Article
Computer Science, Artificial Intelligence
Farrukh Mukhamedov
Summary: This paper investigates the lambda-model for an arbitrary-order Cayley tree with a disordered phase, discussing its relevance in communication theory and its connection to the non-reconstruction problem. Identifying conditions for the extremality of the disordered phase is a natural step when the phase is not extreme.
Article
Physics, Multidisciplinary
R. M. Khakimov, K. O. Umirzakova
Summary: This study investigates fertile hard-core models with three states and an activity parameter on the Cayley tree, identifying regions where the unique translation-invariant Gibbs measure is (not) extremal for two of the models and conditions under which the extremal measure is not unique for one particular model.
THEORETICAL AND MATHEMATICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova
Summary: In this paper, we consider the lambda-model on the Cayley tree of order k = 2 and study translation-invariant Gibbs measures under certain conditions. Furthermore, we investigate whether these Gibbs measures are extremal or non-extremal in the set of all Gibbs measures.
THEORETICAL AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Melissa M. Fuentes
Summary: This paper discusses the impact of graph structure on the maximum number of q-colorings and proves that under certain conditions, a specific type of graph has the maximum number of q-colorings.
SIAM JOURNAL ON DISCRETE MATHEMATICS
(2023)
Article
Mathematics
Samuel L. Krushkal
Summary: This article proves a general theorem that provides a wide collection of univalent functions with equal Grunsky and Teichmuller norms, as well as the Fredholm eigenvalues and reflection coefficients of associated quasicircles. The establishment of exact or approximate values for basic quasiinvariant functionals of Jordan curves is crucial for applications and the numerical aspect of quasiconformal analysis.
Article
Mathematics
Anton Bernshteyn, Tyler Brazelton, Ruijia Cao, Akum Kang
Summary: According to Johansson's theorem, the chromatic number of every triangle-free graph G with maximum degree Delta is at most (C + o(1))Delta/ log Delta, where C is a universal constant greater than 0. Molloy proved that C = 1 using the entropy compression method. In this paper, we show that for every q >= (1 +o(1))Delta/ log Delta, the number of proper q-colorings c(G, q) of G satisfies c(G, q) >= (1 - 1/q)(m) ((1 - o(1))q)(n), where n = |V(G)| and m = |E(G)|. Our result improves previous bounds and has optimal lower bounds in certain cases.
JOURNAL OF COMBINATORIAL THEORY SERIES B
(2023)
Article
Mathematics
Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis
Summary: This study investigates the existence of a threshold for the expected measure of a random polytope under a log-concave probability measure. The study shows that, under certain conditions, the threshold is close to 0.
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics, Applied
Ran Gu, Hui Lei, Yongtang Shi, Yiqiao Wang
Summary: This paper discusses the existence of rainbow-free coloring in random k-uniform hypergraphs, and provides the threshold function and the answer.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ugo Bessi
Summary: This paper explores Kusuoka's measure on fractals and demonstrates how a class of matrix-valued Gibbs measures can be built within the scope of the standard theory. These measures are used to construct self-similar bilinear forms on fractals, and it is shown that Kusuoka's measure and bilinear form can be recovered from the matrix-valued Gibbs measure in a simple way.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Statistics & Probability
Mario Beraha, Jim E. Griffin
Summary: We propose a methodology for modelling and comparing probability distributions within a Bayesian nonparametric framework. Our approach uses dependent normalised random measures and a prior distribution for a collection of discrete random measures. It achieves identified inference through postprocessing posterior samples using Riemannian optimisation. Our approach is validated on simulated data and real-world data sets, providing interesting insights and easily interpretable posterior inference.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2023)
Article
Statistics & Probability
Qian Qin, Galin L. Jones
Summary: Component-wise MCMC algorithms are commonly used for sampling from multivariate probability distributions. In this study, we investigate the convergence rates of deterministic-scan and random-scan samplers and establish a quantitative relationship between them. Our findings show that the deterministic-scan sampler converges faster. We also explore the qualitative relations among the convergence rates of two-component Gibbs samplers and certain conditional Metropolis-Hastings variants.
Article
Mathematics
N. M. Khatamov
Summary: This paper investigates translation-invariant Gibbs measures for the HC-Blume-Capel model with wands having chemical potential on the Cayley tree. It is proven that there is a unique TIGM when eta <= theta(3), and there are exactly three TIGMs when eta > theta(3) in the case of wands with chemical potential. Additionally, the (non)extremality of these measures is studied.
MATHEMATICAL NOTES
(2022)
Article
Physics, Multidisciplinary
Alejandro P. Riascos, Francisco Hernandez Padilla
Summary: In this paper, a framework for comparing differences in occupation probabilities of two random walk processes on networks is presented. The framework considers modifications of the network or the transition probabilities between nodes. A dissimilarity measure is defined using the eigenvalues and eigenvectors of the normalized Laplacian. The framework is used to examine differences in diffusive dynamics, the effect of new edges and rewiring in networks, and divergences in transport in degree-biased random walks and random walks with stochastic reset.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Applied
Hwa-Long Gau, Chi-Kwong Li, Kuo-Zhong Wang, Pei Yuan Wu
Summary: In this paper, the upper and lower bounds of the numerical radius w(FT) of the associated Foguel operator FT on the space P2 are studied. It is shown that for the upper bound, w(FT) = 1 + (1/2)IITII if and only if w(S + T*S*T) = 1 + IITII2. For the lower bound, it is proven that any diagonal T with w(FT) = 1 is compact. Examples of various T's are given to illustrate the attainments of w(FT).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Engineering, Civil
Alok Kumar Samantaray, Adway Mitra, Meenu Ramadas, Rabindra Kumar Panda
Summary: This study introduced a novel technique for grouping locations into spatially coherent homogeneous regions and applied it to assess the impacts of potential climate change on regionalization of hydroclimatic variables. The findings suggest that in future scenarios, the number and distribution of homogeneous regions are projected to change, with wettest regions remaining wetter and moderate-to-heavy rainfall regions shifting to increasingly wetter areas. Despite uncertainties, the changes in hydroclimatic patterns emphasize the importance of considering climate change impacts in water resources management and regional decision making.
JOURNAL OF HYDROLOGY
(2021)
Article
Operations Research & Management Science
Etienne de Klerk, Monique Laurent, Zhao Sun, Juan C. Vera
OPTIMIZATION LETTERS
(2017)
Article
Management
Onur Babat, Juan C. Vera, Luis F. Zuluaga
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2018)
Article
Mathematics, Applied
Denis Assmann, Frauke Liers, Michael Stingl, Juan C. Vera
SIAM JOURNAL ON OPTIMIZATION
(2018)
Article
Computer Science, Theory & Methods
Olga Kuryatnikova, Juan C. Vera
THEORY OF COMPUTING SYSTEMS
(2020)
Article
Business
Lorenz M. Roebers, Aras Selvi, Juan C. Vera
ENGINEERING ECONOMIST
(2019)
Article
Mathematics, Applied
Flavia Bonomo-Braberman, Mitre C. Dourado, Mario Valencia-Pabon, Juan C. Vera
APPLIED MATHEMATICS AND COMPUTATION
(2020)
Article
Computer Science, Software Engineering
Javier Pena, Juan C. Vera, Luis F. Zuluaga
Summary: The paper characterizes the Hoffman constant of a system of linear constraints in relation to a reference polyhedron, and provides a new computational method.
MATHEMATICAL PROGRAMMING
(2021)
Article
Engineering, Multidisciplinary
Javier Pantoja Robayo, Juan C. Vera
Summary: This study introduces a closed-form solution model for energy retailers to hedge price and quantity risks in the electricity market, with a focus on constructing a portfolio of financial instruments based on price and weather indexes.
OPTIMIZATION AND ENGINEERING
(2021)
Article
Mathematics, Applied
Luciano N. Grippo, Adrian Pastine, Pablo Torres, Mario Valencia-Pabon, Juan C. Vera
Summary: This paper discusses the spread of infection in a graph, focusing on the conditions for infection and the minimum set of infected vertices. The P-3-hull number for the Kneser graph K(n, k) is calculated, with exact values determined for n > 2k + 1. Lower and upper bounds are given for the case when n = 2k + 1 using graph homomorphisms.
ELECTRONIC JOURNAL OF COMBINATORICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Rosember Guerra-Urzola, Katrijn Van Deun, Juan C. Vera, Klaas Sijtsma
Summary: PCA is commonly used for exploring and summarizing multivariate data, however, interpreting the components can be challenging due to the linear combination of variables. Various methods have been proposed to sparsify the nonzero coefficients in the components, including rotation-thresholding methods and PCA methods with sparsity inducing penalties or constraints. This study provides guidelines on how to choose among different sparse PCA methods, evaluating their properties and performance through simulation studies and empirical data examples.
Article
Statistics & Probability
Rosember Guerra-Urzola, Niek C. de Schipper, Anya Tonne, Klaas Sijtsma, Juan C. Vera, Katrijn Van Deun
Summary: This study compares penalized PCA methods with their cardinality-constrained counterparts in imposing sparseness on component weights in the least-squares formulation of PCA. Results from a simulation study suggest that using cardinality-constrained methods leads to better recovery of the sparse structure.
ADVANCES IN DATA ANALYSIS AND CLASSIFICATION
(2023)
Article
Operations Research & Management Science
Anne G. Batter, Nikolaus Schweizer, Juan C. Vera
Summary: This paper examines the existence and uniqueness of equilibrium prices in a banking sector model where banks trade contingent convertible bonds with stock price triggers. It is found that if the conversion thresholds are such that bond holders are indifferent about marginal conversions, there exists a unique equilibrium regardless of the network structure. Lower thresholds result in the breakdown of equilibrium, while higher thresholds may lead to multiple equilibria. Additionally, there are complex network effects as one bank's conversion may trigger or prevent further conversions depending on the combination of asset values and conversion triggers.
MATHEMATICS OF OPERATIONS RESEARCH
(2022)
Article
Computer Science, Interdisciplinary Applications
Olga Kuryatnikova, Renata Sotirov, Juan C. Vera
Summary: The maximum k-colorable subgraph (MkCS) problem aims to find an induced k-colorable subgraph with maximum cardinality in a given graph. This paper provides an in-depth analysis of the MkCS problem, considering various semidefinite programming relaxations and their comparisons. The proposed relaxations offer strong bounds for the MkCS problem and outperform existing bounds for most test instances, showing applications in various fields such as network design and genetic research.
INFORMS JOURNAL ON COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Wei Xia, Juan Vera, Luis F. Zuluaga
INFORMS JOURNAL ON COMPUTING
(2020)
Article
Transportation Science & Technology
Thijs Verhaegh, Dennis Huisman, Pieter-Jan Fioole, Juan C. Vera