相关论文: Analysing singularities of a benchmark problem

Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…

We study a class of mathematical and statistical algorithms with the aim of establishing a computer-based framework for fast and reliable automatic abnormality detection on landmark represented image templates. Under this framework, we…

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…

Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…

In Machine Learning, a benchmark refers to an ensemble of datasets associated with one or multiple metrics together with a way to aggregate different systems performances. They are instrumental in (i) assessing the progress of new methods…

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…

This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…

The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is…

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous…

Benchmarking optimization algorithms is fundamental for the advancement of computational intelligence. However, widely adopted artificial test suites exhibit limited correspondence with the diversity and complexity of real-world engineering…

We present an algorithm to efficiently sample the full space of planetary interior density profiles. Our approach uses as few assumptions as possible to pursue an agnostic algorithm. The algorithm avoids the common Markov Chain Monte Carlo…