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Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…
We introduce a fully convolutional fractional scaling component, FCFS. Fully convolutional networks can be applied to any size input and previously did not support non-integer scaling. Our architecture is simple with an efficient single…
We suggest using Fully Homomorphic Encryption (FHE) to be used, not only to keep the privacy of information but also, to verify computations with no additional significant overhead, using only part of the variables length for verification.…
Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from…
We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…
We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank-modulation is a generalization of the rank-modulation scheme, which has…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
International Classification of Diseases (ICD) are the de facto codes used globally for clinical coding. These codes enable healthcare providers to claim reimbursement and facilitate efficient storage and retrieval of diagnostic…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
A standard assumption in the study of logarithmic structures is "fineness", but this assumption is not preserved by intersections, fiber products, and more general limits. We explain how a coherent logarithmic scheme $X$ has a natural…
We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…
In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…
In reversible computing, the management of space is subject to two broad classes of constraints. First, as with general-purpose computation, every allocation must be paired with a matching de-allocation. Second, space can only be safely…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
In this work, we generalize the integer enumeration basis. We also construct bijections between the elements of special sets and the elements of some groups, and treat the special case of the hyperoctohedral groups. Then, we find a code…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…