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We compute structure functions in the Hamiltonian formalism on a momentum lattice using a physically motivated regularisation that links the maximal parton number to the lattice size. We show for the $\phi ^4 _{3+1}$ theory that our method…
The most conspicuous property of a semiflexible polymer is its persistence length, defined as the decay length of tangent correlations along its contour. Using an efficient stochastic growth algorithm to sample polymers embedded in a…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
In this paper we assemble some results about the upper-semicontinuity and lower-semicontinuity of the feasible correspondence and the solution correspondence of linear programming problems allowing variability of all parameters of such…
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence,…
Reliability (survival analysis, to biostatisticians) is a key ingredient for mak- ing decisions that mitigate the risk of failure. The other key ingredient is utility. A decision theoretic framework harnesses the two, but to invoke this…
A formula is derived for stiffness of a polymer chain in terms of the distribution function of end-to-end vectors. This relationship is applied to calculate the stiffness of Gaussian chains (neutral and carrying electric charges at the…
Components in many real-world complex systems depend on each other for the resources required for survival, and may die of a shortage. These patterns of dependencies often take the form of a complex network whose structure potentially…
Perception, localization, planning, and control, high-level functions often organized in a so-called pipeline, are amongst the core building blocks of modern autonomous (ground, air, and underwater) vehicle architectures. These functions…
Nowadays, the consequences of failure and downtime of distributed systems have become more and more severe. As an obvious solution, these systems incorporate protection mechanisms to tolerate faults that could cause systems failures and…
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…
Dependability assurance of systems embedding machine learning(ML) components---so called learning-enabled systems (LESs)---is a key step for their use in safety-critical applications. In emerging standardization and guidance efforts, there…
Load-sharing systems arise in many different reliability applications, for instance, when modeling tensile strength of fibrous composites in textile industry or lifetimes of redundant technical systems in engineering. Sequential order…
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism,…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
A stochastic Lie system on a manifold $M$ is a stochastic differential equation whose dynamics is described by a linear combination with functions depending on $\mathbb{R}^\ell$-valued semi-martigales of vector fields on $M$ spanning a…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…