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ZombieLoad: Cross-Privilege-Boundary Data SamplingMay 14 2019In early 2018, Meltdown first showed how to read arbitrary kernel memory from user space by exploiting side-effects from transient instructions. While this attack has been mitigated through stronger isolation boundaries between user and kernel space, ... More

ConTExT: Leakage-Free Transient ExecutionMay 22 2019Out-of-order execution and speculative execution are among the biggest contributors to performance and efficiency of modern processors. However, they are inconsiderate, leaking secret data during the transient execution of instructions. Many solutions ... More

A Systematic Evaluation of Transient Execution Attacks and DefensesNov 13 2018May 15 2019Research on transient execution attacks including Spectre and Meltdown showed that exception or branch misprediction events might leave secret-dependent traces in the CPU's microarchitectural state. This observation led to a proliferation of new Spectre ... More

NetSpectre: Read Arbitrary Memory over NetworkJul 27 2018In this paper, we present NetSpectre, a generic remote Spectre variant 1 attack. For this purpose, we demonstrate the first access-driven remote Evict+Reload cache attack over network, leaking 15 bits per hour. Beyond retrofitting existing attacks to ... More

ARMageddon: Cache Attacks on Mobile DevicesNov 16 2015Jun 19 2016In the last 10 years, cache attacks on Intel x86 CPUs have gained increasing attention among the scientific community and powerful techniques to exploit cache side channels have been developed. However, modern smartphones use one or more multi-core ARM ... More

Automated Detection, Exploitation, and Elimination of Double-Fetch Bugs using Modern CPU FeaturesNov 03 2017Double-fetch bugs are a special type of race condition, where an unprivileged execution thread is able to change a memory location between the time-of-check and time-of-use of a privileged execution thread. If an unprivileged attacker changes the value ... More

KeyDrown: Eliminating Keystroke Timing Side-Channel AttacksJun 20 2017Besides cryptographic secrets, side-channel attacks also leak sensitive user input. The most accurate attacks exploit cache timings or interrupt information to monitor keystroke timings and subsequently infer typed words and sentences. Previously proposed ... More

Nethammer: Inducing Rowhammer Faults through Network RequestsMay 13 2018A fundamental assumption in software security is that memory contents do not change unless there is a legitimate deliberate modification. Classical fault attacks show that this assumption does not hold if the attacker has physical access. Rowhammer attacks ... More

Higher symmetries in abstract stable homotopy theoriesApr 01 2019This survey offers an overview of an on-going project on uniform symmetries in abstract stable homotopy theories. This project has calculational, foundational, and representation-theoretic aspects, and key features of this emerging field on abstract representation ... More

A Systematic Evaluation of Transient Execution Attacks and DefensesNov 13 2018Modern processor optimizations such as branch prediction and out-of-order execution are crucial for performance. Recent research on transient execution attacks including Spectre and Meltdown showed, however, that exception or branch misprediction events ... More

A Systematic Evaluation of Transient Execution Attacks and DefensesNov 13 2018Feb 20 2019Modern CPU optimizations such as branch prediction and out-of-order execution are crucial for performance. Recent research on transient execution attacks including Spectre and Meltdown showed, however, that exception or branch misprediction events may ... More

Constrained Systems of Conservation Laws: A Geometric TheoryOct 22 2015We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m \geq n$). These constrained systems generalize the system of conservation laws in standard form to a level sufficient ... More

Simultaneous confidence bands for Yule-Walker estimators and order selectionMay 30 2012Let $\{X_k,k\in{\mathbb{Z}}\}$ be an autoregressive process of order $q$. Various estimators for the order $q$ and the parameters ${\bolds \Theta}_q=(\theta_1,...,\theta_q)^T$ are known; the order is usually determined with Akaike's criterion or related ... More

A Rejoinder to Mackintosh and some Remarks on the Concept of General IntelligenceAug 18 2008Aug 19 2008In 2000 Nicholas J. Mackintosh (2000) published an article in "Nature" referring to the concept of general intelligence ("g") claiming that there is clear empirical evidence for the existence of the g factor and psychologists are "united in their support ... More

A short course on $\infty$-categoriesJul 17 2010Jan 21 2015In this short survey we give a non-technical introduction to some main ideas of the theory of $\infty$-categories, hopefully facilitating the digestion of the foundational work of Joyal and Lurie. Besides the basic $\infty$-categorical notions leading ... More

A note on incompressibility of relativistic fluids and the instantaneity of their pressuresJan 29 2016Jun 14 2017We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical limit as $c\rightarrow ... More

On the classification of easy quantum groupsJan 23 2012Dec 05 2013In 2009, Banica and Speicher began to study the compact quantum subgroups of the free orthogonal quantum group containing the symmetric group S_n. They focused on those whose intertwiner spaces are induced by some partitions. These so-called easy quantum ... More

Absolute Continuity Theorem for Random Dynamical Systems on $R^d$Jan 05 2012In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case. Then the absolute ... More

On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operatorsJan 17 2012Nov 06 2012Given a positive, irreducible and bounded C_0-semigroup on a Banach lattice with order continuous norm, we prove that the peripheral point spectrum of its generator is trivial whenever one of its operators dominates a non-trivial compact or kernel operator. ... More

Spectre Attacks: Exploiting Speculative ExecutionJan 03 2018Modern processors use branch prediction and speculative execution to maximize performance. For example, if the destination of a branch depends on a memory value that is in the process of being read, CPUs will try guess the destination and attempt to execute ... More

Another Flip in the Wall of Rowhammer DefensesOct 02 2017Jan 31 2018The Rowhammer bug allows unauthorized modification of bits in DRAM cells from unprivileged software, enabling powerful privilege-escalation attacks. Sophisticated Rowhammer countermeasures have been presented, aiming at mitigating the Rowhammer bug or ... More

Spacetime is Locally Inertial at Points of General Relativistic Shock Wave Interaction between Shocks from Different Characteristic FamiliesSep 17 2014Jun 15 2015We prove that spacetime is locally inertial at points of shock wave collision in General Relativity. The result applies for collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. We give a constructive ... More

Understanding Alternating Minimization for Matrix CompletionDec 03 2013May 14 2014Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still poorly understood. ... More

Holography for General Gauge MediationOct 17 2012Feb 28 2013We construct a holographic model of spontaneous supersymmetry breaking in analogy to AdS/QCD models. Integrating out the bulk theory one obtains an entirely four dimensional effective action that encodes spontaneous supersymmetry breaking effects, coupled ... More

Hybrid Gauge MediationJan 26 2011Sep 19 2011Inspired by four dimensional (de)constructions, we use the framework of "General gauge mediation in five dimensions" to interpolate between gaugino and ordinary gauge mediation. In particular we emphasise that an intermediate hybrid regime of mediation ... More

Convergence of Dynamics and the Perron-Frobenius OperatorSep 16 2016We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent ... More

Non-Euclidean isoperimetric inequalities for nilpotent Lie groupsFeb 14 2019This article treats isoperimetric inequalities for integral currents in the setting of stratified nilpotent Lie groups equipped with left-invariant Riemannian metrics. We prove that for each such group there is a dimension in which no Euclidean isoperimetric ... More

The growth of the first non-Euclidean filling function of the quaternionic Heisenberg GroupFeb 03 2017Dec 22 2017The filling volume functions of the n-th quaternionic Heisenberg group grow, up to dimension n, as fast as the ones of the Euclidean space. We identify the growth rate of the filling volume function in dimension n+1, which is strictly faster than the ... More

Partition C*-algebrasOct 17 2017We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we explain a partition ... More

MeltdownJan 03 2018The security of computer systems fundamentally relies on memory isolation, e.g., kernel address ranges are marked as non-accessible and are protected from user access. In this paper, we present Meltdown. Meltdown exploits side effects of out-of-order ... More

Characterizations of abstract stable homotopy theoriesFeb 24 2016In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a derivator is stable ... More

Transfinite limits in topos theoryFeb 06 2015Feb 02 2016For a coherent site we construct a canonically associated enlarged coherent site, such that cohomology of bounded below complexes is preserved by the enlargement. In the topos associated to the enlarged site transfinite compositions of epimorphisms are ... More

Gauge Mediated Supersymmetry Breaking in Five DimensionsSep 28 2011In this thesis we focus on the construction of models in which a supersymmetry breaking hidden sector is located on one fixed point of an extra dimensional interval and the effects are gauge mediated across this interval to the other fixed point where ... More

Quaternion-Kaehler four-manifolds and Przanowski's functionMay 17 2012Nov 14 2012Quaternion-Kaehler four-manifolds, or equivalently anti-self-dual Einstein manifolds, are locally determined by one scalar function subject to Przanowski's equation. Using twistorial methods we construct a Lax Pair for Przanowski's equation, confirming ... More

Asymptotic support theorem for planar isotropic Brownian flowsJul 07 2010Mar 15 2013It has been shown by various authors that the diameter of a given nontrivial bounded connected set $\mathcal{X}$ grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In case of a planar ... More

Diffraction of the Dart-Rhombus Random TilingNov 10 1999The diffraction spectrum of the dart-rhombus random tiling of the plane is derived in rigorous terms. Using the theory of dimer models, it is shown that it consists of Bragg peaks and an absolutely continuous diffuse background, but no singular continuous ... More

Berry-Esseen theorems under weak dependenceJun 06 2016Let $\{{X}_k\}_{k\geq\mathbb{Z}}$ be a stationary sequence. Given $p\in(2,3]$ moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate $n^{p/2-1}$. For $p\geq4$, we also show a convergence rate of $n^{1/2}$ in $\mathcal{L}^q$-norm, ... More

Uniform change point tests in high dimensionNov 17 2015Feb 14 2016Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve this either by ... More

Expected Coverage of Random Walk Mobility AlgorithmNov 09 2016Unmanned aerial vehicles (UAVs) have been increasingly used for exploring areas. Many mobility algorithms were designed to achieve a fast coverage of a given area. We focus on analysing the expected coverage of the symmetric random walk mobility algorithm ... More

Spacetime is Locally Inertial at Points of General Relativistic Shock Wave Interaction between Shocks from Different Characteristic FamiliesSep 17 2014Feb 07 2017We prove that spacetime is locally inertial at points of shock wave collision in General Relativity. The result applies for collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. We give a constructive ... More

A Proposal of a Damping Term for the Relativistic Euler EquationsNov 25 2015We introduce a damping term for the special relativistic Euler equations in $3$-D and show that the equations reduce to the non-relativistic damped Euler equations in the Newtonian limit. We then write the equations as a symmetric hyperbolic system for ... More

Constrained Systems of Conservation Laws: A Geometric TheoryOct 22 2015Sep 27 2017We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include various examples ... More

On Dirichlet forms and semi-Dirichlet formsDec 23 2014One aim of this note is to give an overview of some developments in the area of Dirichlet forms. A second aim is to review the new book "Semi-{D}irichlet forms and {M}arkov processes" by Yoichi Oshima. The book appeared last year, but first versions were ... More

5D Maximally Supersymmetric Yang-Mills in 4D Superspace: ApplicationsMar 19 2013Jul 15 2013We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation ... More

Eddy currents in accelerator magnetsMar 09 2011This paper covers the main eddy current effects in accelerator magnets - field modification (time delay and field quality) and resistive power losses. In the first part, starting from the Maxwell equations, a basic understanding of the processes is given ... More

General Gauge Mediation and DeconstructionAug 31 2010Dec 06 2010We locate a supersymmetry breaking hidden sector and supersymmetric standard model on different lattice points of an orbifold moose. The hidden sector is encoded in a set of current correlators and the effects of the current correlators are mediated by ... More

A brief history of the Fail Safe Number in Applied ResearchOct 12 2010Rosenthal's (1979) Fail-Safe-Number (FSN) is probably one of the best known statistics in the context of meta-analysis aimed to estimate the number of unpublished studies in meta-analyses required to bring the meta-analytic mean effect size down to a ... More

Optimal eigen expansions and uniform boundsJan 05 2015Feb 14 2016Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$. Uniform asymptotic expansions of the corresponding empirical eigenvalues and eigenfunctions are established ... More

On Time-Reversal Equivariant Hermitian Operator Valued Maps from a 2D-Torus Phase SpaceAug 11 2015In this paper we classify maps from a torus phase space $X$ to $\mathcal{H}_n^*$, the space of $n \times n$, non-singular hermitian operators up to equivariant homotopy. The equivariance is with respect to a time-reversal involution on $X$ and an involution ... More

Constrained Systems of Conservation Laws: A Geometric TheoryOct 22 2015Nov 01 2016We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). These constrained systems generalize the system of conservation laws in standard form to a level sufficient ... More

The 'Regularity Singularity' at Points of General Relativistic Shock Wave InteractionDec 08 2011Sep 18 2014A proof that a new kind of non-removable {\it "regularity singularity"} forms when two shock waves collide within the theory of General Relativity, was first announced in ProcRoySoc A \cite{ReintjesTemple}. In the present paper we give complete proofs ... More

Revisiting the canonicity of canonical triangulationsFeb 15 2016Stable derivators provide an enhancement of triangulated categories as is indicated by the existence of canonical triangulations. In this paper we show that exact morphisms of stable derivators induce exact functors of canonical triangulations, and similarly ... More

Recurrence of singularities for second order isotropic pseudodifferential operatorsDec 28 2017Let $H$ be a self-adjoint isotropic elliptic pseudodifferential operator of order $2$. Denote by $u(t)$ the solution of the Schr\"odinger equation $(i\partial_t - H)u = 0$ with initial data $u(0) = u_0$. If $u_0$ is compactly supported the solution $u(t)$ ... More

Real Equivariant Bordism for elementary abelian 2-groupsJun 29 2012We give a description of real equivariant bordism for elementary abelian 2-groups, which is similar to the description of complex equivariant bordism for the group S^1 x ... x S^1 given by Hanke in 2005.

Higher divergence for nilpotent groupsJul 26 2018The higher divergence of a metric space describes its isoperimetric behaviour at infinity. It is closely related to the higher-dimensional Dehn functions, but has more requirements to the fillings. We prove that these additional requirements do not have ... More

Partition C*-algebras II - Links to Compact Matrix Quantum GroupsOct 24 2017In a recent article, we gave a definition of partition C*-algebras. These are universal C*-algebras based on algebraic relations which are induced from partitions of sets. In this follow up article, we show that often we can associate a Hopf algebra structure ... More

From quaternions to cosmology: spaces of constant curvature, ca. 1873-1925May 01 2003After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th century debates on ... More

Degree-constrained Subgraph Reconfiguration is in PAug 06 2015The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a degree-constrained ... More

Ideles in higher dimensionJul 30 2009May 02 2011We propose a notion of idele class groups of finitely generated fields using the concept of Parshin chains. This new class group allows us to give an idelic interpretation of the higher class field theory of Kato and Saito.

A Tauberian theorem for strong Feller semigroupsOct 16 2013We prove that a weakly ergodic, eventually strong Feller semigroup on the space of measures on a Polish space converges strongly to a projection onto its fixed space.

Pesin's Formula for Random Dynamical Systems on $R^d$Jan 05 2012Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure which is absolutely ... More

Realizability and inscribability for simplicial polytopes via nonlinear optimizationAug 11 2015Oct 26 2015We show that nonlinear optimization techniques can successfully be applied to realize and to inscribe matroid polytopes and simplicial spheres. Thus we obtain a complete classification of neighborly polytopes of dimension $4$, $6$ and $7$ with $11$ vertices, ... More

Computing maximal copies of polytopes contained in a polytopeJul 02 2014Kepler (1619) and Croft (1980) have considered largest homothetic copies of one regular polytope contained in another regular polytope. For arbitrary pairs of polytopes we propose to model this as a quadratically constrained optimization problem. These ... More

Various damage mechanisms in carbon and silicon materials under femtosecond x-ray irradiationMay 19 2018We review the results of our research on damage mechanisms in materials irradiated with femtosecond free-electron-laser (FEL) pulses. They were obtained using our hybrid approach, XTANT (X-ray-induced Thermal And Nonthermal Transitions). Various damage ... More

Algorithms for Timed Consistency ModelsOct 27 2013One of the major challenges in distributed systems is establishing consistency among replicated data in a timely fashion. While the consistent ordering of events has been extensively researched, the time span to reach a consistent state is mostly considered ... More

General Resonance MediationJul 18 2012Mar 25 2013We extend the framework of general gauge mediation to cases where the mediating fields have a nontrivial spectral function, as might arise from strong dynamics. We demonstrate through examples that this setup describes a broad class of possible models ... More

Higher class field theory and the connected componentNov 28 2007Nov 25 2010In this note we present a new self-contained approach to the class field theory of arithmetic schemes in the sense of Wiesend. Along the way we prove new results on space filling curves on arithmetic schemes and on the class field theory of local rings. ... More

Filling Invariants for Carnot GroupsJul 17 2015Oct 05 2015We prove a filling theorem for Carnot groups and compute lower bounds on higher divergence functions for Carnot groups. In application to quaternionic and octonionic Heisenberg Groups we identify their filling functions below the critical dimension.

A Note on an Extension of the Incompressible Euler Equations to Relativity and the Instantaneity of its PressureJan 29 2016We introduce an extension of the incompressible Euler equations to General Relativity and show that the equations proposed correctly reduce to the incompressible Euler equations in the Newtonian limit as $c\rightarrow \infty$. For the case of constant ... More

Derivators, pointed derivators, and stable derivatorsDec 16 2011Feb 13 2012We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category. Moreover, the functors ... More

Monoidal derivators and additive derivatorsMar 22 2012One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce additive derivators ... More

Higher Divergence Functions for Heisenberg GroupsOct 14 2014Sep 29 2015We prove a Filling Theorem for the Heisenberg Groups $H^{2n+1}$: For a given $k$-cycle $a$ we construct a $(k+1)$-chain $b$ (the filling) with boundary $\partial b=a$ and controlled volume. For this filling $b$ we prove a uniform bound on the distance ... More

Making Math Searchable in WikipediaApr 19 2013Wikipedia, the world largest encyclopedia contains a lot of knowledge that is expressed as formulae exclusively. Unfortunately, this knowledge is currently not fully accessible by intelligent information retrieval systems. This immense body of knowledge ... More

On C*-Algebras Generated by Isometries with Twisted Commutation RelationsJul 12 2012In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the circle with itself. ... More

The complete enumeration of 4-polytopes and 3-spheres with nine verticesMar 14 2018Apr 18 2018We describe an algorithm to enumerate polytopes. This algorithm is then implemented to give a complete classification of combinatorial spheres of dimension 3 with 9 vertices and decide polytopality of those spheres. In particular, we completely enumerate ... More

Convergence of Dynamics and the Perron-Frobenius OperatorSep 16 2016Mar 29 2017We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent ... More

Pressure Effects on the 4f Electronic Structure of Light LanthanidesAug 17 2017Jan 23 2019Using the satellite structure of the $L_{\gamma1}$ line in non-resonant x-ray emission spectra, we probe the high-pressure evolution of the bare 4f signature of the early light lanthanides at ambient temperature. For Ce and Pr the satellite peak experiences ... More

Correlated activity of periodically driven binary networksJul 28 2016Experiments showed that excess synchronous spike events are locked to the phase of beta-oscillations in the local field potential (LFP) more strongly than spikes that appear in isolation [Denker et al. 2011, Cereb. Cortex]. To identify the mechanisms ... More

Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolutionNov 12 2014For the simulation of equilibrium states and finite-temperature response functions of strongly-correlated quantum many-body systems, we compare the efficiencies of two different approaches in the framework of the density matrix renormalization group (DMRG). ... More

Exchange-dependent relaxation in the rotating frame for slow and intermediate exchange - modeling off-resonant spin-lock and chemical exchange saturation transferMar 09 2012Dec 30 2012Chemical exchange observed by NMR saturation transfer (CEST) and spin-lock (SL) experiments provide an MRI contrast by indirect detection of exchanging protons. The determination of the relative concentrations and exchange rates is commonly achieved by ... More

Accretion, jets and winds: High-energy emission from young stellar objectsJun 14 2011This article summarizes the processes of high-energy emission in young stellar objects. Stars of spectral type A and B are called Herbig Ae/Be (HAeBe) stars in this stage, all later spectral types are termed classical T Tauri stars (CTTS). Both types ... More

Running of Radiative Neutrino Masses: The Scotogenic Model - REVISITEDJul 22 2015Dec 07 2015A few years ago, it had been shown that effects stemming from renormalisation group running can be quite large in the scotogenic model, where neutrinos obtain their mass only via a 1-loop diagram (or, more generally, in many models in which the light ... More

A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds I - Space-Times of Finite LifetimeJan 23 2013Jan 25 2016We give a functional analytic construction of the fermionic projector on a globally hyperbolic Lorentzian manifold of finite lifetime. The integral kernel of the fermionic projector is represented by a two-point distribution on the manifold. By introducing ... More

The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker UniverseJan 06 2009Feb 06 2013We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the ... More

Analysis of jump processes with nondegenerate jumping kernelsSep 16 2011Dec 21 2011We prove regularity estimates for functions which are harmonic with respect to certain jump processes. The aim of this article is to extend the method of Bass-Levin[BL02] and Bogdan-Sztonyk[BS05] to more general processes. Furthermore, we establish a ... More

Waiting time models of cancer progressionJul 23 2008Feb 03 2009Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is associated with the ... More

The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic WaveSep 15 2016We give a non-perturbative construction of a distinguished state for the quantized Dirac field in Minkowski space in the presence of a time-dependent external field of the form of a plane electromagnetic wave. By explicit computation of the fermionic ... More

Sudden relaminarisation and lifetimes in forced isotropic turbulenceMay 06 2015Sep 24 2015We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from ... More

Preventing False Discovery in Interactive Data Analysis is HardAug 06 2014We show that, under a standard hardness assumption, there is no computationally efficient algorithm that given $n$ samples from an unknown distribution can give valid answers to $n^{3+o(1)}$ adaptively chosen statistical queries. A statistical query asks ... More

Strong Secrecy for Multiple Access ChannelsSep 20 2012We show strongly secret achievable rate regions for two different wiretap multiple-access channel coding problems. In the first problem, each encoder has a private message and both together have a common message to transmit. The encoders have entropy-limited ... More

Mathoid: Robust, Scalable, Fast and Accessible Math Rendering for WikipediaApr 24 2014Wikipedia is the first address for scientists who want to recap basic mathematical and physical laws and concepts. Today, formulae in those pages are displayed as Portable Network Graphics images. Those images do not integrate well into the text, can ... More

On the vanishing of negative homotopy K-theoryJan 29 2016Dec 20 2016We show that the homotopy invariant algebraic K-theory of Weibel vanishes below the negative of the Krull dimension of a noetherian scheme. This gives evidence for a conjecture of Weibel about vanishing of negative algebraic K-groups.

Whether the Metric is Essentially Smooth at Shock Waves in General Relativity Depends on a Hidden Geometric StructureOct 07 2016In General Relativity, the gravitational metric tensor is only known to be Lipschitz continuous at shock waves, a regularity so low that locally inertial frames might not exist. It is an open question whether there exist (singular) coordinate transformations ... More

Degravitation of the Cosmological Constant in BigravityNov 28 2016In this article the phenomenon of degravitation of the cosmological constant is studied in the framework of bigravity. It is demonstrated that despite a sizable value of the cosmological constant its gravitational effect can be only mild. The bigravity ... More

Complex Gated Recurrent Neural NetworksJun 21 2018Oct 27 2018Complex numbers have long been favoured for digital signal processing, yet complex representations rarely appear in deep learning architectures. RNNs, widely used to process time series and sequence information, could greatly benefit from complex representations. ... More

Statistical field theory for neural networksJan 29 2019These notes attempt a self-contained introduction into statistical field theory applied to neural networks of rate units and binary spins. The presentation consists of three parts: First, the introduction of fundamental notions of probabilities, moments, ... More

A finiteness theorem for Galois representations of function fields over finite fields (after Deligne)Aug 01 2012Nov 29 2012Revised: just some typos, reorganized a bit the article. It will be published in the VIASM Annual meeting, Hanoi. We give a detailed account of Deligne's letter to Drinfeld dated June 18, 2011, in which he shows that there are finitely many irreducible ... More

The Fine Classification of Conjunctive Queries and Parameterized Logarithmic Space ComplexityJun 23 2013Jun 25 2013We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of boolean conjunctive queries according to the complexity of this problem. Previous work showed ... More

Improved constraints on $γ$: CKM2014 updateNov 17 2014I report on an updated combination of all currently available tree-level measurements of the CKM angle $\gamma$ from LHCb. This combination currently gives LHCb's most precise value of $\gamma = (73^{+9}_{-10})^\circ$ obtained from $B\to DK$-like decays. ... More

Chow group of 0-cycles with modulus and higher dimensional class field theoryApr 16 2013Nov 24 2015One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of higher dimensional ... More