Related papers: Variant-based Equational Unification under Constru…
In top-down multi-level design methodologies, design descriptions at higher levels of abstraction are incrementally refined to the final realizations. Simulation based techniques have traditionally been used to verify that such model…
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Simulating general quantum processes that describe realistic interactions of quantum systems following a non-unitary evolution is challenging for conventional quantum computers that directly implement unitary gates. We analyze complexities…
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
As the cornerstone of modern power systems, the Unit Commitment Problem (UC) is critical for ensuring operational security and economic efficiency in the ongoing global energy transition. However, existing UC studies typically propose…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
Gauge unification is widely considered to be a desirable feature for extensions of the standard model. Unfortunately the standard model itself does not exhibit a unification of its running gauge couplings but it is required by grand unified…
Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. We develop three variations on VAEs by introducing a second parameterized encoder/decoder pair and,…
Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…
The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…
An algorithm for unification modulo one-sided distributivity is an early result by Tid\'en and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
Tensor-based modulation (TBM) provides a multi-linear spreading framework for blind multi-user separation in unsourced random access. In this paper, we show that TBM is a coded modulation built on a non-binary linear block code over…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…