Related papers: An Efficiently Generated Family of Binary de Bruij…
A self-consistent strategy to complete the dynamical generation of Quark-Level-Linear-Sigma-Model-like Lagrangean theories beyond one loop as proposed in more detail in our manuscript arXiv:0802.1540 [hep-ph] is shortly outlined.
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two…
Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t). The approximation can…
For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly…
Recent improvements in generative adversarial network (GAN) training techniques prove that progressively training a GAN drastically stabilizes the training and improves the quality of outputs produced. Adding layers after the previous ones…
John Tromp introduced the so-called 'binary lambda calculus' as a way to encode lambda terms in terms of 0-1-strings using the de Bruijn representation along with a weighting scheme. Later, Grygiel and Lescanne conjectured that the number…
Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
In this paper, new context of Chinese Remainder Theorem (CRT) based analysis of combinatorial sequence generators has been presented. CRT is exploited to establish fixed patterns in LFSR sequences and underlying cyclic structures of finite…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…
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…
An acoustic reverberator consisting of a network of delay lines connected via scattering junctions is proposed. All parameters of the reverberator are derived from physical properties of the enclosure it simulates. It allows for simulation…
Group synchronization plays a crucial role in global pipelines for Structure from Motion (SfM). Its formulation is nonconvex and it is faced with highly corrupted measurements. Cycle consistency has been effective in addressing these…
Transformer-based models have gained significant traction in sequential recommender systems (SRSs) for their ability to capture user-item interactions effectively. However, these models often suffer from high computational costs and slow…
The main challenge in de novo assembly of NGS data is certainly to deal with repeats that are longer than the reads. This is particularly true for RNA- seq data, since coverage information cannot be used to flag repeated sequences, of which…
The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they…
Fourier methods have a long and proven track record as an excellent tool in data processing. As memory and computational constraints gain importance in embedded and mobile applications, we propose to combine Fourier methods and recurrent…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
For the sequence defined by \[ a(n) = \frac{n^2 - n - 1}{\gcd\big(n^2 - n - 1,\, b(n-3) + n\,b(n-4)\big)} \] Where $b(n) = (n+2)\big(b(n-1) - b(n-2)\big),$ with initial conditions $b(-1) = 0$ and $b(0) = 1$, we find that $a(n)$ contains…