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AlphaStar: An Evolutionary Computation PerspectiveFeb 05 2019Jul 14 2019In January 2019, DeepMind revealed AlphaStar to the world-the first artificial intelligence (AI) system to beat a professional player at the game of StarCraft II-representing a milestone in the progress of AI. AlphaStar draws on many areas of AI research, ... More

Leveling the Playing Field -- Fairness in AI Versus Human Game BenchmarksMar 17 2019Apr 14 2019From the beginning if the history of AI, there has been interest in games as a platform of research. As the field developed, human-level competence in complex games became a target researchers worked to reach. Only relatively recently has this target ... More

AI Researchers, Video Games Are Your Friends!Dec 06 2016If you are an artificial intelligence researcher, you should look to video games as ideal testbeds for the work you do. If you are a video game developer, you should look to AI for the technology that makes completely new types of games possible. This ... More

Leveling the Playing Field -- Fairness in AI Versus Human Game BenchmarksMar 17 2019Aug 29 2019From the beginning if the history of AI, there has been interest in games as a platform of research. As the field developed, human-level competence in complex games became a target researchers worked to reach. Only relatively recently has this target ... More

General Video Game Rule GenerationJun 12 2019We introduce the General Video Game Rule Generation problem, and the eponymous software framework which will be used in a new track of the General Video Game AI (GVGAI) competition. The problem is, given a game level as input, to generate the rules of ... More

Evolution of a Subsumption Architecture NeurocontrollerMay 06 2004An approach to robotics called layered evolution and merging features from the subsumption architecture into evolutionary robotics is presented, and its advantages are discussed. This approach is used to construct a layered controller for a simulated ... More

Neuroevolution in Games: State of the Art and Open ChallengesOct 27 2014Nov 03 2015This paper surveys research on applying neuroevolution (NE) to games. In neuroevolution, artificial neural networks are trained through evolutionary algorithms, taking inspiration from the way biological brains evolved. We analyse the application of NE ... More

General Video Game AI: a Multi-Track Framework for Evaluating Agents, Games and Content Generation AlgorithmsFeb 28 2018Feb 22 2019General Video Game Playing (GVGP) aims at designing an agent that is capable of playing multiple video games with no human intervention. In 2014, The General Video Game AI (GVGAI) competition framework was created and released with the purpose of providing ... More

Evaluation of a Recommender System for Assisting Novice Game DesignersAug 13 2019Game development is a complex task involving multiple disciplines and technologies. Developers and researchers alike have suggested that AI-driven game design assistants may improve developer workflow. We present a recommender system for assisting humans ... More

Deep Reinforcement Learning for General Video Game AIJun 06 2018The General Video Game AI (GVGAI) competition and its associated software framework provides a way of benchmarking AI algorithms on a large number of games written in a domain-specific description language. While the competition has seen plenty of interest, ... More

Autoencoder-augmented Neuroevolution for Visual Doom PlayingJul 12 2017Neuroevolution has proven effective at many reinforcement learning tasks, but does not seem to scale well to high-dimensional controller representations, which are needed for tasks where the input is raw pixel data. We propose a novel method where we ... More

Illuminating Generalization in Deep Reinforcement Learning through Procedural Level GenerationJun 28 2018Nov 29 2018Deep reinforcement learning (RL) has shown impressive results in a variety of domains, learning directly from high-dimensional sensory streams. However, when neural networks are trained in a fixed environment, such as a single level in a video game, they ... More

Evolving controllers for simulated car racingNov 02 2006This paper describes the evolution of controllers for racing a simulated radio-controlled car around a track, modelled on a real physical track. Five different controller architectures were compared, based on neural networks, force fields and action sequences. ... More

Measuring Intelligence through GamesSep 06 2011Artificial general intelligence (AGI) refers to research aimed at tackling the full problem of artificial intelligence, that is, create truly intelligent agents. This sets it apart from most AI research which aims at solving relatively narrow domains, ... More

New And Surprising Ways to Be Mean. Adversarial NPCs with Coupled Empowerment MinimisationJun 04 2018Creating Non-Player Characters (NPCs) that can react robustly to unforeseen player behaviour or novel game content is difficult and time-consuming. This hinders the design of believable characters, and the inclusion of NPCs in games that rely heavily ... More

Active Player ModellingDec 10 2013We argue for the use of active learning methods for player modelling. In active learning, the learning algorithm chooses where to sample the search space so as to optimise learning progress. We hypothesise that player modelling based on active learning ... More

AlphaStar: An Evolutionary Computation PerspectiveFeb 05 2019In January 2019, DeepMind revealed AlphaStar to the world-the first artificial intelligence (AI) system to beat a professional player at the game of StarCraft II-representing a milestone in the progress of AI. AlphaStar draws on many areas of AI research, ... More

AlphaStar: An Evolutionary Computation PerspectiveFeb 05 2019Feb 08 2019In January 2019, DeepMind revealed AlphaStar to the world-the first artificial intelligence (AI) system to beat a professional player at the game of StarCraft II-representing a milestone in the progress of AI. AlphaStar draws on many areas of AI research, ... More

Playing Atari with Six NeuronsJun 04 2018Mar 03 2019Deep reinforcement learning, applied to vision-based problems like Atari games, maps pixels directly to actions; internally, the deep neural network bears the responsibility of both extracting useful information and making decisions based on it. By separating ... More

ELIMINATION from Design to AnalysisMay 15 2019Elimination is a word puzzle game for browsers and mobile devices, where all levels are generated by a constrained evolutionary algorithm with no human intervention. This paper describes the design of the game and its level generation methods, and analysis ... More

Organic Building Generation in MinecraftJun 11 2019This paper presents a method for generating floor plans for structures in Minecraft (Mojang 2009). Given a 3D space, it will auto-generate a building to fill that space using a combination of constrained growth and cellular automata. The result is a series ... More

Deep Learning for Video Game PlayingAug 25 2017Feb 18 2019In this article, we review recent Deep Learning advances in the context of how they have been applied to play different types of video games such as first-person shooters, arcade games, and real-time strategy games. We analyze the unique requirements ... More

DeepMasterPrints: Generating MasterPrints for Dictionary Attacks via Latent Variable EvolutionMay 21 2017Oct 18 2018Recent research has demonstrated the vulnerability of fingerprint recognition systems to dictionary attacks based on MasterPrints. MasterPrints are real or synthetic fingerprints that can fortuitously match with a large number of fingerprints thereby ... More

Diverse Agents for Ad-Hoc Cooperation in HanabiJul 08 2019In complex scenarios where a model of other actors is necessary to predict and interpret their actions, it is often desirable that the model works well with a wide variety of previously unknown actors. Hanabi is a card game that brings the problem of ... More

AAAI-2019 Workshop on Games and Simulations for Artificial IntelligenceMar 06 2019This volume represents the accepted submissions from the AAAI-2019 Workshop on Games and Simulations for Artificial Intelligence held on January 29, 2019 in Honolulu, Hawaii, USA. https://www.gamesim.ai

Deep Interactive EvolutionJan 24 2018This paper describes an approach that combines generative adversarial networks (GANs) with interactive evolutionary computation (IEC). While GANs can be trained to produce lifelike images, they are normally sampled randomly from the learned distribution, ... More

Pitako -- Recommending Game Design Elements in CiceroJul 08 2019Recommender Systems are widely and successfully applied in e-commerce. Could they be used for design? In this paper, we introduce Pitako1, a tool that applies the Recommender System concept to assist humans in creative tasks. More specifically, Pitako ... More

Talakat: Bullet Hell Generation through Constrained Map-ElitesJun 12 2018Jun 14 2018We describe a search-based approach to generating new levels for bullet hell games, which are action games characterized by and requiring avoidance of a very large amount of projectiles. Levels are represented using a domain-specific description language, ... More

Leveling the Playing Field -- Fairness in AI Versus Human Game BenchmarksMar 17 2019Mar 24 2019From the beginning if the history of AI, there has been interest in games as a platform of research. As the field developed, human-level competence in complex games became a target researchers worked to reach. Only relatively recently has this target ... More

DeepTingleMay 09 2017DeepTingle is a text prediction and classification system trained on the collected works of the renowned fantastic gay erotica author Chuck Tingle. Whereas the writing assistance tools you use everyday (in the form of predictive text, translation, grammar ... More

Leveling the Playing Field - Fairness in AI Versus Human Game BenchmarksMar 17 2019From the beginning if the history of AI, there has been interest in games as a platform of research. As the field developed, human-level competence in complex games became a target researchers worked to reach. Only relatively recently has this target ... More

Tree Search vs Optimization Approaches for Map GenerationMar 27 2019Search-based procedural content generation uses stochastic global optimization algorithms to search spaces of game content. However, it has been found that tree search can be competitive with evolution on certain optimization problems. We investigate ... More

A Fast and Efficient Stochastic Opposition-Based Learning for Differential Evolution in Numerical OptimizationAug 09 2019A new variant of stochastic opposition-based learning (OBL) is proposed in this paper. OBL is a relatively new machine learning concept, which consists of simultaneously calculating an original solution and its opposite to accelerate the convergence of ... More

Generative Design in Minecraft (GDMC), Settlement Generation CompetitionMar 27 2018Jul 31 2018This paper introduces the settlement generation competition for Minecraft, the first part of the Generative Design in Minecraft challenge. The settlement generation competition is about creating Artificial Intelligence (AI) agents that can produce functional, ... More

Evolving Game Skill-Depth using General Video Game AI AgentsMar 18 2017Most games have, or can be generalised to have, a number of parameters that may be varied in order to provide instances of games that lead to very different player experiences. The space of possible parameter settings can be seen as a search space, and ... More

Automated Playtesting of Matching Tile GamesJul 15 2019Matching tile games are an extremely popular game genre. Arguably the most popular iteration, Match-3 games, are simple to understand puzzle games, making them great benchmarks for research. In this paper, we propose developing different procedural personas ... More

Intentional Computational Level DesignApr 18 2019The procedural generation of levels and content in video games is a challenging AI problem. Often such generation relies on an intelligent way of evaluating the content being generated so that constraints are satisfied and/or objectives maximized. In ... More

DeepTingleMay 09 2017Mar 27 2019DeepTingle is a text prediction and classification system trained on the collected works of the renowned fantastic gay erotica author Chuck Tingle. Whereas the writing assistance tools you use everyday (in the form of predictive text, translation, grammar ... More

ACM-DE: Adaptive p-best Cauchy Mutation with linear failure threshold reduction for Differential Evolution in numerical optimizationJul 01 2019Differential evolution (DE) is an efficient evolutionary algorithm for optimizing continuous optimization problems. Although DE has been successfully applied to various real-world problems, it suffers from premature convergence where all individuals converge ... More

Empowering Quality Diversity in Dungeon Design with Interactive Constrained MAP-ElitesJun 12 2019We propose the use of quality-diversity algorithms for mixed-initiative game content generation. This idea is implemented as a new feature of the Evolutionary Dungeon Designer, a system for mixed-initiative design of the type of levels you typically find ... More

Automated Playtesting with Procedural Personas through MCTS with Evolved HeuristicsFeb 19 2018This paper describes a method for generative player modeling and its application to the automatic testing of game content using archetypal player models called procedural personas. Theoretically grounded in psychological decision theory, procedural personas ... More

Towards Game-based Metrics for Computational Co-creativitySep 26 2018We propose the following question: what game-like interactive system would provide a good environment for measuring the impact and success of a co-creative, cooperative agent? Creativity is often formulated in terms of novelty, value, surprise and interestingness. ... More

Generating Levels That Teach MechanicsJul 18 2018Oct 01 2018The automatic generation of game tutorials is a challenging AI problem. While it is possible to generate annotations and instructions that explain to the player how the game is played, this paper focuses on generating a gameplay experience that introduces ... More

Data-driven Design: A Case for Maximalist Game DesignMay 30 2018Maximalism in art refers to drawing on and combining multiple different sources for art creation, embracing the resulting collisions and heterogeneity. This paper discusses the use of maximalism in game design and particularly in data games, which are ... More

Deceptive GamesJan 31 2018Feb 04 2018Deceptive games are games where the reward structure or other aspects of the game are designed to lead the agent away from a globally optimal policy. While many games are already deceptive to some extent, we designed a series of games in the Video Game ... More

A Continuous Information Gain Measure to Find the Most Discriminatory Problems for AI BenchmarkingSep 09 2018Sep 11 2018This paper introduces an information-theoretic method for selecting a small subset of problems which gives us the most information about a group of problem-solving algorithms. This method was tested on the games in the General Video Game AI (GVGAI) framework, ... More

Automatic Critical Mechanic Discovery in Video GamesSep 06 2019We present a system that automatically discovers critical mechanics in a variety of video games within the General Video Game Artificial Intelligence (GVG-AI) framework using a combination of game description parsing and playtrace information. Critical ... More

The Case for a Mixed-Initiative Collaborative Neuroevolution ApproachAug 05 2014It is clear that the current attempts at using algorithms to create artificial neural networks have had mixed success at best when it comes to creating large networks and/or complex behavior. This should not be unexpected, as creating an artificial brain ... More

Two-step Constructive Approaches for Dungeon GenerationJun 11 2019This paper presents a two-step generative approach for creating dungeons in the rogue-like puzzle game MiniDungeons 2. Generation is split into two steps, initially producing the architectural layout of the level as its walls and floor tiles, and then ... More

Superstition in the Network: Deep Reinforcement Learning Plays Deceptive GamesAug 12 2019Deep reinforcement learning has learned to play many games well, but failed on others. To better characterize the modes and reasons of failure of deep reinforcement learners, we test the widely used Asynchronous Actor-Critic (A2C) algorithm on four deceptive ... More

General Video Game AI: a Multi-Track Framework for Evaluating Agents, Games and Content Generation AlgorithmsFeb 28 2018Dec 26 2018General Video Game Playing (GVGP) aims at designing an agent that is capable of playing multiple video games with no human intervention. In 2014, The General Video Game AI (GVGAI) competition framework was created and released with the purpose of providing ... More

Pommerman: A Multi-Agent PlaygroundSep 19 2018We present Pommerman, a multi-agent environment based on the classic console game Bomberman. Pommerman consists of a set of scenarios, each having at least four players and containing both cooperative and competitive aspects. We believe that success in ... More

Generative Design in Minecraft: Chronicle ChallengeMay 14 2019We introduce the Chronicle Challenge as an optional addition to the Settlement Generation Challenge in Minecraft. One of the foci of the overall competition is adaptive procedural content generation (PCG), an arguably under-explored problem in computational ... More

DATA AgentSep 28 2018This paper introduces DATA Agent, a system which creates murder mystery adventures from open data. In the game, the player takes on the role of a detective tasked with finding the culprit of a murder. All characters, places, and items in DATA Agent games ... More

The Many AI Challenges of HearthstoneJul 15 2019Games have benchmarked AI methods since the inception of the field, with classic board games such as Chess and Go recently leaving room for video games with related yet different sets of challenges. The set of AI problems associated with video games has ... More

"Press Space to Fire": Automatic Video Game Tutorial GenerationMay 30 2018We propose the problem of tutorial generation for games, i.e. to generate tutorials which can teach players to play games, as an AI problem. This problem can be approached in several ways, including generating natural language descriptions of game rules, ... More

Evolving the Hearthstone MetaJul 02 2019Balancing an ever growing strategic game of high complexity, such as Hearthstone is a complex task. The target of making strategies diverse and customizable results in a delicate intricate system. Tuning over 2000 cards to generate the desired outcome ... More

Who Killed Albert Einstein? From Open Data to Murder Mystery GamesFeb 14 2018This paper presents a framework for generating adventure games from open data. Focusing on the murder mystery type of adventure games, the generator is able to transform open data from Wikipedia articles, OpenStreetMap and images from Wikimedia Commons ... More

AtDelfi: Automatically Designing Legible, Full Instructions For GamesJul 11 2018Sep 17 2018This paper introduces a fully automatic method for generating video game tutorials. The AtDELFI system (AuTomatically DEsigning Legible, Full Instructions for games) was created to investigate procedural generation of instructions that teach players how ... More

Procedural Content Generation through Quality DiversityJul 09 2019Quality-diversity (QD) algorithms search for a set of good solutions which cover a space as defined by behavior metrics. This simultaneous focus on quality and diversity with explicit metrics sets QD algorithms apart from standard single- and multi-objective ... More

Evolving Agents for the Hanabi 2018 CIG CompetitionSep 26 2018Hanabi is a cooperative card game with hidden information that has won important awards in the industry and received some recent academic attention. A two-track competition of agents for the game will take place in the 2018 CIG conference. In this paper, ... More

Obstacle Tower: A Generalization Challenge in Vision, Control, and PlanningFeb 04 2019The rapid pace of research in Deep Reinforcement Learning has been driven by the presence of fast and challenging simulation environments. These environments often take the form of games; with tasks ranging from simple board games, to classic home console ... More

Mapping Hearthstone Deck Spaces through MAP-Elites with Sliding BoundariesApr 24 2019Quality diversity (QD) algorithms such as MAP-Elites have emerged as a powerful alternative to traditional single-objective optimization methods. They were initially applied to evolutionary robotics problems such as locomotion and maze navigation, but ... More

Procedural Content Generation via Machine Learning (PCGML)Feb 02 2017May 07 2018This survey explores Procedural Content Generation via Machine Learning (PCGML), defined as the generation of game content using machine learning models trained on existing content. As the importance of PCG for game development increases, researchers ... More

Obstacle Tower: A Generalization Challenge in Vision, Control, and PlanningFeb 04 2019Jul 01 2019The rapid pace of recent research in AI has been driven in part by the presence of fast and challenging simulation environments. These environments often take the form of games; with tasks ranging from simple board games, to competitive video games. We ... More

Exponential Patterns in Arithmetic Ramsey TheoryJul 28 2016We show that for every finite colouring of the natural numbers there exists $a,b >1$ such that the triple $\{a,b,a^b\}$ is monochromatic. We go on to show the partition regularity of a much richer class of patterns involving exponentiation. For example, ... More

A Fast Method For Bounding The CMB Power Spectrum Likelihood FunctionMar 10 1998As the Cosmic Microwave Background (CMB) radiation is observed to higher and higher angular resolution the size of the resulting datasets becomes a serious constraint on their analysis. In particular current algorithms to determine the location of, and ... More

Isoperimetry in supercritical bond percolation in dimensions three and higherFeb 17 2016We study the isoperimetric subgraphs of the infinite cluster $\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with $d\geq 3$. Specifically, we consider the subgraphs of $\textbf{C}_\infty \cap [-n,n]^d$ which have minimal open ... More

Lepton flavor violation with light vector bosonsFeb 11 2016May 10 2016New sub-GeV vector bosons with couplings to muons but not electrons have been discussed in order to explain the muon's magnetic moment, the gap of high-energy neutrinos in IceCube or the proton radius puzzle. If such a light Z' not only violates lepton ... More

Bond Pricing under Knightian Uncertainty: A Short Rate Model with Drift and Volatility UncertaintyAug 10 2018It is shown how to construct an arbitrage-free short rate model under uncertainty about the drift and the volatility. The uncertainty is represented by a set of priors, which naturally leads to a G-Brownian motion. Within this framework, it is shown how ... More

Connecting Atomistic and Continuous Models of ElastodynamicsJun 06 2016Jun 29 2016We prove long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the interatomic distances ... More

Prospecies of algebras I: Basic propertiesAug 05 2016Mar 06 2017In this paper, we generalise part of the theory of hereditary algebras to the context of prospecies of algebras. Here, a prospecies is a generalisation of Gabriel's concept of species gluing algebras via projective bimodules along a quiver to obtain a ... More

The Massless Nelson Hamiltonian and its DomainJan 17 2019In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form sense) of ... More

Finite F-inveres covers do existAug 15 2018We show that every finite inverse monoid has an idempotent-separating cover by a finite F-inverse monoid. This provides a positive answer to a conjecture of Henckell and Rhodes.

The Kato Square Root Problem for Divergence Form Operators with PotentialDec 26 2018Jan 13 2019The Kato square root problem for divergence form elliptic operators with potential $V:\mathbb{R}^{n} \rightarrow \mathbb{C}$ is the equivalence statement $\left\Vert \left( \mathcal{L}_{A}^{V} \right)^{\frac{1}{2}}u \right\Vert \simeq \left\Vert \nabla ... More

Kalai's squeezed 3-spheres are polytopalOct 22 2001In 1988, Kalai extended a construction of Billera and Lee to produce many triangulated (d-1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Goodman and Pollack, he derived that for every dimension d>=5, most of these ... More

MADCAP - The Microwave Anisotropy Dataset Computational Analysis PackageNov 19 1999Realizing the extraordinary scientific potential of the CMB requires precise measurements of its tiny anisotropies over a significant fraction of the sky at very high resolution. The analysis of the resulting datasets is a serious computational challenge. ... More

On The Absence Of Open Strings In A Lattice-Free Simulation Of Cosmic String FormationNov 10 1995May 02 1996Lattice-based string formation algorithms can, at least in principle, be reduced to the study of the statistics of the corresponding aperiodic random walk. Since in three or more dimensions such walks are transient this approach necessarily generates ... More

The electroweak matter sector from an effective theory perspectiveAug 07 2002The object of this thesis is the study of some open problems in the electroweak matter sector from an effective theory perspective. The topics studied include: General aspects of dynamical symmetry breaking models, studying what traces these mechanisms ... More

Lepton Number Violation with and without Majorana NeutrinosMar 26 2015We discuss the various incarnations of a gauged B-L symmetry: 1) unbroken, it features Dirac neutrinos, neutrinogenesis to create the baryon asymmetry of our Universe, and a potentially light Z' boson; 2) broken by two units, we obtain the standard case ... More

Unbroken B-L SymmetryAug 28 2014Nov 10 2014The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The ... More

Parallel Wavelet Tree ConstructionJul 30 2014Apr 01 2015We present parallel algorithms for wavelet tree construction with polylogarithmic depth, improving upon the linear depth of the recent parallel algorithms by Fuentes-Sepulveda et al. We experimentally show on a 40-core machine with two-way hyper-threading ... More

Multiple harmonic sums and Wolstenholme's theoremFeb 01 2013We give a family of congruences for the binomial coefficients ${kp-1\choose p-1}$ in terms of multiple harmonic sums, a generalization of the harmonic numbers. Each congruence in this family (which depends on an additional parameter $n$) involves a linear ... More

Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systemsMar 12 2007Sep 16 2007For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some system-dependent ... More

Improved Parallel Construction of Wavelet Trees and Rank/Select StructuresOct 11 2016Jan 18 2017Existing parallel algorithms for wavelet tree construction have a work complexity of $O(n\log\sigma)$. This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer sorting and ... More

Isoperimetry in supercritical bond percolation in dimensions three and higherFeb 17 2016Oct 27 2017We study the isoperimetric subgraphs of the infinite cluster $\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with $d\geq 3$. Specifically, we consider the subgraphs of $\textbf{C}_\infty \cap [-n,n]^d$ which have minimal open ... More

Inverse curvature flows in Riemannian warped productsDec 27 2017Jan 24 2018The long-time existence and umbilicity estimates for compact, graphical solutions to expanding curvature flows are deduced in Riemannian warped products of a real interval with a compact fibre. Notably we do not assume the ambient manifold to be rotationally ... More

The Minkowski inequality in de Sitter spaceSep 15 2019The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on round spheres. In this paper we employ a locally constrained inverse mean ... More

Asymptotics to all orders of the Euler--Darboux equation in a triangleJun 08 2018Nov 26 2018In Einstein's theory of relativity, the interaction of two collinearly polarized plane gravitational waves can be described by a Goursat problem for the Euler--Darboux equation in a triangular domain. In this paper, using a representation of the solution ... More

Auslander-Reiten theory of Frobenius-Lusztig kernelsJan 25 2012In this paper we show that the tree class of a component of the stable Auslander-Reiten quiver of a Frobenius-Lusztig kernel is one of the three infinite Dynkin diagrams. For the special case of the small quantum group we show that the periodic components ... More

Orthocompactness and semi-stratifiability in the density topologySep 12 1998The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to determine which subsets ... More

Synchronisation in Invertible Random Dynamical Systems on the CircleFeb 26 2015Jul 05 2015Given a composition of i.i.d. random orientation-preserving homeomorphisms or a memoryless stochastic flow of homeomorphisms on the circle, we show that provided the randomness allows for a sufficient range of possible behaviour on a finite time-scale, ... More

Analytic stability analysis of three-component self-regulatory genetic circuitAug 03 2014Aug 09 2014A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the protein, are ... More

Pinching and asymptotical roundness for inverse curvature flows in Euclidean spaceApr 10 2014Jun 18 2015We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean space, $n\geq 2,$ expanding by arbitrary negative powers of a 1-homogeneous, monotone curvature function $F$ with some concavity properties. We obtain asymptotical roundness, meaning ... More

Power Spectrum Estimators For Large CMB DatasetsDec 08 1997Dec 11 1997Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very serious challenge ... More

Numerical Methods in Cosmological Global Texture SimulationsMar 03 1994Numerical simulations of the evolution of a global topological defect field have two characteristic length scales --- one macrophysical, of order the field correlation length, and the other microphysical, of order the field width. The situation currently ... More

Periods, supercongruences, and their motivic liftsAug 24 2016A period is a complex number arising as the integral of a rational function, with rational coefficients, over a rationally-defined region. Though periods are typically transcendental, the theory of motives predicts a version of Galois theory should hold ... More

The signed permutation group on Feynman graphsDec 08 2015Feb 23 2016The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalizaton group are small, we can expand the ... More

Between ${\cal A}$- and ${\cal B}$-setsNov 01 1998The aim of this paper is to introduce the class of ${\cal A}{\cal B}$-sets as the sets that are the intersection of an open and a semi-regular set. Several classes of well-known topological spaces are characterized via the new concept. A new decomposition ... More

Generalized Selective Modal AnalysisJun 08 1999Jul 27 1999A new approach which generalizes the Selective Modal Analyis (SMA) and algorithms based upon it for solving the generalized eigenvalue problem is described. This approach allows for the systematic consideration of physical properties of the system under ... More