Related papers: Fast Computations on Ordered Nominal Sets
Nominal techniques provide a mathematically principled approach to dealing with names and variable binding in programming languages. This paper explores an attempt to make nominal techniques accessible as an Agda library. We aim for a…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
Sequence optimization, where the items in a list are ordered to maximize some reward has many applications such as web advertisement placement, search, and control libraries in robotics. Previous work in sequence optimization produces a…
The present project aims to use machine learning, specifically neural networks (NN), to learn the trajectories of a set of coupled ordinary differential equations (ODEs) and decrease compute times for obtaining ODE solutions by using this…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a…
We demonstrate the utility of machine learning algorithms for the design of Oscillatory Neural Networks (ONNs). After constructing a circuit model of the oscillators in a machine-learning-enabled simulator and performing Backpropagation…
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for…
In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does…
Preference orderings are orderings of a set of items according to the preferences (of judges). Such orderings arise in a variety of domains, including group decision making, consumer marketing, voting and machine learning. Measuring the…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
The minimal sets within a collection of sets are defined as the ones which do not have a proper subset within the collection, and the maximal sets are the ones which do not have a proper superset within the collection. Identifying extremal…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…
Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic…
Recent advancements in pretraining have demonstrated that modern Large Language Models (LLMs) possess the capability to effectively learn arithmetic operations. However, despite acknowledging the significance of digit order in arithmetic…