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We show that over the class of linear orders with additional binary relations satisfying some monotonicity conditions, monadic first-order logic has the three-variable property. This generalizes (and gives a new proof of) several known…
Most of the research concerting crack propagation in discrete media is concerned with specific types of external loading: displacements on the boundaries, or constant energy fluxes or feeding waves originating from infinity. In this paper…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the…
We approach the problem of heterogeneous dynamic fracture by considering spatiotemporal perturbations to planar crack fronts. Front propagation is governed by local energy balance between the elastic energy per unit area available to…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
In two-dimensional tissues, such as developing germ layers, pair-wise forces (or active stresses) arise from the contractile activity of the cytoskeleton, with dissipation provided by the three-dimensional surroundings. We show analytically…
In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated…
An implicit operation of a class of similar algebras $\mathsf{K}$ is a collection of first order definable partial functions on the members of $\mathsf{K}$ that is globally preserved by homomorphisms. For instance, "taking inverses" can be…
Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some `one particle space' $\K$ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of…
In this thesis, we present a flexible framework for specifying and constructing operads which are suited to reasoning about network construction. The data used to present these operads is called a \emph{network model}, a monoidal variant of…
Motivated by recent experiments on vanadium spinels, $A$V$_2$O$_4$, that show an increasing degree of electronic delocalization for smaller cation sizes, we study the evolution of orbital ordering (OO) between the strong and…
We have developed different network approaches to complex patterns of frictional interfaces (contact areas developments). Here, we analyze the dynamics of static friction. We found, under the correlation measure, the fraction of triangles…
It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions…
Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities $x, y$ is controlled by a homogeneous symmetric kernel $K(x, y)…
There is a connection between the Weyl pseudodifferential calculus and crossed product C*-algebras associated with certain dynamical systems. And in fact both topics are involved in the quantization of a non-relativistic particle moving in…
We consider the bar complex of a monomial non-unital associative algebra $A=k \langle X \rangle / (w_1,...,w_t)$. It splits as a direct sum of complexes $B_w$, defined for any fixed monomial $w=x_1...x_n \in A$. We give a simple argument,…
This paper presents a formulation for brittle fracture in 3D elastic solids within the context of configurational mechanics. The local form of the first law of thermodynamics provides a condition for equilibrium of the crack front. The…