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An Analysis of ALMA Deep Fields and the Perceived Dearth of High-z GalaxiesJun 14 2018Deep, pencil-beam surveys from ALMA at 1.1-1.3mm have uncovered an apparent absence of high-redshift dusty galaxies, with existing redshift distributions peaking around $z\sim1.5-2.5$. This has led to a perceived dearth of dusty systems at $z>4$, and ... More

Characterizing Extragalactic Anomalous Microwave Emission in NGC 6946 with CARMANov 25 2014Using 1 cm and 3 mm CARMA and 2 mm GISMO observations, we follow up the first extragalactic detection of anomalous microwave emission (AME) reported by Murphy et al. 2010 in an extranuclear region (Enuc. 4) of the nearby face-on spiral galaxy NGC 6946. ... More

350 micron Galactic Center Dust Observations with SHARC IIDec 06 2004We present first and preliminary submillimeter continuum images of the Galactic Center region obtained with the new Caltech Submillimeter Observatory facility camera SHARC II. The instrument allows 350 micron observations with unprecedented sensitivity ... More

Taking Census of Massive, Star-Forming Galaxies formed <1 Gyr After the Big BangMar 13 2019Two decades of effort have been poured into both single-dish and interferometric millimeter-wave surveys of the sky to infer the volume density of dusty star-forming galaxies (DSFGs, with SFR>100M$_\odot$ yr$^{-1}$) over cosmic time. Though obscured galaxies ... More

Dust formation, evolution, and obscuration effects in the very high-redshift universeMay 05 2014The evolution of dust at redshifts z>9, and consequently the dust properties, differs greatly from that in the local universe. In contrast to the local universe, core collapse supernovae (CCSNe) are the only source of thermally-condensed dust. Because ... More

SOFIA observations of S106: Dynamics of the warm gasMar 22 2012Context. The HII region/PDR/molecular cloud complex S106 is excited by a single O-star. The full extent of the warm and dense gas close to the star has not been mapped in spectrally resolved high-J CO or [CII] lines, so the kinematics of the warm, partially ... More

The Primordial Inflation Polarization Explorer (PIPER)Jul 21 2016The Primordial Inflation Polarization ExploreR (PIPER) is a balloon-borne telescope designed to measure the polarization of the Cosmic Microwave Background on large angular scales. PIPER will map 85% of the sky at 200, 270, 350, and 600 GHz over a series ... More

SOFIA Far Infrared Imaging Polarimetry of M82 and NGC 253: Exploring the Super-Galactic WindDec 17 2018We present Far-Infrared polarimetry observations of M82 at 53 and $154~\mu \rm{m}$ and NGC 253 at $89~\mu \rm{m}$, which were taken with HAWC+ in polarimetry mode on the Stratospheric Observatory for Infrared Astronomy (SOFIA). The polarization of M82 ... More

The Brightest Galaxies in the Dark Ages: Galaxies' Dust Continuum Emission During the Reionization EraMay 25 2018Though half of cosmic starlight is absorbed by dust and reradiated at long wavelengths (3$\mu$m-3mm), constraints on the infrared through millimeter galaxy luminosity function (the `IRLF') are poor in comparison to the rest-frame ultraviolet and optical ... More

First detections of the [NII] 122 μm line at high redshift: Demonstrating the utility of the line for studying galaxies in the early universeSep 07 2011Sep 09 2011We report the first detections of the [NII] 122 {\mu}m line from a high redshift galaxy. The line was strongly (> 6{\sigma}) detected from SMMJ02399-0136, and H1413+117 (the Cloverleaf QSO) using the Redshift(z) and Early Universe Spectrometer (ZEUS) ... More

Submillimeter Observations of CLASH 2882 and the Evolution of Dust in this GalaxySep 30 2015Two millimeter observations of the MACS J1149.6+2223 cluster have detected a source that was consistent with the location of the lensed MACS1149-JD galaxy at z=9.6. A positive identification would have rendered this galaxy as the youngest dust forming ... More

On the variation of the Poisson structures of certain moduli spacesOct 29 1997Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the fundamental group ... More

Poisson geometry of flat connections for $\roman{SU}(2)$-bundles on surfacesDec 14 1993In earlier work we have shown that the moduli space $N$ of flat connections for the (trivial) $\roman{SU(2)}$-bundle on a closed surface of genus $\ell \geq 2$ inherits a structure of stratified symplectic space with two connected strata $N_Z$ and $N_{(T)}$ ... More

The Casson-Walker-Lescop Invariant and Link InvariantsJul 11 2000Formulas previously presented for the Casson-Walker invariant are generalized to Lescop's extension. These formulas in terms of linking numbers and surgery coefficients compute the change in Lescop's invariant under crossing changes in a framed link presenting ... More

Why Precision?May 22 2012Jun 07 2012Precision measurements together with exact theoretical calculations have led to steady progress in fundamental physics. A brief survey is given on recent developments and current achievements in the field of perturbative precision calculations in the ... More

Structural Relations of Harmonic Sums and Mellin Transforms at Weight w=6Jan 07 2009We derive the structural relations between nested harmonic sums and the corresponding Mellin transforms of Nielsen integrals and harmonic polylogarithms at weight {\sf w = 6}. They emerge in the calculations of massless single--scale quantities in QED ... More

Status of Deeply Inelastic Parton DistributionsNov 12 2007A brief review on the status of unpolarized parton densities and the determination of the QCD scale $\Lambda_{\rm QCD}$ from deep-inelastic scattering data is presented.

On the Anomalous Dimension of the Transversity Distribution $h_1(x,Q^2)$Apr 10 2001May 15 2001We calculate the leading order anomalous dimension of the transversity structure function directly using three different methods, the local light-cone expansion in the forward case, the non-forward case, and the short-distance expansion of the forward ... More

Precision of electro--weak couplings of scalar leptoquarks at TESLASep 28 2000Nov 29 2000We investigate the potential to measure the electro-weak couplings of scalar leptoquarks $\Phi_s$ at TESLA for energies in the range of $\sqrt{s} \simeq 1 \TeV$ using the pair production process $e^+e^- \to \Phi_s \bar{\Phi}_s$.

The Status of the Polarized Parton DensitiesAug 10 2007Aug 13 2007A survey is given on the present knowledge of the polarized parton distribution functions. We give an outlook for further developments desired both on the theoretical as well on the experimental side to complete the understanding of the spin--structure ... More

Analytic Continuation of Mellin Transforms up to two-loop OrderMar 10 2000The analytic continuation of the Mellin transforms to complex values of N for the basic functions $g_i(x)$ of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized splitting functions, ... More

Small $x$ Contributions to the Structure Function $F_L(x,Q^2)$Aug 26 1994The gluon contributions to $F_L(x,Q^2)$ in ${\cal O}(\alpha_s)$ are calculated taking into account the transverse momentum of the initial state parton. In comparison with collinear factorization $F_L(x,Q^2)$, is not affected at large $x$ but takes smaller ... More

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local CouplingsNov 03 2007Nov 25 2007This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, ... More

Duality between Wilson Loops and Scattering AmplitudesOct 21 2008Oct 27 2008We summarise the status of an intriguing new duality between planar maximally helicity violating scattering amplitudes and light-like Wilson loops in N=4 super Yang-Mills. In particular, we focus on the role played by (dual) conformal symmetry, which ... More

A brief introduction to Luttinger liquidsMay 05 2000I give a brief introduction to Luttinger liquids. Luttinger liquids are paramagnetic one-dimensional metals without Landau quasi-particle excitations. The elementary excitations are collective charge and spin modes, leading to charge-spin separation. ... More

Charge-Spin Separation and the Spectral Properties of Luttinger LiquidsOct 21 1993Oct 25 1993We compute the spectral function rho(q,omega) of the one- dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. ... More

DWSB for heterotic flux compactificationsMar 14 2011We investigate the construction of non-supersymmetric vacua in compactifications of heterotic string theory with intrinsic torsion and background fluxes. We do this by using the technique of domain-wall supersymmetry breaking (DWSB) that was developed ... More

Dynamics of gene expression and the regulatory inference problemDec 21 2007Mar 05 2008From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription ... More

Processes, Roles and Their InteractionsFeb 21 2012Taking an interaction network oriented perspective in informatics raises the challenge to describe deterministic finite systems which take part in networks of nondeterministic interactions. The traditional approach to describe processes as stepwise executable ... More

Combined Data Structure for Previous- and Next-Smaller-ValuesFeb 02 2011Let $A$ be a static array storing $n$ elements from a totally ordered set. We present a data structure of optimal size at most $n\log_2(3+2\sqrt{2})+o(n)$ bits that allows us to answer the following queries on $A$ in constant time, without accessing $A$: ... More

Optimal Succinctness for Range Minimum QueriesDec 15 2008Dec 02 2009For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum queries on A ... More

Quasiparticle properties of strongly correlated electron systems with itinerant metamagnetic behaviorApr 18 2008Jul 22 2009A brief account of the zero temperature magnetic response of a system of strongly correlated electrons in strong magnetic field is given in terms of its quasiparticle properties. The scenario is based on the paramagnetic phase of the half-filled Hubbard ... More

Group field theories generating polyhedral complexesJun 28 2015Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in the traditional ... More

Moyal-Weyl deformations of $\mathrm{DGA}$ and $\mathrm{DGCA}$Feb 13 2015Jul 28 2015We consider a natural variant of the Moyal-Weyl product and show that it yields a functorial deformation of differential graded algebras and that we can deform coalgebras in a similar way. The Moyal-Weyl deformation of graded algebras has already been ... More

Some notes on Euler productsDec 21 2014We focus on a well-known convergence phenomenon, the fact that the $\zeta$ zeros are the universal singularities of certain Euler products.

Generalizations of a result of Jarnik on simultaneous approximationOct 24 2014Nov 23 2016Consider a non-increasing function $\Psi$ from the positive reals to the positive reals with decay $o(1/x)$ as $x$ tends to infinity. Jarnik proved in 1930 that there exist real numbers $\zeta_{1},...,\zeta_{k}$ together with $1$ linearly independent ... More

Berkovich skeleta and birational geometrySep 18 2014We give a survey of joint work with Mircea Musta\c{t}\u{a} and Chenyang Xu on the connections between the geometry of Berkovich spaces over the field of Laurent series and the birational geometry of one-parameter degenerations of smooth projective varieties. ... More

Singular propagators in deformation quantization and Shoikhet-Tsygan formalityJan 06 2015Jan 29 2015This paper adds some details to the seminal approach to logarithmic formality \cite{AWRT} and interpolation formality \cite{WR} by Alekseev, Rossi, Torossian and Willwacher: We prove that the interpolation family of Kontsevich formality maps extends to ... More

Continuity Results and Estimates for the Lyapunov Exponent of Brownian Motion in Random PotentialApr 04 2014May 14 2014We collect some applications of the variational formula established by Schr\"oder (1988) and Rue\ss (2013) for the quenched Lyapunov exponent of Brownian motion in stationary and ergodic nonnegative potential. We show for example that the Lyapunov exponent ... More

Two limitations of our knowledge of qualitySep 19 2016This article develops a quality notion that is complementary to the system notion. As a major consequence, it becomes clear why quality can be measured only to a certain extend based on the issues of validity and incompleteness. First, there is an inherent ... More

Counting zeros of holomorphic functions of exponential growthOct 02 2009We consider the number of zeros of holomorphic functions in a bounded domain that depend on a small parameter and satisfy an exponential upper bound near the boundary of the domain and similar lower bounds at finitely many points along the boundary. Roughly ... More

Piecewise constant local martingales with bounded numbers of jumpsDec 23 2016A piecewise constant local martingale $M$ with boundedly many jumps is a uniformly integrable martingale if and only if $M_\infty^-$ is integrable.

The Uniform Integrability of Martingales. On a Question by Alexander ChernyJan 23 2015May 01 2015Let $X$ be a progressively measurable, almost surely right-continuous stochastic process such that $X_\tau \in L^1$ and $E[X_\tau] = E[X_0]$ for each finite stopping time $\tau$. In 2006, Cherny showed that $X$ is then a uniformly integrable martingale ... More

Comment on "Under-reported data analysis with INAR-hidden Markov chains"Dec 17 2018In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the Poisson INAR(1) model ... More

Finding the Maximizers of the Information Divergence from an Exponential FamilyDec 23 2009This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint support and the ... More

A short proof that every finite graph has a tree-decomposition displaying its tanglesNov 09 2015May 31 2016We give a short proof that every finite graph (or matroid) has a tree-decomposition that displays all maximal tangles. This theorem for graphs is a central result of the graph minors project of Robertson and Seymour and the extension to matroids is due ... More

On the cohomology of the holomorph of a finite cyclic groupMar 02 2003Feb 11 2004The mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2 is determined.

Minimal number of points with bad reduction for elliptic curves over P^1Jul 25 2010Jul 22 2011In this work we use elementary methods to discuss the question of the minimal number of points with bad reduction over the projective line for elliptic curves E/k(T) which are non-constant resp. have non-constant j-invariant.

Topic Modeling based on Keywords and ContextOct 07 2017Feb 03 2018Current topic models often suffer from discovering topics not matching human intuition, unnatural switching of topics within documents and high computational demands. We address these concerns by proposing a topic model and an inference algorithm based ... More

Oblivious Sorting and QueuesDec 10 2016We present a deterministic oblivious LIFO (Stack), FIFO, double-ended and double-ended priority queue as well as an oblivious mergesort and quicksort algorithm. Our techniques and ideas include concatenating queues end-to-end, size balancing of multiple ... More

A characterization of the locally finite networks admitting non-constant harmonic functions of finite energyMay 10 2011We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also ... More

From Jantzen to Andersen Filtration via Tilting EquivalenceNov 08 2010Jan 20 2011The space of homomorphisms from a projective object to a Verma module in category O inherits an induced filtration from the Jantzen filtration on the Verma module. On the other hand there is the Andersen filtration on the space of homomorphisms from a ... More

Twilled Lie-Rinehart algebras and differential Batalin-Vilkovisky algebrasNov 10 1998Twilled L(ie)-R(inehart) algebas generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an almost twilled pre-LR algebra, which is a true twilled LR-algebra iff the almost complex structure ... More

Uniqueness and Non-Uniqueness for Spin-Glass Ground States on TreesDec 06 2018We consider a Spin Glass at temperature $T = 0$ where the underlying graph is a locally finite tree. We prove for a wide range of coupling distributions that uniqueness of ground states is equivalent to the maximal flow from any vertex to $\infty$ (where ... More

Lie-Rinehart algebras, descent, and quantizationMar 02 2003A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a smooth manifold. ... More

Kaehler spaces, nilpotent orbits, and singular reductionApr 23 2001Aug 13 2002For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations across the strata ... More

Stratified Kaehler structures on adjoint quotientsApr 06 2004Nov 02 2006Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields ... More

Severi varieties and holomorphic nilpotent orbitsJun 14 2002Jan 29 2004Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding complex projective ... More

Minimal free multi models for chain algebrasMay 10 2004Jan 21 2005Let R be a local ring and A a connected differential graded algebra over R which is free as a graded R-module. Using homological perturbation theory techniques, we construct a minimal free multi model for A having properties similar to that of an ordinary ... More

Group Extended Markov Systems, Amenability, and the Perron-Frobenius OperatorMay 23 2012Jun 04 2013We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a H\"older continuous potential. This extends a result of Day for random ... More

The Local Semicircle Law for Random Matrices with a Fourfold SymmetryJun 15 2015Oct 06 2015We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally ... More

Homological perturbations, equivariant cohomology, and Koszul dualityJan 14 2004Jul 31 2009Our main objective is to demonstrate how homological perturbation theory (HPT) results over the last 40 years immediately or with little extra work give some of the Koszul duality results that have appeared in the last decade. Higher homotopies typically ... More

Relative homological algebra, equivariant de Rham theory, and Koszul dualityJan 14 2004Oct 02 2008Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V the V-valued ... More

Recurrence and pressure for group extensionsMay 21 2012Jun 04 2013We investigate the thermodynamic formalism for recurrent potentials on group extensions of countable Markov shifts. Our main result characterises recurrent potentials depending only on the base space, in terms of the existence of a conservative product ... More

Formal and rigid geometry: an intuitive introduction, and some applicationsJan 19 2007Mar 25 2009We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications to the Milnor ... More

The Cohen-Lenstra Heuristic: Methodology and ResultsDec 25 2009In number theory, great efforts have been undertaken to study the Cohen-Lenstra probability measure on the set of all finite abelian $p$-groups. On the other hand, group theorists have studied a probability measure on the set of all partitions induced ... More

Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusionAug 18 2016We show the existence of locally bounded global solutions to the chemotaxis system \[ u_t = \nabla\cdot(D(u)\nabla u) - \nabla\cdot(\frac{u}{v} \nabla v) \] \[ v_t = \Delta v - uv \] with homogeneous Neumann boundary conditions and suitably regular positive ... More

Algebraic independence of generalized Morita-Miller-Mumford classesOct 06 2009Mar 09 2010The generalized Morita-Miller-Mumford classes of a smooth oriented manifold bundle are defined as the image of the characteristic classes of the vertical tangent bundle under the Gysin homomorphism. We show that if the dimension of the manifold is even, ... More

Line bundles on moduli and related spacesJul 30 2009Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the principal G-circle ... More

Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebrasMar 14 2013Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure ... More

A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivityJan 21 2015We consider the parabolic chemotaxis model \[ u_t=\Delta u - \chi \nabla\cdot(\frac uv \nabla v), \qquad\qquad v_t=\Delta v - v + u\] in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for $\chi\in(0,\chi_0)$ ... More

On intrinsic and extrinsic rational approximation to Cantor setsDec 27 2018Jan 25 2019We provide various new results on a problem proposed by K. Mahler in 1984 concerning rational approximation to fractal sets by rational numbers inside and outside the set in question, respectively. Thereby we complement and generalize recent results of ... More

Berikashvili's functor D and the deformation equationJun 05 1999Berikashvili's functor D defined in terms of twisting cochains is related to deformation theory, gauge theory, Chen's formal power series connections, and the master equation in physics. The idea is advertised that some unification and understanding of ... More

Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel systemOct 25 2017We consider a parabolic-elliptic chemotaxis system generalizing \[ \begin{cases}\begin{split} & u_t=\nabla\cdot((u+1)^{m-1}\nabla u)-\nabla \cdot(u(u+1)^{\sigma-1}\nabla v)\\ & 0 = \Delta v - v + u \end{split}\end{cases} \] in bounded smooth domains $\Omega\subset ... More

Competing interactions and symmetry breaking in the Hubbard-Holstein modelJul 22 2009May 19 2010Competing interactions are often responsible for intriguing phase diagrams in correlated electron systems. Here we analyze the competition of instantaneous short range Coulomb interaction $U$ with the retarded electron-electron interaction induced by ... More

Barbasch-Sahi algebras and Dirac cohomologyAug 26 2016Sep 06 2016We define a class of algebras which are distinguished by a PBW property and an orthogonality condition, and which we call Hopf-Hecke algebras, since they generalize the Drinfeld Hecke algebras defined by Drinfeld. In the course of studying the orthogonality ... More

Index theory in spaces of noncompact manifolds I: Analytical foundationsAug 04 2016We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.

A theoretical study of the dynamics of paramagnetic superrotors in external magnetic fieldsApr 13 2015Apr 20 2015We present a detailed theoretical study of oxygen molecules in high rotational states (molecular superrotors) interacting with an external magnetic field. The system shows rich dynamics, ranging from a spin-selective splitting of the angular distribution ... More

Extended moduli spaces and the Kan construction.II.Lattice gauge theoryJun 14 1995Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant cohomology of the geometric ... More

Symplectic and Poisson structures of certain moduli spaces. II. Projective representations of cocompact discrete planar groupsDec 21 1994Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary infinite orientation ... More

Extensions of Lie-Rinehart algebras and the Chern-Weil constructionJun 01 1997A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for arbitrary extensions of Lie-Rinehart algebras. Some ... More

Geometric limits to geometric optical imaging with infinite, planar, non-absorbing sheetsJan 23 2009May 25 2009New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar, non-absorbing sheet that ... More

Bayesian evidence for non-zero theta_13 and CP-violation in neutrino oscillationsMay 20 2012Aug 31 2012We present the Bayesian method for evaluating the evidence for a non-zero value of the leptonic mixing angle theta_13 and CP-violation in neutrino oscillation experiments. This is an application of the well-established method of Bayesian model selection, ... More

Tunneling HamiltonianFeb 06 2013Mar 07 2013For the description of the transport of electrons across a quantum dot, which is tunnel coupled to leads at different chemical potentials, it is usual to assume that the total Hamiltonian of the composite system of the leads and the quantum dot is the ... More

Trust, but verify: benefits and pitfalls of least-squares refitting in high dimensionsJun 01 2013Least-squares refitting is widely used in high dimensional regression to reduce the prediction bias of l1-penalized estimators (e.g., Lasso and Square-Root Lasso). We present theoretical and numerical results that provide new insights into the benefits ... More

Non-equilibrium dynamics of gene expression and the Jarzynski equalityDec 03 2007In order to express specific genes at the right time, the transcription of genes is regulated by the presence and absence of transcription factor molecules. With transcription factor concentrations undergoing constant changes, gene transcription takes ... More

Statistical mechanics of random two-player gamesOct 22 1999Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate quantities ... More

Spectral properties of Luther-Emery systemsFeb 15 1996We calculate the spectral function of the Luther-Emery model which describes one-dimensional fermions with gapless charge and gapped spin degrees of freedom. We find a true singularity with interaction dependent exponents on the gapped spin dispersion ... More

On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String VacuaAug 13 2012Nov 27 2013Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density of the sum of ... More

Block bootstrap for the empirical process of long-range dependent dataJan 06 2016We consider long-range dependent data. It is shown that the bootstrapped empirical process of these data converges to a semi-degenerate limit. The random part of this limit is always Gaussian. Thus the bootstrap might fail when the original empirical ... More

The homotopy type of a topological stackJan 21 2009The notion of the \emph{homotopy type} of a topological stack has been around in the literature for some time. The basic idea is that an atlas $X \to \mathfrak{X}$ of a stack determines a topological groupoid $\mathbb{X}$ with object space $X$. The homotopy ... More

Elliptic regularity for Dirac operators on families of noncompact manifoldsAug 04 2016Jan 18 2018We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.

Optimally approximating exponential familiesNov 02 2011This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular class of low-dimensional ... More

Fractal Models for Normal Subgroups of Schottky GroupsMay 31 2011Mar 31 2013For a normal subgroup $N$ of the free group $\F_d$ with at least two generators we introduce the radial limit set $\Lr(N,\Phi)$ of $N$ with respect to a graph directed Markov system $\Phi$ associated to $\F_d$. These sets are shown to provide fractal ... More

A spectral method for integral formulations of medium-frequency scattering problemsAug 26 2005A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed efficiently using ... More

Perturbations of selfadjoint operators with periodic classical flowMar 03 2003We consider non-selfadjoint perturbations of a self-adjoint $h$-pseudodifferential operator in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength $\epsilon $ of the perturbation ... More

Infinitely many odd zeta values are irrational. By elementary meansFeb 26 2018In this small note, we provide an elementary proof of the fact that infinitely many odd zeta values are irrational. For the first time, this celebrated theorem been proven by Rivoal and Ball--Rivoal. The original proof uses highly non-elementary methods ... More

A counterexample to Gouvêa's Dimension ConjectureMar 20 2012In this note we provide a counterexample to a conjecture due to F. Gouv\^ea, which says that the Krull dimension of the universal deformation ring - as defined by B. Mazur - associated to an absolutely irreducible residual representation could be expressed ... More

Kaehler quantization and reductionJul 19 2002Apr 08 2004Exploiting a notion of Kaehler structure on a stratified space introduced elsewhere we show that, in the Kaehler case, reduction after quantization coincides with quantization after reduction: Key tools developed for that purpose are stratified polarizations ... More

A Combinatorial Classification of Postcritically Fixed Newton MapsJan 05 2007We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic ones, every component ... More