@article{14739, abstract = {Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.}, author = {Ali, Dashti and Asaad, Aras and Jimenez, Maria-Jose and Nanda, Vidit and Paluzo-Hidalgo, Eduardo and Soriano Trigueros, Manuel}, issn = {1939-3539}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, keywords = {Applied Mathematics, Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Software}, number = {12}, pages = {14069--14080}, publisher = {IEEE}, title = {{A survey of vectorization methods in topological data analysis}}, doi = {10.1109/tpami.2023.3308391}, volume = {45}, year = {2023}, } @article{12164, abstract = {A shared-memory counter is a widely-used and well-studied concurrent object. It supports two operations: An Inc operation that increases its value by 1 and a Read operation that returns its current value. In Jayanti et al (SIAM J Comput, 30(2), 2000), Jayanti, Tan and Toueg proved a linear lower bound on the worst-case step complexity of obstruction-free implementations, from read-write registers, of a large class of shared objects that includes counters. The lower bound leaves open the question of finding counter implementations with sub-linear amortized step complexity. In this work, we address this gap. We show that n-process, wait-free and linearizable counters can be implemented from read-write registers with O(log2n) amortized step complexity. This is the first counter algorithm from read-write registers that provides sub-linear amortized step complexity in executions of arbitrary length. Since a logarithmic lower bound on the amortized step complexity of obstruction-free counter implementations exists, our upper bound is within a logarithmic factor of the optimal. The worst-case step complexity of the construction remains linear, which is optimal. This is obtained thanks to a new max register construction with O(logn) amortized step complexity in executions of arbitrary length in which the value stored in the register does not grow too quickly. We then leverage an existing counter algorithm by Aspnes, Attiya and Censor-Hillel [1] in which we “plug” our max register implementation to show that it remains linearizable while achieving O(log2n) amortized step complexity.}, author = {Baig, Mirza Ahad and Hendler, Danny and Milani, Alessia and Travers, Corentin}, issn = {1432-0452}, journal = {Distributed Computing}, keywords = {Computational Theory and Mathematics, Computer Networks and Communications, Hardware and Architecture, Theoretical Computer Science}, pages = {29--43}, publisher = {Springer Nature}, title = {{Long-lived counters with polylogarithmic amortized step complexity}}, doi = {10.1007/s00446-022-00439-5}, volume = {36}, year = {2023}, } @article{12287, abstract = {We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.}, author = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Wintraecken, Mathijs}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science}, pages = {156--191}, publisher = {Springer Nature}, title = {{Local criteria for triangulating general manifolds}}, doi = {10.1007/s00454-022-00431-7}, volume = {69}, year = {2023}, } @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 = {1936-2455}, 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{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{12129, abstract = {Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.}, author = {Wagner, Uli and Welzl, Emo}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science}, number = {4}, pages = {1227--1284}, publisher = {Springer Nature}, title = {{Connectivity of triangulation flip graphs in the plane}}, doi = {10.1007/s00454-022-00436-2}, volume = {68}, year = {2022}, } @article{12152, abstract = {ESCRT-III filaments are composite cytoskeletal polymers that can constrict and cut cell membranes from the inside of the membrane neck. Membrane-bound ESCRT-III filaments undergo a series of dramatic composition and geometry changes in the presence of an ATP-consuming Vps4 enzyme, which causes stepwise changes in the membrane morphology. We set out to understand the physical mechanisms involved in translating the changes in ESCRT-III polymer composition into membrane deformation. We have built a coarse-grained model in which ESCRT-III polymers of different geometries and mechanical properties are allowed to copolymerise and bind to a deformable membrane. By modelling ATP-driven stepwise depolymerisation of specific polymers, we identify mechanical regimes in which changes in filament composition trigger the associated membrane transition from a flat to a buckled state, and then to a tubule state that eventually undergoes scission to release a small cargo-loaded vesicle. We then characterise how the location and kinetics of polymer loss affects the extent of membrane deformation and the efficiency of membrane neck scission. Our results identify the near-minimal mechanical conditions for the operation of shape-shifting composite polymers that sever membrane necks.}, author = {Jiang, Xiuyun and Harker-Kirschneck, Lena and Vanhille-Campos, Christian Eduardo and Pfitzner, Anna-Katharina and Lominadze, Elene and Roux, Aurélien and Baum, Buzz and Šarić, Anđela}, issn = {1553-7358}, journal = {PLOS Computational Biology}, keywords = {Computational Theory and Mathematics, Cellular and Molecular Neuroscience, Genetics, Molecular Biology, Ecology, Modeling and Simulation, Ecology, Evolution, Behavior and Systematics}, number = {10}, publisher = {Public Library of Science}, title = {{Modelling membrane reshaping by staged polymerization of ESCRT-III filaments}}, doi = {10.1371/journal.pcbi.1010586}, volume = {18}, year = {2022}, } @article{12261, abstract = {Dose–response relationships are a general concept for quantitatively describing biological systems across multiple scales, from the molecular to the whole-cell level. A clinically relevant example is the bacterial growth response to antibiotics, which is routinely characterized by dose–response curves. The shape of the dose–response curve varies drastically between antibiotics and plays a key role in treatment, drug interactions, and resistance evolution. However, the mechanisms shaping the dose–response curve remain largely unclear. Here, we show in Escherichia coli that the distinctively shallow dose–response curve of the antibiotic trimethoprim is caused by a negative growth-mediated feedback loop: Trimethoprim slows growth, which in turn weakens the effect of this antibiotic. At the molecular level, this feedback is caused by the upregulation of the drug target dihydrofolate reductase (FolA/DHFR). We show that this upregulation is not a specific response to trimethoprim but follows a universal trend line that depends primarily on the growth rate, irrespective of its cause. Rewiring the feedback loop alters the dose–response curve in a predictable manner, which we corroborate using a mathematical model of cellular resource allocation and growth. Our results indicate that growth-mediated feedback loops may shape drug responses more generally and could be exploited to design evolutionary traps that enable selection against drug resistance.}, author = {Angermayr, Andreas and Pang, Tin Yau and Chevereau, Guillaume and Mitosch, Karin and Lercher, Martin J and Bollenbach, Mark Tobias}, issn = {1744-4292}, journal = {Molecular Systems Biology}, keywords = {Applied Mathematics, Computational Theory and Mathematics, General Agricultural and Biological Sciences, General Immunology and Microbiology, General Biochemistry, Genetics and Molecular Biology, Information Systems}, number = {9}, publisher = {Embo Press}, title = {{Growth‐mediated negative feedback shapes quantitative antibiotic response}}, doi = {10.15252/msb.202110490}, volume = {18}, year = {2022}, } @article{12280, abstract = {In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.}, author = {Schmid, Laura and Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin}, issn = {1553-7358}, journal = {PLOS Computational Biology}, keywords = {Computational Theory and Mathematics, Cellular and Molecular Neuroscience, Genetics, Molecular Biology, Ecology, Modeling and Simulation, Ecology, Evolution, Behavior and Systematics}, number = {6}, publisher = {Public Library of Science}, title = {{Direct reciprocity between individuals that use different strategy spaces}}, doi = {10.1371/journal.pcbi.1010149}, volume = {18}, year = {2022}, } @article{12286, abstract = {Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes. Our main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$.}, author = {Cooley, Oliver and Kang, Mihyun and Zalla, Julian}, issn = {1077-8926}, journal = {The Electronic Journal of Combinatorics}, keywords = {Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science, Applied Mathematics, Discrete Mathematics and Combinatorics}, number = {4}, publisher = {The Electronic Journal of Combinatorics}, title = {{Loose cores and cycles in random hypergraphs}}, doi = {10.37236/10794}, volume = {29}, year = {2022}, } @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{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 = {1432-0444}, 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 = {1615-3383}, 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{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{14125, abstract = {Motivation: Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed. Results: We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively.}, author = {Stark, Stefan G and Ficek, Joanna and Locatello, Francesco and Bonilla, Ximena and Chevrier, Stéphane and Singer, Franziska and Aebersold, Rudolf and Al-Quaddoomi, Faisal S and Albinus, Jonas and Alborelli, Ilaria and Andani, Sonali and Attinger, Per-Olof and Bacac, Marina and Baumhoer, Daniel and Beck-Schimmer, Beatrice and Beerenwinkel, Niko and Beisel, Christian and Bernasconi, Lara and Bertolini, Anne and Bodenmiller, Bernd and Bonilla, Ximena and Casanova, Ruben and Chevrier, Stéphane and Chicherova, Natalia and D'Costa, Maya and Danenberg, Esther and Davidson, Natalie and gan, Monica-Andreea Dră and Dummer, Reinhard and Engler, Stefanie and Erkens, Martin and Eschbach, Katja and Esposito, Cinzia and Fedier, André and Ferreira, Pedro and Ficek, Joanna and Frei, Anja L and Frey, Bruno and Goetze, Sandra and Grob, Linda and Gut, Gabriele and Günther, Detlef and Haberecker, Martina and Haeuptle, Pirmin and Heinzelmann-Schwarz, Viola and Herter, Sylvia and Holtackers, Rene and Huesser, Tamara and Irmisch, Anja and Jacob, Francis and Jacobs, Andrea and Jaeger, Tim M and Jahn, Katharina and James, Alva R and Jermann, Philip M and Kahles, André and Kahraman, Abdullah and Koelzer, Viktor H and Kuebler, Werner and Kuipers, Jack and Kunze, Christian P and Kurzeder, Christian and Lehmann, Kjong-Van and Levesque, Mitchell and Lugert, Sebastian and Maass, Gerd and Manz, Markus and Markolin, Philipp and Mena, Julien and Menzel, Ulrike and Metzler, Julian M and Miglino, Nicola and Milani, Emanuela S and Moch, Holger and Muenst, Simone and Murri, Riccardo and Ng, Charlotte KY and Nicolet, Stefan and Nowak, Marta and Pedrioli, Patrick GA and Pelkmans, Lucas and Piscuoglio, Salvatore and Prummer, Michael and Ritter, Mathilde and Rommel, Christian and Rosano-González, María L and Rätsch, Gunnar and Santacroce, Natascha and Castillo, Jacobo Sarabia del and Schlenker, Ramona and Schwalie, Petra C and Schwan, Severin and Schär, Tobias and Senti, Gabriela and Singer, Franziska and Sivapatham, Sujana and Snijder, Berend and Sobottka, Bettina and Sreedharan, Vipin T and Stark, Stefan and Stekhoven, Daniel J and Theocharides, Alexandre PA and Thomas, Tinu M and Tolnay, Markus and Tosevski, Vinko and Toussaint, Nora C and Tuncel, Mustafa A and Tusup, Marina and Drogen, Audrey Van and Vetter, Marcus and Vlajnic, Tatjana and Weber, Sandra and Weber, Walter P and Wegmann, Rebekka and Weller, Michael and Wendt, Fabian and Wey, Norbert and Wicki, Andreas and Wollscheid, Bernd and Yu, Shuqing and Ziegler, Johanna and Zimmermann, Marc and Zoche, Martin and Zuend, Gregor and Rätsch, Gunnar and Lehmann, Kjong-Van}, issn = {1367-4811}, journal = {Bioinformatics}, keywords = {Computational Mathematics, Computational Theory and Mathematics, Computer Science Applications, Molecular Biology, Biochemistry, Statistics and Probability}, number = {Supplement_2}, pages = {i919--i927}, publisher = {Oxford University Press}, title = {{SCIM: Universal single-cell matching with unpaired feature sets}}, doi = {10.1093/bioinformatics/btaa843}, volume = {36}, 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}, } @article{11683, abstract = {The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity.}, author = {Henzinger, Monika H and Rao, Satish and Gabow, Harold N.}, issn = {0196-6774}, journal = {Journal of Algorithms}, keywords = {Computational Theory and Mathematics, Computational Mathematics, Control and Optimization}, number = {2}, pages = {222--250}, publisher = {Elsevier}, title = {{Computing vertex connectivity: New bounds from old techniques}}, doi = {10.1006/jagm.1999.1055}, volume = {34}, year = {2000}, }