how many cages midscribe an egg the midscribability theorem which was first proved by o schramm states that given a smooth strictly convex body k r 3 and a convex polyhedron p there exists a convex polyhedron q r 3 combi natorially equivalent to p which midscribes k here the word midscribe means that all its edges are tangent to the boundary surface of k b y using the intersection number technique together with the teichmuller theory of pack ings this paper provides an alternative approach to this theorem furthermore by combining schramm s method with the above ones we obtain a rigidity result as well that is such a polyhedron is unique under the normalization condition

stable equilibrium of systems of generalized volterra type abstract in this paper the global stability of systems of the generalized volterra type dx i dt x i j 1 n a ij x j b i i 1 n is investigated it is shown that a stable equilibrium point of 1 must be a solution of corresponding linear complementarity problem further when the structure of 1 is restricted the known stability condition is proved to be necessary and sufficient for the existence of a stable equilibrium point for every b rn some structures satisfying these restrictions are given

stability analysis for lotka volterra systems based on an algorithm of real root isolation based on the theory of monotone flows of solutions of systems of differential equations the routh hurwitz theorem and a real root isolation algorithm of multivariate polynomials are applied to a class of lotka volterra diffusion systems an algorithm to determine the location of equilibria and the stability of the nonlinear dynamics systems is implemented in maple

finding density functionals with machine learning machine learning is used to approximate density functionals for the model problem of the kinetic energy of noninteracting fermions in 1d mean absolute errors below 1 text text mathrm kcal mathrm mol on test densities similar to the training set are reached with fewer than 100 training densities a predictor identifies if a test density is within the interpolation region via principal component analysis a projected functional derivative finds highly accurate self consistent densities the challenges for application of our method to real electronic structure problems are discussed

critical behaviour of the 3d xy model a monte carlo study we present the results of a study of the three dimensional xy model on a simple cubic lattice using the single cluster updating algorithm combined with improved estimators we have measured the susceptibility and the correlation length for various couplings in the high temperature phase on lattices of size up to l 112 at the transition temperature we studied the fourth order cumulant and other cumulant like quantities on lattices of size up to l 64 from our numerical data we obtain for the critical coupling kc 0 45420 2 and for the static critical exponents v 1 976 6 and v 0 662 7

permanence of dispersal population model with time delays permanence of a dispersal single species population model is considered where environment is partitioned into several patches and the species requires some time to disperse between the patches the model is described by delay differential equations the existence of food rich patches and small dispersions among the patches are proved to be sufficient to ensure partial permanence of the model it is also shown that partial permanence ensures permanence if each food poor patch is connected to at least one food rich patch and if each pair in food rich patches is connected furthermore it is proved that partial persistence is ensured even under large dispersion among food rich patches if the dispersion time is relatively small

local stability and lyapunov functionals for n dimensional quasipolynomial conservative systems abstract we present a method for determining the local stability of equilibrium points of conservative generalizations of the lotka volterra equations these generalizations incorporate both an arbitrary number of species including odd dimensional systems and nonlinearities of arbitrarily high order in the interspecific interaction terms the method combines a reformulation of the equations in terms of a poisson structure and the construction of their lyapunov functionals via the energy casimir method these lyapunov functionals are a generalization of those traditionally known for lotka volterra systems examples are given

a unique representation of polyhedral types centering via mobius transformations for n 3 distinct points in the d dimensional unit sphere there exists a mobius transformation such that the barycenter of the transformed points is the origin this mobius transformation is unique up to post composition by a rotation we prove this lemma and apply it to prove the uniqueness part of a representation theorem for 3 dimensional polytopes as claimed by ziegler 1995 for each polyhedral type there is a unique representative up to isometry with edges tangent to the unit sphere such that the origin is the barycenter of the points where the edges touch the sphere

unsupervised learning of phase transitions from principal component analysis to variational autoencoders we examine unsupervised machine learning techniques to learn features that best describe configurations of the two dimensional ising model and the three dimensional xy model the methods range from principal component analysis over manifold and clustering methods to artificial neural network based variational autoencoders they are applied to monte carlo sampled configurations and have a priori no knowledge about the hamiltonian or the order parameter we find that the most promising algorithms are principal component analysis and variational autoencoders their predicted latent parameters correspond to the known order parameters the latent representations of the models in question are clustered which makes it possible to identify phases without prior knowledge of their existence furthermore we find that the reconstruction loss function can be used as a universal identifier for phase transitions

hard spin mean field theory a systematic derivation and exact correlations in one dimension hard spin mean field theory is an improved mean field approach which has proven to give accurate results especially for frustrated spin systems with relatively little computational effort in this work the previous phenomenological derivation is supplanted by a systematic and generic derivation that opens the possibility for systematic improvements especially for the calculation of long range correlation functions a first level of improvement suffices to recover the exact long range values of the correlation functions in one dimension

global stability and predator dynamics in a model of prey dispersal in a patchy environment on considere un systeme d equations differentielles autonomes non lineaires on determine l equilibre de ce systeme

network inference using asynchronously updated kinetic ising model network structures are reconstructed from dynamical data by respectively naive mean field nmf and thouless anderson palmer tap approximations tap approximation adds simple corrections to the nmf approximation taking into account the effect of the focused spin on itself via its influence on other neighboring spins for tap approximation we use two methods to reconstruct the network a iterative method b casting the inference formula to a set of cubic equations and solving it directly we investigate inference of the asymmetric sherrington kirkpatrick as k model using asynchronous update the solutions of the set of cubic equations depend on temperature t in the as k model and a critical temperature t c 2 1 is found the two methods for tap approximation produce the same results when the iterative method is convergent compared to nmf tap is somewhat better at low temperatures but approaches the same performance as temperature increases both nmf and tap approximation reconstruct better for longer data length l but for the degree of improvement tap performs better than nmf

vector field divergence of predictive model output as indication of phase transitions we introduce an alternative method to identify phase boundaries in physical systems it is based on training a predictive model such as a neural network to infer a physical system s parameters from its state the deviation of the inferred parameters from the underlying correct parameters will be most susceptible and diverge maximally in the vicinity of phase boundaries therefore peaks in the vector field divergence of the model s predictions are used as indication of phase transitions our method is applicable for phase diagrams of arbitrary parameter dimension and without prior information about the phases application to both the two dimensional ising model and the dissipative kuramoto hopf model show promising results

stable propagation algorithm for the minimization of the bethe free energy we propose a new propagation algorithm for the minimization of the bethe free energy for a generic lattice model with pair interactions the algorithm turns out to be more stable than belief propagation as it reaches a fixed point also for highly frustrated systems such as spin glasses and faster than the provably convergent double loop algorithms

analysis of dynamic ising model by a variational approximate method estimation of transfer entropy transfer entropy is an important index for investigating the causal relationship between random variables it is known that a phase transition can be detected by transfer entropy in this work i propose a method for obtaining the transfer entropy by applying the variational approximation method to a dynamic ising model our method is also effective for dynamics that do not satisfy the detailed balance condition our method finds the transfer entropy by solving a transcendental equation when compared with the transfer entropy obtained by monte carlo sampling it was found that they qualitatively matched near the transition point moreover the match was obtained with good accuracy in the region deviated from the transition point

the effect of dispersal on permanence in a predator prey population growth model abstract in this paper we consider a periodic predator prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation we assume a volterra within patch dynamic under the assumption that the average of dispersal rate from patch 1 to patch 2 is less than that of the intrinsic growth rate of prey in patch 1 we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques in 1

minimal surfaces from circle patterns geometry from combinatorics the theory of polyhedral surfaces and more generally the field of discrete differential geometry are presently emerging on the border of differential and discrete geometry whereas classical differential geometry investigates smooth geometric shapes such as surfaces and discrete geometry studies geometric shapes with a finite number of elements polyhedra the theory of polyhedral surfaces aims at a development of discrete equivalents of the geometric notions and methods of surface theory the latter appears then as a limit of the refinement of the discretization current progress in this field is to a large extent stimulated by its relevance for computer graphics and visualization one of the central problems of discrete differential geometry is to find proper discrete analogues of special classes of surfaces such as minimal con stant mean curvature isothermic surfaces etc usually one can suggest vari ous discretizations with the same continuous limit which have quite different geometric properties the goal of discrete differential geometry is to find a dis cretization which inherits as many essential properties of the smooth geometry as possible our discretizations are based on quadrilateral meshes i e we discretize parametrized surfaces for the discretization of a special class of surfaces it is natural to choose an adapted parametrization in this paper we investigate conformai discretizations of surfaces i e discretizations in terms of circles and spheres and introduce a new discrete model for minimal surfaces see figures 1 and 2 in comparison with direct methods see in particular 23 leading

ising model for neural data model quality and approximate methods for extracting functional connectivity we study pairwise ising models for describing the statistics of multineuron spike trains using data from a simulated cortical network we explore efficient ways of finding the optimal couplings in

the c convergence of hexagonal disk packings to the riemann map let omega mathop subset limits ne c be a simply connected domain the rodin sullivan theorem states that a sequence of disk packings in the unit disk u converges in a well defined sense to a conformal map from to u moreover it is known that the first and second derivatives converge as well here it is proven that for hexagonal disk packings the convergence is c this is done by studying mobius invariants of the disk packings that are discrete analogs of the schwarzian derivative

periodic solution of a lotka volterra predator prey model with dispersion and time delays a periodic lotka volterra predator prey model with dispersion and time delays is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory and by means of a suitable lyapunov functional a set of easily verifiable sufficient conditions are derived for the existence uniqueness and global stability of positive periodic solutions of the system sufficient conditions are also established for the uniform persistence of the system numerical simulations are presented to illustrate our main results

existence of stable equilibrium point for dynamical systems of volterra type this paper presents sufficient conditions for the existence of a nonnegative and stable equilibrium point of a dynamical system of volterra type 1 ddt xi t xi t fi x1 t xn t qi i 1 n for every q q1 qn t rn results of a nonlinear complementarity problem are applied to obtain the conditions system 1 has a nonnegative and stable equilibrium point if i f x f1 x fn x t is a continuous and differentiable m function and it satisfies a certain surjectivity property or ii f x is continuous and strongly monotone on r 0n

permanence and extinction analysis for a delayed periodic predator prey system with holling type ii response function and diffusion abstract in this paper it is studied that two species predator prey lotka volterra type dispersal system with delay and holling type ii response function in which the prey species can disperse among n patches while the density independent predator species is confined to one of the patches and cannot disperse sufficient conditions of integrable form for the boundedness permanence extinction and the existence of positive periodic solution are established respectively

variational principles for circle patterns and koebe s theorem we prove existence and uniqueness results for patterns of circles with prescribed intersection angles on constant curvature surfaces our method is based on two new functionals one for the euclidean and one for the hyperbolic case we show how colin de verdiere s bragger s and rivin s functionals can be derived from ours

permanence and extinction in logistic and lotka volterra systems with diffusion abstract in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments differing from former studies our discussion includes the important situation in conservation biology in which species live in a weak patchy environment in the sense that species will become extinct in some of the isolated patches for the single population model we show that identical species can persist for some diffusion rates and can also vanish for another set of restrictions on the diffusion rates although the single endangered species will vanish in some isolated patches without contributions from other patches furthermore we consider the existence uniqueness and global stability of the positive periodic solution for prey predator systems we can make both the prey and the predator species permanent by choosing the diffusion rates appropriately even if the prey species has a negative intrinsic growth rate in some patches moreover we introduce an exotic competitive species y into the habitat occupied by the native species x competitive permanence and competitive exclusion both are considered the implications of these results are significant for the conservation of endangered species

automatic alignment of genus zero surfaces a new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero the algorithm takes as input a pair of surfaces that are topological 2 spheres each surface given by a distinct triangulation the algorithm then constructs a map f between the two surfaces first each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm the two mappings are then composed with a mobius transformation to generate the function f the mobius transformation is chosen by minimizing an energy that measures the distance of f from an isometry we illustrate our approach using several real life data sets we show first that the algorithm allows for accurate automatic and landmark free nonrigid registration of brain surfaces we then validate our approach by comparing shapes of proteins we provide numerical experiments to demonstrate that the distances computed with our algorithm between low resolution surface based representations of proteins are highly correlated with the corresponding distances computed between high resolution atomistic models for the same proteins

global stability in generalized lotka volterra diffusion systems abstract this paper analyzes the existence conditions of a nonnegative global stable equilibrium point in generalized lotka volterra systems with diffusion for a patchtype environment applying the extended stability theory of lasalle and complementarity theorem several structures of patches with a globally stable equilibrium are derived it is shown that diffusion cannot be destabilizing for systems with such structures

examples of renormalization group transformations for image sets using the example of configurations generated with the worm algorithm for the two dimensional ising model we propose renormalization group rg transformations inspired by the tensor rg that can be applied to sets of images we relate criticality to the logarithmic divergence of the largest principal component we discuss the changes in link occupation under the rg transformation suggest ways to obtain data collapse and compare with the two state tensor rg approximation near the fixed point

inference of kinetic ising model on sparse graphs based on dynamical cavity method we propose an approach to the inference of kinetic ising model which asks to reconstruct couplings and external fields from given time dependent output of original system our approach gives an exact result on tree graphs and a good approximation on sparse graphs it can be seen as an extension of belief propagation inference of static ising model to kinetic ising model while existing mean field methods to the kinetic ising inference e g naive mean field tap equation and simply mean field use approximations which calculate magnetizations and correlations at time t from statistics of data at time t 1 dynamical cavity method can use statistics of data at times earlier than t 1 to capture more correlations at different time steps extensive numerical experiments show that our inference method is superior to existing mean field approaches on diluted networks

searching predator and prey dominance in discrete predator prey systems with dispersion the model for this study is an extension of a discrete time predator prey model of hassell and comins that includes dispersion in a patchy habitat in a single patch system it is shown that irrespective of initial population densities a prey species with a high growth rate dominates the system with the resulting existence or extinction of the searching predator with a numerical example it is shown that if the searching predator preys exclusively on the prey species that has a high growth rate then a spectrum of dynamical behavior including predator induced coexistence exclusionary dynamics and hopf bifurcation could occur in the single patch system if the searching predator preys exclusively on the prey species that has a low growth rate then both the predator and its preferred prey species go extinct an example is given illustrating that searching predator diffusion could change a system with stable coexistence of prey to extinction of prey species in a two patch system it is shown that the

how to cage an egg this paper proves that given a convex polyhedron p subset mathbb r 3 and a smooth strictly convex body k subset mathbb r 3 there is some convex polyhedron q combinatorically equivalent to p which midscribes k that is all the edges of q are tangent to k furthermore with some stronger smoothness conditions on k the space of all such q is a six dimensional differentiable manifold