TY - CHAP AB - We prove that there is no strongly regular graph (SRG) with parameters (460; 153; 32; 60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs. AU - Bondarenko, Andriy AU - Mellit, Anton AU - Prymak, Andriy AU - Radchenko, Danylo AU - Viazovska, Maryna ID - 61 T2 - Contemporary Computational Mathematics TI - There is no strongly regular graph with parameters (460; 153; 32; 60) ER - TY - JOUR AB - Blood platelets are critical for hemostasis and thrombosis, but also play diverse roles during immune responses. We have recently reported that platelets migrate at sites of infection in vitro and in vivo. Importantly, platelets use their ability to migrate to collect and bundle fibrin (ogen)-bound bacteria accomplishing efficient intravascular bacterial trapping. Here, we describe a method that allows analyzing platelet migration in vitro, focusing on their ability to collect bacteria and trap bacteria under flow. AU - Fan, Shuxia AU - Lorenz, Michael AU - Massberg, Steffen AU - Gärtner, Florian R ID - 6354 IS - 18 JF - Bio-Protocol KW - Platelets KW - Cell migration KW - Bacteria KW - Shear flow KW - Fibrinogen KW - E. coli SN - 2331-8325 TI - Platelet migration and bacterial trapping assay under flow VL - 8 ER - TY - CHAP AB - This chapter finds an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface. On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs bundles, whose mirror was proposed by Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin’s proposal. AU - Hausel, Tamás AU - Mellit, Anton AU - Pei, Du ID - 6525 SN - 9780198802013 T2 - Geometry and Physics: Volume I TI - Mirror symmetry with branes by equivariant verlinde formulas ER - TY - JOUR AB - We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1. AU - Lee, Jii AU - Schnelli, Kevin ID - 690 IS - 1-2 JF - Probability Theory and Related Fields TI - Local law and Tracy–Widom limit for sparse random matrices VL - 171 ER - TY - JOUR AB - We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision. AU - Shekhovtsov, Alexander AU - Swoboda, Paul AU - Savchynskyy, Bogdan ID - 703 IS - 7 JF - IEEE Transactions on Pattern Analysis and Machine Intelligence SN - 01628828 TI - Maximum persistency via iterative relaxed inference with graphical models VL - 40 ER -