Long fully commutative elements in affine Coxeter groups

An element of a Coxeter group $W$ is called fully commutative if any two of its reduced decompositions can be related by a series of transpositions of adjacent commuting generators. In the preprint "Fully commutative elements in finite and affine Coxeter groups" (arXiv:1402.2166), R. Biagioli and the authors proved among other things that, for each irreducible affine Coxeter group, the sequence counting fully commutative elements with respect to length is ultimately periodic. In the present work, we study this sequence in its periodic part for each of these groups, and in particular we determine the minimal period. We also observe that in type $A$ affine we get an instance of the cyclic sieving phenomenon.Comment: 17 pages, 9 figure

Capturing CFLs with Tree Adjoining Grammars

We define a decidable class of TAGs that is strongly equivalent to CFGs and is cubic-time parsable. This class serves to lexicalize CFGs in the same manner as the LCFGs of Schabes and Waters but with considerably less restriction on the form of the grammars. The class provides a normal form for TAGs that generate local sets in much the same way that regular grammars provide a normal form for CFGs that generate regular sets.Comment: 8 pages, 3 figures. To appear in proceedings of ACL'9

A flexible flight display research system using a ground-based interactive graphics terminal

Requirements and research areas for the air transportation system of the 1980 to 1990's were reviewed briefly to establish the need for a flexible flight display generation research tool. Specific display capabilities required by aeronautical researchers are listed and a conceptual system for providing these capabilities is described. The conceptual system uses a ground-based interactive graphics terminal driven by real-time radar and telemetry data to generate dynamic, experimental flight displays. These displays are scan converted to television format, processed, and transmitted to the cockpits of evaluation aircraft. The attendant advantages of a Flight Display Research System (FDRS) designed to employ this concept are presented. The detailed implementation of an FDRS is described. The basic characteristics of the interactive graphics terminal and supporting display electronic subsystems are presented and the resulting system capability is summarized. Finally, the system status and utilization are reviewed

Fully commutative elements and lattice walks

International audienceAn element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge in the finite case. In this work we deal with any finite or affine Coxeter group $W$, and we enumerate fully commutative elements according to their Coxeter length. Our approach consists in encoding these elements by various classes of lattice walks, and we then use recursive decompositions of these walks in order to obtain the desired generating functions. In type $A$, this reproves a theorem of Barcucci et al.; in type $\tilde{A}$, it simplifies and refines results of Hanusa and Jones. For all other finite and affine groups, our results are new.Un élément d’un groupe de Coxeter $W$ est dit totalement commutatif si deux de ses décompositions réduites peuvent toujours être reliées par une suite de transpositions de générateurs adjacents qui commutent. Ces éléments ont été étudiés en détail par Stembridge dans le cas où $W$ est fini. Dans ce travail, nous considérons $W$ fini ou affine, et énumérons les éléments totalement commutatifs selon leur longueur de Coxeter. Notre approche consiste à encoder ces éléments par diverses classes de chemins du plan que nous décomposons récursivement pour obtenir les fonctions génératrices voulues. Pour le type $A$ cela redonne un théorème de Barcucci et al.; pour $\tilde{A}$, cela simplifie et précise des résultats de Hanusa et Jones. Pour tous les autres groupes finis et affines, nos résultats sont nouveaux

Light-sheet microscopy: a tutorial

This paper is intended to give a comprehensive review of light-sheet (LS) microscopy from an optics perspective. As such, emphasis is placed on the advantages that LS microscope configurations present, given the degree of freedom gained by uncoupling the excitation and detection arms. The new imaging properties are first highlighted in terms of optical parameters and how these have enabled several biomedical applications. Then, the basics are presented for understanding how a LS microscope works. This is followed by a presentation of a tutorial for LS microscope designs, each working at different resolutions and for different applications. Then, based on a numerical Fourier analysis and given the multiple possibilities for generating the LS in the microscope (using Gaussian, Bessel, and Airy beams in the linear and nonlinear regimes), a systematic comparison of their optical performance is presented. Finally, based on advances in optics and photonics, the novel optical implementations possible in a LS microscope are highlighted.Peer ReviewedPostprint (published version

Tree-Based Reconstructive Partitioning: A Novel Low-Data Level Generation Approach

Procedural Content Generation (PCG) is the algorithmic generation of content, often applied to games. PCG and PCG via Machine Learning (PCGML) have appeared in published games. However, it can prove difficult to apply these approaches in the early stages of an in-development game. PCG requires expertise in representing designer notions of quality in rules or functions, and PCGML typically requires significant training data, which may not be available early in development. In this paper, we introduce Tree-based Reconstructive Partitioning (TRP), a novel PCGML approach aimed to address this problem. Our results, across two domains, demonstrate that TRP produces levels that are more playable and coherent, and that the approach is more generalizable with less training data. We consider TRP to be a promising new approach that can afford the introduction of PCGML into the early stages of game development without requiring human expertise or significant training data.Comment: 9 pages, 3 figures, The 19th AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment (AIIDE 2023

Procedural Content Generation in 3 Dimensions using Wave Function Collapse in Minecraft

This investigation into the effectiveness of Wave Function Collapse as a Procedural Content Generation Technique (PCG) in Minecraft sets out to determine whether this method can be used easily by players and game designers to generate content that mimics the original content. We also set out to determine whether this technique can be implemented by game designers or community modders easily enough to improve the default generation of settlements in Minecraft. We grade the effectiveness of our output using metrics provided by the Generative Design in Minecraft Competition in order to test whether generated content is effective. Tests were conducted on terrain that was taken from an existing Minecraft world, and featured a mixture of structures ranging from simple to complex in design meant to simulate structures that players would build near the beginning of the game. Unfortunately, our conclusion is that in it’s most basic form, Wave Function Collapse is unsuited as a PCG tool for Minecraft. During the course of our testing, we found that the run times for simple algorithms were too long to be effective, and the algorithm fails to generate content for many of the test cases regularly. In order to make it more suitable, a number of improvements are suggested including global constraints, weight balancing, and layering PCG methods. Overall, this approach has potential, but requires more work before it is a suitable replacement to current PCG methods for Minecraft settlement generation

An Investigation of the Effects of Front-Line Employees\u27 Work-Family Conflict on Customer Satisfaction through Exhaustion and Emotional Displays

The present study investigates the distal effects of front-line employees\u27 work-family conflict on customer satisfaction. Based on data from 200 paired employee-customer interactions at six hotels, a Structural Equation Modeling was conducted to test the hypothesized model and the results supported most of our predictions. Specifically, participants\u27 FIW (family interfering with work) was positively linked to physical, emotional, and mental exhaustion, while WIF (work interfering with family) did not have such associations. Further, individuals with higher levels of physical exhaustion were more likely to manage their emotions by faking positive emotions and suppressing negative emotions, whereas participants with higher levels of emotional exhaustion were more likely to fake positive emotions. Although faking positive emotions enhances the employee\u27s role performance, such actions failed to enhance customer satisfaction. The current research extends our knowledge of work-family conflict on employee-customer interactions and suggests that hospitality organizations need to be aware of the critical effects of employees\u27 family affairs on work behaviors and ultimately on customer satisfaction