Related papers: On Multisequences and their extensions
This report will add some supplements to the recently finished report series on the distance function wavelets (DFW). First, we define the general distance in terms of the Riesz potential, and then, the distance function Abel wavelets are…
We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…
We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
When extending the Ehrhart lattice point enumerator $L_P(t)$ to allow real dilation parameters $t$, we lose the invariance under integer translations that exists when $t$ is restricted to be an integer. This paper studies this phenomenon;…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
Current progress in artificial intelligence is centered around so-called large language models that consist of neural networks processing long sequences of high-dimensional vectors called tokens. Statistical physics provides powerful tools…
A scaling theory is used to derive the dependence of the average number <k> of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions…
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this…
We derive bounds on the number of switches at an arbitrary set of positions in a circular sequence of permutations and relate them to the diameter of Multipermutohedra.
In this paper we study multi-parameter projection theorems for fractal sets. With the help of these estimates, we recover results about the size of $A \cdot A+...+A \cdot A$, where $A$ is a subset of the real line of a given Hausdorff…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable…
The transcription of handwritten text on images is one task in machine learning and one solution to solve it is using multi-dimensional recurrent neural networks (MDRNN) with connectionist temporal classification (CTC). The RNNs can contain…
The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
Long-term time-series forecasting is essential for planning and decision-making in economics, energy, and transportation, where long foresight is required. To obtain such long foresight, models must be both efficient and effective in…