Results for "Lukas Simon"

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Impersonating LoRaWAN gateways using Semtech Packet ForwarderApr 24 2019Low Power Wide Area Network (LPWAN) technologies like the Long Range Wide Area Network (LoRaWAN) standard provide the foundation of applications realizing communication and intelligent interaction between almost any kind of object. These applications ... More
Analysis of the Linearized Problem of Quantitative Photoacoustic TomographyFeb 15 2017Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative transfer equation ... More
GPdoemd: a Python package for design of experiments for model discriminationOct 05 2018Mar 08 2019Model discrimination identifies a mathematical model that usefully explains and predicts a given system's behaviour. Researchers will often have several models, i.e. hypotheses, about an underlying system mechanism, but insufficient experimental data ... More
Coulomb Blockade Spectroscopy of $\mathrm{MoS}_2$ NanotubesApr 11 2019Apr 28 2019We demonstrate low-temperature transport spectroscopy measurements on a quantum dot lithographically defined in a multiwall MoS2 nanotube. At T=300mK, clear Coulomb blockade is observed, with charging energies in the range of 1meV. In single electron ... More
Micromagnetics of rare-earth efficient permanent magnetsMar 28 2019The development of permanent magnets containing less or no rare-earth elements is linked to profound knowledge of the coercivity mechanism. Prerequisites for a promising permanent magnet material are a high spontaneous magnetization and a sufficiently ... More
The Little Bundles OperadJan 15 2019Feb 10 2019Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy quotient we build an aspherical topological operad that we call the little ... More
Optomechanics with one-dimensional gallium phosphide photonic crystal cavitiesDec 03 2018Gallium phosphide offers an attractive combination of a high refractive index ($n>3$ for vacuum wavelengths up to 4 {\mu}m) and a wide electronic bandgap (2.26 eV), enabling optical cavities with small mode volumes and low two-photon absorption at telecommunication ... More
Simulation of magnetic active polymers for versatile microfluidic devicesMay 30 2013We propose to use a compound of magnetic nanoparticles (20-100 nm) embedded in a flexible polymer (Polydimethylsiloxane PDMS) to filter circulating tumor cells (CTCs). The analysis of CTCs is an emerging tool for cancer biology research and clinical cancer ... More
A digit reversal property for Stern polynomialsOct 01 2016Nov 15 2017We consider the following polynomial generalization of Stern's diatomic series: let $s_1(x,y)=1$, and for $n\geq 1$ set $s_{2n}(x,y)=s_n(x,y)$ and $s_{2n+1}(x,y)=x\,s_n(x,y)+y\,s_{n+1}(x,y)$. The coefficient $[x^iy^j]s_n(x,y)$ is the number of hyperbinary ... More
On the Hilbert series of the GrassmannianDec 15 2017We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods and show that its h-polynomial coincides with the k-Narayana polynomial. We give a simplified formula for the h-polynomial of Schubert varieties. Finally, we use ... More
Linearizability of Saturated PolynomialsJul 09 2015Mar 11 2019Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this is sharp for ... More
Smooth Siegel disks without number theory: A remark on a proof by Buff and CheritatOct 26 2005X. Buff and A. Cheritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of A. Avila, we give yet another simplification of their proof. The main tool used is a harmonic function introduced ... More
On eigenvalue and eigenvector estimates for nonnegative definite operatorsMar 16 2005In this article we further develop a perturbation approach to the Rayleigh--Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of the theory to nonnegative definite operators . The perturbation argument ... More
Gorensteinness and iteration of Cox rings for Fano type varietiesMar 19 2019Apr 08 2019We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of ... More
Decomposing Sets of InversionsNov 15 2011Aug 06 2012In this note we consider the question how the set of inversions of a permutation $\pi \in S_n$ can be partitioned into two subset, such that those are itself inversion sets of permutations. This is archived by exploiting a connection to a graph theoretical ... More
SL(n)-Contravariant $L_p$-Minkowski ValuationsOct 26 2014All SL(n)-contravariant $L_p$-Minkowski valuations on polytopes are completely classified. The prototypes of such valuations turn out to be the asymmetric $L_p$-projection body operators.
Motion planning in high-dimensional spacesJun 19 2018Jul 19 2018Motion planning is a key tool that allows robots to navigate through an environment without collisions. The problem of robot motion planning has been studied in great detail over the last several decades, with researchers initially focusing on systems ... More
Small Sets with Large Difference SetsMay 24 2017For every $\epsilon > 0$ and $k \in \mathbb{N}$, Haight constructed a set $A \subset \mathbb{Z}_N$ ($\mathbb{Z}_N$ stands for the integers modulo $N$) for a suitable $N$, such that $A-A = \mathbb{Z}_N$ and $|kA| < \epsilon N$. Recently, Nathanson posed ... More
Newton-Machian analysis of Neo-tychonian model of planetary motionsJan 25 2013Feb 06 2013The calculation of the trajectories in the Sun-Earth-Mars system will be performed in two different models, both in the framework of Newtonian mechanics. First model is well-known Copernican system, which assumes the Sun is at rest and all the planets ... More
Relative convergence estimates for the spectral asymptotic in the Large Coupling LimitFeb 13 2009We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational Linear Algebra ... More
The structure of DGA resolutions of monomial idealsOct 20 2016Jun 20 2018Let $I \subset k[x_1, \dotsc, x_n]$ be a squarefree monomial ideal a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $k[x_1, \dotsc, x_n]/I$. In particular, we characterize the possible vectors of ... More
Algebraic Multilevel Methods for Markov ChainsNov 12 2017Dec 30 2017A new algebraic multilevel algorithm for computing the second eigenvector of a column-stochastic matrix is presented. The method is based on a deflation approach in a multilevel aggregation framework. In particular a square and stretch approach, first ... More
Sharp bounds for the valence of certain harmonic polynomialsOct 25 2005D. Khavinson and G. Swiatek proved that harmonic polynomials p(z)+q(z), where p is holomorphic, q is antiholomorphic, and deg p = n > 1 = deg q, can have at most 3n-2 complex zeros. We show that this bound is sharp for all n by proving a conjecture of ... More
The Linear Ordering Polytope via RepresentationsSep 23 2011Oct 25 2011Let $P_n$ denote the $n$-th linear ordering polytope. We define projections from $P_n$ to the $n$-th permutahedron and to the $(n-1)$-st linear ordering polytope. Both projections are equivariant with respect to the natural $\Sn$-action and they project ... More
Generalized Monotone Triangles: an extended Combinatorial Reciprocity TheoremJul 18 2012In a recent work, the combinatorial interpretation of the polynomial alpha(n;k1,k2,...,kn) counting the number of Monotone Triangles with bottom row k1 < k2 < ... < kn was extended to weakly decreasing sequences k1 >= k2 >= ... >= kn. In this case the ... More
Heights and totally $p$-adic numbersApr 20 2015Oct 28 2015We study the behavior of canonical height functions $\widehat{h}_f$, associated to rational maps $f$, on totally $p$-adic fields. In particular, we prove that there is a gap between zero and the next smallest value of $\widehat{h}_f$ on the maximal totally ... More
Completing the classification of representations of $\mathrm{SL}_n$ with complete intersection invariant ringDec 05 2018We present a full list of all representations of the special linear group $\mathrm{SL}_n$ over the complex numbers with complete intersection invariant ring, completing the classification of Shmelkin. For this task, we combine three techniques. Firstly, ... More
A non-Golod ring with a trivial product on its Koszul homologyNov 16 2015Jan 30 2017We present a monomial ideal $\mathfrak{a} \subset S$ such that $S/\mathfrak{a}$ is not Golod, even though the product on its Koszul homology is trivial. This constitutes a counterexample to a well-known result by Berglund and J\"ollenbeck (the error can ... More
Approaching Cusick's conjecture on the sum-of-digits functionApr 18 2019Cusick's conjecture on the binary sum of digits $s(n)$ of a nonnegative integer $n$ states the following: for all nonnegative integers $t$ we have \[ c_t=\lim_{N\rightarrow\infty}\frac 1N\left\lvert\{n<N:s(n+t)\geq s(n)\}\right\rvert>1/2. \] We prove ... More
Linearity in minimal resolutions of monomial idealsFeb 24 2017Mar 24 2017Let $S = k[x_1, \dotsc, x_n]$ be a polynomial ring over a field $k$ and let $M$ be a graded $S$-module with minimal free resolution $\mathbb{F}_\bullet$. Its linear part $lin(\mathbb{F}_\bullet)$ is obtained by deleting all non-linear entries from the ... More
SL(n)-Covariant $L_p$-Minkowski ValuationsSep 18 2012Jul 01 2015All continuous SL(n)-covariant $L_p$-Minkowski valuations defined on convex bodies are completely classified. The $L_p$-moment body operators turn out to be the nontrivial prototypes of such maps.
A response-matrix-centred approach to presenting cross-section measurementsMar 15 2019Mar 21 2019The current canonical approach to publishing cross-section data is to unfold the reconstructed distributions. Detector effects like efficiency and smearing are undone mathematically, yielding distributions in true event properties. This is an ill-posed ... More
Stanley depth and simplicial spanning treesOct 14 2014Mar 09 2015We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection with the simplicial spanning trees of skeletons of a simplex. We apply ... More
Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic TomographyJan 22 2018Feb 08 2018The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate ... More
Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic TomographyJan 22 2018Mar 28 2018The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate ... More
Single-stage reconstruction algorithm for quantitative photoacoustic tomographyJan 19 2015Mar 25 2015The development of efficient and accurate image reconstruction algorithms is one of the cornerstones of computed tomography. Existing algorithms for quantitative photoacoustic tomography currently operate in a two-stage procedure: First an inverse source ... More
Analysis of the Block Coordinate Descent Method for Non-linear Ill-Posed ProblemsFeb 13 2019Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates simultaneously. ... More
Design and modeling of a transistor vertical-cavity surface-emitting laserFeb 15 2011A multiple quantum well (MQW) transistor vertical-cavity surface-emitting laser (T-VCSEL) is designed and numerically modeled. The important physical models and parameters are discussed and validated by modeling a conventional VCSEL and comparing the ... More
Gap control in phosphorene/BN structures from first principles calculationsJul 27 2016Using both DFT as well as $G_0W_0$ calculations, we investigate static and dynamic effects on the phosphorene band gap upon deposition and encapsulation on/in BN multilayers. We demonstrate how competing long- and short-range effects cause the phosphorene ... More
ConFusion: Sensor Fusion for Complex Robotic Systems using Nonlinear OptimizationJun 19 2018Mar 01 2019We present ConFusion, an open-source package for online sensor fusion for robotic applications. ConFusion is a modular framework for fusing measurements from many heterogeneous sensors within a moving horizon estimator. ConFusion offers greater flexibility ... More
Highly selective dry etching of GaP in the presence of Al$_\textrm{x}$Ga$_{1-\textrm{x}}$PJan 19 2018We present an inductively coupled-plasma reactive-ion etching process that simultaneously provides both a high etch rate and unprecedented selectivity for gallium phosphide (GaP) in the presence of aluminum gallium phosphide (Al$_\textrm{x}$Ga$_{1-\textrm{x}}$P). ... More
ConFusion: Sensor Fusion for Complex Robotic Systems using Nonlinear OptimizationJun 19 2018Oct 09 2018We present ConFusion, an open-source package for online sensor fusion for robotic applications. ConFusion is a modular framework for fusing measurements from many heterogeneous sensors within a moving horizon estimator. ConFusion offers greater flexibility ... More
vh@nnlo-v2: New physics in Higgs StrahlungFeb 13 2018May 14 2018Introducing version 2 of the code vh@nnlo, we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions ... More
Towards Blockchain-based Auditable Storage and Sharing of IoT DataMay 22 2017Nov 14 2017Today the cloud plays a central role in storing, processing, and distributing data. Despite contributing to the rapid development of IoT applications, the current IoT cloud-centric architecture has led into a myriad of isolated data silos that hinders ... More
vh@nnlo-v2: New physics in Higgs StrahlungFeb 13 2018Introducing version 2 of the code vh@nnlo, we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions ... More
Droplet: Decentralized Authorization for IoT Data StreamsJun 06 2018Nov 14 2018This paper presents Droplet, a decentralized data access control service, which operates without intermediate trust entities. Droplet enables data owners to securely and selectively share their encrypted data while guaranteeing data confidentiality against ... More
Design Considerations of Biaxially Tensile-Strained Germanium-on-Silicon LasersNov 18 2015Dec 14 2015Physical models of Ge energy band structure and material loss were implemented in LASTIP(TM), a 2D simulation tool for edge emitting laser diodes. The model calculation is able to match experimental data available. Important design parameters of a Fabry-Perot ... More
Learning Taxonomies of Concepts and not Words using Contextualized Word Representations: A Position PaperJan 31 2019Taxonomies are semantic hierarchies of concepts. One limitation of current taxonomy learning systems is that they define concepts as single words. This position paper argues that contextualized word representations, which recently achieved state-of-the-art ... More
The Symmetric signature of cyclic quotient singularitiesMar 21 2016The symmetric signature is an invariant of local domains which was recently introduced by Brenner and the first author in an attempt to find a replacement for the $F$-signature in characteristic zero. In the present note we compute the symmetric signature ... More
Rank Revealing Gaussian Elimination by the Maximum Volume ConceptFeb 08 2018A Gaussian elimination algorithm is presented that reveals the numerical rank of a matrix by yielding small entries in the Schur complement. The algorithm uses the maximum volume concept to find a square nonsingular submatrix of maximum dimension. The ... More
The stable 4-genus of alternating knotsMay 13 2015Nov 21 2016We show that the difference between the genus and the stable topological 4-genus of alternating knots is either zero or at least 1/3.
Nonlinear plastic modes in disordered solidsJul 24 2015Oct 27 2015We propose a framework within which a robust mechanical definition of precursors to plastic instabilities, often termed `soft-spots', naturally emerges. They are shown to be collective displacements (modes) $\hat{z}_0$ that correspond to local minima ... More
Heavy hyperplanes in multiarrangements and their freenessMar 18 2016Only few categories of free arrangements are known in which Terao's conjecture holds. One of such categories consists of $3$-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements ... More
New Quantum Obstructions to SlicenessJan 28 2015Apr 28 2016It is well-known that generic perturbations of the complex Frobenius algebra used to define Khovanov cohomology each give rise to Rasmussen's concordance invariant s. This gives a concordance homomorphism to the integers and a strong lower bound on the ... More
Soft See-Saw: Radiative Origin of Neutrino Masses in SUSY TheoriesSep 23 2016Radiative neutrino mass generation within supersymmetric (SUSY) construction is studied. The mechanism is considered where the lepton number violation is originating from the soft SUSY breaking terms. This requires extensions of the MSSM with states around ... More
On weakly formulated Sylvester equations and applicationsJul 26 2005We use a ``weakly formulated'' Sylvester equation $$A^{1/2}TM^{-1/2}-A^{-1/2}TM^{1/2}=F$$ to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis ... More
Centro-Affine Tensor ValuationsSep 13 2015We completely classify all measurable $\operatorname{SL}(n)$-covariant symmetric tensor valuations on convex polytopes containing the origin in their interiors. It is shown that essentially the only examples of such valuations are the moment tensor and ... More
Reconstruction theorem for complex polynomialsFeb 01 2015May 01 2015Recently Takens' Reconstruction Theorem was studied in the complex analytic setting by Forn{\ae}ss and Peters \cite{FP}. They studied the real orbits of complex polynomials, and proved that for non-exceptional polynomials ergodic properties such as measure ... More
Asymptotic normality of the likelihood moment estimators for a stationary linear process with heavy-tailed innovationsMay 25 2016A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently proved that the ... More
Multi-time formulation of particle creation and annihilation via interior-boundary conditionsAug 13 2018Sep 21 2018Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of linear conditions ... More
Random Set Solutions to Stochastic Wave EquationsMar 15 2019This paper is devoted to three topics. First, proving a measurability theorem for multifunctions with values in non-metrizable spaces, which is required to show that solutions to stochastic wave equations with interval parameters are random sets; second, ... More
Neuromodulation of Neuromorphic CircuitsMay 15 2018Mar 21 2019We present a novel methodology to enable control of a neuromorphic circuit in close analogy with the physiological neuromodulation of a single neuron. The methodology is general in that it only relies on a parallel interconnection of elementary voltage-controlled ... More
LOOL: Mathematica package for evaluating leading order one loop functionsJul 10 2014One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the evaluation. ... More
Supplementary kinetic constants of charged particlesDec 21 2006We put forward: (A) An improved description of classical, kinetic properties of a charged pointlike physical particle that consists, in addition to its mass and charge, also of the Eliezer and Bhabha kinetic constants; and (B) a proposal to evaluate these ... More
Framework for finite alternative theories to a quantum field theory. II-UnitarityOct 24 2003We generalized the 't Hooft-Veltman method of unitary regulators to put forward a path-integral framework for finite, alternative theories to a given quantum field theory. And we demonstrated that the proposed framework is feasible by providing a finite ... More
Diagnostics of Plasma Properties in Broad Line Region of AGNsSep 23 2003The Boltzmann-plot (BPT) method for laboratory plasma diagnostic was used for a quick estimate of physical conditions in the Broad Line Region (BLR) of 14 Active Galactic Nuclei (AGNs). For the BLR of nine AGNs, where PLTE exist, the estimated electron ... More
Realistic regularization of the QED Green functionsMar 13 2000Jul 02 2001Generalizing the 't Hooft and Veltman method of unitary regulators, we demonstrate for the first time the existence of local, Lorentz-invariant, physically motivated Lagrangians of quantum-electrodynamic phenomena such that: (i) Feynman diagrams are finite ... More
Szemerédi's theorem in the primesSep 14 2017Green and Tao famously proved in 2005 that any subset of the primes of fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to zero sufficiently ... More
Formulae for Line Bundle Cohomology on Calabi-Yau ThreefoldsAug 29 2018Sep 26 2018We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by systematising ... More
Dynamic Flows with Adaptive Route ChoiceNov 18 2018Nov 23 2018We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest ... More
Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences, IINov 05 2015Nov 15 2017We prove that the Thue--Morse sequence $\mathbf t$ along subsequences indexed by $\lfloor n^c\rfloor$ is normal, where $1<c<3/2$. That is, for $c$ in this range and for each $\omega\in\{0,1\}^L$, where $L\geq 1$, the set of occurrences of $\omega$ as ... More
On classical upper bounds for slice generaNov 08 2016Apr 05 2019We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound for another version of the slice genus proposed here: the minimal genus of ... More
Dissecting Adam: The Sign, Magnitude and Variance of Stochastic GradientsMay 22 2017Jun 20 2018The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of stochastic ... More
On conditional moments of high-dimensional random vectors given lower-dimensional projectionsMay 09 2014Sep 06 2016One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also shared, in ... More
Linearized Filtering of Affine Processes Using Stochastic Riccati EquationsJan 23 2018We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for its law, for some time $t > 0 $, conditional on all observations up to this time $ t $. This is a general, possibly high dimensional filtering problem ... More
Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov--Poisson equationsNov 10 2012A rigorous convergence analysis of the Strang splitting algorithm with a discontinuous Galerkin approximation in space for the Vlasov--Poisson equations is provided. It is shown that under suitable assumptions the error is of order $\mathcal{O}(\tau^2+h^q ... More
Compressible multi-component flow in porous media with Maxwell-Stefan diffusionMay 21 2019We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan theory in a thermodynamically ... More
Rolling G_2 ModuliAug 28 2003We study the time evolution of freely rolling moduli in the context of M-theory on a G_2 manifold. This free evolution approximates the correct dynamics of the system at sufficiently large values of the moduli when effects from non-perturbative potentials ... More
Continuants, run lengths, and Barry's modified Pascal triangleOct 17 2017We show that the $n$'th diagonal sum of Barry's modified Pascal triangle can be described as the continuant of the run lengths of the binary representation of $n$. We also obtain an explicit description for the row sums.
The $v_n$-periodic Goodwillie tower on Wedges and CofibresDec 08 2016Jul 04 2017We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge $X \vee Y$ of spaces (using the Hilton-Milnor theorem) and on the cofibre $\mathrm{cof}(f)$ of a map $f: X \rightarrow Y$. We deduce some consequences for ... More
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torusJul 21 2006For a general class of linear collisional kinetic models in the torus, including in particular the linearized Boltzmann equation for hard spheres, the linearized Landau equation with hard and moderately soft potentials and the semi-classical linearized ... More
Bad practices in evaluation methodology relevant to class-imbalanced problemsDec 04 2018For research to go in the right direction, it is essential to be able to compare and quantify performance of different algorithms focused on the same problem. Choosing a suitable evaluation metric requires deep understanding of the pursued task along ... More
An explicit generating function arising in counting binomial coefficients divisible by powers of primesApr 24 2016Nov 08 2017For a prime $p$ and nonnegative integers $j$ and $n$ let $\vartheta_p(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are exactly divisible by $p^j$. Moreover, for a finite sequence $w=(w_{r-1}\cdots w_0)\neq (0,\ldots,0)$ in ... More
Combinatorial Reciprocity for Monotone TrianglesNov 11 2011The number of Monotone Triangles with bottom row k1 < k2 < ... < kn is given by a polynomial alpha(n; k1,...,kn) in n variables. The evaluation of this polynomial at weakly decreasing sequences k1 >= k2 >= ... >= kn turns out to be interpretable as signed ... More
The Homology of Connective Morava $E$-theory with coefficients in $\mathbb{F}_p$Apr 24 2017Let $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;\mathbb{F}_p)$ for any prime $p$ and $n \leq 4$ up to possible multiplicative extensions when $n$ is $3$ or $4$. We ... More
Convergence analysis of Strang splitting for Vlasov-type equationsJul 09 2012May 01 2013A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step \tau. ... More
Stability of steady states in kinetic Fokker-Planck equations for Bosons and FermionsJul 31 2007We study a class of nonlinear kinetic Fokker-Planck type equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence of classical solutions in the perturbative regime and prove ... More
Lonely runners in function fieldsNov 03 2017Dec 26 2018The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture asserts that ... More
Canonical threefold singularities with a torus action of complexity one and $k$-empty polytopesJul 20 2018We classify the canonical threefold singularities that allow an effective two-torus action. This extends classification results of Mori on terminal threefold singularities and of Ishida and Iwashita on toric canonical threefold singularities. Our classification ... More
The Tu--Deng Conjecture holds almost surelyJul 25 2017Jul 10 2018The Tu--Deng Conjecture is concerned with the sum of digits $w(n)$ of $n$ in base~$2$ (the Hamming weight of the binary expansion of $n$) and states the following: assume that $k$ is a positive integer and $1\leq t<2^k-1$. Then \[\Bigl \lvert\Bigl\{(a,b)\in\bigl\{0,\ldots,2^k-2\bigr\}^2:a+b\equiv ... More
Divisibility of binomial coefficients by powers of twoOct 30 2017For nonnegative integers $j$ and $n$ let $\Theta(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are not divisible by $2^{j+1}$. In this paper we prove that the family $j\mapsto\Theta(j,n)$ usually follows a normal distribution. ... More
Deterministic Control of Stochastic Reaction-Diffusion EquationsMay 22 2019We consider the control of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise via deterministic controls. Existence of optimal controls and necessary conditions for optimality are derived. Using adjoint calculus, we ... More
Edge rings satisfying Serre's condition R_1Feb 22 2012Aug 06 2012A combinatorial criterion for the edge ring of a finite connected graph to satisfy Serre's condition R_1 is studied.
On the inverse Klain mapJun 23 2012Nov 15 2012The continuity of the inverse Klain map is investigated and the class of centrally symmetric convex bodies at which every valuation depends continuously on its Klain function is characterized. Among several applications, it is shown that McMullen's decomposition ... More
An introduction to matrix convex sets and free spectrahedraNov 09 2016Sep 06 2018The purpose of this paper is to give a self-contained overview of the theory of matrix convex sets and free spectrahedra. We will give new proofs and generalizations of key theorems. However we will also introduce various new concepts and results as well. ... More
The Action of Young Subgroups on the Partition ComplexJan 04 2018Mar 06 2018We study the restrictions, the strict fixed points, and the strict quotients of the partition complex $|\Pi_n|$, which is the $\Sigma_n$-space attached to the poset of proper nontrivial partitions of the set $\{1,\ldots,n\}$. We express the space of fixed ... More
Deformation Theory and Partition Lie AlgebrasApr 15 2019May 15 2019A theorem of Lurie and Pridham establishes a correspondence between formal moduli problems and differential graded Lie algebras in characteristic zero, thereby formalising a well-known principle in deformation theory. We introduce a variant of differential ... More
Reduced dynamical systemsFeb 12 2019We consider the dynamics of complex rational maps on the Riemann sphere. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini-Study distances between finitely many initial elements of the orbit and the ... More
The Discrete Langevin Machine: Bridging the Gap Between Thermodynamic and Neuromorphic SystemsJan 16 2019Apr 18 2019A formulation of Langevin dynamics for discrete systems is derived as a new class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a novel network architecture which is implemented by the Langevin machine. The ... More
On the exactness of Lasserre relaxations for compact convex basic closed semialgebraic setsApr 24 2017Feb 28 2018Consider a finite system of non-strict real polynomial inequalities and suppose its solution set $S\subseteq\mathbb R^n$ is convex, has nonempty interior and is compact. Suppose that the system satisfies the Archimedean condition, which is slightly stronger ... More