Related papers: On Multisequences and their extensions
Recently, large language models (LLMs) have shown remarkable capabilities including understanding context, engaging in logical reasoning, and generating responses. However, this is achieved at the expense of stringent computational and…
It is known that in the Minkowski sum of $r$ polytopes in dimension $d$, with $r<d$, the number of vertices of the sum can potentially be as high as the product of the number of vertices in each summand. However, the number of vertices for…
We describe constructions of extended formulations that establish a certain relaxed version of the Hirsch conjecture and prove that if there is a pivot rule for the simplex algorithm for which one can bound the number of steps by a…
Recent research in feature learning has been extended to sequence data, where each instance consists of a sequence of heterogeneous items with a variable length. However, in many real-world applications, the data exists in the form of…
We investigate the class of sequences $w(n)$ that can serve as almost-everywhere convergence Weyl multipliers for all rearrangements of multiple trigonometric systems. We show that any such sequence must satisfy the bounds $\log n\lesssim…
In this note we use the analogy between the Catalan sequence and the Rueppel sequence to derive a variety of conjectures surrounding the Hankel transforms of a number of sequences closely related to the Rueppel sequence. Use is made of the…
Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…
A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden…
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…
Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context,…
Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…
In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
Accurate forecasting of long-term time series has important applications for decision making and planning. However, it remains challenging to capture the long-term dependencies in time series data. To better extract long-term dependencies,…
In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and…
We consider the number of linear extensions of an N-free order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The…
We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive…