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Splitting and merging are long standing issues in PIC codes. I propose a novel algorithm devoted to exact splitting for Particle-In-Cell (PIC) codes relying on Adaptive Mesh Refinement (AMR) grids. AMR grids have - by definition - a…

We consider the problem of designing a coding scheme that allows both sparsity and privacy for distributed matrix-vector multiplication. Perfect information-theoretic privacy requires encoding the input sparse matrices into matrices…

We determine conditions on classical group algebra codes so that they have pre-orientation for cup products and copy-cup gates. This defines quantum codes that have constant-depth $\operatorname{CZ}$ and $\operatorname{CCZ}$ gates…

Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst…

Logic locking as a solution for semiconductor intellectual property (IP) confidentiality has received considerable attention in academia, but has yet to produce a viable solution to protect against known threats. In part due to a lack of…

Bi-clustering refers to the task of finding sub-matrices (indexed by a group of columns and a group of rows) within a matrix of data such that the elements of each sub-matrix (data and features) are related in a particular way, for…

In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…

Given integers $k_1, k_2$ with $0\le k_1<k_2$, the determinations of all positive integers $q$ for which there exists a perfect Splitter $B[-k_1, k_2](q)$ set is a wide open question in general. In this paper, we obtain new necessary and…

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

In this paper we consider combinatorial secure codes in traitor tracing for protecting copyright of multimedia content. First, we introduce a new notion of secure codes with list decoding (SCLDs) for collusion-resistant multimedia…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

Group testing enables to identify infected individuals in a population using a smaller number of tests than individual testing. To achieve this, group testing algorithms commonly assume knowledge of the number of infected individuals;…

Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…

We present the notion of \emph{reasonable utility} for binary mechanisms, which applies to all utility functions in the literature. This notion induces a partial ordering on the performance of all binary differentially private (DP)…

Secret sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q > n, where n is the number of shares,…

An `obfuscation' for encrypted computing is quantified exactly here, leading to an argument that security against polynomial-time attacks has been achieved for user data via the deliberately `chaotic' compilation required for security…

In this work, we develop a method named Twinning, for partitioning a dataset into statistically similar twin sets. Twinning is based on SPlit, a recently proposed model-independent method for optimally splitting a dataset into training and…

Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e. random graphs…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

Two-party split learning has emerged as a popular paradigm for vertical federated learning. To preserve the privacy of the label owner, split learning utilizes a split model, which only requires the exchange of intermediate representations…