相关论文: Analysis and Comparison of Known and Randomly Gene…
Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of random vectors, namely probability measures or more simply…
We present the algorithm for generating strictly saturated random sequential adsorption packings built of rounded polygons. It can be used to study various properties of such packings built of a wide variety of different shapes and in…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
A new construction of authentication codes with arbitration from pseudo-symplectic geometry over finite fields is given. The parameters and the probabilities of deceptions of the codes are also computed.
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
There is a great need for improved statistical sampling in a range of physical, chemical and biological systems. Even simulations based on correct algorithms suffer from statistical error, which can be substantial or even dominant when slow…
LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such codes is trying to avoid cycles of short length in the associated Tanner graph, i.e. obtaining…
In its many variants, randomized benchmarking (RB) is a broadly used technique for assessing the quality of gate implementations on quantum computers. A detailed theoretical understanding and general guarantees exist for the functioning and…
Statistical machine learning often uses probabilistic algorithms, such as Markov Chain Monte Carlo (MCMC), to solve a wide range of problems. Many accelerators are proposed using specialized hardware to address sampling inefficiency, the…
Cloud-based and distributed computations are of growing interest in modern control systems. However, these technologies require performing computations on not necessarily trustworthy platforms and, thus, put the confidentiality of sensitive…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of $n$-qubit circuits rely on efficient procedures for…
Randomness extractors, which extract high quality (almost-uniform) random bits from biased random sources, are important objects both in theory and in practice. While there have been significant progress in obtaining near optimal…
Approximate Membership Query structures (AMQs) rely on randomisation for time- and space-efficiency, while introducing a possibility of false positive and false negative answers. Correctness proofs of such structures involve subtle…
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
Complex information-processing systems, for example quantum circuits, cryptographic protocols, or multi-player games, are naturally described as networks composed of more basic information-processing systems. A modular analysis of such…
Random number generators (RNG) are an important resource in many areas: cryptography (both quantum and classical), probabilistic computation (Monte Carlo methods), numerical simulations, industrial testing and labeling, hazard games,…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…