Related papers: Using Linear Difference Equations to Model Nonline…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
An external description for nonperiodically sampled multivariable linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use…
Equations system constructors of hierarchical circuits play a central role in device modeling, nonlinear equations solving, and circuit design automation. However, existing constructors present limitations in applications to different…
A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Henon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
We introduce an algorithm to generate multivariate series of symbols from a finite alphabet with a given hierarchical structure of similarities. The target hierarchical structure of similarities is arbitrary, for instance the one obtained…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
The proliferation of sensor devices monitoring human activity generates voluminous amount of temporal sequences needing to be interpreted and categorized. Moreover, complex behavior detection requires the personalization of multi-sensor…
Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
We present significant extensions to diffusion-based sequence generation models, blurring the line with autoregressive language models. We introduce hyperschedules, which assign distinct noise schedules to individual token positions,…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature…
In this paper, we will present a new key exchange cryptosystem based on linear algebra, which take less operations but weaker in security than Diffie-Hellman's one.
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…