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The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with…
The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence…
We describe a highly robust method, applicable to both electromagnetic and matter-wave beams, that can produce a beam consisting of a lattice of orbital angular momentum (OAM) states coupled to a two-level system. We also define efficient…
Denoising Diffusion Probabilistic models have emerged as simple yet very powerful generative models. Unlike other generative models, diffusion models do not suffer from mode collapse or require a discriminator to generate high-quality…
We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a…
Score-based generative models (SGMs) have demonstrated unparalleled sampling quality and diversity in numerous fields, such as image generation, voice synthesis, and tabular data synthesis, etc. Inspired by those outstanding results, we…
Achieving expressive 3D motion reconstruction and automatic generation for isolated sign words can be challenging, due to the lack of real-world 3D sign-word data, the complex nuances of signing motions, and the cross-modal understanding of…
Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently,…
We describe proofs of the standard generating formulas for unsigned and signed Stirling numbers of the first kind that follow from a natural combinatorial interpretation based on cycle-colored permutations.
Digital circles not only play an important role in various technological settings, but also provide a lively playground for more fundamental number-theoretical questions. In this paper, we present a new recursive algorithm for the…
Speculative decoding has emerged as a widely adopted method to accelerate large language model inference without sacrificing the quality of the model outputs. While this technique has facilitated notable speed improvements by enabling…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
Speculative generation has emerged as a promising technique to accelerate inference in large language models (LLMs) by leveraging parallelism to verify multiple draft tokens simultaneously. However, the fundamental limits on the achievable…
Sequences with good randomness properties are quite important for stream ciphers. In this paper, a new class of quaternary sequences is constructed by using generalized cyclotomic classes of $\mathbb{Z}_{2p^m}$ $(m\geq1)$. The exact values…
A set $\mathcal{S}$ of derangements (fixed-point-free permutations) of a set $V$ generates a digraph with vertex set $V$ and arcs $(x,x^\sigma)$ for $x\in V$ and $\sigma\in\mathcal{S}$. We address the problem of characterising those…
We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of two-photon spectral states, from highly…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
This paper presents a twist to the generation of binary random sequences by starting with decimal sequences. Rather than representing the prime reciprocal sequence directly in base 2, we first right the prime reciprocal in base 10 and then…
With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship between multiple neural signals. Correlation-based methods are a set of…