Related papers: Super Solutions of the Model RB
Let $E$ be a complete, separable metric space and $A$ be an operator on $C_b(E)$. We give an abstract definition of viscosity sub/supersolution of the resolvent equation $\lambda u-Au=h$ and show that, if the comparison principle holds,…
Relation between problem hardness and solution space structure is an important research aspect. Model d-k-CSP generates very hard instances when $r=1$ and $r$ is near 1, where $r$ represents normalized constraint density. We find that when…
Image super-resolution (SR) is a field in computer vision that focuses on reconstructing high-resolution images from the respective low-resolution image. However, super-resolution is a well-known ill-posed problem as most methods rely on…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
A superredundant clause is a clause that is redundant in the resolution closure of a formula. The converse concept of superirredundancy ensures membership of the clause in all minimal CNF formulae that are equivalent to the given one. This…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive.…
Multidimensional continuous-domain inverse problems are often solved by the minimization of a loss functional, formed as the sum of a data fidelity and a regularization. In this work, we present a new construction where the regularization…
Most of the recent literature on image Super-Resolution (SR) can be classified into two main approaches. The first one involves learning a corruption model tailored to a specific dataset, aiming to mimic the noise and corruption in…
Concerning a class of diffusive logistic equations, Ni [1, Abstract] proposed an optimization problem to consider the supremum of the ratio of the L^1 norms of species and resources by varying the diffusion rates and the profiles of…
We introduce the notion of $\mathcal{N}=1$ abstract super loop equations, and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be thought of as a supersymmetric generalization of the…
The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…
We derive several new bounds for the problem of difference sets with local properties, such as establishing the super-linear threshold of the problem. For our proofs, we develop several new tools, including a variant of higher moment…
The relativistic membrane equation can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, a new blow-up theorem is established. As an application, it demonstrates the formation of…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…