Related papers: Two examples of Wilf-collapse
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under…
We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a…
Collapse models are phenomenological models introduced to solve the measurement problem in quantum mechanics. They modify the Schr\"odinger equation by adding non-linear and stochastic terms, which induce the wavefunction collapse in space.…
Recent advances in interpretable Machine Learning (iML) and eXplainable AI (XAI) construct explanations based on the importance of features in classification tasks. However, in a high-dimensional feature space this approach may become…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…
The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…
Collapse models describe the breakdown of the quantum superposition principle when moving from microscopic to macroscopic scales. They are among the possible solutions to the quantum measurement problem and thus describe the emergence of…
Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
A family of concurrent data predictors is derived from the decision tree classifier by removing the limitation of sequentially evaluating attributes. By evaluating attributes concurrently, the decision tree collapses into a flat structure.…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
Recently, Scullard and Ziff noticed that a broad class of planar percolation models are self-dual under a simple condition that, in a parametrized version of such a model, reduces to a single equation. They state that the solution of the…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
For a set of permutation patterns $\Pi$, let $F^\text{st}_n(\Pi,q)$ be the st-polynomial of permutations avoiding all patterns in $\Pi$. Suppose $312\in\Pi$. For a class of permutation statistics which includes inversion and descent…
Theories including a collapse mechanism have been presented various years ago. They are based on a modification of standard quantum mechanics in which nonlinear and stochastic terms are added to the evolution equation. Their principal…
Implicit bias describes the phenomenon where optimization-based training algorithms, without explicit regularization, show a preference for simple estimators even when more complex estimators have equal objective values. Multiple works have…
A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
A permutation is defined to be cycle-up-down if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and analytically that these permutations are enumerated by the…