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Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is…
Given a non-necessarily commutative unital ring $R$ and a unital partial representation $\Theta $ of a group $G$ into the Picard semigroup $\mathbf{PicS} (R)$ of the isomorphism classes of partially invertible $R$-bimodules, we construct an…
This work proposes an extension to Structured Grammatical Evolution (SGE) called Co-evolutionary Probabilistic Structured Grammatical Evolution (Co-PSGE). In Co-PSGE each individual in the population is composed by a grammar and a genotype,…
Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing…
Humans easily interpret expressions that describe unfamiliar situations composed from familiar parts ("greet the pink brontosaurus by the ferris wheel"). Modern neural networks, by contrast, struggle to interpret novel compositions. In this…
Classical splines feature prominently in approximation theory and numerical analysis, while GKM theory arises in the study of equivariant cohomology. More recently, generalized splines have been studied which simultaneously generalize both…
Compositional generalization allows efficient learning and human-like inductive biases. Since most research investigating compositional generalization in NLP is done on English, important questions remain underexplored. Do the necessary…
Let $G$ be a finitely generated group. We show that for any finite generating set $A$, the language consisting of all geodesics in $Cay(G,A)$ with a contracting property is a regular language. As an application, we show that any finitely…
Sequential processes in real-world often carry a combination of simple subsystems that interact with each other in certain forms. Learning such a modular structure can often improve the robustness against environmental changes. In this…
We introduce a categorical language in which it is possible to talk about DNA sequencing, alignment methods, CRISPR, homologous recombination, haplotypes, and genetic linkage. This language takes the form of a class of limit-sketches whose…
The general translator formalism and computing specific implementations are proposed. The implementation of specific elements necessary to process the source and destination information within the translators are presented. Some common…
Motivated by work on bio-operations on DNA strings, we consider an outfix-guided insertion operation that can be viewed as a generalization of the overlap assembly operation on strings studied previously. As the main result we construct a…
Polymorphism in programming languages enables code reuse. Here, we show that polymorphism has broad applicability far beyond computations for technical computing: parallelism in distributed computing, presentation of visualizations of…
A generalized top-spin analysis proposed some time ago in the context of Standard Model and subsequently studied in varying contexts is now applied primarily to the case of $e^+e^-\rightarrow t\bar{t}$ with transversely polarized beams.…
There are many structures (algebras, categories, etc) with natural gradings such that the degree 0 components are not semisimple. Particular examples include tensor algebras with non-semisimple degree 0 parts, extension algebras of standard…
In synchronous rewriting, the productions of two rewriting systems are paired and applied synchronously in the derivation of a pair of strings. We present a new synchronous rewriting system and argue that it can handle certain phenomena…
Cross-lingual word embeddings transfer knowledge between languages: models trained on high-resource languages can predict in low-resource languages. We introduce CLIME, an interactive system to quickly refine cross-lingual word embeddings…
Do language models (LMs) offer insights into human language learning? A common argument against this idea is that because their architecture and training paradigm are so vastly different from humans, LMs can learn arbitrary inputs as easily…
Speculative decoding accelerates autoregressive speech generation by letting a fast draft model propose tokens that a larger target model verifies. However, for speech LLMs that generate acoustic tokens, exact token matching is overly…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…