Related papers: Super Solutions of the Model RB
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…
We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable…
In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satisfiable to a region where almost all…
In this paper we study the solution space structure of model RB, a standard prototype of Constraint Satisfaction Problem (CSPs) with growing domains. Using rigorous the first and the second moment method, we show that in the solvable phase…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR…
In this work we provide a method for building up a strictly positive supersolution for the steady state of a degenerated logistic equation type, i.e., when the weight function vanishes on the boundary of the domain. This degenerated system…
This paper focuses on the fundamental aspects of super-resolution, particularly addressing the stability of super-resolution and the estimation of two-point resolution. Our first major contribution is the introduction of two…
In mathematics, a super-resolution problem can be formulated as acquiring high-frequency data from low-frequency measurements. This extrapolation problem in the frequency domain is well-known to be unstable. We propose a model-based…
This paper focuses on the superset model problem that arises in the context of regression. To address this problem, we take the Bayesian approach to measure its uncertainty. An illustrative example with the real dataset is provided.
The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
Real-world Super-Resolution (SR) has been traditionally tackled by first learning a specific degradation model that resembles the noise and corruption artifacts in low-resolution imagery. Thus, current methods lack generalization and lose…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…
We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong…