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In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on.…
Dictionary learning methods can be split into: i) class specific dictionary learning ii) class shared dictionary learning. The difference between the two categories is how to use discriminative information. With the first category, samples…
One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
In this article, we continue the study of monadic distributive lattices (or m-lattices) which are a natural generalization of monadic Heyting algebras, introduced by Monteiro and Varsavsky and developed exhaustively by Bezhanishvili. First,…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical…
Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…
Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…
We revisit the definition of Cartesian differential categories, showing that a slightly more general version is useful for a number of reasons. As one application, we show that these general differential categories are comonadic over…
We use a theory of colax Reedy diagrams to show that the category of Segal M-precategories with fixed set of objects has a model structure for a symmetric monoidal model category M = (M,\otimes,I). What is relevant here is when M is…
Clustering temporal and dynamically changing multivariate time series from real-world fields, called temporal clustering for short, has been a major challenge due to inherent complexities. Although several deep temporal clustering…
This thesis proposes a framework based on a notion of combinatorial cell complex (cc) whose cells are defined simply as finite sets of vertices. The cells of a cc are subject to four axioms involving a rank function that assigns a rank (or…
We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a…
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…
Conventional multi-label classification (MLC) methods assume that all samples are fully labeled and identically distributed. Unfortunately, this assumption is unrealistic in large-scale MLC data that has long-tailed (LT) distribution and…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…
We introduce a new type of weakly enriched categories over a given symmetric monoidal model category M; these are called Co-Segal categories. Their definition derives from the philosophy of classical (enriched) Segal categories. We study…
Supervised contrastive learning (SCL) frameworks treat each class as independent and thus consider all classes to be equally important. This neglects the common scenario in which label hierarchy exists, where fine-grained classes under the…