Related papers: The Method(!) of "Guess and Check"
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…
In software testing, a set of test cases is constructed according to some predefined selection criteria. The software is then examined against these test cases. Three interesting observations have been made on the current artifacts of…
Although quantum states nicely explain experiments, the outcomes of experiments are not states. Instead, outcomes correspond to probability distributions. Twenty years ago we proved categorically that probability distributions leave open a…
Some important problems in quantitative QCD will certainly yield to hard work and adequate investment of resources, others appear difficult but may be accessible, and still others will require essentially new ideas. Here I identify several…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
The greedy walk is a walk on a point process that always moves from its current position to the nearest not yet visited point. We consider here various point processes on two lines. We look first at the greedy walk on two independent…
We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of square-root log n.
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
Current large language models reason in isolation. Although it is common to sample multiple reasoning paths in parallel, these trajectories do not interact, and often fail in the same redundant ways. We introduce LACE, a framework that…
Programmers often use an iterative process of hypothesis generation ("perhaps this function is called twice?") and hypothesis testing ("let's count how many times this breakpoint fires") to understand the behavior of unfamiliar or…
In this note, we consider random walks in the quarter plane with arbitrary big jumps. We announce the extension to that class of models of the analytic approach of [G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
The solvability of the three-dimensional O($N$) scalar field theory in the large $N$ limit makes it an ideal toy model exhibiting "walking" behavior, expected in some SU($N$) gauge theories with a large number of fermion flavors. We study…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle…
We propose a new approach for solving a class of discrete decision making problems under uncertainty with positive cost. This issue concerns multiple and diverse fields such as engineering, economics, artificial intelligence, cognitive…
Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an…