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Simulation offers a scalable and efficient alternative to real-world data collection for learning visuomotor robotic policies. However, the simulation-to-reality, or Sim2Real distribution shift -- introduced by employing simulation-trained…
The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated…
Reconciling a gene tree with a species tree is an important task that reveals much about the evolution of genes, genomes, and species, as well as about the molecular function of genes. A wide array of computational tools have been devised…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Pruning is the art of cutting unwanted and unhealthy plant branches and is one of the difficult tasks in the field robotics. It becomes even more complex when the plant branches are moving. Moreover, the reproducibility of robot pruning…
We argue for supplementing the process of training a prediction algorithm by setting up a scheme for detecting the moment when the distribution of the data changes and the algorithm needs to be retrained. Our proposed schemes are based on…
Reservoir computing is a brain inspired approach for information processing, well suited to analogue implementations. We report a photonic implementation of a reservoir computer that exploits frequency domain multiplexing to encode neuron…
One requirement of maintaining digital information is storage. With the latest advances in the digital world, new emerging media types have required even more storage space to be kept than before. In fact, in many cases it is required to…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical…
In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated by the problem of computing free presentations of the…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
Operating system (OS) updates introduce numerical perturbations that impact the reproducibility of computational pipelines. In neuroimaging, this has important practical implications on the validity of computational results, particularly…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
This paper introduces a novel anti-unification algorithm for the generalization of variadic structures with binders, designed as a flexible tool for structural code comparison. By combining nominal techniques for handling variable binding…
Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers.…
We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework.…
To achieve reliability in distributed storage systems, data has usually been replicated across different nodes. However the increasing volume of data to be stored has motivated the introduction of erasure codes, a storage efficient…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…