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Probability of Physical Association of 104 Blended Companions to \textit{Kepler} Objects of Interest Using Visible and Near-Infrared Adaptive Optics PhotometrySep 29 2016We determine probabilities of physical association for stars in blended Kepler Objects of Interest, and find that $14.5\%^{+3.8\%}_{-3.4\%}$ of companions within $\sim4\arcsec$ are consistent with being physically unassociated with their primary. This ... More

Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)Oct 24 2014Jun 20 2015Explicit solutions of the cubic Fermat equation are constructed in ring class fields $\Omega_f$, with conductor $f$ prime to $3$, of any imaginary quadratic field $K$ whose discriminant satisfies $d_K \equiv 1$ (mod $3$), in terms of the Dedekind $\eta$-function. ... More

Periodic points of algebraic functions and Deuring's class number formulaDec 11 2017Jan 01 2018The exact set of periodic points in $\overline{\mathbb{Q}}$ of the algebraic function $\widehat{F}(z)=(-1\pm \sqrt{1-z^4})/z^2$ is shown to consist of the coordinates of certain solutions $(x,y)=(\pi, \xi)$ of the Fermat equation $x^4+y^4=1$ in ring class ... More

Product formulas for the $5$-division points on the Tate normal form and the Rogers-Ramanujan continued fractionDec 19 2016Jun 11 2018Explicit formulas are proved for the $5$-torsion points on the Tate normal form $E_5$ of an elliptic curve having $(X,Y)=(0,0)$ as a point of order $5$. These formulas express the coordinates of points in $E_5[5] - \langle(0,0)\rangle$ as products of ... More

Algebraic Geometry of Matrix Product StatesOct 10 2012Sep 10 2014We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix product state ... More

Closed-Loop Policies for Operational Tests of Safety-Critical SystemsJul 25 2017May 19 2018Manufacturers of safety-critical systems must make the case that their product is sufficiently safe for public deployment. Much of this case often relies upon critical event outcomes from real-world testing, requiring manufacturers to be strategic about ... More

Imitating Driver Behavior with Generative Adversarial NetworksJan 24 2017The ability to accurately predict and simulate human driving behavior is critical for the development of intelligent transportation systems. Traditional modeling methods have employed simple parametric models and behavioral cloning. This paper adopts ... More

An Efficient Automated Validation Procedure for Exoplanet Transit CandidatesJun 07 2012Oct 03 2012Surveys searching for transiting exoplanets have found many more candidates than they have been able to confirm as true planets. This situation is especially acute with the Kepler survey, which has found over 2300 candidates but has confirmed only 77 ... More

An estimate of the circulation generated by a bluff bodyMay 30 2006Mar 01 2008A loss in circulation is sometimes cited in connection with bluff-body wakes as a result of comparing the circulation actually observed downstream with a well-known theoretical estimate of the total circulation generated by a cylinder. In an effort to ... More

A Complete Set of Invariants for LU-Equivalence of Density OperatorsJul 13 2015Nov 21 2016We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants below a certain degree. This implicitly gives a finite complete set of invariants for local unitary equivalence. ... More

Magneto-seismological insights into the penumbral chromosphere and evidence for wave damping in spiculesMay 13 2014The observation of propagating magneto-hydrodynamic kink waves in magnetic structures and measurement of their properties (amplitude, phase speed) can be used to diagnose the plasma conditions in the neighbourhood of the magnetic structure via magneto-seismology ... More

Chromospheric jets around the edges of sunspotsMay 10 2012May 11 2012Evidence is beginning to be put forward that demonstrates the role of the chromosphere in supplying energy and mass to the corona. We aim to assess the role of chromospheric jets in active region dynamics. Using a combination of the Hinode/SOT Ca II H ... More

Robotic Laser-Adaptive-Optics Imaging of 715 Kepler Exoplanet Candidates using Robo-AODec 17 2013Jun 03 2014The Robo-AO Kepler Planetary Candidate Survey is designed to observe every Kepler planet candidate host star with laser adaptive optics imaging to search for blended nearby stars, which may be physically associated companions and/or responsible for transit ... More

Population-Weighted Density, Density-Weighted Population, Granularity, Paradoxes: a RecapitulationDec 14 2014Jan 31 2015Quantifying the population density of an urban area is a fraught issue. Measures of density are often defined differently from place to place or applied inconsistently, and arguments abound over just how much of the land surrounding a city should and ... More

Dimension of Marginals of Kronecker Product ModelsNov 10 2015A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. ... More

Transformation Double Categories Associated to 2-Group ActionsDec 31 2013Jan 11 2016Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in category-theoretic terms, ... More

On the edge energy of grapheneDec 12 2017Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma({\bf n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In the case of ... More

The Robo-AO KOI Survey: laser adaptive optics imaging of every Kepler exoplanet candidateAug 01 2016The Robo-AO Kepler Planetary Candidate Survey is observing every Kepler planet candidate host star (KOI) with laser adaptive optics imaging to hunt for blended nearby stars which may be physically associated companions. With the unparalleled efficiency ... More

Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behaviorDec 23 2009Jun 25 2010Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus reverse-engineering attempts. ... More

Piece of CAKE: A Comprehensive Queue Management Solution for Home GatewaysApr 20 2018May 25 2018The last several years has seen a renewed interest in smart queue management to curb excessive network queueing delay, as people have realised the prevalence of bufferbloat in real networks. However, for an effective deployment at today's last mile connections, ... More

Discerning Exoplanet Migration Models Using Spin-Orbit MeasurementsOct 19 2010We investigate the current sample of exoplanet spin-orbit measurements to determine whether a dominant planet migration channel can be identified, and at what confidence. We use the predictions of Kozai migration plus tidal friction (Fabrycky and Tremaine ... More

On the Low False Positive Probabilities of Kepler Planet CandidatesJan 28 2011Jun 10 2011We present a framework to conservatively estimate the probability that any particular planet-like transit signal observed by the Kepler mission is in fact a planet, prior to any ground-based follow-up efforts. We use Monte Carlo methods based on stellar ... More

The mildly nonlinear imprint of structure on the CMBDec 03 1999Dec 05 1999I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included ... More

Are pre-main-sequence stars older than we thought?Jul 14 2009We fit the colour-magnitude diagrams of stars between the zero-age main-sequence and terminal-age main sequence in young clusters and associations. The ages we derive are a factor 1.5 to 2 longer than the commonly used ages for these regions, which are ... More

On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnetJun 28 1999The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schr\"odinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izergin ... More

A Structured Variational Auto-encoder for Learning Deep Hierarchies of Sparse FeaturesFeb 28 2016In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian units allow spike-and-slab ... More

What Bell DidAug 08 2014On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier arguments of Einstein, Podolsky and Rosen. ... More

Reply to WernerAug 08 2014Reinhard Werner authored a comment on my paper "What Bell Did", disputing the conclusion and argumentation of the paper. This is my reply.

Euclidean-valued group cohomology is always reducedOct 11 2013Nov 25 2013If G is a countable discrete group acting linearly on a finite-dimensional vector space over any topological field, then the groups of coboundaries are closed for the product topology in all degrees, and hence the cohomology is reduced in all degrees. ... More

Correlation functions, null polygonal Wilson loops, and local operatorsOct 18 2011Jul 30 2012We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By ... More

The LSST Data Processing Software Stack: Summer 2015 ReleaseNov 20 2015The Large Synoptic Survey Telescope (LSST) is an 8-m optical ground-based telescope being constructed on Cerro Pachon in Chile. LSST will survey half the sky every few nights in six optical bands. The data will be transferred to NCSA and within 60 seconds ... More

The Labyrinth of Quantum LogicFeb 06 2018Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of "classical" is often not precisely specified. ... More

Evolutionary Innovations and Where to Find Them: Routes to Open-Ended Evolution in Natural and Artificial SystemsJun 05 2018Feb 21 2019This paper presents a high-level conceptual framework to help orient the discussion and implementation of open-endedness in evolutionary systems. Drawing upon earlier work by Banzhaf et al., three different kinds of open-endedness are identified: exploratory, ... More

Discrete Hashimoto surfaces and a doubly discrete smokering flowJul 25 2000B\"acklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schr\"odinger equation ... More

A Geometric Embedding for Standard Analytic ModulesMar 28 2005Jun 11 2007In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector bundle defined ... More

The geometry of model spaces for probability-preserving actions of sofic groupsDec 04 2015Jun 06 2016Bowen's notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the `model spaces'. The metric ... More

The elementary obstruction and the Weil restrictionDec 20 2007Mar 31 2009In this text we investigate the good behaviour of the elementary obstruction, introduced by Colliot-Thelene and Sansuc. This is an obstruction to the existence of a rational points on certain algebraic varieties. Assuming some conditions on the Picard ... More

On the regularity over positively graded algebrasDec 20 2006Aug 30 2007We study the relationship between the Tor-regularity and the local-regularity over a positively graded algebra defined over a field which coincide if the algebra is a standard graded polynomial ring. In this case both are characterizations of the so-called ... More

Radio detection of cosmic rays with the Auger Engineering Radio ArrayMay 13 2019The Auger Engineering Radio Array (AERA) complements the Pierre Auger Observatory with 150 radio-antenna stations measuring in the frequency range from 30 to 80 MHz. With an instrumented area of 17 km$^2$, the array constitutes the largest cosmic-ray ... More

Uniform stability of linear evolution equations, with applications to parallel transportsFeb 12 2015I prove the bistability of linear evolution equations $x' = A(t)x$ in a Banach space $E$, where the operator-valued function $A$ is of the form $A(t) = f'(t)G(t,f(t))$ for a binary operator-valued function $G$ and a scalar function $f$. The constant that ... More

Behaviour of entropy under bounded and integrable orbit equivalenceApr 04 2016Nov 07 2016Let $G$ and $H$ be infinite finitely generated amenable groups. This paper studies two notions of equivalence between actions of such groups on standard Borel probability spaces. They are defined as stable orbit equivalences in which the associated cocycles ... More

Towards a Noether-like conservation law theorem for one dimensional reversible cellular automataDec 01 2003Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics. We take the ... More

Electroweak Physics Results from NuTeVMay 22 2002NuTeV has performed precise measurements of neutral-current to charged-current cross section ratios using intense high energy neutrino and anti-neutrino beams on a primarily steel target at the Fermilab Tevatron. A null hypothesis test of the standard ... More

Beyond the RPA on the cheap: improved correlation energies with the efficient "Radial Exchange Hole" kernelAug 27 2012The "ACFD-RPA" correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here we present a parameter-free exchange-correlation ... More

Inner Accretion Disk Edges in a Kerr-Like SpacetimeApr 30 2013Jun 06 2013According to the no-hair theorem, astrophysical black holes are uniquely described by the Kerr metric. In order to test this theorem with observations in either the electromagnetic or gravitational-wave spectra, several Kerr-like spacetimes have been ... More

Beyond the Standard Model Higgs Boson Searches at the TevatronDec 02 2010Results are presented for beyond the Standard Model Higgs boson searches using up to 4.2 fb-1 of data from Run II at the Tevatron. No significant excess is observed in any of the channels so 95% confidence level limits are presented.

Sgr A* and General RelativityDec 11 2015May 09 2016General relativity has been widely tested in weak gravitational fields but still stands largely untested in the strong-field regime. According to the no-hair theorem, black holes in general relativity depend only on their masses and spins and are described ... More

Invariant Set Theory: Violating Measurement Independence without Fine Tuning, Conspiracy, Constraints on Free Will or RetrocausalityJul 07 2015Nov 06 2015Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe $U$ can be considered a deterministic dynamical system evolving precisely on a (suitably constructed) fractal dynamically ... More

The ECMWF Ensemble Prediction System: Looking Back (more than) 25 Years and Projecting Forward 25 YearsMar 16 2018This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast ... More

Modern Python at the Large Synoptic Survey TelescopeDec 01 2017The LSST software systems make extensive use of Python, with almost all of it initially being developed solely in Python 2. Since LSST will be commissioned when Python 2 is end-of-lifed it is critical that we have all our code support Python 3 before ... More

Time Symmetric Quantum Theory Without RetrocausalityJul 24 2017In their recent paper "Is a Time Symmetric Interpretation of Quantum Theory Possible Without Retrocausality?", Matthew Leifer and Matthew Pusey argue that the answer to their title question is "no". Unfortunately, the central proof offered in the paper ... More

Gluing and deformations of asymptotically cylindrical special LagrangiansSep 27 2017We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, ... More

Contrastive Explanation: A Structural-Model ApproachNov 07 2018The topic of causal explanation in artificial intelligence has gathered interest in recent years as researchers and practitioners aim to increase trust and understanding of intelligent decision-making and action. While different sub-fields have looked ... More

Free Semialgebraic GeometryFeb 28 2019This is a survey article on the currently very active research area of free (=non-commutative) real algebra and geometry. We first review some of the important results from the commutative theory, and then explain similarities and differences as well ... More

Comparing invariants of SK1Mar 08 2010Mar 18 2010In this text, we compare several invariants of the reduced Whitehead group SK1 of a central simple algebra. For biquaternion algebras, we compare a generalised invariant of Suslin as constructed by the author in a previous article to an invariant introduced ... More

A Characterization of Morphic Words with Polynomial GrowthMar 24 2019A morphic word is obtained by iterating a morphism to generate an infinite word, and then applying a coding. We characterize morphic words with polynomial growth in terms of a new type of infinite word called a $\textit{zigzag word}$. A zigzag word is ... More

LLL & ABCJul 24 2003Dec 11 2003This note is an observation that the LLL algorithm applied to prime powers can be used to find "good" examples for the ABC and Szpiro conjectures.

Observable Equivalence between General Relativity and Shape DynamicsMar 29 2012In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with General Relativity ... More

Shape DynamicsAug 26 2011General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads to a constraint ... More

Reduction of a Quantum TheoryDec 21 2006This paper serves as a preparation of work that focuses on extracting cosmological sectors from Loop Quantum Gravity. We start with studying the extraction of subsystems from classical systems. A classical Hamiltonian system can be reduced to a subsystem ... More

Deducing the Density Hales-Jewett Theorem from an infinitary removal lemmaMar 09 2009Apr 19 2011We offer a new proof of Furstenberg and Katznelson's density version of the Hales-Jewett Theorem: For any $\delta > 0$ there is some $N_0 \geq 1$ such that whenever $A \subseteq [k]^N$ with $N \geq N_0$ and $|A|\geq \delta k^N$, $A$ contains a \textbf{combinatorial ... More

Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groupsMay 27 2011Jul 01 2016Let $G$ be a connected nilpotent Lie group. Given probability-preserving $G$-actions $(X_i,\Sigma_i,\mu_i,u_i)$, $i=0,1,...,k$, and also polynomial maps $\phi_i:\mathbb{R}\to G$, $i=1,...,k$, we consider the trajectory of a joining $\lambda$ of the systems ... More

An alternative ending to "Pleasant extensions retaining algebraic structure''Oct 06 2009May 24 2010The culmination of the papers (arXiv:0905.0518, arXiv:0910.0909) was a proof of the norm convergence in $L^2(\mu)$ of the quadratic nonconventional ergodic averages \frac{1}{N}\sum_{n=1}^N(f_1\circ T_1^{n^2})(f_2\circ T_1^{n^2}T_2^n)\quad\quad f_1,f_2\in ... More

On semidefinite representations of non-closed setsJul 16 2009Dec 17 2009Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinitely representable sets. Both kinds of sets are of practical use in polynomial optimization, since they occur as feasible sets in semidefinite ... More

The one-arm exponent for mean-field long-range percolationNov 11 2014Consider a long-range percolation model on $\mathbb{Z}^d$ where the probability that an edge $\{x,y\} \in \mathbb{Z}^d \times \mathbb{Z}^d$ is open is proportional to $\|x-y\|_2^{-d-\alpha}$ for some $\alpha >0$ and where $d > 3 \min\{2,\alpha\}$. We ... More

Multiple recurrence and the structure of probability-preserving systemsJun 02 2010Jun 08 2010In 1975 Szemer\'edi proved the long-standing conjecture of Erd\H{o}s and Tur\'an that any subset of $\bbZ$ having positive upper Banach density contains arbitrarily long arithmetic progressions. Szemer\'edi's proof was entirely combinatorial, but two ... More

Who discovered positron annihilation?Sep 13 2018In the early 1930s, the positron, pair production, and, at last, positron annihilation were discovered. Over the years, several scientists have been credited with the discovery of the annihilation radiation. Commonly, Thibaud and Joliot have received ... More

Formal Semantics and Soundness of a Translation from Event-B Actions to SQL StatementsJun 08 2016The EventB2SQL tool translates Event-B models to persistent Java applications that store the state of the model in a relational database. Most Event-B assignments are translated directly to SQL database modification statements, which can then be executed ... More

Black Hole Formation in Lovelock GravityAug 10 2014We first derive the Hamiltonian for Lovelock gravity and find that it takes the same form as in general relativity when written in terms of the Misner-Sharp mass function. We then minimally couple the action to matter fields to find Hamilton's equations ... More

Distribution and Generalized Center in Planar NearringsJul 05 2016Nov 10 2016Planar nearrings play an important role in nearring theory, both from the structural side as being close to generalised nearfields, as well as from an applications perspective, in geometry and designs. We investigate the distributive elements of planar ... More

Closed Systems of Invertible MapsDec 21 2015We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have connections ... More

X-ray Probes of Black Hole Accretion Disks for Testing the No-Hair TheoremJan 12 2015The spins of a number of supermassive and stellar-mass black holes have been measured based on detections of thermal continuum emission and relativistically broadened iron lines in their x-ray spectra. Likewise, quasiperiodic variability has been observed ... More

Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons LearnedJun 26 2014Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines ... More

Implementing and Automating Fixed-Form Variational Posterior Approximation through Stochastic Linear RegressionJan 09 2014We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer details on ... More

Determining the CKM Parameter Vcd from nuN Charm ProductionAug 14 1997The formalism for extracting the CKM parameter $V_{cd}$ from $\nu N$ production of charm is discussed in some detail. The various model assumptions needed are clearly pointed out. A direct determination from neutrino induced dimuon production requires ... More

Unfolding algorithms and tests using RooUnfoldMay 05 2011The RooUnfold package provides a common framework to evaluate and use different unfolding algorithms, side-by-side. It currently provides implementations or interfaces for the Iterative Bayes, Singular Value Decomposition, and TUnfold methods, as well ... More

Search for Supersymmetric Neutral Higgs Bosons at the TevatronOct 26 2007Recent preliminary results obtained by the CDF and DO Collaborations on searches for Higgs bosons beyond the Standard Model at Run II of the Tevatron are discussed. The data, corresponding to integrated luminosities of up to 1 fb-1, are compared to theoretical ... More

General relativity as a two-dimensional CFTMay 21 2015The tree-level scattering amplitudes of general relativity encode the full non-linearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative expansion of the Einstein-Hilbert ... More

Evolution in Virtual WorldsOct 17 2017This chapter discusses the possibility of instilling a virtual world with mechanisms for evolution and natural selection in order to generate rich ecosystems of complex organisms in a process akin to biological evolution. Some previous work in the area ... More

Requirements for Open-Ended Evolution in Natural and Artificial SystemsJul 27 2015Open-ended evolutionary dynamics remains an elusive goal for artificial evolutionary systems. Many ideas exist in the biological literature beyond the basic Darwinian requirements of variation, differential reproduction and inheritance. I argue that these ... More

Artificial Life and the Web: WebAL Comes of AgeJul 22 2014A brief survey is presented of the first 18 years of web-based Artificial Life ("WebAL") research and applications, covering the period 1995-2013. The survey is followed by a short discussion of common methodologies employed and current technologies relevant ... More

Devil's crevasse and macroscopic entanglement in two-component Bose-Einstein condensatesMay 22 2013Spin coherent states are the matter equivalent of optical coherent states, where a large number of two component particles form a macroscopic state displaying quantum coherence. Here we give a detailed study of entanglement generated between two spin-1/2 ... More

Experimental summary of the $52^{\rm nd}$ Rencontres de Moriond session on Electroweak Interactions and Unified TheoriesJul 17 2017Jul 18 2017A summary, from an experimental perspective, of the $52^{\rm nd}$ Rencontres de Moriond session on Electroweak Interactions and Unified Theories is presented.

Explanation in Artificial Intelligence: Insights from the Social SciencesJun 22 2017Aug 15 2018There has been a recent resurgence in the area of explainable artificial intelligence as researchers and practitioners seek to make their algorithms more understandable. Much of this research is focused on explicitly explaining decisions or actions to ... More

Beyond Worst-Case AnalysisJun 26 2018In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like linear programming, ... More

Radio Detection of Cosmic Rays -- Achievements and Future PotentialApr 18 2017When modern efforts for radio detection of cosmic rays started about a decade ago, hopes were high but the true potential was unknown. Since then, we have achieved a detailed understanding of the radio emission physics and have consequently succeeded ... More

Gluing and deformation of asymptotically cylindrical Calabi-Yau manifolds in complex dimension threeMar 27 2017We develop some consequences of the connection between Calabi-Yau structures and torsion-free $G_2$ structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching asymptotically ... More

Prediction of Infinite Words with AutomataMar 08 2016In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the predictor's guesses ... More

Extendability of parallel sections in vector bundlesJul 07 2014Aug 26 2015We address the following question: Given a differentiable manifold $M$ what are the open subsets $U$ of $M$ such that, for all vector bundles $E$ over $M$ and all linear connections $\nabla$ on $E$, any $\nabla$-parallel section in $E$ defined on $U$ ... More

On the geometry of a class of invariant measures and a problem of AldousAug 16 2008In his 1985 survey of notions of exchangeability, Aldous introduced a form of exchangeability corresponding to the symmetries of the infinite discrete cube, and asked whether these exchangeable probability measures enjoy a representation theorem similar ... More

Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applicationsMay 05 2009Nov 11 2009We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such extensions rests on ... More

Pleasant extensions retaining algebraic structure, IMay 05 2009Sep 07 2014In two recent papers we introduced some new techniques for constructing an extension of a probability-preserving system $T:\mathbb{Z}^d\curvearrowright (X,\mu)$ that enjoys certain desirable properties in connexion with the asymptotic behaviour of some ... More

Positive Polynomials and Sequential Closures of Quadratic ModulesJul 21 2008Let S be a basic closed semi-algebraic set in R^n and P the corresponding preordering in R[X_1,...,X_n]. We examine for which polynomials f there exist identities f+\ep q \in P for all \ep>0. These are precisely the elements of the sequential closure ... More

Non-conventional ergodic averages for several commuting actions of an amenable groupSep 17 2013Jun 19 2014Let $(X,\mu)$ be a probability space, $G$ a countable amenable group and $(F_n)_n$ a left F\o lner sequence in $G$. This paper analyzes the non-conventional ergodic averages \[\frac{1}{|F_n|}\sum_{g \in F_n}\prod_{i=1}^d (f_i\circ T_1^g\cdots T_i^g)\] ... More

Ergodic-theoretic implementations of the Roth density-increment argumentMay 27 2011Jul 21 2013We exhibit proofs of two ergodic-theoretic results in the study of multiple recurrence using an analog of the density-increment argument of Roth and Gowers: Furstenberg's Multiple Recurrence Theorem (which implies Szemer\'edi's Theorem), and a two-dimensional ... More

Detection and effects of meteoric smoke particles in the atmosphereJan 16 2018Sep 03 2018These are the lecture notes of a trial lecture on the given topic "The detection and effects of meteoric debris in the atmosphere and why we should care". I have shortened the title a little, while I have expanded on the contents. First, I discuss some ... More

High Energy Muon Momentum Estimation from Multiple Coulomb Scattering in Dense DetectorsMay 09 1997A method is described for estimating muon track momentum from the distribution of hits along tracks in dense calorimeters due to multiple Coulomb scattering (MCS). The method requires only well-aligned conventional drift chambers or similar tracking devices ... More

Background field approach to electromagnetic properties of baryonsNov 15 2011Dec 13 2011We investigate the self-energies of particles in an external magnetic field $B$. The dependence is generally of the type $\sqrt{P(B)}$ with $P$ a polynomial in $B$ and the participating masses. The non-analytic point depends on the mass and charge constellations, ... More

On exchangeable random variables and the statistics of large graphs and hypergraphsJan 10 2008May 26 2008De Finetti's classical result of [18] identifying the law of an exchangeable family of random variables as a mixture of i.i.d. laws was extended to structure theorems for more complex notions of exchangeability by Aldous [1,2,3], Hoover [41,42], Kallenberg ... More

On local search and LP and SDP relaxations for k-Set PackingJul 27 2015Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set problem. In this ... More