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In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this…
This paper considers quasi-reductivity - essentially, the property that an evaluation cannot get "stuck" due to a missing case in pattern matching - in the context of term rewriting with logical constraints.
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
This paper designs an alogrithm to compute the minimal combinations of finite sets in Euclidean spaces, and applys the algorithm of study the moment maps and geometric invariant stability of hypersurfaces. The classical example of cubic…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
The concept of operator left residuation has been introduced by the authors in a previous paper. Modifications of so-called quantum structures, in particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and Boolean posets…
This article proposes modifications to standard low order finite element approximations of the Stokes system with the goal of improving both the approximation quality and the parallel algebraic solution process. Different from standard…
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…
In the wake of the explosive growth in smartphones and cyberphysical systems, there has been an accelerating shift in how data is generated away from centralised data towards on-device generated data. In response, machine learning…
The bottom-left algorithm is a simple heuristic for the Strip Packing Problem. It places the rectangles in the given order at the lowest free position in the strip, using the left most position in case of ties. Despite its simplicity, the…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…