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M-STAR: A Modular, Evidence-based Software Trustworthiness FrameworkJan 17 2018Despite years of intensive research in the field of software vulnerabilities discovery, exploits are becoming ever more common. Consequently, it is more necessary than ever to choose software configurations that minimize systems' exposure surface to these ... More

Analyzing Business Process Anomalies Using AutoencodersMar 03 2018Businesses are naturally interested in detecting anomalies in their internal processes, because these can be indicators for fraud and inefficiencies. Within the domain of business intelligence, classic anomaly detection is not very frequently researched. ... More

Beyond the Hype: On Using Blockchains in Trust Management for AuthenticationNov 13 2017Trust Management (TM) systems for authentication are vital to the security of online interactions, which are ubiquitous in our everyday lives. Various systems, like the Web PKI (X.509) and PGP's Web of Trust are used to manage trust in this setting. In ... More

BINet: Multi-perspective Business Process Anomaly ClassificationFeb 08 2019In this paper, we introduce BINet, a neural network architecture for real-time multi-perspective anomaly detection in business process event logs. BINet is designed to handle both the control flow and the data perspective of a business process. Additionally, ... More

A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph TransformationMay 14 2018In the communication systems domain, constructing and maintaining network topologies via topology control (TC) algorithms is an important cross-cutting research area. Network topologies are usually modeled using attributed graphs whose nodes and edges ... More

PABO: Mitigating Congestion via Packet Bounce in Data Center NetworksFeb 21 2018Aug 03 2018In today's data center, a diverse mix of throughput-sensitive long flows and delay-sensitive short flows are commonly presented in shallow-buffered switches. Long flows could potentially block the transmission of delay-sensitive short flows, leading to ... More

I Trust my Zombies: A Trust-enabled BotnetDec 11 2017Defending against botnets has always been a cat and mouse game. Cyber-security researchers and government agencies attempt to detect and take down botnets by playing the role of the cat. In this context, a lot of work has been done towards reverse engineering ... More

A Systematic Approach to Constructing Incremental Topology Control Algorithms Using Graph TransformationMay 09 2018Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee certain required ... More

Search-based Methods to Bound Diagnostic Probabilities in Very Large Belief NetsMar 20 2013Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to find the most ... More

Flat Space Limit of (Higher-Spin) Cardy FormulaAug 29 2014Apr 18 2015In this note I derive the flat space limit of the modified Cardy formula associated with inner horizons and show that it reproduces the correct Galilean conformal field theory counting of flat space cosmology microstates. l also determine the entropy ... More

Twisted K-theory, old and newJan 27 2007Aug 23 2007Twisted K-theory has its origins in the author's PhD thesis [27] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper with P. Donovan http://www.numdam.org/item?id=PMIHES_1970__38__5_0 The objective of this paper is to revisit the subject ... More

Element Abundances through the Cosmic AgesMar 12 2003The horizon for studies of element abundances has expanded dramatically in the last ten years. Once the domain of astronomers concerned chiefly with stars and nearby galaxies, this field has now become a key component of observational cosmology, as technological ... More

Friendly Artificial Intelligence: the Physics ChallengeSep 02 2014Sep 03 2014Relentless progress in artificial intelligence (AI) is increasingly raising concerns that machines will replace humans on the job market, and perhaps altogether. Eliezer Yudkowski and others have explored the possibility that a promising future for humankind ... More

Cosmological neutrino bounds for non-cosmologistsMar 24 2005I briefly review cosmological bounds on neutrino masses and the underlying gravitational physics at a level appropriate for readers outside the field of cosmology. For the case of three massive neutrinos with standard model freezeout, the current 95% ... More

The importance of quantum decoherence in brain processesJul 05 1999Nov 10 1999Based on a calculation of neural decoherence rates, we argue that that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally ... More

The Interpretation of Quantum Mechanics: Many Worlds or Many Words?Sep 15 1997As cutting-edge experiments display ever more extreme forms of non-classical behavior, the prevailing view on the interpretation of quantum mechanics appears to be gradually changing. A (highly unscientific) poll taken at the 1997 UMBC quantum mechanics ... More

On the dimensionality of spacetimeFeb 25 1997Apr 05 1997Some superstring theories have more than one effective low-energy limit, corresponding to classical spacetimes with different dimensionalities. We argue that all but the 3+1-dimensional one might correspond to ``dead worlds'', devoid of observers, in ... More

How to make maps from CMB data without losing informationNov 18 1996Mar 17 1997The next generation of CMB experiments can measure cosmological parameters with unprecedented accuracy - in principle. To achieve this in practice when faced with such gigantic data sets, elaborate data analysis methods are needed to make it computationally ... More

An icosahedron-based method for pixelizing the celestial sphereOct 14 1996For power spectrum estimation it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind the ``COBE sky cube" was defined. This paper has as central theme to further improve on this elegant ... More

How did it all begin?Aug 20 2005How did it all begin? Although this question has undoubtedly lingered for as long as humans have walked the Earth, the answer still eludes us. Yet since my grandparents were born, scientists have been able to refine this question to a degree I find truly ... More

Dark matter and dark energy from pockets of gravity created by quantum tunneling of the inflaton potentialSep 17 2013Dec 13 2013It is usually assumed that during the reheating period of inflation the inflaton field behaves coherently and follows a classical path. It is pointed out that a background inflaton field \phi_0 falling down a potential density V(\phi) can and frequently ... More

Quantization and SemiclassicsSep 01 2010This course is aimed at graduate students in physics in mathematics and designed to give a comprehensive introduction to Weyl quantization and semiclassics via Egorov's theorem. Chapter 2 gives a quick overview of classical and quantum mechanics on R^d. ... More

Configuration Space Methods and Time Ordering for Scalar Propagators in (Anti and) de Sitter SpacetimesJun 13 2007Aug 29 2007In this master thesis a configuration space method presented by C. Dullemond and E. van Beveren for computing all propagators of a scalar field (Wightman, Hadamard and Schwinger functions,retarded, advanced and Feynman propagator) is reviewed for four-dimensional ... More

Multiple Space Debris Collecting Mission -- Optimal Mission PlanningApr 05 2014This paper addresses the problem of planning successive Space Debris Collecting missions so that they can be achieved at minimal cost by a generic vehicle. The problem mixes combinatorial optimization to select and order the debris among a list of candidates, ... More

Low-Thrust Transfer Between Circular Orbits Using Natural PrecessionMar 02 2015The minimum-fuel low-thrust transfer between circular orbits is formulated using the Edelbaum's averaged dynamics with the addition of the nodal precession due to the first zonal term. The extremal analysis shows that an optimal transfer is composed of ... More

Modified logarithmic Sobolev inequalities for canonical ensemblesJun 06 2013Jun 19 2014In this paper, we prove modified logarithmic Sobolev inequalities for canonical ensembles with superquadratic single-site potential. These inequalities were introduced by Bobkov and Ledoux, and are closely related to concentration of measure and transport-entropy ... More

Simulating Linear Logic in 1-Only Linear LogicSep 09 2017Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than (modalized) ... More

A sharp symmetrized form of Talagrand's transport-entropy inequality for the Gaussian measureJun 17 2018This note presents a sharp transport-entropy inequality that improves on Talagrand's inequality for the Gaussian measure, arising as a dual formulation of the functional Santal\'o inequality. We also discuss some extensions and connections with concentration ... More

Stein kernels and moment mapsApr 12 2018Jun 16 2018We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Amp\`ere equation. As a consequence, we show how regularity bounds on these maps control the rate of convergence in the classical central limit ... More

The Nonexistence of Noncompact Type-I Ancient 3-d $κ$-Solutions of Ricci Flow with Positive CurvatureJan 26 2018In this short paper, we show there do not exist three-dimensional noncompact $\kappa$-solutions of Ricci flow that have positive curvature and satisfy a Type-I bound. This represents progress towards the proof of Perelman's conjecture that the only complete ... More

Inflaton vacuum fluctuations as dark matter and the potential V(phi) as dark energyDec 13 2017Jan 21 2019It is shown, using quantum field theory in curved spacetime, how the expansion of the universe during inflation produces an aggregate of particles and inflaton vacuum fluctuations at a temperature of 5x10^17GeV and dense enough to make reheating unnecessary. ... More

Conformal Group Actions on Generalized Kuramoto OscillatorsDec 16 2018Dec 18 2018This paper unifies the recent results on generalized Kuramoto Model reductions. Lohe took a coupled system of $N$ bodies on $S^d$ governed by the Kuramoto equations $\dot{x_i} = \Omega x_i + X - \langle x_i, X \rangle x_i$ and used the method of Watanabe ... More

Higher-order Stein kernels for Gaussian approximationDec 06 2018We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics on the space ... More

Deformation and rigidity of simplicial group actions on treesJul 02 2001May 08 2002We study a notion of deformation for simplicial trees with group actions (G-trees). Here G is a fixed, arbitrary group. Two G-trees are related by a deformation if there is a finite sequence of collapse and expansion moves joining them. We show that this ... More

On uniqueness of JSJ decompositions of finitely generated groupsOct 17 2001May 22 2003We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the ... More

A Free Boundary Problem for the Parabolic Poisson KernelOct 19 2015We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nystr\"om, and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson kernel ... More

Splittings of generalized Baumslag-Solitar groupsFeb 02 2005Mar 11 2006We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity ... More

Error estimates for the finite element approximation of bilinear boundary control problemsJan 11 2019In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin coefficient from ... More

Two-parameter Asymptotics in Magnetic Weyl CalculusSep 18 2008May 28 2010This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter \eps, the case of small coupling $\lambda$ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl ... More

Partial flag incidence algebrasMay 05 2016The $n^{th}$ partial flag incidence algebra of a poset $P$ is the set of functions from $P^n$ to some ring which are zero on non-partial flag vectors. These partial flag incidence algebras for $n>2$ are not commutative, not unitary, and not associative. ... More

Genealogical distance under selectionApr 21 2018We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding distance in ... More

Return Probabilities of Random WalksDec 14 2015Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely determines the random ... More

A zero point energy explanation of a peak in liquid helium's dynamic structure factorMay 27 1997Recent high resolution experiments show a strong peak at Q = 1.9 Ang^{-1} in liquid helium's dynamic structure factor that exhibits a singular dependence on temperature. The theoretical situation is briefly reviewed, and the comment is made that the simplest ... More

Towards a q-analogue of the Harer-Zagier formula via rook placementsDec 10 2014In 1986 Harer and Zagier computed a certain matrix integral to determine an influential closed-form formula for the number of (orientable) one-face maps on n vertices colored from N colors. Kerov (1997) provided a proof which computed the same matrix ... More

Abelian gauge symmetries and fluxed instantons in compactifications of type IIB and F-theoryFeb 15 2014We discuss the role of Abelian gauge symmetries in type IIB orientifold compactifications and their F-theory uplift. Particular emphasis is placed on U(1)s which become massive through the geometric St\"uckelberg mechanism in type IIB. We present a proposal ... More

On Regularity of J-holomorphic MapsSep 03 2014We provide a short proof that an $L^2_1$ and $J$-holomorphic curve is in fact smooth. As an application, we deduce a removal of singularity theorem for curves of finite energy.

Exploiting the Statistics of Learning and InferenceFeb 26 2014Mar 04 2014When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by exploiting their inherent ... More

Practical Issues in Constructing a Bayes' Belief NetworkMar 27 2013Bayes belief networks and influence diagrams are tools for constructing coherent probabilistic representations of uncertain knowledge. The process of constructing such a network to represent an expert's knowledge is used to illustrate a variety of techniques ... More

Twisted bundles and twisted K-theoryDec 12 2010We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and bundles of modules ... More

Le theoreme de periodicite en K-theorie hermitienneOct 26 2008Bott periodicity plays an important role in topological K-theory. The purpose of this paper is to extend the periodicity theorem in a discrete context, where all classical groups are involved and not just the general linear group. The present paper generalizes ... More

Clifford modules and twisted K-theoryJan 17 2008The purpose of this shord paper is to make the link between the fundamental work of Atiyah, Bott and Shapiro (MR0167985/29/5250) and twisted K-theory (MR0282363/43/8075). This link was implicit for a long time in the literature (for the description of ... More

The First Galaxies: Clues from Element AbundancesJan 06 2000It has recently become possible to measure directly the abundances of several chemical elements in a variety of environments at redshifts up to z = 5. In this review I summarise the latest observations of Lyman break galaxies, damped Lyman alpha systems ... More

Deuterium at High Redshifts: Recent Advances and Open IssuesJan 19 2006Among the light elements created in the Big Bang, deuterium is one of the most difficult to detect but is also the one whose abundance depends most sensitively on the density of baryons. Thus, although we still have only a few positive identifications ... More

How to measure CMB power spectra without losing informationNov 21 1996Mar 12 1997A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties: (1) It is unbeatable in the sense that no other method can measure C_l with smaller error ... More

Nuclear War from a Cosmic PerspectiveMay 01 2015May 21 2015I discuss the impact of computer progress on nuclear war policy, both by enabling more accurate nuclear winter simulations and by affecting the probability of war starting accidentally. I argue that from a cosmic perspective, humanity's track record of ... More

What does inflation really predict?Oct 12 2004Mar 11 2005If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Omega_tot), dark energy (rho_Lambda, ... More

Rational curves in the moduli of supersingular K3 surfacesJul 30 2015We show how to construct non-isotrivial families of supersingular K3 surfaces over rational curves using a relative form of the Artin-Tate isomorphism and twisted analogues of Bridgeland's results on moduli spaces of stable sheaves on elliptic surfaces. ... More

The Large Hadron Electron Collider ProjectAug 20 2009A Conceptual Design Report (CDR) for the Large Hadron Electron Collider, the LHeC, is being prepared, to which an introduction was given for the plenary panel discussion on the future of deep inelastic scattering held at DIS09. This is briefly summarised ... More

Improved Measures of Integrated InformationJan 11 2016Nov 29 2016Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated and classified ... More

The pentagram map and Y-patternsMay 04 2010Apr 15 2011The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its "shortest" diagonals, and output the smaller polygon which they cut out. We employ the machinery of cluster algebras to obtain ... More

Twisted sheaves and the period-index problemNov 09 2005May 25 2007We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber's ... More

Moduli of twisted orbifold sheavesMar 23 2008Feb 02 2010We study stacks of slope-semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope-semistable sheaves on smooth projective surfaces. ... More

Remarks on the stack of coherent algebrasMar 02 2006Jun 20 2006We consider the stack of coherent algebras with proper support, a moduli problem generalizing Alexeev and Knutson's stack of branchvarieties to the case of an Artin stack. The main results are proofs of the existence of Quot and Hom spaces in greater ... More

Derivation degree sequences of non-free arrangementsJul 19 2018In this note we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements, free arrangements ... More

Markov chains under nonlinear expectationMar 09 2018In this paper, we consider nonlinear continuous-time Markov chains with a finite state space. We define so-called $Q$-operators as an extension of $Q$-matrices to a nonlinear setup, where the nonlinearity is due to parameter uncertainty. The main result ... More

Fast MLE Computation for the Dirichlet MultinomialMay 01 2014Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading through the ... More

Structure of a condensate for the Bose fluid in a vesselJan 10 2012Mar 09 2014We discuss a possibility of a fragmented structure of the condensate for an interacting Bose systems placed in a vessel. See also Erratum.

Cycles positifs dans les variétés abéliennesSep 12 2011Sep 13 2011In the first part, we study the structure of the R-algebra generated by the Hodge classes on the self-product A^e of a very general principally polarized abelian variety A. In the second part, we compare various notions of positivity for cycles of higher ... More

Improved Measures of Integrated InformationJan 11 2016Jul 18 2016Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated and classified ... More

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problemAug 15 2011Aug 15 2012We analyze cosmology assuming unitary quantum mechanics, using a tripartite partition into system, observer and environment degrees of freedom. This generalizes the second law of thermodynamics to "The system's entropy can't decrease unless it interacts ... More

Comparing and combining CMB datasetsSep 01 1998Feb 08 1999One of the best ways of spotting previously undetected systematic errors in CMB experiments is to compare two independent observations of the same region. We derive a set of tools for comparing and combining CMB data sets, applicable also in the common ... More

Removing real-world foregrounds from CMB mapsDec 03 1997Feb 20 1998Most work on foreground removal has treated the case where the frequency dependence of all components is perfectly known and independent of position. In contrast, real-world foregrounds are generally not perfectly correlated between frequencies, with ... More

Measuring cosmological parameters with galaxy surveysJun 19 1997Dec 16 1997We assess the accuracy with which future galaxy surveys can measure cosmological parameters by deriving a handy approximation that we validate numerically. We find that galaxy surveys are quite complementary to future Cosmic Microwave Background (CMB) ... More

CMB mapping experiments: a designer's guideMay 24 1997Jul 29 1997We apply state-of-the art data analysis methods to a number of fictitious CMB mapping experiments, including 1/f noise, distilling the cosmological information from time-ordered data to maps to power spectrum estimates, and find that in all cases, the ... More

Does the universe in fact contain almost no information?Mar 07 1996At first sight, an accurate description of the state of the universe appears to require a mind-bogglingly large and perhaps even infinite amount of information, even if we restrict our attention to a small subsystem such as a rabbit. In this paper, it ... More

A method for extracting maximum resolution power spectra from microwave sky mapsDec 18 1994Jul 25 1996A method for extracting maximal resolution power spectra from microwave sky maps is presented and applied to the 2 year COBE data, yielding a power spectrum that is consistent with a standard n=1, Q=20 micro-Kelvin model. By using weight functions that ... More

The Mathematical UniverseApr 05 2007Oct 08 2007I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe ... More

Parallel UniversesFeb 07 2003I survey physics theories involving parallel universes, which form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic universe, which contains Hubble ... More

Cosmological constraints from current CMB and SN 1a data: a brute force 8 parameter analysisSep 16 1998Feb 02 1999We describe constraints on a ``standard'' 8 parameter open cold dark matter (CDM) model from the most recent CMB and SN1a data. Our parameters are the densities of CDM, baryons, vacuum energy and curvature, the reionization optical depth, and the normalization ... More

Doppler peaks and all that: CMB anisotropies and what they can tell usNov 30 1995The power spectrum of fluctuations in the cosmic microwave background (CMB) depends on most of the key cosmological parameters. Accurate future measurements of this power spectrum might therefore allow us to determine h, Omega, Omega_b, Lambda, n, T/S, ... More

ESTIMATING MICROWAVE POWER SPECTRAFeb 06 1995A new method for estimating the power spectrum $C_l$ from cosmic microwave background (CMB) maps was recently presented by the author and applied to the 2 year COBE data. It was found that the spectral resolution $\Delta l$ for COBE could be more than ... More

Dark matter from primordial metric fields and the term (grad g_{00})^2Jul 03 2011It is a well-known truism, inspired on the general theory of relativity, that gravity gravitates. Here we suggest the possibility that dark matter may be caused by the gravitation of the metric. At first sight this seems impossible since the gravitational ... More

From algebraic K-theory to hermitian K-theorySep 26 2005We introduce a new morphism between algebraic and hermitian K-theory. The topological analog is the Adams operation in real K-theory. From this morphism, we deduce a lower bound for the higher algebraic K-theory of a ring A in terms of the classical Witt ... More

Multiple Space Debris Collecting Mission - Debris selection and Trajectory optimizationJul 01 2011A possible mean to stabilize the LEO debris population is to remove each year 5 heavy debris like spent satellites or launchers stages from that space region. This paper investigates the DeltaV requirement for such a Space Debris Collecting mission. The ... More

Optimal Latent Representations: Distilling Mutual Information into Principal PairsFeb 09 2019Principal component analysis (PCA) is generalized from one to two random vectors, decomposing the correlations between them into a set of "principal pairs" of correlated scalars. For the special case of Gaussian random vectors, PCA decomposes the information ... More

A gradient flow approach to large deviations for diffusion processesMay 15 2014In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such processes. An equivalence ... More

A Two-Phase Free Boundary Problem for Harmonic MeasureSep 15 2014Sep 27 2016We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro and prove a sharp H\"older regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must ... More

Period and index in the Brauer group of an arithmetic surface (with an appendix by Daniel Krashen)Feb 09 2007May 27 2009In this paper we introduce two new ways to split ramification of Brauer classes on surfaces using stacks. Each splitting method gives rise to a new moduli space of twisted stacky vector bundles. By studying the structure of these spaces we prove new results ... More

Numerical Solution of the Simple Monge-Ampère Equation with Non-convex Dirichlet Data on Non-convex DomainsMay 12 2017Jun 01 2017The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Amp\`ere equation is known independently of the convexity of the domain or Dirichlet boundary data -- when the Monge-Amp\`ere equation is posed as Bellman ... More

Stabilization of the Witt groupSep 27 2005Using an idea due to R.Thomason, we define a "homology theory" on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find P. Balmer's higher Witt groups. ... More

Compactified moduli of projective bundlesJun 11 2007May 25 2009We present a method for compactifying stacks of $\PGL_n$-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are irreducible and carry ... More

Family size decomposition of genealogical treesMar 07 2019We study the path of family size decompositions of varying depth of genealogical trees. We prove that this decomposition as a function on (equivalence classes of) ultra-metric measure spaces to the Skorohod space describing the family sizes at different ... More

Geometric Cycles in Floer TheorySep 03 2014We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.

Geometric HomologySep 03 2014The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately addressed. In particular, ... More

Asymptotic Symmetry Algebras in Non-Anti-de-Sitter Higher-Spin Gauge TheoriesOct 24 2012We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdS higher-spin gravity with a focus on AdS$_2\times\mathbb{R}$ and $\mathbb{H}_2\times\mathbb{R}$. We find a consistent set of boundary conditions for spin-3 gravity in the non-principal ... More

On the Choice of Regions for Generalized Belief PropagationJul 11 2012Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a science until this ... More

Many Worlds in ContextMay 13 2009Mar 24 2010Everett's Many-Worlds Interpretation of quantum mechanics is discussed in the context of other physics disputes and other proposed kinds of parallel universes. We find that only a small fraction of the usual objections to Everett's theory are specific ... More

Measuring the metric: a parametrized post-Friedmanian approach to the cosmic dark energy problemJan 22 2001Sep 17 2002We argue for a ``parametrized post-Friedmanian'' approach to linear cosmology, where the history of expansion and perturbation growth is measured without assuming that the Einstein Field Equations hold. As an illustration, a model-independent analysis ... More

Measuring quantum states: an experimental setup for measuring the spatial density matrixJul 25 1996To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure the state is. ... More

Consciousness as a State of MatterMay 02 2014Nov 07 2015I examine the hypothesis that consciousness can be understood as a state of matter, "perceptronium", with distinctive information processing abilities. I explore five basic principles that may distinguish conscious matter from other physical systems such ... More