvex Smooth Optimization


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Gentle, Geometric Introduction to Copositive Optimization


Convex (?) Co-Clustering of Tensors

uk: Математика, природничі науки

uk: вхід без авторизації


keywords:
Mathematics
Operations research
mathematical programming
Computer science
Data mining

uk: Математика, природничі науки

uk: вхід без авторизації

name: Matrix Completion with Non-Linear Models


keywords:
Mathematics
Biology and other natural sciences
Manifolds and cell complexes
Mathematical biology

uk: Математика, природничі науки

uk: вхід без авторизації

name: Using DNA supercoiling to control DNA minicircle shape


uk: Математика, природничі науки

uk: вхід без авторизації

name: Knotting in open subarcs of closed knots


uk: Математика, природничі науки

uk: вхід без авторизації

name: Applications of R-graphs to DNA modeling


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Diagrammatic Approach for Determining the Braid Index of Alternating Links, Part I


uk: Математика, природничі науки

uk: вхід без авторизації

name: The geometry of Spherically confined random polygons


uk: Математика, природничі науки

uk: вхід без авторизації

name: Protein Knots: Folding, Stability, Degradation and Design


Geometry of Polygonal Knot Space

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: An exploration of the effects of excluded volume on knotting, size and scaling in self avoiding random walks in 3-space


Slipknotting in random knot diagrams

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Additivity of topological balance lengths and a slow growth in the effective scaling exponent of knotted random polygons


uk: Математика, природничі науки

uk: вхід без авторизації

name: Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Natural Map from Random Walks to Equilateral Polygons in Any Dimension


uk: Математика, природничі науки

uk: вхід без авторизації

name: Structural entanglements in proteins and their complexes


Developing models for chromatin folding

uk: Математика, природничі науки

uk: вхід без авторизації

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


Comparing Metrics on Spaces of Curves

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Diagrammatic Approach for Determining the Braid Index of Alternating Links, Part II


Knotting and Linking in Macromolecules

uk: Математика, природничі науки

uk: вхід без авторизації


On the number of unknot diagrams

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Sampling Finite Sets: From Partitions to Orthoschemes


Entanglement in Biology

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Uncovering the Molecular Details Behind Disease-Associated Leptin Mutations and the Role of the Pierced Lasso Topology


uk: Математика, природничі науки

description: We prove that the dynatomic curves associated with iteration of zd+c in any fixed characteristic (not dividing d) have gonalities tending to infinity. This implies a uniform upper bound on the number of L-rational preperiodic points of zd+c as L varies over extensions of bounded degree over a fixed function field K and c varies over nonconstant elements of L. It also reduces the strong uniform boundedness conjecture for preperiodic points over number fields to the conjecture for periodic points. This is joint work with John R. Doyle.

uk: вхід без авторизації

name: Gonality of dynatomic curves and the strong uniform boundedness conjecture for preperiodic points over function fields


uk: Математика, природничі науки

description: This talk concerns joint work with Xander Faber. Let K be a nonarchimedean local field of characteristic 0 and residue characteristic p>0. Let q=pf be the order of its residue field, and let CK be the completion of an algebraic closure of K. The group of continuous automorphisms Galc(CK/K) acts on the Berkovich Projective Line P1CK. We show that the Galois invariant locus in P1CK is a densely branched tree which properly contains the path-closure of P1(K), and is contained in a tube of path-distance radius 1/(p−1)∗[1+1/(p−1)] around the path-closure. The radius can probably be improved to 1/(p−1). The Galois invariant locus has q+1 branches at each type II point in the locus corresponding to a disc D(a,pb), with b rational, and no other branches. We construct a conjecturally dense subset of the Galois invariant locus. We also establish a conjecture of Benedetto, that each Galois invariant point is defined over a totally ramified extension of K.

uk: вхід без авторизації

name: The Galois Invariant Locus in the Berkovich Projective Line


uk: Математика, природничі науки

description: Let A be a non-isotrivial family of abelian varieties over a smooth irreducible curve S. Suppose the generic fiber of A is simple and call R its endomorphism ring. We consider an irreducible curve C in the n-fold fibered power of A and suppose that everything is defined over a number field k. Then C defines n points P1,...Pn points on A(k(C)). Then, there are at most finitely many points c on the curve such that the specialized P1(c),...Pn(c) are dependent over R, unless they were already identically dependent. This, combined with earlier works of the authors and of Habegger and Pila, gives a general unlikely intersections statement for (not necessarily simple) families of abelian varieties. The proof of these theorems uses a method introduced by Pila and Zannier and combines results coming from o-minimality with some Diophantine ingredients. These results have applications to the study of the solvability of some Diophantine equations in polynomials.

uk: вхід без авторизації

name: Unlikely Intersections on families of abelian varieties (Part I)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Unlikely Intersections on families of abelian varieties (Part II)


uk: Математика, природничі науки

description: Let f:S^2 —> S^2 be a postcritically finite branched covering from the 2-sphere to itself with postcritical set P. Thurston studied the dynamics of f using an induced holomorphic self-map T(f) of the Teichmuller space of complex structures on (S^2, P). Koch found that this holomorphic dynamical system on Teichmuller space descends to algebraic dynamical systems: 1. T(f) always descends to a multivalued self map H(f) of the moduli space M_{0,P} of markings of the Riemann sphere by the finite set P 2. When P contains a point x at which f is fully ramified, under certain combinatorial conditions on f, the inverse of T(f) descends to a rational self-map M(f) of projective space CP^n. When, in addition, x is a fixed point of f, i.e. f is a `topological polynomial’, the induced self-map M(f) is regular. The dynamics of H(f) and M(f) may be studied via numerical invariants called dynamical degrees: the k-th dynamical degree of an algebraic dynamical system measures the asymptotic growth rate, under iteration, of the degrees of k-dimensional subvarieties. I will introduce the dynamical systems T(f), H(f) and M(f), and dynamical degrees. I will then discuss why it is useful to study H(f) (resp. M(f)) simultaneously on several compactifications of M_{0,P}. We find that the dynamical degrees of H(f) (resp. M(f)) are algebraic integers whose properties are constrained by the dynamics of f on the finite set P. In particular, when M(f) exists, then the more f resembles a topological polynomial, the more M(f) : CP^n - - -> CP^n behaves like a regular map.

uk: вхід без авторизації

name: Algebraic dynamics from topological and holomorphic dynamics


uk: Математика, природничі науки

description: Rational functions of degree d > 1 in one variable are parametrized by a quasi-projective variety. From the point of view of arithmetic geometry, it is natural to study points on this variety through the machinery of Weil heights, while the dynamical interpretation suggests other measures of complexity, such as the "critical height" introduced by Silverman. This talk will present some recent work relating the critical height to Weil heights on moduli space, and then go on to suggest some further directions involving variants of the critical height.

uk: вхід без авторизації

name: The critical height of a rational function (and some depleted variants)


Solenoidal manifolds

uk: Математика, природничі науки

description: We present several results about solenoidal manifolds motivated by results by Dennis Sullivan in [1] with commentaries developed in [2]. Solenoidal manifolds of dimension n are topological spaces which are locally homeomorphic to the product of a Cantor set with an open subset of Rn. We will give some applications to 3-dimensional manifolds. References: [1] D. Sullivan, Solenoidal manifolds, J. Singul. 9 (2014), 203–205. [2] A. Verjovsky, Commentaries on the paper “Solenoidal manifolds” by Dennis Sullivan. J. Singul. 9 (2014), 245–251.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Consider a rational map R of degree d>1 with coefficients over a non-archimedean field Cp, with p≥2 a fixed prime number. If R has a cycle of Siegel disks and has good reduction, then it was shown by Rivera-Letelier (2000) that a new rational map Q can be constructed from R, in such a way that Q will exhibit a cycle of m-Herman rings. In this talk, we address the case of rational maps with bad reduction and provide an extension of Rivera-Letelier's result for this case.

uk: вхід без авторизації

name: Rational maps with bad reduction and domains of quasi-periodicity


uk: Математика, природничі науки

description: I shall explain how the study of positivity properties of numerical cycles allows one to understand the asymptotic behaviour of sequences of degrees of iterates of rational maps over any normal projective variety.

uk: вхід без авторизації

name: Degrees of iterates of dominant rational self-maps on normal projective varieties


uk: Математика, природничі науки

description: I will present a recent joint work with S. Vishkautsan where we provide an explicit bound on the number of periodic points of a rational function of degree at least 2 defined over a number field. The bound depends only on the number of primes of bad reduction and the degree of the function, and is linear in the degree. We show that under stronger assumptions (but not so strong, in terms of ramification) the dependence on the degree of the map in the bounds can be removed.

uk: вхід без авторизації

name: Scarcity of periodic points for rational functions over a number field


uk: Математика, природничі науки

description: Recent studies have questioned the degree to which interactive ocean circulations are important for making useful predictions of the next decade. We investigate this question by identifying the most predictable patterns of global sea surface temperature in coupled atmosphere-ocean models. Remarkably, the most predictable patterns in models that include interactive ocean circulation are very similar to predictable patterns in models without interactive ocean circulations (i.e., models whose ocean is represented by a 50m-deep slab ocean mixed layer with no interactive currents). In addition, these patterns can be skillfully predicted in observational data using empirical models trained on simulations from either type of climate model. These results suggest that interactive ocean circulation is not essential for the spatial structure of multi-year predictability previously identified in coupled models and observations. However, the time scale of predictability, and the relation of these predictable patterns to other climate variables, is sensitive to whether the model supports interactive ocean circulations or not, especially over the North Atlantic. To understand this sensitivity, a hierarchy of ocean models coupled to stochastic atmospheric models are examined, ranging from slab mixed-layer models to a stochastically forced Stommel box model. The box model is able to reproduce many statistical characteristics of sea surface temperatures that are relevant to predictability. This model is then used to suggest hypotheses that can be tested about the role of ocean dynamics in multi-year predictability.

uk: вхід без авторизації

name: The role of ocean dynamics in multi-year predictability


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


uk: Математика, природничі науки

uk: вхід без авторизації

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


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

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