Results for "Jakob Schiøtz"

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Vibrationally Mediated Control of Single Electron Transmission in Weakly Coupled Molecule-Metal JunctionsJan 04 2010Mar 25 2010We propose a mechanism which allows one to control the transmission of single electrons through a molecular junction. The principle utilizes the emergence of transmission sidebands when molecular vibrational modes are coupled to the electronic state mediating ... More
Origin of power laws for reactions at metal surfaces mediated by hot electronsNov 10 2009Dec 01 2009A wide range of experiments have established that certain chemical reactions at metal surfaces can be driven by multiple hot electron mediated excitations of adsorbates. A high transient density of hot electrons is obtained by means of femtosecond laser ... More
Hot electron mediated desorption rates calculated from excited state potential energy surfacesOct 15 2008Jan 07 2009We present a model for Desorption Induce by (Multiple) Electronic Transitions (DIET/DIMET) based on potential energy surfaces calculated with the Delta Self-Consistent Field extension of Density Functional Theory. We calculate potential energy surfaces ... More
Delta Self-Consistent Field as a method to obtain potential energy surfaces of excited molecules on surfacesJul 21 2008We present a modification of the $\Delta$SCF method of calculating energies of excited states, in order to make it applicable to resonance calculations of molecules adsorbed on metal surfaces, where the molecular orbitals are highly hybridized. The $\Delta$SCF ... More
Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electronsMar 11 2010We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation ... More
Memory effects in non-adiabatic molecular dynamics at metal surfacesJun 11 2010We study the effect of temporal correlation in a Langevin equation describing non-adiabatic dynamics at metal surfaces. For a harmonic oscillator the Langevin equation preserves the quantum dynamics exactly and it is demonstrated that memory effects are ... More
Robust Structural Identification via Polyhedral Template MatchingMar 16 2016Apr 18 2016Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common Neighbour Analysis, ... More
Electrochemical control of quantum interference in anthraquinone-based molecular switchesMay 04 2010Using first-principles calculations we analyze the electronic transport properties of a recently proposed anthraquinone based electrochemical switch. Robust conductance on/off ratios of several orders of magnitude are observed due to destructive quantum ... More
Microscopic Calculation of Flow Stress in Cu-Mg Metallic GlassJun 14 2004We have carried out shear-deformation simulations on amorphous Mg-Cu systems at zero temperature and pressure, containing 2048-131072 atoms. At the largest size a smooth stress-strain curve is obtained with a well-defined flow stress. In the smallest ... More
Simulation of Cu-Mg metallic glass: Thermodynamics and StructureSep 29 2003We have obtained effective medium theory (EMT) interatomic potential parameters suitable for studying Cu-Mg metallic glasses. We present thermodynamic and structural results from simulations of such glasses over a range of compositions. We have produced ... More
Rich Ground State Chemical Ordering in Nanoparticles: Exact Solution of a Model for Ag-Au ClustersDec 20 2017Jun 13 2018We show that nanoparticles can have very rich ground state chemical order. This is illustrated by determining the chemical ordering of Ag-Au 309-atom Mackay icosahedral nanoparticles. The energy of the nanoparticles is described using a cluster expansion ... More
Calculation of Elastic Green's Functions for Lattices with CavitiesDec 17 1996In this Brief Report, we present an algorithm for calculating the elastic Lattice Greens Function of a regular lattice, in which defects are created by removing lattice points. The method is computationally efficient, since the required matrix operations ... More
A deep learning approach to identify local structures in atomic-resolution transmission electron microscopy imagesFeb 08 2018Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have developed a ... More
A deep learning approach to identify local structures in atomic-resolution transmission electron microscopy imagesFeb 08 2018Feb 09 2018Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have developed a ... More
Atomic-scale modeling of the deformation of nanocrystalline metalsDec 07 1998Nanocrystalline metals, i.e. metals with grain sizes from 5 to 50 nm, display technologically interesting properties, such as dramatically increased hardness, increasing with decreasing grain size. Due to the small grain size, direct atomic-scale simulations ... More
Atomic-scale simulations of nanocrystalline metalsFeb 11 1999Nanocrystalline metals, i.e. metals in which the grain size is in the nanometer range, have a range of technologically interesting properties including increased hardness and yield strength. We present atomic-scale simulations of the plastic behavior ... More
Infinite-Dimensional Supermanifolds via Multilinear BundlesOct 12 2018Jan 22 2019In this paper, we provide an accessible introduction to the theory of locally convex supermanifolds in the categorical approach. In this setting, a supermanifold is a functor $\mathcal{M}\colon\mathbf{Gr}\to\mathbf{Man}$ from the category of Grassmann ... More
On the 3-torsion Part of the Homology of the Chessboard ComplexMar 26 2012Let $1 \le m \le n$. We prove various results about the chessboard complex $M_{m,n}$, which is the simplicial complex of matchings in the complete bipartite graph $K_{m,n}$. First, we demonstrate that there is nonvanishing 3-torsion in $H_d(M_{m,n};Z)$ ... More
Arakelov motivic cohomology IIMay 17 2012Oct 19 2013We show that the constructions done in part I generalize their classical counterparts: firstly, the classical Beilinson regulator is induced by the abstract Chern class map from $BGL$ to the Deligne cohomology spectrum. Secondly, Arakelov motivic cohomology ... More
Mixed Artin-Tate motives over number ringsMar 05 2010Aug 05 2010This paper studies Artin-Tate motives over number rings. As a subcategory of geometric motives, the triangulated category of Artin-Tate motives DATM(S) is generated by motives of schemes that are finite over the base S. After establishing stability of ... More
Non-elementary proper forcingOct 12 2009May 08 2011We introduce a simplified framework for ord-transitive models and Shelah's non elementary proper (nep) theory. We also introduce a new construction for the countable support nep iteration.
Preserving Non-Null with Suslin+ forcingNov 25 2002Feb 09 2005We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah's "preserving a little implies preserving much": If I is a Suslin ccc ideal ... More
Uniform central limit theorems for the Grenander estimatorNov 24 2014Jun 26 2015We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness s>1/2. We do ... More
Discovering and Proving Infinite Binomial Sums IdentitiesJul 07 2015Oct 29 2015We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of generating series. ... More
Classification of Rigid Irregular $G_2$-ConnectionsSep 12 2016Jul 16 2018Using the Katz-Arinkin algorithm we give a classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ having differential Galois group $G_2$, the exceptional simple algebraic group, and slopes having numerator ... More
New entropic uncertainty relations for prime power dimensionsSep 30 2011We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple probability ... More
A Computer Algebra Toolbox for Harmonic Sums Related to Particle PhysicsNov 04 2010In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums and generalized ... More
Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebrasMar 22 2012Jul 12 2012We study the Borcherds superalgebra obtained by adding an odd (fermionic) null root to the set of simple roots of a simple finite-dimensional Lie algebra. We compare it to the Kac-Moody algebra obtained by replacing the odd null root by an ordinary simple ... More
Exceptional Lie algebras and M-theoryDec 08 2009In this thesis we study algebraic structures in M-theory, in particular the exceptional Lie algebras arising in dimensional reduction of its low energy limit, eleven-dimensional supergravity. We focus on e8 and its infinite-dimensional extensions e9 and ... More
Permanental Point Processes on Real Tori, Theta Functions and Monge-Ampère EquationsApr 19 2016May 18 2016Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge-Amp\`ere equations on real tori. We show convergence in law of the associated point processes and explain connections to complex Monge-Amp\`ere equations and ... More
Exceptional geometry and Borcherds superalgebrasJul 31 2015Jun 20 2016We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view. By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to e_{n+1}, the ... More
Discovering and Proving Infinite Pochhammer Sum IdentitiesFeb 28 2019We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as specializations ... More
On the graph-theoretical interpretation of Pearson correlations in a multivariate process and a novel partial correlation measureOct 18 2013The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger causality and encode ... More
Tagging, Folksonomy & Co - Renaissance of Manual Indexing?Jan 10 2007Jan 26 2007This paper gives an overview of current trends in manual indexing on the Web. Along with a general rise of user generated content there are more and more tagging systems that allow users to annotate digital resources with tags (keywords) and share their ... More
Even more simple cardinal invariantsJun 03 2007Jul 16 2007Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.
A logarithmic view towards semistable reductionMay 18 2003The geometric condition of T. Saito for trivial action of the wild monodromy of a smooth proper curve over the generic point of a trait is transformed to the condition of logarithmic smooth reduction. The proof emphasizes methods and results from logarithmic ... More
The Role of Type III Factors in Quantum Field TheoryNov 17 2004Dec 04 2004One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite ... More
f-cohomology and motives over number ringsMar 05 2010Mar 16 2015This paper is concerned with an interpretation of f-cohomology, a modification of motivic cohomology of motives over number fields, in terms of motives over number rings. Under standard assumptions on mixed motives over finite fields, number fields and ... More
Exact Sequences for the Homology of the Matching ComplexMar 26 2012Building on work by Bouc and by Shareshian and Wachs, we provide a toolbox of long exact sequences for the reduced simplicial homology of the matching complex $M_n$, which is the simplicial complex of matchings in the complete graph $K_n$. Combining these ... More
Five-Torsion in the Homology of the Matching Complex on 14 VerticesMar 26 2012J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing ... More
On the birational section conjecture with local conditionsMar 14 2012Sep 17 2015A birationally liftable Galois section s of a hyperbolic curve X/k over a number field k yields an adelic point x(s) in the smooth completion of X. We show that x(s) is X-integral outside a set of places of Dirichlet density 0, or s is cuspidal. The proof ... More
The Brauer-Manin obstruction for sections of the fundamental groupOct 26 2009We establish Grothendieck's section conjecture for an open subset of the Reichardt-Lind curve, and introduce the notion of a Brauer-Manin obstruction for sections of the fundamental group extension.
A monodromy criterion for extending curvesAug 23 2004Nov 10 2004A family of proper smooth curves of genus $\geq 2$, parametrised by an open dense subset $U$ of a normal variety $S$, extends to $S$ if the natural map $\pi_1(U) \to \pi_1(S)$ on fundamental groups is an isomorphism. The criterion of this note is actually ... More
Affine anabelian curves in positive characteristicJun 18 2002An investigation of morphisms that coincide topologically is used to generalize to all characteristics and partly reprove Tamagawa's theorem on the Grothendieck conjecture in anabelian geometry for affine hyperbolic curves. The theorem now deals with ... More
Conic bundles and iterated root stacksSep 25 2017Jun 21 2018We generalize a classical result by V. G. Sarkisov about standard models for conic bundles to the case of a not necessarily algebraically closed perfect field, using iterated root stacks, destackification, and resolution of singularities.
Discovering and Proving Infinite Pochhammer Sum IdentitiesFeb 28 2019Apr 10 2019We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as specializations ... More
Ab initio van der Waals interactions in simulations of water alter structure from mainly tetrahedral to high-density-likeJan 29 2011May 03 2011The structure of liquid water at ambient conditions is studied in ab initio molecular dynamics simulations using van der Waals (vdW) density-functional theory, i.e. using the new exchange-correlation functionals optPBE-vdW and vdW-DF2. Inclusion of the ... More
Connecting generalized parton distributions and light-cone wave functionsSep 26 2000The relation of generalized (skewed) quark distributions to nucleon wave functions is discussed in the context of light-cone quantization.
Wide Angle Compton ScatteringOct 16 2000We present the handbag contribution to Wide Angle Compton Scattering (WACS) at moderately large momentum transfer obtained with a proton distribution amplitude close to the asymptotic form. In comparison it is found to be significantly larger than results ... More
Proton-Proton Elastic Scattering; Landshoff Contributions in the Diquark ModelJun 08 1994Independent multiple scattering (`Landshoff') contributions to proton-proton elastic scattering at wide angles are calculated in the quark-diquark model. Results confirm previous observations about the magnitude of these contributions. The use of the ... More
The Classification of Rigid Irregular $G_2$-ConnectionsSep 12 2016Sep 28 2016Using the Katz-Arinkin algorithm we give a complete classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ having differential Galois group $G_2$, the exceptional simple algebraic group. In addition to hypergeometric ... More
A note on the Thom isomorphism in geometric (co)homologyMar 31 2004Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
Conditional independence testing based on a nearest-neighbor estimator of conditional mutual informationSep 05 2017Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional ... More
Encoding changing country codes for the Semantic Web with ISO 3166 and SKOSJan 25 2008This paper shows how authority files can be encoded for the Semantic Web with the Simple Knowledge Organisation System (SKOS). In particular the application of SKOS for encoding the structure, management, and utilization of country codes as defined in ... More
On the average distribution of primes represented by binary quadratic formsDec 05 2013We investigate the average distribution of primes represented by positive definite integral binary quadratic forms, the average being taken over negative fundamental discriminants in long ranges. In particular, we prove corresponding results of Bombieri-Vinogradov ... More
On the period-index problem in light of the section conjectureFeb 28 2008Period and index of a curve $X/K$ over a $p$-adic local field $K$ such that the fundamental group $\pi_1(X/K)$ admits a splitting are shown to be powers of $p$. As a consequence, examples of curves over number fields are constructed where having sections ... More
More Torsion in the Homology of the Matching ComplexMar 26 2012Mar 28 2012A matching on a set $X$ is a collection of pairwise disjoint subsets of $X$ of size two. Using computers, we analyze the integral homology of the matching complex $M_n$, which is the simplicial complex of matchings on the set $\{1, >..., n\}$. The main ... More
Special L-values of geometric motivesMar 05 2010Aug 03 2015This paper proposes a conjecture on special values of L-functions of geometric motives over Z. This includes L-functions of mixed motives over Q and Hasse-Weil zeta-functions of schemes over Z. We conjecture the following: the order of L(M, s) at s=0 ... More
Algebraic K-theory of the infinite placeFeb 23 2012Jun 05 2014In this note, we show that the algebraic K-theory of generalized archimedean valuation rings occurring in Durov's compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces. We also show that the ... More
Demystifying Gauge SymmetryJan 29 2019Gauge symmetries are often highlighted as a fundamental cornerstone of modern physics. But at the same time, it is commonly emphasized that gauge symmetries are not a fundamental feature of nature but merely redundancies in our description. We argue that ... More
Optimal trajectory trackingDec 23 2015This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of so-called exactly ... More
Bosons in Rapid RotationAug 20 2008Some recent progress in the mathematical physics of rapidly rotating, dilute Bose gases in anharmonic traps is reviewed.
Coupled Kähler-Ricci solitons on toric Fano manifoldsNov 27 2017Oct 05 2018We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled K\"ahler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson ... More
On the Number of Periodic Points of Quadratic Dynamical Systems Modulo a PrimeNov 02 2016In 2004 Vasiga and Shallit studied the number of periodic points of two particular discrete quadratic maps modulo prime numbers. They found the asymptotic behaviour of the sum of the number of periodic points for all primes less than some bound, assuming ... More
Inverse Mellin Transform of Holonomic SequencesJun 09 2016We describe a method to compute the inverse Mellin transform of holonomic sequences, that is based on a method to compute the Mellin transform of holonomic functions. Both methods are implemented in the computer algebra package HarmonicSums.
Linear structures in nonlinear optimal controlApr 05 2016We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task also known ... More
Practical Concurrent Priority QueuesSep 23 2015Priority queues are abstract data structures which store a set of key/value pairs and allow efficient access to the item with the minimal (maximal) key. Such queues are an important element in various areas of computer science such as algorithmics (i.e. ... More
Proceedings Seventh Workshop on Intersection Types and Related SystemsMar 15 2015This volume contains a final and revised selection of papers presented at the Seventh Workshop on Intersection Types and Related Systems (ITRS 2014), held in Vienna (Austria) on July 18th, affiliated with TLCA 2014, Typed Lambda Calculi and Applications ... More
Collaborative thesaurus tagging the Wikipedia wayApr 10 2006Apr 27 2006This paper explores the system of categories that is used to classify articles in Wikipedia. It is compared to collaborative tagging systems like del.icio.us and to hierarchical classification like the Dewey Decimal Classification (DDC). Specifics and ... More
Revealing digital documents. Concealed structures in dataMay 29 2011This short paper gives an introduction to a research project to analyze how digital documents are structured and described. Using a phenomenological approach, this research will reveal common patterns that are used in data, independent from the particular ... More
On groups with unbounded Cayley graphsNov 29 2018Jan 29 2019We show that every non-trivial compact connected group and every non-trivial general or special linear group over an infinite field admits a generating set such that the associated Cayley graph has infinite diameter.
Trading degree for dimension in the section conjecture: The non-abelian Shapiro LemmaFeb 10 2009This note aims at providing evidence for the section conjecture of anabelian geometry by establishing its behaviour under Weil restriction of scalars. In particular, the etale fundamental group of the Weil restriction is determined by means of a Shapiro ... More
On cuspidal sections of algebraic fundamental groupsAug 29 2008Rational points in the boundary of a hyperbolic curve over a field with sufficiently nontrivial Kummer theory are the source for an abundance of sections of the fundamental group exact sequence. We follow and refine Nakamura's approach towards these boundary ... More
Constructing pairs of dual bandlimited frame wavelets in $L^2(\mathbb{R}^n)$Sep 22 2010Given a real, expansive dilation matrix we prove that any bandlimited function $\psi \in L^2(\mathbb{R}^n)$, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, ... More
On some Hermite series identities and their applications to Gabor analysisNov 30 2015We prove some infinite series identities for the Hermite functions. From these identities we disprove the Gabor frame set conjecture for Hermite functions of order $4m+2$ and $4m+3$ for $m \in \{0\} \cup \mathbb{N}$. The results hold not only for Hermite ... More
Topics in the Mathematical Physics of Cold Bose GasesFeb 04 2014Feb 14 2014In these notes of six lectures on selected topics in the theory of cold, dilute Bose gases, presented at the 5th Warsaw School of Statistical Physics in June 2013, the following topics are discussed: 1) The concept of BEC, 2) the ground state energy of ... More
Quasi-symmetric functions and the Chow ring of the stack of expanded pairsJun 27 2018We show that the Hopf algebra of quasi-symmetric functions arises naturally as the integral Chow ring of the algebraic stack of expanded pairs originally described by J. Li, using a more combinatorial description in terms of configurations of line bundles. ... More
Simulations of mechanics and structure of nanomaterials --- from nanoscale to coarser scalesAug 19 1998We discuss how simulations of mechanical properties of materials require descriptions at many different length scales --- from the nanoscale where an atomic description is appropriate, through a mesoscale where dislocation based descriptions may be useful, ... More
Physics at the LHC -- From Standard Model measurements to Searches for New PhysicsJun 29 2012The successful operation of the {\em Large Hadron Collider} (LHC) during the past two years allowed to explore particle interaction in a new energy regime. Measurements of important Standard Model processes like the production of high-\pt\ jets, $W$ and ... More
Spin-dependent Fragmentation FunctionsJun 26 2002I will give an overview on fragmentation functions with particular emphasis on spin-dependence. A straightforward classification scheme permits to label all independent fragmentation functions for a given physical situation in an unambiguous way. In the ... More
Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's AlgorithmJan 02 2018We describe how the extension of a solver for linear differential equations by Kovacic's algorithm helps to improve a method to compute the inverse Mellin transform of holonomic sequences. The method is implemented in the computer algebra package HarmonicSums. ... More
Three-algebras, triple systems and 3-graded Lie superalgebrasMay 15 2009Dec 08 2009The three-algebras used by Bagger and Lambert in N=6 theories of ABJM type are in one-to-one correspondence with a certain type of Lie superalgebras. We show that the description of three-algebras as generalized Jordan triple systems naturally leads to ... More
Simple transitive $2$-representations of Soergel bimodules in type $B_2$Sep 04 2015Jun 17 2016We prove that every simple transitive $2$-representation of the fiat $2$-category of Soergel bimodules (over the coinvariant algebra) in type $B_2$ is equivalent to a cell $2$-representation. We also describe some general properties of the $2$-category ... More
Stability of position control of traveling waves in reaction-diffusion systemsDec 30 2013We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on the reduced ... More
SST polarization model and polarimeter calibrationOct 20 2010A telescope polarization model for the SST [Swedish 1-m Solar Telescope] is developed and the parameters of this model are fitted to polarization measurements made with a 1-meter linear polarizer in front of the entrance window. In this model, the 1-meter ... More
Gauge Coupling Unification without SupersymmetryAug 30 2018Oct 16 2018We investigate the prospects to achieve unification of the gauge couplings in models without supersymmetry. We restrict our discussion to $SU(5), SO(10)$ and $E_6$ models that mimic the structure of the Standard Model as much as possible ("conservative ... More
Pitowsky's Kolmogorovian models and Super-DeterminismJun 22 2016Sep 28 2016In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed "spin-$\frac12$ functions" and later "Kolmogorovian models", which employs a nonstandard notion of probability. We describe Pitowsky's analysis ... More
Geometric Brauer residue via root stacksMar 12 2018Jun 21 2018We reinterpret the residue map for the Brauer group of a smooth variety using a root stack construction and Weil restriction for algebraic stacks, and apply the result to find a geometric representative of for the residue of a Brauer class associated ... More
Birational p-adic Galois sections in higher dimensionsFeb 13 2012This note explores the consequences of Koenigsmann's model theoretic argument from the proof of the birational p-adic section conjecture for curves in the context of higher dimensional varieties over p-adic local fields.
Polar sets of anisotropic Gaussian random fieldsAug 03 2012This paper studies polar sets of anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical ... More
Confidence sets in nonparametric calibration of exponential Lévy modelsFeb 29 2012Sep 19 2013Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential L\'evy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration method for the ... More
Symmetry Groups of Principal Bundles Over Non-Compact BasesOct 31 2013Nov 06 2013In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact base M. This ... More
Convolutional Neural FabricsJun 08 2016Oct 28 2016Despite the success of CNNs, selecting the optimal architecture for a given task remains an open problem. Instead of aiming to select a single optimal architecture, we propose a "fabric" that embeds an exponentially large number of architectures. The ... More
Higgs Boson Searches at Hadron CollidersApr 13 2005The investigation of the dynamics responsible for electroweak symmetry breaking is one of the prime tasks of experiments at present and future colliders. Experiments at the Tevatron ppbar Collider and at the CERN Large Hadron Collider (LHC) must be able ... More
Convolutional Neural FabricsJun 08 2016Jun 09 2016Despite the success of convolutional neural networks, selecting the optimal architecture for a given task remains an open problem. Instead of aiming to select a single optimal architecture, we propose a $"$fabric$"$ that embeds an exponentially large ... More
The optical Möbius strip cavity: Tailoring geometric phases and far fieldsNov 09 2017Feb 13 2018The M\"{o}bius strip, a long sheet of paper whose ends are glued together after a $180^{\circ}$ twist, has remarkable geometric and topological properties. Here, we consider dielectric M\"{o}bius strips of finite width and investigate the interplay between ... More
Controlling the position of traveling waves in reaction-diffusion systemsApr 08 2013Jan 17 2014We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a pre-specified protocol of motion. Given this protocol, the control function is found as the solution ... More
Constrained Quantum Systems as an Adiabatic ProblemMay 11 2010We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to earlier works ... More
Effective Hamiltonians for Constrained Quantum SystemsJul 02 2009Dec 10 2009We consider the time-dependent Schr\"odinger equation on a Riemannian manifold $\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\mathcal{C}$. When we scale the potential in the directions normal to ... More
A Sacks Real out of NowhereMar 11 2007Apr 29 2009There is a proper countable support iteration of length $\omega$ adding no new reals at finite stages and adding a Sacks real in the limit.