Related papers: Tredoku Patterns
In this paper, we study the problem of learning a model for human pose estimation as mixtures of compositional sub-trees in two layers of prediction. This involves estimating the pose of a sub-tree followed by identifying the relationships…
In this talk I pay tribute to Toshimitsu Yamazaki who died earlier this year. Yamazaki's leading contributions to Hadronic Physics, in particular to Strangeness Nuclear Physics in Japan and elsewhere, are well known. Two of the five…
The broken stick problem is the following classical question. You have a segment $[0,1]$. You choose two points on this segment at random. They divide the segment into three smaller segments. Show that the probability that the three…
Over the years, several Bridges papers have delved into the concept of danceability of a knot diagram. Inspired by dancing on non-orientable surfaces, in this paper, we expand danceability to twisted virtual knot diagrams. This paper is…
Discovering patterns in a sequence is an important aspect of data mining. One popular choice of such patterns are episodes, patterns in sequential data describing events that often occur in the vicinity of each other. Episodes also enforce…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
In this paper, we introduce the concept of triad. Using this notion, we study, revisit, discover and rediscover some basic properties of ludics from a very general point of view.
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent…
Frieze patterns are combinatorial objects that are deeply related to cluster theory. Determinants of frieze patterns arise from triangular regions of the frieze, and they have been considered in previous works by Broline-Crowe-Isaacs, and…
We give a comprehensive treatment on how $F$-signatures, splitting primes, splitting ratios, and test modules behave under finite covers. To this end, we expand on the notion of transposability along a section section of the relative…
We provide an overview of recent work which aims to understand patterns of vanishing Yukawa couplings that arise in models of particle physics derived from string theory. These patterns are seemingly linked to a plethora of different…
In 1966 Mark Kac asked the famous question 'Can one hear the shape of a drum?'. While this was later shown to be false in general, it was proved by C. Durso that one can hear the shape of a triangle. After an introduction to the general…
This article presents a whirlwind tour of some results surrounding the Koebe-Andre'ev-Thurston Theorem, Bill Thurston's seminal circle packing theorem that appears in Chapter 13 of The Geometry and Topology of Three-Manifolds. It will…
Starting from expressions in Connor et al. (1988) [1], we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna and Callen (1984) [2] and by Nishimura et al (1998) [3], but for more realistic…
We revisit the elegant observation of T. Cover '65 which, perhaps, is not as well-known to the broader community as it should be. The first goal of the tutorial is to explain---through the prism of this elementary result---how to solve…
This paper presents a novel construction method for symmetric Sudoku-type games based on Lee distance perfect codes and diameter perfect codes. The proposed method utilizes the tiling property of these codes to define the structure of the…
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically…
In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. In 2011 Wolf computed the "Skewes number" for twin primes, i.e., the first prime at which a reversal of the Hardy-Littlewood…
I review the basic ideas of "trace dynamics", as formulated in my 2004 Cambridge University Press book "Quantum Theory as an Emergent Phenomenon", and then discuss how they have influenced much of my work of the last two decades.
A beautiful theorem of Thomas Price links the Fibonacci numbers and the Lucas polynomials to the plane geometry of an ellipse, generalizing a classic problem about circles. We give a brief history of the circle problem, an account of…