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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

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

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

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

Accuracy of position determination in Ca$^{2+}$ signalingJul 19 2019A living cell senses its environment and responds to external signals. In this work, we study theoretically, the precision at which cells can determine the position of a spatially localized transient extracellular signal. To this end, we focus on the ... 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

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

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

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

Positional information readout in $Ca^{2+}$ signalingJun 23 2017Living cells respond to spatial signals. Signal transmission to the cell interior often involves the release of second messengers like $Ca^{2+}$ . They will eventually trigger a physiological response by activating kinases that in turn activate target ... More

Positional information readout in $Ca^{2+}$ signalingJun 23 2017Jul 19 2019Living cells respond to spatial signals. Signal transmission to the cell interior often involves the release of second messengers like $Ca^{2+}$ . They will eventually trigger a physiological response by activating kinases that in turn activate target ... 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

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

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

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

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

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.

Filling Invariants of Stratified Nilpotent Lie GroupsJul 17 2015Feb 03 2017Filling invariants are measurements of a metric space describing the behaviour of isoperimetric inequalities. In this article we examine filling functions and higher divergence functions. We prove for a class of stratified nilpotent Lie groups that in ... 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

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

Phason Dynamics in One-Dimensional LatticesFeb 09 2010In quasicrystals, the phason degree of freedom and the inherent anharmonic potentials lead to complex dynamics which cannot be described by the usual phonon modes of motion. We have constructed simple one-dimensional model systems, the dynamic Fibonacci ... More

Structure factors of harmonic and anharmonic Fibonacci chains by molecular dynamics simulationsApr 11 2007The dynamics of quasicrystals is characterized by the existence of phason excitations in addition to the usual phonon modes. In order to investigate their interplay on an elementary level we resort to various one-dimensional model systems. The main observables ... 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

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

Effects of helicity on dissipation in homogeneous box turbulenceAug 29 2018Oct 04 2018The dimensionless dissipation coefficient $\beta=\varepsilon L/U^3$ is an important characteristic of statistically stationary homogeneous turbulence. In studies of $\beta$, the external force is typically isotropic and large-scale, and its helicity $H_f$ ... 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

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

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

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 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

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

Obstructing Visibilities with One ObstacleJul 01 2016Sep 01 2016Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon $C$ and a finite set $P$ of points in general position ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fallout: Reading Kernel Writes From User SpaceMay 29 2019Recently, out-of-order execution, an important performance optimization in modern high-end processors, has been revealed to pose a significant security threat, allowing information leaks across security domains. In particular, the Meltdown attack leaks ... More

The Complexity of Drawing Graphs on Few Lines and Few PlanesJul 21 2016It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the minimum number of lines in $\mathbb{R}^d$ ... More

A graphite-prism definition for Avogadro's "integer"Jan 25 2012Aug 05 2015The new International System of Units may let us select an integer value for Avogadro's number. Some might prefer an integer that's divisible by 12, so that an integer number of $^{12}C$ atoms may be associated (to first order) with a gram's mass. For ... More

Semi-implicit finite-difference method with predictor-corrector algorithm for solution of diffusion equation with nonlinear termsNov 26 2015We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm and provides ... More

Drawing Graphs on Few Lines and Few PlanesJul 05 2016Sep 01 2016We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections to other challenging ... More

The large-scale dynamics of magnetic helicityMay 05 2016In this Letter we investigate the dynamics of magnetic helicity in magnetohydrodynamic (MHD) turbulent flows focusing at scales larger than the forcing scale. Our results show a non-local inverse cascade of magnetic helicity, which occurs directly from ... More

On the vanishing of negative homotopy K-theoryJan 29 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.

Detecting multi-atomic composite states in optical latticesSep 20 2006We propose and discuss methods for detecting quasi-molecular complexes which are expected to form in strongly interacting optical lattice systems. Particular emphasis is placed on the detection of composite fermions forming in Bose-Fermi mixtures. We ... More

A renormalizable effective theory for leading logarithms in ChPTJan 17 2007We argue that the linear sigma model at small external momenta is an effective theory for the leading logarithms of chiral perturbation theory. Based on this assumption an attempt is made to sum these leading logarithms using the standard renormalization ... More

Correlated activity of periodically driven binary networksJul 28 2016Oct 21 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

Relative perturbation bounds with applications to empirical covariance operatorsFeb 08 2018The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and limit theorems. ... More

Tunneling of quasiholes in the fractional quantum Hall regimeMar 03 2004The elementary low energy excitations in the fractional quantum Hall (FQH) regime are known to be fractionally charged quasiparticles and quasiholes. This work focusses on quasiholes in a finite system of a few electrons treated by exact numerical diagonalization. ... More

Intertwiner spaces of quantum group subrepresentationsNov 07 2018We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to this $(N-1)$-dimensional ... More

Optimal metric regularity in General Relativity follows from the RT-equations by elliptic regularity theory in $L^p$-spacesAug 20 2018Aug 23 2018We prove existence of solutions to the Regularity Transformation equations (RT-equations), and thereby demonstrate that regularity singularities do not exist in General Relativity, when the connection $\Gamma$ of the gravitational metric satisfies $\Gamma, ... More

The Regularity Transformation Equations: An elliptic mechanism for smoothing gravitational metrics in General RelativityMay 02 2018Sep 24 2018Regularity singularities are points in spacetime where the gravitational metric tensor of General Relativity fails to be at least two levels more regular than its curvature tensor. Whether regularity singularities exist for shock wave solutions constructed ... More

Natural Supersymmetry and Dynamical Flavour with Metastable VacuaApr 04 2014We show how gauged flavour breaking and N = 1 supersymmetry breaking can be dynamically aligned to produce natural models. Supersymmetry is broken in a metastable vacuum, while a weakly gauged flavour symmetry is identified with an SU(3)_F subgroup of ... More

The combinatorics of an algebraic class of easy quantum groupsDec 05 2013Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group and the orthogonal group as well as Wang's quantum permutation group and ... More

Convergence of Positive Operator SemigroupsMay 03 2017Jan 26 2019We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a purely algebraic ... More

On a Convergence Theorem for Semigroups of Positive Integral OperatorsJun 04 2017We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive $C_0$-semigroup on an $L^p$-space is strongly convergent in case that it has a strictly positive fixed point and contains an integral operator. Our proof ... More

Comparability and regularity estimates for symmetric nonlocal Dirichlet formsSep 30 2011The aim of this work is to study comparability of nonlocal Dirichlet forms. We provide sufficient conditions on the kernel for local and global comparability. As an application we prove a-priori estimates in H\"{o}lder spaces for solutions to integrodifferential ... More

Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by SemigroupsJan 10 2019Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by partitions of finite ... More

Intertwiner spaces of quantum group subrepresentationsNov 07 2018Mar 30 2019We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to this $(N-1)$-dimensional ... More

Quantum groups based on spatial partitionsSep 08 2016We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so called easy ... More

The classification of tensor categories of two-colored noncrossing partitionsSep 03 2015Our basic objects are partitions of finite sets of points into disjoint subsets. We investigate sets of partitions which are closed under taking tensor products, composition and involution, and which contain certain base partitions. These so called categories ... More

Regularity estimates for elliptic nonlocal operatorsSep 28 2015Nov 25 2015We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general, possibly singular, ... More

Sandpile monomorphisms and harmonic functionsApr 27 2019The abelian sandpile model is a cellular automaton defined on a finite convex domain $\Gamma\subset\mathbb{Z}^2$ of the standard square lattice $\mathbb{Z}^2$. Its recurrent configurations form an abelian group, the sandpile group. Little is known about ... More

Solving systems of linear equations on a quantum computerFeb 05 2013Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers, making for one ... More

Semi-implicit finite-difference method with predictor-corrector algorithm for solution of diffusion equation with nonlinear termsNov 26 2015Jul 04 2019We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm and provides ... 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

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

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

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

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

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

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

Observing small-scale $γ$-ray anisotropies with the Cherenkov Telescope ArrayJun 05 2018Aug 22 2018Disentangling the composition of the diffuse gamma-ray background (DGRB) is a major challenge in gamma-ray astronomy. It is presumed that at the highest energies, the DGRB is dominated by relatively few, still unresolved point sources. This conjecture ... More

Mean ergodicity vs weak almost periodicitySep 07 2017Mar 06 2018We provide explicit examples of positive and power-bounded operators on $c_0$ and $\ell^\infty$ which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and ... More

Pure Measures, Density Measures and the Dual of L-infinityOct 05 2017Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The main results ... More