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The ring of cyclic quasi-symmetric functions and its non-Escher subring are introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; for the non-Escher subring they arise as toric $P$-partition…
We introduce a new basis for quasisymmetric functions, which arise from a specialization of nonsymmetric Macdonald polynomials to standard bases, also known as Demazure atoms. Our new basis is called the basis of quasisymmetric Schur…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…
We study the growth rate of harmonic functions in two aspects: gradient estimate and frequency. We obtain the sharp gradient estimate of positive harmonic function in geodesic ball of complete surface with nonnegative curvature. On complete…
We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that…
Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing…
Periodic solution parameters, in chaotic dynamical systems, form periodic windows with characteristic distribution in two-parameter spaces. Recently, general properties of this organization have been reported, but a theoretical explanation…
A sequence $(x_{n})$ of points in a topological group is called $\Delta$-quasi-slowly oscillating if $(\Delta x_{n})$ is quasi-slowly oscillating, and is called quasi-slowly oscillating if $(\Delta x_{n})$ is slowly oscillating. A function…
We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of $b$ frequencies, $b\leq d+2$, in arbitrary dimension $d$ and for arbitrary non…
A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not…
We numerically investigate hyperuniformity in two-dimensional frictionless jammed packings of bidisperse systems. Hyperuniformity is characterized by the suppression of density fluctuations at large length scales, and the structure factor…
We investigate the applicability of divisible residuated lattices (DRLs) as a general evaluation framework for soft constraint satisfaction problems (soft CSPs). DRLs are in fact natural candidates for this role, since they form the…
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…