Related papers: Computational Complexity of Avalanches in the Kada…
The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections.…
Knapsack problems (KPs) are common in industry, but solving KPs is known to be NP-hard and has been tractable only at a relatively small scale. This paper examines KPs in a slightly generalized form and shows that they can be solved nearly…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Consider the Abelian sandpile measure on $\mathbb{Z}^d$, $d \ge 2$, obtained as the $L \to \infty$ limit of the stationary distribution of the sandpile on $[-L,L]^d \cap \mathbb{Z}^d$. When adding a grain of sand at the origin, some region,…
The scaling properties of waves of topplings in the sandpile model on the Sierpinski gasket are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is found. Predictions for scaling…
It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
We demonstrate a polynomial approach to express the decision version of the directed Hamiltonian Cycle Problem (HCP), which is NP-Complete, as the Solvability of a Polynomial Equation with a constant number of variables, within a bounded…
We prove that path puzzles with complete row and column information--or equivalently, 2D orthogonal discrete tomography with Hamiltonicity constraint--are strongly NP-complete, ASP-complete, and #P-complete. Along the way, we newly…
This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
In this paper we investigate computational properties of the Diophantine problem for spherical equations in some classes of finite groups. We classify the complexity of different variations of the problem, e.g., when $G$ is fixed and when…
In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Cl\'ement…
The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite…
We study random 2-dimensional complexes in the Linial - Meshulam model and prove that for the probability parameter satisfying $$p\ll n^{-46/47}$$ a random 2-complex $Y$ contains several pairwise disjoint tetrahedra such that the 2-complex…
Quantitative extensions of logic programming often require the solution of so called second level inference tasks, i.e., problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication,…
In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL)…
We investigate the sandpile model on the two--dimensional Sierpinski gasket fractal. We find that the model displays novel critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes and topplings and…