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Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of…
In this paper, in order to characterize the critical error linear complexity spectrum (CELCS) for $2^n$-periodic binary sequences, we first propose a decomposition based on the cube theory. Based on the proposed $k$-error cube…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable…
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…
Sparse linear regression is the well-studied inference problem where one is given a design matrix $\mathbf{A} \in \mathbb{R}^{M\times N}$ and a response vector $\mathbf{b} \in \mathbb{R}^M$, and the goal is to find a solution $\mathbf{x}…
The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…
We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conventional languages using…
We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…
The problem of estimating frequency moments of a data stream has attracted a lot of attention since the onset of streaming algorithms [AMS99]. While the space complexity for approximately computing the $p^{\rm th}$ moment, for $p\in(0,2]$…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction…
The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its…
While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
Token-based time series large language models (TS-LLMs) have emerged as a promising direction for time series analysis and reasoning. However, prior studies largely overlook the inherent continuity and ordinality of time series tokens,…