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Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing many points of a cartesian product. In 2000, Elekes and Rónyai proved that if the graph of a polynomial f(x, y) contains cn2 points of an n × n × n cartesia ...
The high failure rate expected for future supercomputers requires the design of new fault tolerant solutions. Most checkpointing protocols are designed to work with any message-passing application but suffer from scalability issues at extreme scale. We tak ...
Given a collection C of curves in the plane, its string graph is defined as the graph with vertex set C, in which two curves in C are adjacent if and only if they intersect. Given a partially ordered set (P,
We study global behavior of radial solutions for the nonlinear wave equation with the focusing energy critical nonlinearity in three and five space dimensions. Assuming that the solution has energy at most slightly more than the ground states and gets away ...
Extensive research on antiviral small molecules starting in the early 1970s has led to the identification of 10-carboxymethyl-9-acridanone (CMA) as a potent type I interferon (IFN) inducer. Up to date, the mode of action of this antiviral molecule has rema ...
We provide strong evidence that the S = 1 bilinear-biquadratic Heisenberg model with nearest-neighbor interactions on the square lattice possesses an extended three-sublattice phase induced by quantum fluctuations for sufficiently large biquadratic interac ...
Over the last ten years, Diffusion-weighted Imaging (DWI) has become an important tool to investigate white matter (WM) anomalies in schizophrenia. Despite technological improvement and the exponential use of this technique, discrepancies remain and little ...
We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group and infinite projected entangled-pair states. For the triangular lattice we confir ...
In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...