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Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural NetworksJul 05 2016Our goal is to combine the rich multi-step inference of symbolic logical reasoning together with the generalization capabilities of vector embeddings and neural networks. We are particularly interested in complex reasoning about the entities and relations ... More

Question Answering on Knowledge Bases and Text using Universal Schema and Memory NetworksApr 27 2017Existing question answering methods infer answers either from a knowledge base or from raw text. While knowledge base (KB) methods are good at answering compositional questions, their performance is often affected by the incompleteness of the KB. Au contraire, ... More

Row-less Universal SchemaApr 21 2016Universal schema jointly embeds knowledge bases and textual patterns to reason about entities and relations for automatic knowledge base construction and information extraction. In the past, entity pairs and relations were represented as learned vectors ... More

Syntax Helps ELMo Understand Semantics: Is Syntax Still Relevant in a Deep Neural Architecture for SRL?Nov 12 2018Do unsupervised methods for learning rich, contextualized token representations obviate the need for explicit modeling of linguistic structure in neural network models for semantic role labeling (SRL)? We address this question by incorporating the massively ... More

Topic Models Conditioned on Arbitrary Features with Dirichlet-multinomial RegressionJun 13 2012Although fully generative models have been successfully used to model the contents of text documents, they are often awkward to apply to combinations of text data and document metadata. In this paper we propose a Dirichlet-multinomial regression (DMR) ... More

Word Representations via Gaussian EmbeddingDec 20 2014May 01 2015Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation and its relationships, ... More

Dependency Parsing with Dilated Iterated Graph CNNsMay 01 2017Jul 21 2017Dependency parses are an effective way to inject linguistic knowledge into many downstream tasks, and many practitioners wish to efficiently parse sentences at scale. Recent advances in GPU hardware have enabled neural networks to achieve significant ... More

Structured Prediction Energy NetworksNov 19 2015Jun 23 2016We introduce structured prediction energy networks (SPENs), a flexible framework for structured prediction. A deep architecture is used to define an energy function of candidate labels, and then predictions are produced by using back-propagation to iteratively ... More

Free subgroups of special linear groupsMar 31 2014Nov 05 2014We present a proof of the following claim. Suppose that $n$ is an integer such that $n>1$ and that $k$ is any field. Suppose that $g$ is an element of $\mathrm{SL}(n,k)$ of infinite order. Then the set $\{h\in\mathrm{SL}(n,k)\mid <g,h>$ is a free group ... More

Film Edge Nonlocal Spin ValvesMar 28 2009Spintronics is a new paradigm for integrated digital electronics. Recently established as a niche for nonvolatile magnetic random access memory (MRAM), it offers new functionality while demonstrating low power and high speed performance. However, to reach ... More

Learning with Scope, with Application to Information Extraction and ClassificationDec 12 2012In probabilistic approaches to classification and information extraction, one typically builds a statistical model of words under the assumption that future data will exhibit the same regularities as the training data. In many data sets, however, there ... More

On Lazard's Valuation and CAD ConstructionJan 26 2015Feb 09 2015In 1990 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results ... More

Lexicon Infused Phrase Embeddings for Named Entity ResolutionApr 22 2014Most state-of-the-art approaches for named-entity recognition (NER) use semi supervised information in the form of word clusters and lexicons. Recently neural network-based language models have been explored, as they as a byproduct generate highly informative ... More

Energy and Policy Considerations for Deep Learning in NLPJun 05 2019Recent progress in hardware and methodology for training neural networks has ushered in a new generation of large networks trained on abundant data. These models have obtained notable gains in accuracy across many NLP tasks. However, these accuracy improvements ... More

Inference by Minimizing Size, Divergence, or their SumMar 15 2012We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the ... More

Compositional Vector Space Models for Knowledge Base CompletionApr 24 2015May 27 2015Knowledge base (KB) completion adds new facts to a KB by making inferences from existing facts, for example by inferring with high likelihood nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop relational synonyms like this, ... More

Training for Fast Sequential Prediction Using Dynamic Feature SelectionOct 30 2014Dec 19 2014We present paired learning and inference algorithms for significantly reducing computation and increasing speed of the vector dot products in the classifiers that are at the heart of many NLP components. This is accomplished by partitioning the features ... More

End-to-End Learning for Structured Prediction Energy NetworksMar 16 2017Jul 15 2017Structured Prediction Energy Networks (SPENs) are a simple, yet expressive family of structured prediction models (Belanger and McCallum, 2016). An energy function over candidate structured outputs is given by a deep network, and predictions are formed ... More

Generalizing to Unseen Entities and Entity Pairs with Row-less Universal SchemaJun 18 2016Jan 09 2017Universal schema predicts the types of entities and relations in a knowledge base (KB) by jointly embedding the union of all available schema types---not only types from multiple structured databases (such as Freebase or Wikipedia infoboxes), but also ... More

Latent Relation Representations for Universal SchemasJan 18 2013Jan 28 2013Traditional relation extraction predicts relations within some fixed and finite target schema. Machine learning approaches to this task require either manual annotation or, in the case of distant supervision, existing structured sources of the same schema. ... More

Anytime Belief Propagation Using Sparse DomainsNov 14 2013Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important ... More

Distantly Labeling Data for Large Scale Cross-Document CoreferenceMay 24 2010Cross-document coreference, the problem of resolving entity mentions across multi-document collections, is crucial to automated knowledge base construction and data mining tasks. However, the scarcity of large labeled data sets has hindered supervised ... More

Paper Matching with Local Fairness ConstraintsMay 28 2019Automatically matching reviewers to papers is a crucial step of the peer review process for venues receiving thousands of submissions. Unfortunately, common paper matching algorithms often construct matchings suffering from two critical problems: (1) ... More

Nonparametric Bayes Pachinko AllocationJun 20 2012Recent advances in topic models have explored complicated structured distributions to represent topic correlation. For example, the pachinko allocation model (PAM) captures arbitrary, nested, and possibly sparse correlations between topics using a directed ... More

Generalizing to Unseen Entities and Entity Pairs with Row-less Universal SchemaJun 18 2016Universal schema predicts the types of entities and relations in a knowledge base (KB) by jointly embedding the union of all available schema types---not only types from multiple structured databases (such as Freebase or Wikipedia infoboxes), but also ... More

Ask the GRU: Multi-Task Learning for Deep Text RecommendationsSep 07 2016Sep 09 2016In a variety of application domains the content to be recommended to users is associated with text. This includes research papers, movies with associated plot summaries, news articles, blog posts, etc. Recommendation approaches based on latent factor ... More

A Conditional Random Field for Discriminatively-trained Finite-state String Edit DistanceJul 04 2012The need to measure sequence similarity arises in information extraction, object identity, data mining, biological sequence analysis, and other domains. This paper presents discriminative string-edit CRFs, a finitestate conditional random field model ... More

Simultaneously Self-Attending to All Mentions for Full-Abstract Biological Relation ExtractionFeb 28 2018Most work in relation extraction forms a prediction by looking at a short span of text within a single sentence containing a single entity pair mention. This approach often does not consider interactions across mentions, requires redundant computation ... More

Unsupervised Latent Tree Induction with Deep Inside-Outside Recursive AutoencodersApr 03 2019We introduce deep inside-outside recursive autoencoders (DIORA), a fully-unsupervised method for discovering syntax that simultaneously learns representations for constituents within the induced tree. Our approach predicts each word in an input sentence ... More

Unsupervised Latent Tree Induction with Deep Inside-Outside Recursive AutoencodersApr 03 2019Apr 04 2019We introduce deep inside-outside recursive autoencoders (DIORA), a fully-unsupervised method for discovering syntax that simultaneously learns representations for constituents within the induced tree. Our approach predicts each word in an input sentence ... More

Coherent electrical control of a single high-spin nucleus in siliconJun 03 2019Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, e.g. in chemistry, medicine, materials science and mining. Nuclear spins also featured in early ideas and demonstrations ... More

Efficient Non-parametric Estimation of Multiple Embeddings per Word in Vector SpaceApr 24 2015There is rising interest in vector-space word embeddings and their use in NLP, especially given recent methods for their fast estimation at very large scale. Nearly all this work, however, assumes a single vector per word type ignoring polysemy and thus ... More

Learning Soft Linear Constraints with Application to Citation Field ExtractionMar 06 2014Oct 17 2014Accurately segmenting a citation string into fields for authors, titles, etc. is a challenging task because the output typically obeys various global constraints. Previous work has shown that modeling soft constraints, where the model is encouraged, but ... More

Bethe Projections for Non-Local InferenceMar 04 2015Jun 18 2015Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained ... More

Multilingual Relation Extraction using Compositional Universal SchemaNov 19 2015Mar 03 2016Universal schema builds a knowledge base (KB) of entities and relations by jointly embedding all relation types from input KBs as well as textual patterns expressing relations from raw text. In most previous applications of universal schema, each textual ... More

Fast and Accurate Entity Recognition with Iterated Dilated ConvolutionsFeb 07 2017Jul 22 2017Today when many practitioners run basic NLP on the entire web and large-volume traffic, faster methods are paramount to saving time and energy costs. Recent advances in GPU hardware have led to the emergence of bi-directional LSTMs as a standard method ... More

Hierarchical Losses and New Resources for Fine-grained Entity Typing and LinkingJul 13 2018Extraction from raw text to a knowledge base of entities and fine-grained types is often cast as prediction into a flat set of entity and type labels, neglecting the rich hierarchies over types and entities contained in curated ontologies. Previous attempts ... More

SemEval 2017 Task 10: ScienceIE - Extracting Keyphrases and Relations from Scientific PublicationsApr 10 2017May 02 2017We describe the SemEval task of extracting keyphrases and relations between them from scientific documents, which is crucial for understanding which publications describe which processes, tasks and materials. Although this was a new task, we had a total ... More

Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural NetworksJul 05 2016May 01 2017Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and large-scale knowledge ... More

Probabilistic Embedding of Knowledge Graphs with Box Lattice MeasuresMay 17 2018Embedding methods which enforce a partial order or lattice structure over the concept space, such as Order Embeddings (OE) (Vendrov et al., 2016), are a natural way to model transitive relational data (e.g. entailment graphs). However, OE learns a deterministic ... More

Linguistically-Informed Self-Attention for Semantic Role LabelingApr 23 2018Nov 12 2018Current state-of-the-art semantic role labeling (SRL) uses a deep neural network with no explicit linguistic features. However, prior work has shown that gold syntax trees can dramatically improve SRL decoding, suggesting the possibility of increased ... More

Distributional Inclusion Vector Embedding for Unsupervised Hypernymy DetectionOct 02 2017May 29 2018Modeling hypernymy, such as poodle is-a dog, is an important generalization aid to many NLP tasks, such as entailment, coreference, relation extraction, and question answering. Supervised learning from labeled hypernym sources, such as WordNet, limits ... More

Active Bias: Training More Accurate Neural Networks by Emphasizing High Variance SamplesApr 24 2017Jan 06 2018Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD): the variance ... More

Finer Grained Entity Typing with TypeNetNov 15 2017We consider the challenging problem of entity typing over an extremely fine grained set of types, wherein a single mention or entity can have many simultaneous and often hierarchically-structured types. Despite the importance of the problem, there is ... More

Multi-step Retriever-Reader Interaction for Scalable Open-domain Question AnsweringMay 14 2019This paper introduces a new framework for open-domain question answering in which the retriever and the reader iteratively interact with each other. The framework is agnostic to the architecture of the machine reading model, only requiring access to the ... More

Building Dynamic Knowledge Graphs from Text using Machine Reading ComprehensionOct 12 2018We propose a neural machine-reading model that constructs dynamic knowledge graphs from procedural text. It builds these graphs recurrently for each step of the described procedure, and uses them to track the evolving states of participant entities. We ... More

Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural NetworksJul 05 2016Oct 13 2016Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and large-scale knowledge ... More

Bethe Projections for Non-Local InferenceMar 04 2015Nov 28 2016Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained ... More

An Online Hierarchical Algorithm for Extreme ClusteringApr 06 2017Many modern clustering methods scale well to a large number of data items, N, but not to a large number of clusters, K. This paper introduces PERCH, a new non-greedy algorithm for online hierarchical clustering that scales to both massive N and K--a problem ... More

Learning Dynamic Feature Selection for Fast Sequential PredictionMay 22 2015We present paired learning and inference algorithms for significantly reducing computation and increasing speed of the vector dot products in the classifiers that are at the heart of many NLP components. This is accomplished by partitioning the features ... More

Supervised Hierarchical Clustering with Exponential LinkageJun 19 2019In supervised clustering, standard techniques for learning a pairwise dissimilarity function often suffer from a discrepancy between the training and clustering objectives, leading to poor cluster quality. Rectifying this discrepancy necessitates matching ... More

Search-Guided, Lightly-supervised Training of Structured Prediction Energy NetworksDec 22 2018In structured output prediction tasks, labeling ground-truth training output is often expensive. However, for many tasks, even when the true output is unknown, we can evaluate predictions using a scalar reward function, which may be easily assembled from ... More

An Integrated, Conditional Model of Information Extraction and Coreference with Applications to Citation MatchingJul 11 2012Although information extraction and coreference resolution appear together in many applications, most current systems perform them as ndependent steps. This paper describes an approach to integrated inference for extraction and coreference based on conditionally-trained ... More

Attending to All Mention Pairs for Full Abstract Biological Relation ExtractionOct 23 2017Nov 15 2017Most work in relation extraction forms a prediction by looking at a short span of text within a single sentence containing a single entity pair mention. However, many relation types, particularly in biomedical text, are expressed across sentences or require ... More

Singularities and Catastrophes in Economics: Historical Perspectives and Future DirectionsJul 12 2019Economic theory is a mathematically rich field in which there are opportunities for the formal analysis of singularities and catastrophes. This article looks at the historical context of singularities through the work of two eminent Frenchmen around the ... More

Efficient Graph-based Word Sense Induction by Distributional Inclusion Vector EmbeddingsApr 09 2018May 29 2018Word sense induction (WSI), which addresses polysemy by unsupervised discovery of multiple word senses, resolves ambiguities for downstream NLP tasks and also makes word representations more interpretable. This paper proposes an accurate and efficient ... More

Go for a Walk and Arrive at the Answer: Reasoning Over Paths in Knowledge Bases using Reinforcement LearningNov 15 2017Dec 30 2018Knowledge bases (KB), both automatically and manually constructed, are often incomplete --- many valid facts can be inferred from the KB by synthesizing existing information. A popular approach to KB completion is to infer new relations by combinatory ... More

Learning a Natural Language Interface with Neural ProgrammerNov 28 2016Learning a natural language interface for database tables is a challenging task that involves deep language understanding and multi-step reasoning. The task is often approached by mapping natural language queries to logical forms or programs that provide ... More

Learning a Natural Language Interface with Neural ProgrammerNov 28 2016Mar 02 2017Learning a natural language interface for database tables is a challenging task that involves deep language understanding and multi-step reasoning. The task is often approached by mapping natural language queries to logical forms or programs that provide ... More

Low-Rank Hidden State Embeddings for Viterbi Sequence LabelingAug 02 2017In textual information extraction and other sequence labeling tasks it is now common to use recurrent neural networks (such as LSTM) to form rich embedded representations of long-term input co-occurrence patterns. Representation of output co-occurrence ... More

OpenKI: Integrating Open Information Extraction and Knowledge Bases with Relation InferenceApr 12 2019In this paper, we consider advancing web-scale knowledge extraction and alignment by integrating OpenIE extractions in the form of (subject, predicate, object) triples with Knowledge Bases (KB). Traditional techniques from universal schema and from schema ... More

Embedded-State Latent Conditional Random Fields for Sequence LabelingSep 28 2018Complex textual information extraction tasks are often posed as sequence labeling or \emph{shallow parsing}, where fields are extracted using local labels made consistent through probabilistic inference in a graphical model with constrained transitions. ... More

Topological rigidity in totally disconnected locally compact groupsOct 04 2012Nov 05 2014In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising this to the ... More

A proposed characterisation of the intrinsically justified reflection principlesMar 31 2014Aug 03 2016Building on previous work of Tait, Koellner, and myself exploring the question of which reflection principles are intrinsically justified on the basis of the iterative conception of set, we formulate a new reflection principle, which subsumes all previously ... More

All large-cardinal axioms not known to be inconsistent with ZFC are justifiedDec 21 2017Dec 30 2017In other work we have outlined how, building on ideas of Welch and Roberts, one can motivate believing in the existence of supercompact cardinals. After making this observation we strove to formulate a justification for large-cardinal axioms of greater ... More

A Consistency Proof for Some Restrictions of Tait's Reflection PrinciplesSep 22 2010Sep 05 2012A new large-cardinal property is introduced which enables one to give a relative consistency proof of restricted versions of the reflection principles discussed by Tait in his essay "Constructing Cardinals from Below".

The choiceless cardinals are inconsistentDec 27 2017Feb 25 2018We give a proof of the Kunen inconsistency in ZF.

Intrinsically justified reflection principlesMar 31 2014Dec 21 2017We are concerned with the distinction between intrinsic and extrinsic justifications for large-cardinal axioms, as outlined in for example Section 3 of the 1964 version of G\"odel's essay on the continuum problem. William Tait and Peter Koellner have ... More

Controlling systematics in ground-based CMB surveys with partial boresight rotationMay 29 2019Future CMB experiments will require exquisite control of systematics in order to constrain the $B$-mode polarisation power spectrum. One class of systematics that requires careful study is instrumental systematics. The potential impact of such systematics ... More

New Large Cardinal Axioms and the Ultimate-L ProgramDec 10 2018Mar 09 2019We will consider a number of new large-cardinal properties, the $\alpha$-tremendous cardinals for each limit ordinal $\alpha>0$, the hyper-tremendous cardinals, the $\alpha$-enormous cardinals for each limit ordinal $\alpha>0$, and the hyper-enormous ... More

A Local-to-Global Result for Topological Spherical BuildingsSep 22 2010Oct 17 2012Suppose that \Delta, \Delta' are two buildings each arising from a semisimpe algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter diagram has no isolated nodes. We give conditions under which ... More

Rigidity of the group topology for closed Weyl transitive groups of automorphisms of a regular locally finite buildingFeb 12 2014Nov 05 2014We prove that if $G$ is a group of automorphisms of a regular locally finite building which is closed in the compact-open topology and acts Weyl transitively on the building, then $G$ admits just one Hausdorff locally compact $\sigma$-compact topology ... More

Chromium single photon emitters in diamond fabricated by ion implantationJan 25 2010Controlled fabrication and identification of bright single photon emitters is at the heart of quantum optics and materials science. Here we demonstrate a controlled engineering of a chromium bright single photon source in bulk diamond by ion implantation. ... More

Automatically Extracting Action Graphs from Materials Science Synthesis ProceduresNov 18 2017Nov 28 2017Computational synthesis planning approaches have achieved recent success in organic chemistry, where tabulated synthesis procedures are readily available for supervised learning. The syntheses of inorganic materials, however, exist primarily as natural ... More

The Materials Science Procedural Text Corpus: Annotating Materials Synthesis Procedures with Shallow Semantic StructuresMay 16 2019Jul 13 2019Materials science literature contains millions of materials synthesis procedures described in unstructured natural language text. Large-scale analysis of these synthesis procedures would facilitate deeper scientific understanding of materials synthesis ... More

The Materials Science Procedural Text Corpus: Annotating Materials Synthesis Procedures with Shallow Semantic StructuresMay 16 2019Materials science literature contains millions of materials synthesis procedures described in unstructured natural language text. Large-scale analysis of these synthesis procedures would facilitate deeper scientific understanding of materials synthesis ... More

Height growth on semisimple groupsDec 23 2015Jan 04 2016A condition is given, under which a general lattice point counting function is asymptotic to the corresponding ball volume growth function. This is then used to give height asymptotics in the style of the Batyrev-Manin Conjecture for certain intrinsically ... More

A prime geodesic theorem for higher rank buildingsSep 13 2016We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.

Accounting for parameter uncertainty in two-stage designs for Phase II dose-response studiesAug 03 2014Aug 05 2014In this paper we consider two-stage adaptive dose-response study designs, where the study design is changed at an interim analysis based on the information collected so far. In a simulation study, two approaches will be compared for these type of designs; ... More

Storing quantum information for 30 seconds in a nanoelectronic deviceFeb 28 2014The spin of an electron or a nucleus in a semiconductor [1] naturally implements the unit of quantum information -- the qubit -- while providing a technological link to the established electronics industry [2]. The solid-state environment, however, may ... More

Inorganic Materials Synthesis Planning with Literature-Trained Neural NetworksDec 31 2018Leveraging new data sources is a key step in accelerating the pace of materials design and discovery. To complement the strides in synthesis planning driven by historical, experimental, and computed data, we present an automated method for connecting ... More

High-fidelity adiabatic inversion of a $^{31}\mathrm{P}$ electron spin qubit in natural siliconDec 17 2013The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit gate ... More

A Systematic Classification of Knowledge, Reasoning, and Context within the ARC DatasetJun 01 2018Feb 04 2019The recent work of Clark et al. introduces the AI2 Reasoning Challenge (ARC) and the associated ARC dataset that partitions open domain, complex science questions into an Easy Set and a Challenge Set. That paper includes an analysis of 100 questions with ... More

Bell's inequality violation with spins in siliconApr 13 2015Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high ... More

Inorganic Materials Synthesis Planning with Literature-Trained Neural NetworksDec 31 2018Feb 17 2019Leveraging new data sources is a key step in accelerating the pace of materials design and discovery. To complement the strides in synthesis planning driven by historical, experimental, and computed data, we present an automated method for connecting ... More

Measuring the Viscosity and Time Correlation Functions in a Microscopic Model of a MicroemulsionJun 04 1999Jun 05 1999A dynamical lattice model is used to study the viscosity and the velocity-velocity autocorrelation function in a microemulsion phase. We find evidence of anomalous viscosities in these phases (relative to water-rich and/or oil-rich phases), in qualitative ... More

Exploring quantum chaos with a single nuclear spinMar 15 2017Oct 09 2018Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete ... More

On Shafarevich-Tate groups and the arithmetic of Fermat CurvesOct 31 2002We extend the results of the first author on nontrivial elements in the Shafarevich-Tate group of the jacobian of a quotient of a Fermat curve of prime degree, and use the methods of the second author to derive a result bounding the quadratic points on ... More

Bigness in compatible systemsAug 13 2009Apr 21 2010Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if rho is an l-adic representation of the absolute Galois group of a number field for which the residual representation rho-bar comes from a modular ... More

Average liar count for degree-2 Frobenius pseudoprimesJul 17 2017In this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham, generalizing arguments of Erd\H{o}s and Pomerance, and Monier. These bounds are provided for both Jacobi symbol plus ... More

Quaternionic Kähler Manifolds of Cohomogeneity OneAug 21 1998Nov 24 1998Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler manifolds with a cohomogeneity-two action of a semi-simple group preserving each ... More

Twisted Poincare Series and Zeta functions on finite quotients of buildingsJun 23 2016In the case where $G=$SL$_{2}(F)$ for a non-archimedean local field $F$ and $\Gamma$ is a discrete torsion-free cocompact subgroup of $G$, there is a known relationship between the Ihara zeta function for the quotient of the Bruhat-Tits tree of $G$ by ... More

On Creativity of Elementary Cellular AutomataMay 11 2013We map cell-state transition rules of elementary cellular automata (ECA) onto the cognitive control versus schizotypy spectrum phase space and interpret cellular automaton behaviour in terms of creativity. To implement the mapping we draw analogies between ... More

Modifying hyperkaehler manifolds with circle symmetryOct 24 2005Oct 25 2005A construction is introduced for modifying hyperkaehler manifolds with tri-Hamiltonian circle action, that in favourable situations increases the second Betti number by one. This is based on the symplectic cut construction of Lerman. In 4 or 8 dimensions ... More

Logical Modelling of Physarum PolycephalumMay 20 2011We propose a novel model of unconventional computing where a structural part of computation is presented by dynamics of plasmodium of Physarum polycephalum, a large single cell. We sketch a new logical approach combining conventional logic with process ... More

Non-Abelian Cut Constructions and Hyperkähler ModificationsFeb 09 2010We discuss a general framework for cutting constructions and reinterpret in this setting the work on non-Abelian symplectic cuts by Weitsman. We then introduce two analogous non-Abelian modification constructions for hyperk\"ahler manifolds: one modifies ... More

Hypertoric manifolds and hyperKähler moment mapsJul 14 2016We discuss various aspects of moment map geometry in symplectic and hyperK\"ahler geometry. In particular, we classify complete hyperK\"ahler manifolds of dimension $4n$ with a tri-Hamiltonian action of a torus of dimension $n$, without any assumption ... More

Toric Hypersymplectic QuotientsApr 30 2004May 06 2004We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The image of the hypersymplectic moment ... More

Electron spin relaxation of single phosphorus donors in metal-oxide-semiconductor nanoscale devicesDec 17 2018We analyze the electron spin relaxation rate $1/T_1$ of individual ion-implanted $^{31}P$ donors, in a large set of metal-oxide-semiconductor (MOS) silicon nanoscale devices, with the aim of identifying spin relaxation mechanisms peculiar to the environment ... More

A Dressed Spin Qubit in SiliconMar 15 2016Coherent dressing of a quantum two-level system provides access to a new quantum system with improved properties - a different and easily tuneable level splitting, faster control, and longer coherence times. In our work we investigate the properties of ... More