Related papers: Algorithmic resolution via weighted blowings up
We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the…
We consider the sensitivity of algorithms for the maximum matching problem against edge and vertex modifications. Algorithms with low sensitivity are desirable because they are robust to edge failure or attack. In this work, we show a…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
In this paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
We consider the 1D cubic NLS on $\mathbb R$ and prove a blow-up result for functions that are of borderline regularity, i.e. $H^s$ for any $s<-\frac 12$ for the Sobolev scale and $\mathcal F L^\infty$ for the Fourier-Lebesgue scale. This is…
This paper is a follow up to a previous work that presented an algorithm to efficiently find all of the equilibria of the Kuramoto model with nonuniform coupling described by a rank one matrix. The algorithm was shown experimentally to be…
In this paper we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar $n$-body problem. Our approach is based on Albouy-Kaloshin's work on finiteness of central configurations for the…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Cluster analysis plays an important role in decision making process for many knowledge-based systems. There exist a wide variety of different approaches for clustering applications including the heuristic techniques, probabilistic models,…
Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role…
This paper is concerned with a cubic nonlinear Schr\"odinger system modeling the interaction between an optical beam and its third harmonic in a material with Kerr-type nonlinear response. We are mainly interested in the so-called…
The low rank approximation of matrices is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block…
For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quantized singular sources. In particular the uniqueness result…
We study spherical charged black holes in the presence of a cosmological constant with corrections motivated by the theory of loop quantum gravity. The effective theory is constructed at the Hamiltonian level by introducing certain…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…
In this short paper, we are concerned with the blowup phenomenon of stochastic parabolic equations. By using comparison principle and the results of deterministic parabolic equations, we obtain blowup results of solutions for stochastic…
In this paper, we obtain the exact blow-up profiles of solutions of the Keller-Segel-Patlak system in the space with dimensions $N\ge 3$, which solves an open problem proposed by P. Souplet and M. Winkler in 2019. To establish this…