Related papers: Signum Function Method for Generation of Correlate…

This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet…

An approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness…

While diffusion models excel at generating high-quality images from text prompts, they struggle with visual consistency when generating image sequences. Existing methods generate each image independently, leading to disjointed narratives -…

We present a theoretical and experimental study of the generation of photon pairs through the process of spontaneous four wave mixing (SFWM) in a few-mode, birefringent fiber. Under these conditions, multiple SFWM processes are in fact…

Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as…

We propose generative neural network methods to generate DNA sequences and tune them to have desired properties. We present three approaches: creating synthetic DNA sequences using a generative adversarial network; a DNA-based variant of…

The focus of this work is to show how to combine Zech's logarithms and each of the cycle joining and cross-join pairing methods to construct binary de Bruijn sequences of any order. A basic implementation is supplied as a proof-of-concept.…

Recurrent Neural Networks (RNNs) are extensively used for time-series modeling and prediction. We propose an approach for automatic construction of a binary classifier based on Long Short-Term Memory RNNs (LSTM-RNNs) for detection of a…

This paper investigates the randomness properties of a function of the divisor pairs of a natural number. This function, the antecedents of which go to very ancient times, has randomness properties that can find applications in…

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child…

When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…

In this paper we consider a discrete-time dynamical system on the real line by random iteration of two functions. These functions are assumed to satisfy appropriate monotonicity conditions; optionally, a symmetry condition may be imposed.…

Background: Neuro-symbolic methods enhance the reliability of neural network classifiers through logical constraints, but they lack native support for ontologies. Objectives: We aim to develop a neuro-symbolic method that reliably outputs…

Analogously to de Bruijn sequences, Orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., recursive…

Machine-learning techniques have been recently used with spectacular results to generate artefacts such as music or text. However, these techniques are still unable to capture and generate artefacts that are convincingly structured. In this…

As the basis of generative AI, an autoregressive model requires the generation of a new token depending on all the previously generated tokens, which brings high quality but also restricts the model to generate tokens one by one, forming a…

We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The…

The primary objective of this section is to demonstrate that the actual pseudorandom measures of our construction are significantly smaller than the theoretical upper bounds derived from the Weil theorem. Regarding the family of sequences,…

Using a recently developed strong-coupling method, we present a comprehensive theory for doublon production processes in modulation spectroscopy of a three-dimensional system of ultracold fermionic atoms in an optical lattice with a trap.…

Generating plausible and fluent sentence with desired properties has long been a challenge. Most of the recent works use recurrent neural networks (RNNs) and their variants to predict following words given previous sequence and target…