Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Exact solution for a metapopulation version of Schelling's model.

ABSTRACT: In 1971, Schelling introduced a model in which families move if they have too many neighbors of the opposite type. In this paper, we will consider a metapopulation version of the model in which a city is divided into N neighborhoods, each of which has L houses. There are ?NL red families and ?NL blue families for some ? < 1/2. Families are happy if there are ? ?(c)L families of the opposite type in their neighborhood and unhappy otherwise. Each family moves to each vacant house at rates that depend on their happiness at their current location and that of their destination. Our main result is that if neighborhoods are large, then there are critical values ?(b) < ?(d) < ?(c), so that for ? < ?(b), the two types are distributed randomly in equilibrium. When ? > ?(b), a new segregated equilibrium appears; for ?(b) < ? < ?(d), there is bistability, but when ? increases past ?(d) the random state is no longer stable. When ?(c) is small enough, the random state will again be the stationary distribution when ? is close to 1/2. If so, this is preceded by a region of bistability.

SUBMITTER: Durrett R

PROVIDER: S-EPMC4191761 | biostudies-literature | 2014 Sep

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

Exact solution for first-order synchronization transition in a generalized Kuramoto model.

Project description:First-order, or discontinuous, synchronization transition, i.e. an abrupt and irreversible phase transition with hysteresis to the synchronized state of coupled oscillators, has attracted much attention along the past years. We here report the analytical solution of a generalized Kuramoto model, and derive a series of exact results for the first-order synchronization transition, including i) the exact, generic, solutions for the critical coupling strengths for both the forward and backward transitions, ii) the closed form of the forward transition point and the linear stability analysis for the incoherent state (for a Lorentzian frequency distribution), and iii) the closed forms for both the stable and unstable coherent states (and their stabilities) for the backward transition. Our results, together with elucidating the first-order nature of the transition, provide insights on the mechanisms at the basis of such a synchronization phenomenon.

| S-EPMC4248286 | biostudies-literature

Exact solution of the Eigen model with general fitness functions and degradation rates.

Project description:We present an exact solution of Eigen's quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasispecies under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady-state solution shows a multicenter behavior.

| S-EPMC1458773 | biostudies-literature

Exact solution of the Zwanzig-Lauritzen model of polymer crystallization under tension.

Project description:We solve a two-dimensional model for polymer chain folding in the presence of mechanical pulling force (f) exactly using equilibrium statistical mechanics. Using analytically derived expression for the partition function we determine the phase diagram for the model in the f-temperature (T) plane. A square root singularity in the susceptibility indicates a second order phase transition from a folded to an unfolded state at a critical force (fc) in the thermodynamic limit of infinitely long polymer chain. The temperature dependence of fc shows a reentrant phase transition, which is reflected in an increase in fc as T increases below a threshold value. As a result, for a range of f values, the unfolded state is stable at both low and high temperatures. The high temperature unfolded state is stabilized by entropy whereas the low temperature unfolded state is dominated by favorable energy. The exact calculation could serve as a benchmark for testing approximate theories that are used in analyzing single molecule pulling experiments.

| S-EPMC3612122 | biostudies-other

Exact solution for the Anisotropic Ornstein-Uhlenbeck process.

Project description:Active-Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models also include random noise in particle displacement (a Wiener process), resulting in diffusive motion at short time scales. On the other hand, Ornstein-Uhlenbeck processes apply Langevin dynamics to the particles' velocity and predict motion that is not diffusive at short time scales. Experiments show that migrating cells have gradually varying speeds at intermediate and long time scales, with short-time diffusive behavior. While Ornstein-Uhlenbeck processes can describe the moderate-and long-time speed variation, Active-Matter models for over-damped particles can explain the short-time diffusive behavior. Isotropic models cannot explain both regimes, because short-time diffusion renders instantaneous velocity ill-defined, and prevents the use of dynamical equations that require velocity time-derivatives. On the other hand, both models correctly describe some of the different temporal regimes seen in migrating biological cells and must, in the appropriate limit, yield the same observable predictions. Here we propose and solve analytically an Anisotropic Ornstein-Uhlenbeck process for polarized particles, with Langevin dynamics governing the particle's movement in the polarization direction and a Wiener process governing displacement in the orthogonal direction. Our characterization provides a theoretically robust way to compare movement in dimensionless simulations to movement in experiments in which measurements have meaningful space and time units. We also propose an approach to deal with inevitable finite-precision effects in experiments and simulations.

| S-EPMC10022481 | biostudies-literature

Exact closure and solution for spatial correlations in single-file diffusion.

Project description:In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.

| S-EPMC8956262 | biostudies-literature

Exact solution for the Poisson field in a semi-infinite strip.

Project description:The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

| S-EPMC5415694 | biostudies-literature

EXACT: a collaboration toolset for algorithm-aided annotation of images with annotation version control.

Project description:In many research areas, scientific progress is accelerated by multidisciplinary access to image data and their interdisciplinary annotation. However, keeping track of these annotations to ensure a high-quality multi-purpose data set is a challenging and labour intensive task. We developed the open-source online platform EXACT (EXpert Algorithm Collaboration Tool) that enables the collaborative interdisciplinary analysis of images from different domains online and offline. EXACT supports multi-gigapixel medical whole slide images as well as image series with thousands of images. The software utilises a flexible plugin system that can be adapted to diverse applications such as counting mitotic figures with a screening mode, finding false annotations on a novel validation view, or using the latest deep learning image analysis technologies. This is combined with a version control system which makes it possible to keep track of changes in the data sets and, for example, to link the results of deep learning experiments to specific data set versions. EXACT is freely available and has already been successfully applied to a broad range of annotation tasks, including highly diverse applications like deep learning supported cytology scoring, interdisciplinary multi-centre whole slide image tumour annotation, and highly specialised whale sound spectroscopy clustering.

| S-EPMC7902667 | biostudies-literature

The metapopulation genetic algorithm: An efficient solution for the problem of large phylogeny estimation.

Project description:Large phylogeny estimation is a combinatorial optimization problem that no future computer will ever be able to solve exactly in practical computing time. The difficulty of the problem is amplified by the need to use complex evolutionary models and large taxon samplings. Hence, many heuristic approaches have been developed, with varying degrees of success. Here, we report on a heuristic approach, the metapopulation genetic algorithm, involving several populations of trees that are forced to cooperate in the search for the optimal tree. Within each population, trees are subjected to evaluation, selection, and mutation events, which are directed by using inter-population consensus information. The method proves to be both very accurate and vastly faster than existing heuristics, such that data sets comprised of hundreds of taxa can be analyzed in practical computing times under complex models of maximum-likelihood evolution. Branch support values produced by the metapopulation genetic algorithm might closely approximate the posterior probabilities of the corresponding branches.

| S-EPMC124960 | biostudies-literature

Exact model reduction of combinatorial reaction networks.

Project description:BACKGROUND: Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. RESULTS: We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. CONCLUSION: The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

| S-EPMC2570670 | biostudies-literature

Exact invariant solution reveals the origin of self-organized oblique turbulent-laminar stripes.

Project description:Wall-bounded shear flows transitioning to turbulence may self-organize into alternating turbulent and laminar regions forming a stripe pattern with non-trivial oblique orientation. Different experiments and flow simulations identify oblique stripe patterns as the preferred solution of the well-known Navier-Stokes equations, but the origin of stripes and their oblique orientation remains unexplained. In concluding his lectures, Feynman highlights the unexplained stripe pattern hidden in the solution space of the Navier-Stokes equations as an example demonstrating the need for improved theoretical tools to analyze the fluid flow equations. Here we exploit dynamical systems methods and demonstrate the existence of an exact equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles oblique stripe patterns in plane Couette flow. The stripe equilibrium emerges from the well-studied Nagata equilibrium and exists only for a limited range of pattern angles. This suggests a mechanism selecting the non-trivial oblique orientation angle of turbulent-laminar stripes.

| S-EPMC6533313 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data