Related papers: Computational Complexity of Avalanches in the Kada…
The discrete modeling of the Geiger-mode APD is considered. Results of modeling and experimental measurements with the SiPM show that the known formula for the charge of the avalanche pulse Q=dU*Cd underestimates its value. In addition, it…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
We present a directed unloading sand box type avalanche model, driven by slowly lowering the retaining wall at the bottom of the slope. The avalanche propagation in the two dimensional surface is related to the space-time configurations of…
We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…
We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for…
We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
We introduce a natural stochastic extension, called SSP, of the abelian sandpile model(ASM), which shares many mathematical properties with ASM, yet radically differs in its physical behavior, for example in terms of the shape of the steady…
We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…
We consider the average-case complexity of some otherwise undecidable or open Diophantine problems. More precisely, consider the following: (I) Given a polynomial f in Z[v,x,y], decide the sentence \exists v \forall x \exists y f(v,x,y)=0,…
We consider the isotropic two-dimensional abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from…
Using the theory of resolving classes, we show that if $X$ is a CW complex of finite type such that $\map_*(X, S^{2n+1})\sim *$ for all sufficiently large $n$, then $\map_*(X, K) \sim *$ for every simply-connected finite-dimensional CW…
We study here a variant of the Abelian Sandpile Model, where the playground is a cylinder of width $w$ and of circumference c. When c << w, we describe a phenomenon which has not been observed in other geometries: the probability…
We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven…
In this paper, we reinterpret quadratic Lyapunov functions as solutions to a performance estimation saddle point problem. This allows us to automatically detect the existence of such a Lyapunov function and thus numerically check that a…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
In complexity theory, there exists a famous unsolved problem whether NP can be P or not. In this paper, we discuss this aspect in SAT (satisfiability) problem, and it is shown that the SAT can be solved in plynomial time by means of quantum…
Shallow landslides pose a significant threat to people and infrastructure. While often modeled based on limit equilibrium analysis, finite or discrete elements, continuum particle-based approaches like the Material Point Method (MPM) have…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…