2,766 research outputs found
Approximately Sampling Elements with Fixed Rank in Graded Posets
Graded posets frequently arise throughout combinatorics, where it is natural
to try to count the number of elements of a fixed rank. These counting problems
are often -complete, so we consider approximation algorithms for
counting and uniform sampling. We show that for certain classes of posets,
biased Markov chains that walk along edges of their Hasse diagrams allow us to
approximately generate samples with any fixed rank in expected polynomial time.
Our arguments do not rely on the typical proofs of log-concavity, which are
used to construct a stationary distribution with a specific mode in order to
give a lower bound on the probability of outputting an element of the desired
rank. Instead, we infer this directly from bounds on the mixing time of the
chains through a method we call .
A noteworthy application of our method is sampling restricted classes of
integer partitions of . We give the first provably efficient Markov chain
algorithm to uniformly sample integer partitions of from general restricted
classes. Several observations allow us to improve the efficiency of this chain
to require space, and for unrestricted integer partitions,
expected time. Related applications include sampling permutations
with a fixed number of inversions and lozenge tilings on the triangular lattice
with a fixed average height.Comment: 23 pages, 12 figure
Universality in a class of fragmentation-coalescence processes
We introduce and analyse a class of fragmentation-coalescence processes
defined on finite systems of particles organised into clusters. Coalescent
events merge multiple clusters simultaneously to form a single larger cluster,
while fragmentation breaks up a cluster into a collection of singletons. Under
mild conditions on the coalescence rates, we show that the distribution of
cluster sizes becomes non- random in the thermodynamic limit. Moreover, we
discover that in the limit of small fragmentation rate these processes exhibit
self-organised criticality in the cluster size distribution, with universal
exponent 3/2.Comment: 17 pages, 1 figur
Effects of gabergic phenols on the dynamic and structure of lipid bilayers: A molecular dynamic simulation approach
γ-Aminobutyric acid (GABA) is the major inhibitory neurotransmitter in the vertebrate and invertebrate nervous system. GABAA receptors are activated by GABA and their agonists, and modulated by a wide variety of recognized drugs, including barbiturates, anesthetics, and benzodiazepines. The phenols propofol, thymol, chlorothymol, carvacrol and eugenol act as positive allosteric modulators on GABAA-R receptor. These GABAergic phenols interact with the lipid membrane, therefore, their anesthetic activity could be the combined result of their specific activity (with receptor proteins) as well as nonspecific interactions (with surrounding lipid molecules) modulating the supramolecular organization of the receptor environment. Therefore, we aimed to contribute to a description of the molecular events that occur at the membrane level as part of the mechanism of general anesthesia, using a molecular dynamic simulation approach. Equilibrium molecular dynamics simulations indicate that the presence of GABAergic phenols in a DPPC bilayer orders lipid acyl chains for carbons near the interface and their effect is not significant at the bilayer center. Phenols interacts with the polar interface of phospholipid bilayer, particularly forming hydrogen bonds with the glycerol and phosphate group. Also, potential of mean force calculations using umbrella sampling show that propofol partition is mainly enthalpic driven at the polar region and entropic driven at the hydrocarbon chains. Finally, potential of mean force indicates that propofol partition into a gel DPPC phase is not favorable. Our in silico results were positively contrasted with previous experimental data.Fil: Miguel, Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; ArgentinaFil: Villarreal, Marcos Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; ArgentinaFil: Garcia, Daniel Asmed. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; Argentin
Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows
The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches designed to minimize the number of cells used to augment/stabilize the least-squares stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cellaverage gradients is described. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet engine flowpath is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the preferred gradient method for a realistic 3-D geometry on a non-hex-dominant grid
Spatial SINR Games of Base Station Placement and Mobile Association
We study the question of determining locations of base stations that may
belong to the same or to competing service providers. We take into account the
impact of these decisions on the behavior of intelligent mobile terminals who
can connect to the base station that offers the best utility. The signal to
interference and noise ratio is used as the quantity that determines the
association. We first study the SINR association-game: we determine the cells
corresponding to each base stations, i.e., the locations at which mobile
terminals prefer to connect to a given base station than to others. We make
some surprising observations: (i) displacing a base station a little in one
direction may result in a displacement of the boundary of the corresponding
cell to the opposite direction; (ii) A cell corresponding to a BS may be the
union of disconnected sub-cells. We then study the hierarchical equilibrium in
the combined BS location and mobile association problem: we determine where to
locate the BSs so as to maximize the revenues obtained at the induced SINR
mobile association game. We consider the cases of single frequency band and two
frequency bands of operation. Finally, we also consider hierarchical equilibria
in two frequency systems with successive interference cancellation
Self-Organized Criticality and Thermodynamic formalism
We introduce a dissipative version of the Zhang's model of Self-Organized
Criticality, where a parameter allows to tune the local energy dissipation. We
analyze the main dynamical features of the model and relate in particular the
Lyapunov spectrum with the transport properties in the stationary regime. We
develop a thermodynamic formalism where we define formal Gibbs measure,
partition function and pressure characterizing the avalanche distributions. We
discuss the infinite size limit in this setting. We show in particular that a
Lee-Yang phenomenon occurs in this model, for the only conservative case. This
suggests new connexions to classical critical phenomena.Comment: 35 pages, 15 Figures, submitte
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
Opinion Polarization by Learning from Social Feedback
We explore a new mechanism to explain polarization phenomena in opinion
dynamics in which agents evaluate alternative views on the basis of the social
feedback obtained on expressing them. High support of the favored opinion in
the social environment, is treated as a positive feedback which reinforces the
value associated to this opinion. In connected networks of sufficiently high
modularity, different groups of agents can form strong convictions of competing
opinions. Linking the social feedback process to standard equilibrium concepts
we analytically characterize sufficient conditions for the stability of
bi-polarization. While previous models have emphasized the polarization effects
of deliberative argument-based communication, our model highlights an affective
experience-based route to polarization, without assumptions about negative
influence or bounded confidence.Comment: Presented at the Social Simulation Conference (Dublin 2017
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