Related papers: Applications of Finite Fields to Dynamical Systems…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…
Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically driven, dynamically evolving field from finite…
Combinatorial algorithms for minimization of functions of many variables, which take their values in finite totally ordered sets, are developed. For that the decomposition of the functions by Boolean polynomials is used. The modified SFM…
We know that for a finite field $F$, every function on $F$ can be given by a polynomial with coefficients in $F$. What about the converse? i.e. if $R$ is a ring (not necessarily commutative or with unity) such that every function on $R$ can…
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Dynamic Fault Trees (DFTs) are a prominent model in reliability engineering. They are strictly more expressive than static fault trees, but this comes at a price: their interpretation is non-trivial and leaves quite some freedom. This paper…
This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…
In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…
A transcendental entire function f is called geometrically finite if the intersection of the set of singular values with the Fatou set is compact and the intersection of the postsingular set with the Julia set is finite. (In particular,…
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses,…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F…