Related papers: The Necklace Process: A Generating Function Approa…
A point process on a space is a random bag of elements of that space. In this paper we explore programming with point processes in a monadic style. To this end we identify point processes on a space X with probability measures of bags of…
Bulgarian Solitaire is an interesting self-map on the set of integer partitions of a fixed number $n$. As a finite dynamical system, its long-term behavior is well-understood, having recurrent orbits parametrized by necklaces of beads with…
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire…
The degree-restricted random process is a natural algorithmic model for generating graphs with degree sequence D_n=(d_1, \ldots, d_n): starting with an empty n-vertex graph, it sequentially adds new random edges so that the degree of each…
We present a probabilistic modeling framework and adaptive sampling algorithm wherein unsupervised generative models are combined with black box predictive models to tackle the problem of input design. In input design, one is given one or…
Germ order is a non-standard stochastic order defined through the comparison of the generating functions of the processes. This order was first introduced for branching random walks with a constant breeding law and independent dispersal of…
Jewelry has been an integral part of human culture since ages. One of the most popular styles of jewelry is created by putting together precious and semi-precious stones in diverse patterns. While technology is finding its way in the…
This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…
We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices…
Random sampling is a technique for signal acquisition which is gaining popularity in practical signal processing systems. Nowadays, event-driven analog-to-digital converters make random sampling feasible in practical applications. A process…
Conditional selective inference requires an exact characterization of the selection event, which is often unavailable except for a few examples like the lasso. This work addresses this challenge by introducing a generic approach to estimate…
The topological underpinnings are presented for a new algorithm which answers the question: `Is a given knot the unknot?' The algorithm uses the braid foliation technology of Bennequin and of Birman and Menasco. The approach is to consider…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
We introduce a new matrix product, that we call the wreath product of matrices. The name is inspired by the analogous product for graphs, and the following important correspondence is proven: the wreath product of the adjacency matrices of…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
This work analyses the quantum state of twin photons and twin beams generated by parametric-down conversion in a hexagonally poled photonic crystal,characterized by the simultaneous presence of two nonlinear processes sustained by two…
How do we estimate the probability of an abundant objects' formation, with minimal context or assumption about is origin? To explore this we have previously introduced the concept of pathway assembly (as pathway complexity), in a graph…
We develop a full-fledged analysis of an algorithmic decision process that, in a multialternative choice problem, produces computable choice probabilities and expected decision times.
Bubble-nucleation processes of a Lennard-Jones liquid are studied by molecular dynamics simulations. Waiting time, which is the lifetime of a superheated liquid, is determined for several system sizes, and the apparent finite-size effect of…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…