Geometry problem solving has garnered increasing attention due to its potential applications in intelligent education field. Inspired by the observation that text often introduces ambiguities that diagrams can clarify, this paper presents Pi-GPS, a n...
A topology on a set $X$ is the same as a projection (i.e. an idempotent linear operator) $cl:2^X\to 2^X$ satisfying $A\subset cl(A)$ for all $A\subset X$. That's a good way to summarize Kuratowski's closure operator. Basic geometry on a set $X$ is...
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to prove via algebraic geometry a recursion between the volumes of modu...
We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two observed v...
This paper presents Roof-GAN, a novel generative adversarial network that generates structured geometry of residential roof structures as a set of roof primitives and their relationships. Given the number of primitives, the generator produces a struc...
A library for mental poker (and other card games). Based on the Barnett-Smart protocol and the Bayer-Groth argument of correct shuffle (⭐ 118)
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping manifests itse...
Light-cone cuts have recently been proposed as a method to reconstruct the conformal metric of a holographic spacetime. We explore how additional information about the bulk geometry gets encoded in the structure of these light-cone cuts. In particula...
We highlight a fundamental connection between information geometry and variational Bayes (VB) and discuss its consequences for machine learning. Under certain conditions, a VB solution always requires estimation or computation of natural gradients. W...
We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions...
We study aspects of quantum cosmology in the presence of a modified space-time geometry. In particular, within the context of Gravity's Rainbow modified geometry, motivated from quantum gravity corrections at the Planck energy scale, we show that the...
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical
We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic variety fo...
We demonstrate a watt-level, kHz nanosecond-pulse ASE source with its pulse-width being close to its round-trip time. The ASE uses a Nd:GdVO4 high gain bounce geometry structure without an output coupler. Using an EOQ (electro-optics Q-switch) device...
Well-known text (WKT) is a text markup language for representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used
Notation for spin coefficients for metrics of neutral signature in four dimensions is introduced. The utility and interpretation of spin coefficients is explored through themes in null geometry familiar from (complex) general relativity. Four-dimen...
The preparation of a coherent heavy-hole spin via ionization of a spin-polarized electron-hole pair in an InAs/GaAs quantum dot in a Voigt geometry magnetic field is investigated. For a dot with a 17 ueV bright-exciton fine-structure splitting, the f...
Phase plotting is a useful way of visualising functions on complex space. We reinvent the method in the context of hyperbolic geometry, and we use it to plot functions on various representative surfaces for hyperbolic space, illustrating with direct...
A 2008 general overview on Weil-Petersson geometry is offered. A preliminary plan for the subsequent CBMS lectures at Central Connecticut State University is included. Mirzakhani's solution of Witten-Kontsevich is not included - this work essentially...
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations exist, it is...