@article{11447,
abstract = {Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks.},
author = {Saona Urmeneta, Raimundo J and Kondrashov, Fyodor and Khudiakova, Kseniia},
issn = {1522-9602},
journal = {Bulletin of Mathematical Biology},
keywords = {Computational Theory and Mathematics, General Agricultural and Biological Sciences, Pharmacology, General Environmental Science, General Biochemistry, Genetics and Molecular Biology, General Mathematics, Immunology, General Neuroscience},
number = {8},
publisher = {Springer Nature},
title = {{Relation between the number of peaks and the number of reciprocal sign epistatic interactions}},
doi = {10.1007/s11538-022-01029-z},
volume = {84},
year = {2022},
}
@article{10842,
abstract = {We determine the unique factorization of some polynomials over a finite local commutative ring with identity explicitly. This solves and generalizes the main conjecture of Qian, Shi and Solé in [13]. We also give some applications to enumeration of certain generalized double circulant self-dual and linear complementary dual (LCD) codes over some finite rings together with an application in asymptotic coding theory.},
author = {Köse, Seyda and Özbudak, Ferruh},
issn = {1936-2447},
journal = {Cryptography and Communications},
keywords = {Applied Mathematics, Computational Theory and Mathematics, Computer Networks and Communications},
number = {4},
pages = {933--948},
publisher = {Springer Nature},
title = {{Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes}},
doi = {10.1007/s12095-022-00557-8},
volume = {14},
year = {2022},
}
@article{8940,
abstract = {We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.},
author = {Boissonnat, Jean-Daniel and Kachanovich, Siargey and Wintraecken, Mathijs},
issn = {0179-5376},
journal = {Discrete & Computational Geometry},
keywords = {Theoretical Computer Science, Computational Theory and Mathematics, Geometry and Topology, Discrete Mathematics and Combinatorics},
number = {1},
pages = {386--434},
publisher = {Springer Nature},
title = {{Triangulating submanifolds: An elementary and quantified version of Whitney’s method}},
doi = {10.1007/s00454-020-00250-8},
volume = {66},
year = {2021},
}
@article{10211,
abstract = {We study the problem of recovering an unknown signal 𝑥𝑥 given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator 𝑥𝑥^L and a spectral estimator 𝑥𝑥^s. The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine 𝑥𝑥^L and 𝑥𝑥^s. At the heart of our analysis is the exact characterization of the empirical joint distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of 𝑥𝑥^L and 𝑥𝑥^s, given the limiting distribution of the signal 𝑥𝑥. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form 𝜃𝑥𝑥^L+𝑥𝑥^s and we derive the optimal combination coefficient. In order to establish the limiting distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s), we design and analyze an approximate message passing algorithm whose iterates give 𝑥𝑥^L and approach 𝑥𝑥^s. Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.},
author = {Mondelli, Marco and Thrampoulidis, Christos and Venkataramanan, Ramji},
issn = {1615-3375},
journal = {Foundations of Computational Mathematics},
keywords = {Applied Mathematics, Computational Theory and Mathematics, Computational Mathematics, Analysis},
publisher = {Springer},
title = {{Optimal combination of linear and spectral estimators for generalized linear models}},
doi = {10.1007/s10208-021-09531-x},
year = {2021},
}
@article{11446,
abstract = {Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of Sn-equivariant maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.},
author = {Avvakumov, Sergey and Kudrya, Sergey},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science},
number = {3},
pages = {1202--1216},
publisher = {Springer Nature},
title = {{Vanishing of all equivariant obstructions and the mapping degree}},
doi = {10.1007/s00454-021-00299-z},
volume = {66},
year = {2021},
}
@article{8767,
abstract = {Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.},
author = {Kaveh, Kamran and McAvoy, Alex and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {1553-7358},
journal = {PLOS Computational Biology},
keywords = {Ecology, Modelling and Simulation, Computational Theory and Mathematics, Genetics, Ecology, Evolution, Behavior and Systematics, Molecular Biology, Cellular and Molecular Neuroscience},
number = {11},
publisher = {Public Library of Science},
title = {{The Moran process on 2-chromatic graphs}},
doi = {10.1371/journal.pcbi.1008402},
volume = {16},
year = {2020},
}
@article{8459,
abstract = {Nuclear magnetic resonance (NMR) is a powerful tool for observing the motion of biomolecules at the atomic level. One technique, the analysis of relaxation dispersion phenomenon, is highly suited for studying the kinetics and thermodynamics of biological processes. Built on top of the relax computational environment for NMR dynamics is a new dispersion analysis designed to be comprehensive, accurate and easy-to-use. The software supports more models, both numeric and analytic, than current solutions. An automated protocol, available for scripting and driving the graphical user interface (GUI), is designed to simplify the analysis of dispersion data for NMR spectroscopists. Decreases in optimization time are granted by parallelization for running on computer clusters and by skipping an initial grid search by using parameters from one solution as the starting point for another —using analytic model results for the numeric models, taking advantage of model nesting, and using averaged non-clustered results for the clustered analysis.},
author = {Morin, Sébastien and Linnet, Troels E and Lescanne, Mathilde and Schanda, Paul and Thompson, Gary S and Tollinger, Martin and Teilum, Kaare and Gagné, Stéphane and Marion, Dominique and Griesinger, Christian and Blackledge, Martin and d’Auvergne, Edward J},
issn = {1367-4803},
journal = {Bioinformatics},
keywords = {Statistics and Probability, Computational Theory and Mathematics, Biochemistry, Molecular Biology, Computational Mathematics, Computer Science Applications},
number = {15},
pages = {2219--2220},
publisher = {Oxford University Press},
title = {{Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data}},
doi = {10.1093/bioinformatics/btu166},
volume = {30},
year = {2014},
}