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Early-warning indicators in the dynamic regimeSep 23 2016Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the fluctuations around ... More

Nonlinear softening as a predictive precursor to climate tippingMar 15 2011Dec 09 2011Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious ... More

Climate tipping as a noisy bifurcation: a predictive techniqueJul 08 2010Nov 30 2010It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that determines the ... More

Longtime behavior of coupled wave equations for semiconductor lasersAug 09 2013Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial differential ... More

Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equationsOct 12 2010Feb 26 2015In this paper we prove that periodic boundary-value problems (BVPs) for delay differential equations are locally equivalent to finite-dimensional algebraic systems of equations. We rely only on regularity assumptions that follow those of the review by ... More

Effects of periodic forcing on a Paleoclimate delay modelAug 07 2018Jan 11 2019We present a study of a delay differential equation (DDE) model for the Mid-Pleistocene Transition (MPT). We investigate the behavior of the model when subjected to periodic forcing. The unforced model has a bistable region consisting of a stable equilibrium ... More

Generic stabilizability for time-delayed feedback controlAug 23 2015Apr 24 2016Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current output and the ... More

Relative equilibria and relative periodic solutions in systems with time-delay and $S^{1}$ symmetryJun 14 2013Dec 03 2016We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the number of CW ... More

Characteristic matrices for linear periodic delay differential equationsMay 25 2010Jan 21 2011Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way can have a discrete ... More

Small-scale instabilities in dynamical systems with slidingNov 12 2008Jul 12 2010We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations. We consider ... More

Relative equailibria and relative periodic solutions in systems with time-delay and $S^{1}$ symmetryJun 14 2013We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the number of CW ... More

Bifurcation analysis of delay-induced resonances of the El-Nino Southern OscillationSep 13 2011May 28 2014Models of global climate phenomena of low to intermediate complexity are very useful for providing an understanding at a conceptual level. An important aspect of such models is the presence of a number of feedback loops that feature considerable delay ... More

Using feedback control and Newton iterations to track dynamically unstable phenomena in experimentsMar 18 2009If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is a combination ... More

Derivation of Delay Equation Climate Models Using the Mori-Zwanzig FormalismFeb 08 2019Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism ... More

The Mid-Pleistocene Transition induced by delayed feedback and bistabilityDec 20 2017Nov 09 2018The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate dynamics that was ... More

Probability of noise and rate-induced tippingJun 27 2016We propose a formula to approximate the probability of rate-induced tipping with additive white noise occurring for small to moderate equilibrium drift speeds. Early-warning indicators have generally been used on historical tipping events as a form of ... More

Early-warning indicators for rate-induced tippingSep 05 2015Sep 23 2016A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a prototypical model for rate-induced tipping, the saddle-node normal form ... More

On the Stability of a Chain of Phase OscillatorsJan 25 2011Jun 02 2011We study a chain of $N+1$ phase oscillators with asymmetric but uniform coupling. This type of chain possesses $2^{N}$ ways to synchronize in so-called travelling wave states, i.e. states where the phases of the single oscillators are in relative equilibrium. ... More

Universality in quantum parametric correlationsMay 03 1999Jul 30 1999We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations. Under certain ... More

Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillatorsJan 30 2015Apr 24 2015We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we ... More

Controlling unstable chaos: Stabilizing chimera states by feedbackOct 28 2013Dec 18 2013We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it loses its attractivity. ... More

Evolution of the L1 halo family in the radial solar sail CRTBPAug 15 2013Jul 28 2014We present a detailed investigation of the dramatic changes that occur in the $\mathcal{L}_1$ halo family when radiation pressure is introduced into the Sun-Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used ... More

Systematic experimental exploration of bifurcations with non-invasive controlSep 17 2012Mar 15 2013We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular non-invasive control schemes, such as (Pyragas) time-delayed ... More

Shock-Sensitivity in Shell-Like Structures: with Simulations of Spherical Shell BucklingSep 20 2015Oct 06 2015Under increasing compression, an unbuckled shell is in a metastable state which becomes increasingly precarious as the buckling load is approached. So to induce premature buckling a lateral disturbance will have to overcome a decreasing energy barrier ... More

Nonlinear dynamic interactions between flow-induced galloping and shell-like bucklingJan 10 2014For an elastic system that is non-conservative but autonomous, subjected for example to time-independent loading by a steadily flowing fluid (air or water), a dangerous bifurcation, such as a sub-critical bifurcation, or a cyclic fold, will trigger a ... More

Extremum seeking via continuation techniques for optimizing biogas production in the chemostatFeb 13 2013May 13 2013We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach ... More

On the stability of periodic orbits in delay equations with large delayJan 06 2011Dec 05 2012We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set ... More

Temporal dissipative solitons in time-delay feedback systemsJan 11 2019Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, spot or pulse solutions, these states play an important role in data transmission using optical ... More

Equation-Free Analysis of Macroscopic Behavior in Traffic and Pedestrian FlowFeb 03 2014Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are explicitly ... More

DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equationsJun 27 2014Sep 06 2016DDEBIFTOOL is a collection of Matlab routines for numerical bifurcation analysis of systems of delay differential equations with discrete constant and state-dependent delays. The package supports continuation and stability analysis of steady state solutions ... More

Implicit Methods for Equation-Free Analysis: Convergence Results and Analysis of Emergent Waves in Microscopic Traffic ModelsJan 25 2013Jul 09 2014We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time stepper converges ... More

A method for the reconstruction of unknown non-monotonic growth functions in the chemostatAug 08 2012Jan 10 2013We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out ... More

The Mid-Pleistocene Transition induced by delayed feedback and bistabilityDec 20 2017The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate dynamics that was ... More

Semiclassical Transition from an Elliptical to an Oval BilliardNov 14 1996Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. In many situations, ... More

Wavefunctions, Green's functions and expectation values in terms of spectral determinantsJun 27 2007We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The wavefunctions, ... More

Spectral statistics in chaotic systems with a point interactionMar 08 2000Aug 14 2000We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order ... More

Dynamics of symmetric dynamical systems with delayed switchingApr 02 2008We study dynamical systems that switch between two different vector fields depending on a discrete variable and with a delay. When the delay reaches a problem-dependent critical value so-called event collisions occur. This paper classifies and analyzes ... More

Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systemsSep 06 2002We consider the semiclassical approximation to the spectral form factor K(tau) for two-dimensional uniformly hyperbolic systems, and derive the first off-diagonal correction for small tau. The result agrees with the tau^2-term of the form factor for the ... More

Semiclassical Treatment of Diffraction in Billiard Systems with a Flux LineMar 31 1999In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical approximation for ... More

Geometrical theory of diffraction and spectral statisticsOct 06 1999We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential can lead to ... More

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace FormulaOct 31 1997We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit ... More

Experimental continuation of periodic orbits through a foldApr 02 2008Jun 12 2008We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be ... More

Uniform Approximation for Period-Quadrupling BifurcationsAug 21 1997We derive a uniform approximation for semiclassical contributions of periodic orbits to the spectral density which is valid for generic period-quadrupling bifurcations in systems with a mixed phase space. These bifurcations involve three periodic orbits ... More

Singular compactness and definability for $Σ$-cotorsion and Gorenstein modulesApr 24 2018May 25 2018We introduce a general version of singular compactness theorem which makes it possible to show that being a $\Sigma$-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed along the way, ... More

Semiclassical expansion of parametric correlation functions of the quantum time delayAug 24 2006We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factor $K(\tau,x,y,M)$, that depends on the number of open channels ... More

Bifurcations of Periodic Orbits and Uniform ApproximationsJan 22 1997We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective ... More

The countable Telescope Conjecture for module categoriesJan 25 2008May 16 2008By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A, B) is of finite type." We prove a modification of this ... More

Semiclassical universality of parametric spectral correlationsAug 07 2006We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor $K(\tau,x)$ which ... More

Semiclassical Theory of Chaotic Quantum TransportMay 08 2002We present a refined semiclassical approach to the Landauer conductance and Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for systems with uniformly hyperbolic dynamics that including off-diagonal contributions to double sums over ... More

The semiclassical relation between open trajectories and periodic orbits for the Wigner time delayNov 28 2007The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how ... More

Particle creation and annihilation at interior boundaries: One-dimensional modelsNov 10 2015We describe creation and annihilation of particles at external sources in one spatial dimension in terms of interior-boundary conditions (IBCs). We derive explicit solutions for spectra, (generalised) eigenfunctions, as well as Green functions, spectral ... More

Introduction to Multi-Agent SimulationMar 27 2008When designing systems that are complex, dynamic and stochastic in nature, simulation is generally recognised as one of the best design support technologies, and a valuable aid in the strategic and tactical decision making process. A simulation model ... More

A First Approach on Modelling Staff Proactiveness in Retail Simulation ModelsAug 15 2011There has been a noticeable shift in the relative composition of the industry in the developed countries in recent years; manufacturing is decreasing while the service sector is becoming more important. However, currently most simulation models for investigating ... More

GKZ Hypergeometric StructuresNov 14 2005This text is based on lectures by the author in the Summer School `Algebraic Geometry and Hypergeometric Functions' in Istanbul in June 2005. It gives a review of some of the basic aspects of the theory of hypergeometric structures of Gelfand, Kapranov ... More

Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systemsOct 12 2012Mar 29 2013We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.

An improved analytic Method for calculating $π(x)$Oct 26 2014Nov 06 2015We present an improved version of the analytic method for calculating $\pi(x)$, the number of prime numbers not exceeding $x$. We implemented this method in cooperation with J. Franke, T. Kleinjung and A. Jost and calculated the value $\pi(10^{25})$.

The ring of arithmetical functions with unitary convolution: General TruncationsMay 23 2002Let A denote the ring of arithmetical functions with unitary convolution, and let V be a finite subset of the positive integers having the property that for every v in V, all unitary divisors of v lie in V. We study the truncation A_V, an artinian monomial ... More

Orthogonal Pure States in Operator TheoryNov 13 2002Jun 05 2003We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by continuous functions, ... More

Ranking Function Synthesis for Linear Lasso ProgramsJan 21 2014The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting invariants. We extend ... More

Arithmetic of fuzzy numbers and intervals -- a new perspective with examplesOct 16 2013The article guides the reader through four consecutive definitions of progressing scope. Fuzzy intervals are represented as an ordered pair of functions, and fuzzy numbers are defined as a subcase. The four arithmetic operations are defined utilizing ... More

AdS_3 Partition Functions ReconstructedJul 08 2007Nov 02 2007For pure gravity in AdS_3, Witten has given a recipe for the construction of holomorphically factorizable partition functions of pure gravity theories with central charge c=24k. The partition function was found to be a polynomial in the modular invariant ... More

Sheaves on P2 and generalized Appell functionsJul 28 2014Feb 23 2016A closed expression is given for the generating function of (virtual) Poincar\'e polynomials of moduli spaces of semi-stable sheaves on the projective plane $\mathbb{P}^2$ with arbitrary rank $r$ and Chern classes. This generating function is known to ... More

On the space of elliptic generaMay 28 2008Jan 27 2009Invariance under modular transformations and spectral flow restrict the possible spectra of superconformal field theories (SCFT). This paper presents a technique to calculate the number of constraints on the polar spectra of N=(2,2) and N=(4,0) SCFT's ... More

Strong-coupling approach to ground-state properties of the Anderson lattice-modelSep 05 1996A Slave-Boson perturbational approach to ground-state properties of the $U\to\infty$ periodic Anderson model is derived as an expansion around the Atomic Limit ($V=0$). In the case of zero temperature any constraint-integral or limiting procedure can ... More

On the hydrino state of the relativistic hydrogen atomJul 27 2005Aug 05 2005The Klein-Gordon equation of the hydrogen atom has a low-lying eigenstate, called hydrino state, with square integrable wavefunction. The corresponding spinor solution of Dirac's equation is not square integrable. For this reason the hydrino state has ... More

Refinement-Cut: User-Guided Segmentation Algorithm for Translational ScienceJun 07 2014In this contribution, a semi-automatic segmentation algorithm for (medical) image analysis is presented. More precise, the approach belongs to the category of interactive contouring algorithms, which provide real-time feedback of the segmentation result. ... More

PCG-Cut: Graph Driven Segmentation of the Prostate Central GlandOct 12 2013Prostate cancer is the most abundant cancer in men, with over 200,000 expected new cases and around 28,000 deaths in 2012 in the US alone. In this study, the segmentation results for the prostate central gland (PCG) in MR scans are presented. The aim ... More

Winding strings and AdS_3 black holesJun 13 2002Sep 19 2002We start a systematic study of string theory in AdS_3 black hole backgrounds. Firstly, we analyse in detail the geodesic structure of the BTZ black hole, including spacelike geodesics. Secondly, we study the spectrum for massive and massless scalar fields, ... More

Hamlet and Pfister forms (A tragedy in four acts)Nov 13 2009In the mid-1960s A. Pfister discovered extraordinary, strongly multiplicative forms which are now called Pfister forms. From that time on, these forms played a dominant role in the theory of quadratic forms. One of the key properties of a Pfister form ... More

Arithmetic of fuzzy numbers and intervals -- a new perspective with examplesOct 16 2013Oct 27 2016This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the inversion of cumulative ... More

A characterization of Morita equivalence pairs of quantalesNov 15 2002We characterize the pairs of sup-lattices which occur as pairs of Morita equivalence bimodules between quantales in terms of the mutual relation between the sup-lattices.

Weak and quasi-polynomial tractability of approximation of infinitely differentiable functionsJan 21 2013Apr 03 2013We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of dimensionality. We show ... More

Blank measurement based time-alignment in LC-MSMay 09 2012Here are presenting the blank based time-alignment (BBTA) as a strong analytical approach for treatment of non-linear shift in time occurring in HPLC-MS data. Need of such tool in recent large dataset produced by analytical chemistry and so-called omics ... More

Jacob's ladders and new orthogonal systems generated by Jacobi polynomialsOct 18 2010Nov 18 2010Is is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the classical Jacobi's polynomials, i.e. the Legendre polynomials, Chebyshev polynomials of the first and the second kind,...

Lindel\" of hypothesis and the order of the mean-value of $|ζ(s)|^{2k-1}$ in the critical stripJan 14 2015The main subject of this paper is the mean-value of the function $|\zeta(s)|^{2k-1}$ in the critical strip. On Lindel\" of hypothesis we give a solution to this question for some class of disconnected sets. This paper is English version of our paper \cite{5}. ... More

Jacob's ladders, reverse iterations and new infinite set of $L_2$-orthogonal systems generated by the Riemann $\zf$-functionFeb 10 2014It is proved in this paper that continuum set of $L_2$-orthogonal systems generated by the Riemann zeta-function on the critical line corresponds to every fixed $L_2$-orthogonal system on a fixed segment. This theorem serves as a resource for new set ... More

Jacob's ladders and the three-points interaction of the Riemann zeta-function with itselfJul 26 2011It is proved that some set of the values of $|\zeta(\sigma_0+i\vp_1(t))|^2$ on every fixed line $\sigma=\sigma_0>1$ generates a corresponding set of the values of $|\zeta(\frac 12+it)|^2$ on the critical line $\sigma=\frac 12$ (i.e. we have an analogue ... More

Riemann hypothesis and some new asymptotically multiplicative integrals which contain the remainder of the prime-counting function $π(x)$Nov 02 2010A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.

Jacob's ladders and the $\tilde{Z}^2$-transformation of a polynomials in $\ln \vp_1(t)$May 12 2010Jun 18 2010It is proved in this paper that there is a nonlocal asymptotic splitting (in the integral sense) of the function $Z^4(t)$ into two factors. The corresponding formula cannot be obtained in the known theories of Balasubramanian, Heath-Brown and Ivic.

Canonical Formulation of Spin in General RelativityJun 21 2011The present thesis aims at an extension of the canonical formalism of Arnowitt, Deser, and Misner from self-gravitating point-masses to objects with spin. This would allow interesting applications, e.g., within the post-Newtonian (PN) approximation. The ... More

Introduction to representations of the canonical commutation and anticommutation relationsNov 08 2005Nov 09 2005Lecture notes of a minicourse given at the Summer School on Large Coulomb Systems - QED in Nordfjordeid, 2003, devoted to representations of the CCR and CAR. Quasifree states, the Araki-Woods and Araki-Wyss representations, and the lattice of von Neumenn ... More

Effectively closed sets of measures and randomnessApr 16 2008We show that if a real $x$ is strongly Hausdorff $h$-random, where $h$ is a dimension function corresponding to a convex order, then it is also random for a continuous probability measure $\mu$ such that the $\mu$-measure of the basic open cylinders shrinks ... More

Fixed points in models of continuous opinion dynamics under bounded confidenceJun 10 2008We present two models of continuous opinion dynamics under bounded confidence which are representable as nonnegative discrete dynamical systems, namely the Hegselmann-Krause model (Hegselmann and Krause, Journal of Artificial Societies and Social Simulation ... More

Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensusAug 21 2007We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount of ressource ... More

Terrestrial Gravity FluctuationsJul 21 2015The article reviews the current state of the field, and also presents new analyses especially with respect to the impact of seismic scattering on gravity perturbations, active gravity noise cancellation, and time-domain models of gravity perturbations ... More

A tropical approach to secant dimensionsMay 12 2006Sep 05 2006Tropical geometry yields good lower bounds, in terms of certain combinatorial-polyhedral optimisation problems, on the dimensions of secant varieties. In particular, it gives an attractive pictorial proof of the theorem of Hirschowitz that all Veronese ... More

On realization of generalized effect algebrasAug 07 2012A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice $L({\mathcal H})$ of all closed subspaces of a separable complex Hilbert space. ... More

Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravityApr 23 2013May 01 2013In the time-space symmetric version of dynamical triangulation, a non-perturbative version of quantum Einstein gravity, numerical simulations without matter have shown two phases, with spacetimes that are either crumpled or elongated like branched polymers, ... More

Simulations in Early Universe TheoryOct 26 2005We give an impression of the type of results that have been obtained with numerical lattice simulations of field theory in the early universe.

Remarks on the quantum gravity interpretation of 4D dynamical triangulationAug 15 1996We review some of the phenomenology in 4D dynamical triangulation and explore its interpretation in terms of a euclidean effective action of the continuum form $\intx \sqrt{g} [\mu -\frac{1}{16\pi G} R + \cdots]$.

A reduction of proof complexity to computational complexity for $AC^0[p]$ Frege systemsNov 11 2013Aug 22 2014We give a general reduction of lengths-of-proofs lower bounds for constant depth Frege systems in DeMorgan language augmented by a connective counting modulo a prime $p$ (the so called $AC^0[p]$ Frege systems) to computational complexity lower bounds ... More

Finiteness for the k-factor model and chirality varietiesNov 21 2008This paper deals with two families of algebraic varieties arising from applications. First, the k-factor model in statistics, consisting of n-times-n covariance matrices of n observed Gaussian variables that are pairwise independent given k hidden Gaussian ... More

Deconvolution with unknown error distributionMay 23 2007Aug 21 2009We consider the problem of estimating a density $f_X$ using a sample $Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an unknown density. We assume that an additional sample $\epsilon_1,...,\epsilon_m$ from $f_{\epsilon}$ is observed. ... More

Sextic surfaces with ten triple pointsApr 04 2003All families of sextic surfaces with the maximal number of isolated triple points are found.

Weak uniform structures on probability distributionsJul 20 2010Nov 21 2010In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be considered to be ... More

On purity and applications to coderived and singularity categoriesDec 04 2014Given a locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. Moreover, the full subcategory of compact objects ... More

Derived equivalences induced by big cotilting modulesAug 08 2013Jun 02 2014We prove that given a Grothendieck category G with a tilting object of finite projective dimension, the induced triangle equivalence sends an injective cogenerator of G to a big cotilting module. Moreover, every big cotilting module can be constructed ... More

Simple curve singularitiesJun 19 2013We classify simple parametrisations of complex curve singularities. Simple means that all neighbouring singularities fall in finitely many equivalence classes. We take the neighbouring singularities to be the ones occurring in the versal deformation of ... More

Geometric structures invariant to symmetriesJul 01 2012We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit description. This ... More

Photoinduced two-proton knockout and ground-state correlations in nucleiMay 31 1996A factorized and analytical form for the A($\gamma$,pp) and A(e,e$'$pp) cross section is proposed. In the suggested scheme the two-proton knockout cross sections can be directly analyzed in terms of the ground-state correlation functions. Central, spin-spin ... More