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We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…
In the recent years, there has been active research on self-orthogonal embeddings of linear codes since they yielded some optimal self-orthogonal codes. LCD codes have a trivial hull so they are counterparts of self-orthogonal codes. So it…
Realistic 3D-conformations of protein structures can be embedded in a cubic lattice using exclusively integer numbers, additions, subtractions and boolean operations.
The purpose of this paper is to construct non-trivial cocycles of the space $Emb(\mathbb{R}^j, \mathbb{R}^{n})$ of long embeddings. We construct the cocycles by integral over configuration spaces, associated with Bott-Cattaneo-Rossi graphs…
Minimal linear codes are algebraic objects which gained interest in the last twenty years, due to their link with Massey's secret sharing schemes. In this context, Ashikhmin and Barg provided a useful and a quite easy to handle sufficient…
Probabilistic amplitude shaping (PAS) is on track to become the de facto coded modulation standard for communication systems aiming to operate close to channel capacity at high transmission rates. The essential component of PAS that breeds…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
Hulls of linear codes have been of interest and extensively studied due to their rich algebraic structures and wide applications. In this paper, alternative characterizations of hulls of linear codes are given as well as their applications.…
In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…
Embedding learning for categorical features is crucial for the deep learning-based recommendation models (DLRMs). Each feature value is mapped to an embedding vector via an embedding learning process. Conventional methods configure a fixed…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a graphical model in order to define a new code.…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
We demonstrate that traits are a natural way to support correctness-by-construction (CbC) in an existing programming language in the presence of traditional post-hoc verification (PhV). With Correctness-by-Construction, programs are…
Given a tiling $\mathcal{T}$ of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes $\mathcal{T}\times\mathbb{R}$.…
In this paper we study a class of embeddings of tent inverse limit spaces. We introduce techniques relying on the Milnor-Thurston kneading theory and use them to study sets of accessible points and prime ends of given embeddings. We…