相关论文: Residue Number System Comparison revisited, a soft…

Synchronous computation models simplify the design and the verification of fault-tolerant distributed systems. For efficiency reasons such systems are designed and implemented using an asynchronous semantics. In this paper, we bridge the…

A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…

A new variant of the GMRES method is presented for solving linear systems with the same matrix and subsequently obtained multiple right-hand sides. The new method keeps such properties of the classical GMRES algorithm as follows. Both bases…

Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a…

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…

Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…

Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS)…

Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity,…

Reciprocal recommender systems (RRSs) are crucial in online two-sided matching platforms, such as online job or dating markets, as they need to consider the preferences of both sides of the match. The concentration of recommendations to a…

The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…

Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…

Sequences of linear systems arise in the predictor-corrector method when computing the Pareto front for multi-objective optimization. Rather than discarding information generated when solving one system, it may be advantageous to recycle…

Inspired by recent findings on the fractal geometry of language, we introduce Recursive INference Scaling (RINS) as a complementary, plug-in recipe for scaling inference time in language and multimodal systems. RINS is a particular form of…

Large language models (LLMs) frequently generate multiple candidate responses for a given prompt, yet selecting the most reliable one remains challenging, especially when correctness diverges from surface-level majority agreement. Existing…

Recurrent Neural Networks (RNNs) are widely used for sequential processing but face fundamental limitations with continual inference due to state saturation, requiring disruptive hidden state resets. However, reset-based methods impose…

It is well known that n integers in the range [1,n^c] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these algorithms use O(n)…

In medical device comparison studies, equivalency test is commonly used to demonstrate two measurement methods agree up to a pre-specified performance goal based on the paired repeated measures. Such equivalency test often involves…

Optical neural networks (ONN) based on micro-ring resonators (MRR) have emerged as a promising alternative to significantly accelerating the massive matrix-vector multiplication (MVM) operations in artificial intelligence (AI) applications.…

Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…

This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process…