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Directional time frequency analysis via continuous frameFeb 15 2014Grafakos and Sansing \cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L^2(\mr^n)$ based on Gabor systems in $\ltr;$ the key tool is the "ridge idea," which lifts a function of one variable to a function of several ... More

Optimal leverage from non-ergodicityFeb 17 2009Aug 09 2010In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies ... More

Menger 1934 revisitedOct 07 2011Karl Menger's 1934 paper on the St. Petersburg paradox contains mathematical errors that invalidate his conclusion that unbounded utility functions, specifically Bernoulli's logarithmic utility, fail to resolve modified versions of the St. Petersburg ... More

The time resolution of the St. Petersburg paradoxNov 19 2010Mar 23 2011A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel ... More

The sum of log-normal variates in geometric Brownian motionFeb 08 2018Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology ... More

Insurance makes wealth grow fasterJul 16 2015Jul 13 2017Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, ... More

Tuning- and order parameter in the SOC ensembleDec 11 2009The one-dimensional Oslo model is studied under self-organized criticality (SOC) conditions and under absorbing state (AS) conditions. While the activity signals the phase transition under AS conditions by a sudden increase, this is not the case under ... More

Amplitude noise and coherence degradation of femtosecond supercontinuum generation in all-normal-dispersion fibersFeb 04 2019Supercontinuum (SC) generation via femtosecond (fs) pumping in all-normal-dispersion (ANDi) fiber is predicted to offer completely coherent broadening mechanisms, potentially allowing for substantially reduced noise levels in comparison to those obtained ... More

Stochastic Market EfficiencyJan 24 2011It is argued that the simple trading strategy of leveraging or deleveraging an investment in the market portfolio cannot outperform the market. Such stochastic market efficiency places strong constraints on the possible stochastic properties of the market. ... More

Universality under conditions of self-tuningFeb 11 2009Aug 09 2010We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same finite-size scaling ... More

The time interpretation of expected utility theoryJan 11 2018Decision theory is the model of individual human behavior employed by neoclassical economics. Built on this model of individual behavior are models of aggregate behavior that feed into models of macroeconomics and inform economic policy. Neoclassical ... More

Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"Apr 04 2008In [Braz. J. Phys. 30, 27 (2000)] Dickman et al. suggested that self-organized criticality can be produced by coupling the activity of an absorbing state model to a dissipation mechanism and adding an external drive. We analyzed the proposed mechanism ... More

The evolutionary advantage of cooperationJun 10 2015The present study asks how cooperation and consequently structure can emerge in many different evolutionary contexts. Cooperation, here, is a persistent behavioural pattern of individual entities pooling and sharing resources. Examples are: individual ... More

Self-organized Criticality and Absorbing States: Lessons from the Ising ModelNov 29 2004We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it can be used for ... More

Ergodicity breaking in geometric Brownian motionSep 20 2012Mar 14 2013Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any ... More

An evolutionary advantage of cooperationJun 10 2015May 24 2018Cooperation is a persistent behavioral pattern of entities pooling and sharing resources. Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism ... More

Rational insurance with linear utility and perfect informationJul 16 2015We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the expectation value of wealth, buying insurance is only ... More

Rain: Relaxations in the skyApr 04 2002We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in Nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the ... More

A recipe for irreproducible resultsJun 23 2017Recent studies have shown that many results published in peer-reviewed scientific journals are not reproducible. This raises the following question: why is it so easy to fool myself into believing that a result is reliable when in fact it is not? Using ... More

Leverage efficiencyJan 24 2011Jul 13 2017Peters (2011a) defined an optimal leverage which maximizes the time-average growth rate of an investment held at constant leverage. We test the hypothesis that this optimal leverage is attracted to 1, such that leveraging an investment in the market portfolio ... More

Defect states and spin-orbital physics in doped vanadates Y1-xCaxVO3Jan 17 2013We present a model for typical charged defects in weakly doped Y1-xCaxVO3 perovskites and study how they influence the magnetic and orbital order. Starting from a multiband Hubbard model, we show that the charge carriers introduced by doping are bound ... More

Critical phenomena in atmospheric precipitationJun 02 2006Critical phenomena near continuous phase transitions are typically observed on the scale of wavelengths of visible light[1]. Here we report similar phenomena for atmospheric precipitation on scales of tens of kilometers. Our observations have important ... More

Frames containing a Riesz basis and preservation of this property under perturbationSep 22 1995Aldroubi has shown how one can construct any frame $\gtu$ starting with one frame $\ftu $,using a bounded operator $U$ on $l^2(N)$. We study the overcompleteness of the frames in terms of properties of $U$. We also discuss perturbation of frames in the ... More

Classifying Tight Weyl-Heisenberg FramesDec 30 1998A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions ... More

Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$Sep 22 1995We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. ... More

Weyl-Heisenberg frames for subspaces of L^2(R)Nov 24 1998We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R), wou conditions are significantly weaker than the previous known conditions. ... More

Evaluating gambles using dynamicsMay 03 2014Jun 05 2015Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions ... More

Simultaneous Object Detection and Semantic SegmentationMay 06 2019Both object detection in and semantic segmentation of camera images are important tasks for automated vehicles. Object detection is necessary so that the planning and behavior modules can reason about other road users. Semantic segmentation provides for ... More

Theory of optical spectral weights in Mott insulators with orbital degrees of freedomMar 18 2004Jun 09 2004Introducing partial sum rules for the optical multiplet transitions, we outline a unified approach to magnetic and optical properties of strongly correlated transition metal oxides. On the example of LaVO$_3$ we demonstrate how the temperature and polarization ... More

Spin-orbital entanglement near quantum phase transitionsJun 17 2007Spin-orbital entanglement in the ground state of a one-dimensional SU(2)$\otimes$SU(2) spin-orbital model is analyzed using exact diagonalization of finite chains. For $S=1/2$ spins and $T=1/2$ pseudospins one finds that the quantum entanglement is similar ... More

Orbitally induced string formation in the spin-orbital polaronsMay 14 2009We study the spectral function of a single hole doped into the (a,b) plane of the Mott insulator LaVO$_3$, with antiferromagnetic (AF) spin order of S=1 spins accompanied by alternating orbital (AO) order of active $\{d_{yz},d_{zx}\}$ orbitals. Starting ... More

Compass-Heisenberg Model on the Square Lattice : Spin Order and ExcitationsMay 10 2010Sep 13 2010We explore the physics of the anisotropic compass model under the influence of perturbing Heisenberg interactions and present the phase diagram with multiple quantum phase transitions. The macroscopic ground state degeneracy of the compass model is lifted ... More

50 Years of Bailey's lemmaOct 12 2009Oct 14 2009This is a paper published in 2001 based on a talk given in 1999 celebrating the 50th anniversary of W. N. Bailey's influential q-series paper "Identities of the Rogers-Ramanujan type". In no more than 13 pages I give a brief but reasonably complete overview ... More

On the generalised Selberg integral of Richards and ZhengAug 22 2007In a recent paper Richards and Zheng compute the determinant of a matrix whose entries are given by beta-type integrals, thereby generalising an earlier result by Dixon and Varchenko. They then use their result to obtain a generalisation of the famous ... More

Dimerization versus Orbital Moment Ordering in the Mott insulator YVO$_3$Jun 25 2003We use exact diagonalization combined with mean-field theory to investigate the phase diagram of the spin-orbital model for cubic vanadates. The spin-orbit coupling competes with Hund's exchange and triggers a novel phase, with the ordering of $t_{2g}$ ... More

The importance of the Selberg integralOct 22 2007It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name. One of these is the Selberg integral, an n-dimensional generalization of the Euler beta integral. We trace its sudden ... More

A Complexity View of RainfallJan 25 2002We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number ... More

Far from equilibrium: Wealth reallocation in the United StatesMay 18 2016Studies of wealth inequality often assume that an observed wealth distribution reflects a system in equilibrium. This constraint is rarely tested empirically. We introduce a simple model that allows equilibrium but does not assume it. To geometric Brownian ... More

How well can Charge Transfer Inefficiency be corrected? A parameter sensitivity study for iterative correctionJun 25 2015Radiation damage to space-based Charge-Coupled Device (CCD) detectors creates defects which result in an increasing Charge Transfer Inefficiency (CTI) that causes spurious image trailing. Most of the trailing can be corrected during post-processing, by ... More

Fractional and Complex Pseudo-Splines and the Construction of Parseval FramesFeb 27 2016Apr 16 2016Pseudo-splines of integer order $(m,\ell)$ were introduced by Daubechies, Han, Ron, and Shen as a family which allows interpolation between the classical B-splines and the Daubechies' scaling functions. The purpose of this paper is to generalize the pseudo-splines ... More

Testing for simultaneous jumps in case of asynchronous observationsJun 23 2016This paper proposes a novel test for simultaneous jumps in a bivariate It\^o semimartingale when observation times are asynchronous and irregular. Inference is built on a realized correlation coefficient for the jumps of the two processes which is estimated ... More

One-dimensional orbital fluctuations and the exotic magnetic properties of YVO$_3$Jun 17 2007Starting from the Mott insulator picture for cubic vanadates, we derive and investigate the model of superexchange interactions between V$^{3+}$ ions, with nearly degenerate $t_{2g}$ orbitals occupied by two electrons each. The superexchange interactions ... More

Ultra-low-noise supercontinuum generation with a flat near-zero normal dispersion fiberDec 10 2018Apr 23 2019A pure silica photonic crystal fiber with a group velocity dispersion ($\beta_2$) of 4 ps$^2$/km at 1.55 $\mu$m and less than 7 ps$^2$/km from 1.32 $\mu$m to the zero dispersion wavelength (ZDW) 1.80 $\mu$m was designed and fabricated. The dispersion ... More

The A_{2n}^{(2)} Rogers-Ramanujan identitiesSep 20 2013Nov 05 2013The famous Rogers-Ramanujan and Andrews--Gordon identities are embedded in a doubly-infinite family of Rogers-Ramanujan-type identities labelled by positive integers m and n. For fixed m and n the product side corresponds to a specialised character of ... More

Laws of large numbers for Hayashi-Yoshida-type functionalsMar 15 2018In high-frequency statistics and econometrics sums of functionals of increments of stochastic processes are commonly used and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. ... More

Dedekind's eta-function and Rogers-Ramanujan identitiesJan 11 2010Jan 22 2010We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)} eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities.

Positivity preserving transformations for q-binomial coefficientsFeb 26 2003Several new transformations for q-binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well ... More

Photoemission spectra of LaMnO3 controlled by orbital excitationsApr 25 2001We investigate the spectral function of a hole moving in the orbital-ordered ferromagnetic planes of LaMnO$_3$, and show that it depends critically on the type of orbital ordering. While the hole does not couple to the spin excitations, it interacts strongly ... More

Evolution of Spin-Orbital-Lattice Coupling in the $R$VO$_3$ PerovskitesMay 11 2008We introduce a microscopic model which unravels the physical mechanisms responsible for the observed phase diagram of the $R$VO$_3$ perovskites. It reveals a nontrivial interplay between superexchange, the orbital-lattice coupling due to the GdFeO$_3$-like ... More

Weyl-Heisenberg Frames, Translation Invariant Systems and the Walnut RepresentationOct 29 1999We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions ... More

Reiter's polaron wavefunction applied to a $t_{2g}$ orbital t-J modelNov 24 2008Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with $t_{2g}$ orbital degrees of freedom. While the number of excitations ... More

Fingerprints of spin-orbital physics in cubic Mott insulators: Magnetic exchange interactions and optical spectral weightsJan 17 2006The temperature dependence and anisotropy of optical spectral weights associated with different multiplet transitions is determined by the spin and orbital correlations. To provide a systematic basis to exploit this close relationship between magnetism ... More

Escape angles in bulk chi(2) soliton interactionsOct 16 2000Nov 06 2001We develop a theory for non-planar interaction between two identical type I spatial solitons propagating at opposite, but arbitrary transverse angles in quadratic nonlinear (or so-called chi(2)) bulk media. We predict quantitatively the outwards escape ... More

Perturbations of Weyl-Heisenberg framesAug 22 2000We develop a usable perturbation theory for Weyl-Heisenberg frames. In particular, we prove that if $(E_{mb}T_{na}g)_{m,n\inmathbb Z}$ is a WH-frame and $h$ is a function which is close to $g$ in the Wiener Amalgam space norm, then $(E_{mb}T_{na}h)_{m,n\in ... More

Frames of translatesNov 24 1998We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural numbers, then ... More

Avalanche Behavior in an Absorbing State Oslo ModelMay 19 2004Jul 15 2004Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this article, we transform the ... More

Spectral properties of orbital polarons in Mott insulatorsNov 23 2008We address the spectral properties of Mott insulators with orbital degrees of freedom, and investigate cases where the orbital symmetry leads to Ising-like superexchange in the orbital sector. The paradigm of a hole propagating by its coupling to quantum ... More

Hole propagation in the Kitaev-Heisenberg model: From quasiparticles in quantum Neel states to non-Fermi liquid in the Kitaev phaseAug 15 2013Jul 11 2014We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the t-J-like Kitaev-Heisenberg model on a honeycomb lattice: the Neel antiferromagnetic, stripe, zigzag and Kitaev spin-liquid phase. We find coherent propagation ... More

Hidden Quasiparticles and Incoherent Photoemission Spectra in Na2IrO3Feb 01 2013Aug 02 2013We study two Heisenberg-Kitaev t-J-like models on a honeycomb lattice, focusing on the zigzag magnetic phase of Na$_2$IrO$_3$, and investigate hole motion by exact diagonalization and variational methods. The spectral functions are quite distinct from ... More

Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori RulesApr 18 2006We point out that large composite spin-orbital fluctuations in Mott insulators with $t_{2g}$ orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, ... More

Spin-wave theory for dimerized ferromagnetic chainsJun 09 2009We describe a Peierls dimerization which occurs in ferromagnetic spin chains at finite temperature, within the modified spin-wave theory. Usual spin-wave theory is modified by introducing a Lagrange multiplier which enforces a nonmagnetic state at finite ... More

Frame Properties of Operator OrbitsApr 10 2018Aug 05 2018We consider sequences in a Hilbert space $\mathcal H$ of the form $(T^nf_0)_{n\in I},$ with a linear operator $T$, the index set being either $I = \mathbb N$ or $I = \mathbb Z$, a vector $f_0\in \mathcal H$, and answer the following two related questions: ... More

On Ladder Logic Bombs in Industrial Control SystemsFeb 17 2017In industrial control systems, devices such as Programmable Logic Controllers (PLCs) are commonly used to directly interact with sensors and actuators, and perform local automatic control. PLCs run software on two different layers: a) firmware (i.e. the ... More

Weak product spaces of Dirichlet seriesOct 07 2015Sep 23 2016Let $\mathscr{H}^2$ denote the space of ordinary Dirichlet series with square summable coefficients, and let $\mathscr{H}^2_0$ denote its subspace consisting of series vanishing at $+\infty$. We investigate the weak product spaces $\mathscr{H}^2\odot\mathscr{H}^2$ ... More

Constant term identities and Poincare polynomialsSep 05 2012Apr 05 2013In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald's constant term identities admit an extra set of free parameters, thereby linking them ... More

Preheating in an Asymptotically Safe Quantum Field TheoryMar 08 2016We consider reheating in a class of asymptotically safe quantum field theories recently studied in \cite{Litim:2014uca, Litim:2015iea}. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. ... More

Optimization and projection of coated structures with orthotropic infill materialAug 14 2018The purpose of this work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. By making use of the relaxed design space, we can obtain designs ... More

A Nekrasov-Okounkov formula for Macdonald polynomialsJun 15 2016Feb 19 2018We prove a Macdonald polynomial analogue of the celebrated Nekrasov-Okounkov hook-length formula from the theory of random partitions. As an application we obtain a proof of one of the main conjectures of Hausel and Rodriguez-Villegas from their work ... More

Bubble generation in a twisted and bent DNA-like modelAug 31 2004The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed ... More

Bounded Littlewood identitiesJun 09 2015Feb 19 2018We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of bounded Littlewood ... More

Quasiperiodic Envelope SolitonsJul 26 1999We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping ... More

The MUSE Data Reduction Pipeline: Status after Preliminary Acceptance EuropeJun 30 2015MUSE, a giant integral field spectrograph, is about to become the newest facility instrument at the VLT. It will see first light in February 2014. Here, we summarize the properties of the instrument as built and outline functionality of the data reduction ... More

Wind and Wave Extremes over the World Oceans from Very Large EnsemblesJul 21 2014Global return values of marine wind speed and significant wave height are estimated from very large aggregates of archived ensemble forecasts at +240-h lead time. Long lead time ensures that the forecasts represent independent draws from the model climate. ... More

Experimental observation of plasmons in a graphene monolayer resting on a two-dimensional subwavelength silicon gratingJan 15 2013Mar 22 2013We experimentally demonstrate graphene-plasmon polariton excitation in a continuous graphene monolayer resting on a two-dimensional subwavelength silicon grating. The subwavelength silicon grating is fabricated by a nanosphere lithography technique with ... More

Orbital dynamics in ferromagnetic transition metal oxidesDec 08 1998We consider a model of strongly correlated $e_g$ electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO$_3$. It is found that the classical orbital order with alternating occupied $e_g$ orbitals has a full rotational ... More

Nonlinearity and disorder: Classification and stability of nonlinear impurity modesSep 03 2000We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schr\"odinger ... More

Coherent Transport and Concentration of Particles in Optical Traps using Varying Transverse Beam ProfilesFeb 04 2005Tailored time-dependent variations of the transverse profile together with longitudinal phase shifts of laser beams are studied. It is shown theoretically that a standing wave setup and real-time beam forming techniques (e.g. by computer-addressed holograms) ... More

Detecting N-particle interference patterns with linear balanced N-port analyzersMar 11 2003A standard two-path interferometer fed into a linear N-port analyzer with coincidence detection of its output ports is analyzed. The N-port is assumed to be implemented as a discrete Fourier transformation $\cal F$, i.e., to be balanced. For unbound bosons ... More

Dialling up Energy Point Spectra in Polynomial Quantum Harmonic Oscillators and Violation of the Sturm-Liouville Nodal Ordering TheoremJan 10 2019Harmonic quantum oscillators are building blocks of quantum theory particularly field theory. Here I show that a polynomial of degree~$N$ of a harmonic oscillator Hamiltonian allows us to devise a fully solvable continuous quantum system for which the ... More

Strong-interaction approximation for transfer matrix methodJun 08 2010Using transfer-matrix method a correspondence between $2D$ classical spin systems ($2D$ Ising model and six-vertex model) and $1D$ quantum spin systems is considered. We find the transfer matrix in two limits - in a well-known strong-anisotropy limit ... More

On extensions of wavelet systems to dual pairs of framesJan 05 2014It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems are generated ... More

Debian Astro: An open computing platform for astronomyNov 22 2016Debian Astro is a Debian Pure Blend that aims to distribute the available astronomy software within the Debian operating system. Using Debian as the foundation has unique advantages for end-users and developers such as an easy installation and upgrading ... More

Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changesMay 02 2014Jun 17 2014In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand ... More

Bright and Dark Helices of LightMay 21 2009Jun 12 2012Laser beams can be made to form bright and dark intensity helices of light. Such helices have a pitch length on the order of a wavelength and may have applications in lithography and the manipulation of particles through optical forces. The formation ... More

Data-Driven Design: Exploring new Structural Forms using Machine Learning and Graphic StaticsSep 23 2018The aim of this research is to introduce a novel structural design process that allows architects and engineers to extend their typical design space horizon and thereby promoting the idea of creativity in structural design. The theoretical base of this ... More

Self-testing properties of Gisin's elegant Bell inequalityJun 07 2017Oct 05 2017An experiment in which the Clauser-Horne-Shimony-Holt inequality is maximally violated is self-testing (i.e., it certifies in a device-independent way both the state and the measurements). We prove that an experiment maximally violating Gisin's elegant ... More

Uncertainty is complementary to ComplementarityAug 03 1999For any ideal two-path interferometer it is shown that the wave-particle duality of quantum mechanics implies Heisenberg's uncertainty relation and vice versa. It is conjectured that complementarity and uncertainty are two aspects of the same general ... More

Galaxy cluster strong lensing: image deflections from density fluctuations along the line of sightOct 24 2011Dec 08 2011A standard method to study the mass distribution in galaxy clusters is through strong lensing of background galaxies in which the positions of multiple images of the same source constrain the surface mass distribution of the cluster. However, current ... More

Equivalence between free and harmonically trapped quantum particlesAug 23 2010It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle subjected to a sudden ... More

Imprinting interference fringes in massive optomechanical systemsJun 01 2011Dec 07 2011An interferometric scheme for the creation of momentum superposition states of mechanical oscillators, using a quantum mirror kicked by free photons is analyzed. The scheme features ultra-fast preparation with immediate detection and should allow for ... More

Optical Lenses for Atomic BeamsOct 24 2008Jan 14 2009Superpositions of paraxial laser beam modes to generate atom-optical lenses based on the optical dipole force are investigated theoretically. Thin, wide, parabolic, cylindrical and circular atom lenses with numerical apertures much greater than those ... More

Six problems in frame theoryAug 23 2013We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their role.

Convolutional LSTM Networks for Subcellular Localization of ProteinsMar 06 2015Machine learning is widely used to analyze biological sequence data. Non-sequential models such as SVMs or feed-forward neural networks are often used although they have no natural way of handling sequences of varying length. Recurrent neural networks ... More

GPU-based Online Track Reconstruction for the ALICE TPC in Run 3 with Continuous Read-OutMay 14 2019In LHC Run 3, ALICE will increase the data taking rate significantly to 50 kHz continuous read-out of minimum bias Pb-Pb collisions. The reconstruction strategy of the online-offline computing upgrade foresees a first synchronous online reconstruction ... More

Approaching the Heisenberg limit with two mode squeezed statesNov 27 2002Two mode squeezed states can be used to achieve Heisenberg limit scaling in interferometry: a phase shift of $\delta \phi \approx 2.76 / < N >$ can be resolved. The proposed scheme relies on balanced homodyne detection and can be implemented with current ... More

Quantum Statistics Can Suppress Classical InterferenceOct 10 2001Classical optical interference experiments correspond to a measurement of the first-order correlation function of the electromagnetic field. The converse of this statement: experiments that measure the first order correlation functions do not distinguish ... More

De Broglie Wavelength Reduction for a Multi-photon Wave PacketOct 09 2001An experiment is proposed that permits the observation of the reduced de Broglie wavelengths of two and four-photon wave packets using present technology. It is suggested to use a Mach-Zehnder setup and feed both input ports with light generated by a ... More

Wide cylindrical or spherical optical potentials from laser beam superpositionsApr 28 2009Superpositions of paraxial Laguerre-Gauss laser beam modes to generate optical potentials based on the optical dipole force are investigated theoretically. Parabolic and other monomial potentials with even powers, in cylindrical and spherical symmetry, ... More

A geometric classification of the path components of the space of locally stable maps $S^3\to \mathbb{R}^4$Dec 13 2013Locally stable maps $S^3\to\mathbb{R}^4$ are classified up to homotopy through locally stable maps. The equivalence class of a map $f$ is determined by three invariants: the isotopy class $\sigma(f)$ of its framed singularity link, the generalized normal ... More

Measurement of the dark matter velocity anisotropy profile in galaxy clustersOct 20 2008Dark matter particles form halos that contribute the major part of the mass of galaxy clusters. The formation of these cosmological structures have been investigated both observationally and in numerical simulations, which have confirmed the existence ... More