TY - JOUR AB - Given a fixed finite metric space (V,μ), the {\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs. AU - Dvorak, Martin AU - Kolmogorov, Vladimir ID - 10045 JF - Mathematical Programming KW - minimum 0-extension problem KW - metric labeling problem KW - discrete metric spaces KW - metric extensions KW - computational complexity KW - valued constraint satisfaction problems KW - discrete convex analysis KW - L-convex functions SN - 0025-5610 TI - Generalized minimum 0-extension problem and discrete convexity ER - TY - JOUR AB - We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1-E)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time 0(mE-1), beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in 0(mE-1 log E-1). Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-E)-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is 0(mE-1), where m is the sum of the number of initially existing and inserted edges. AU - Zheng, Da Wei AU - Henzinger, Monika H ID - 15121 JF - Mathematical Programming SN - 0025-5610 TI - Multiplicative auction algorithm for approximate maximum weight bipartite matching ER - TY - JOUR AB - Water is known to play an important role in collagen self-assembly, but it is still largely unclear how water–collagen interactions influence the assembly process and determine the fibril network properties. Here, we use the H2O/D2O isotope effect on the hydrogen-bond strength in water to investigate the role of hydration in collagen self-assembly. We dissolve collagen in H2O and D2O and compare the growth kinetics and the structure of the collagen assemblies formed in these water isotopomers. Surprisingly, collagen assembly occurs ten times faster in D2O than in H2O, and collagen in D2O self-assembles into much thinner fibrils, that form a more inhomogeneous and softer network, with a fourfold reduction in elastic modulus when compared to H2O. Combining spectroscopic measurements with atomistic simulations, we show that collagen in D2O is less hydrated than in H2O. This partial dehydration lowers the enthalpic penalty for water removal and reorganization at the collagen–water interface, increasing the self-assembly rate and the number of nucleation centers, leading to thinner fibrils and a softer network. Coarse-grained simulations show that the acceleration in the initial nucleation rate can be reproduced by the enhancement of electrostatic interactions. These results show that water acts as a mediator between collagen monomers, by modulating their interactions so as to optimize the assembly process and, thus, the final network properties. We believe that isotopically modulating the hydration of proteins can be a valuable method to investigate the role of water in protein structural dynamics and protein self-assembly. AU - Giubertoni, Giulia AU - Feng, Liru AU - Klein, Kevin AU - Giannetti, Guido AU - Rutten, Luco AU - Choi, Yeji AU - Van Der Net, Anouk AU - Castro-Linares, Gerard AU - Caporaletti, Federico AU - Micha, Dimitra AU - Hunger, Johannes AU - Deblais, Antoine AU - Bonn, Daniel AU - Sommerdijk, Nico AU - Šarić, Anđela AU - Ilie, Ioana M. AU - Koenderink, Gijsje H. AU - Woutersen, Sander ID - 15116 IS - 11 JF - Proceedings of the National Academy of Sciences of the United States of America SN - 0027-8424 TI - Elucidating the role of water in collagen self-assembly by isotopically modulating collagen hydration VL - 121 ER - TY - GEN AB - This zip file contains data, and analysis for the paper "Elucidating the role of water in collagen self-assembly by isotopically modulating collagen hydration". AU - Giubertoni, G. AU - Woutersen, S. ID - 15126 TI - Dataset Collagen Self Assembly in H2O and D2O ER - TY - THES AB - Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in discrete geometry that have captivated mathematicians for centuries, if not millennia. This thesis seeks to cast new light on these structures by illustrating specific instances where a topological perspective, specifically through discrete Morse theory and persistent homology, provides valuable insights. At first glance, the topology of these geometric objects might seem uneventful: point sets essentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which is a contractible space, and the topology of a network primarily involves the enumeration of connected components and cycles within the network. However, beneath this apparent simplicity, there lies an array of intriguing structures, a small subset of which will be uncovered in this thesis. Focused on three case studies, each addressing one of the mentioned objects, this work will showcase connections that intertwine topology with diverse fields such as combinatorial geometry, algorithms and data structures, and emerging applications like spatial biology. AU - Cultrera di Montesano, Sebastiano ID - 15094 SN - 2663 - 337X TI - Persistence and Morse theory for discrete geometric structures ER -