Related papers: On modular decompositions of system signatures
The article is focused on studying how to predict the failure times of coherent systems from the early failure times of their components. Both the cases of independent and dependent components are considered by assuming that they are…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…
The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates paths into high-dimensional feature vectors, capturing their…
We address the problem of estimating the state of a differentially flat system from measurements that may be corrupted by an adversarial attack. In cyber-physical systems, malicious attacks can directly compromise the system's sensors or…
A method for the numerical simulation of signed probability distributions for the case of tossing $1/n$-th of a coin is presented and illustrated by examples.
A partition of a positive integer $n$ is a representation of $n$ as a sum of a finite number of positive integers (called parts). A trapezoidal number is a positive integer that has a partition whose parts are a decreasing sequence of…
Sylvester showed that the partition of an integer into a set of positive integers can be represented as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. The wave itself is a weighted sum of the…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. The only…
In this paper we present an extension of Stanley's theorem related to partitions of positive integers. Stanley's theorem states a relation between "the sum of the numbers of distinct members in the partitions of a positive integer $n$" and…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…
We study a sound verification method for parametric component-based systems. The method uses a resource logic, a new formal specification language for distributed systems consisting of a finite yet unbounded number of components. The logic…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
We develop the rudiments of a tropical homology theory, based on "triples" and "systems." Results include a version of Schanuel's lemma, projective dimension, the homology semi-module, and a weak Snake lemma.
We propose a new formal criterion for evaluating secure compilation schemes for unsafe languages, expressing end-to-end security guarantees for software components that may become compromised after encountering undefined behavior---for…