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On the Dynamics and Origin of Haumea's MoonsAug 08 2013The dwarf planet Haumea has two large satellites, Namaka and Hi'iaka, which orbit at relatively large separations. Both moons have significant eccentricities and inclinations, in a pattern that is consistent with a past orbital resonance (Ragozzine and ... More

Secular Resonance Between Iapetus and the Giant PlanetsSep 24 2018Using numerical integrations, we find that the orbital eccentricity of Saturn's moon Iapetus undergoes prominent multi-Myr oscillations. We identify the responsible resonant argument to be $\varpi-\varpi_{g5}+\Omega-\Omega_{eq}$, with the terms being ... More

Dynamical Evidence for a Late Formation of Saturn's MoonsMar 23 2016We explore the past evolution of Saturn's moons using direct numerical integrations. We find that the past Tethys-Dione 3:2 orbital resonance predicted in standard models likely did not occur, implying that the system is less evolved than previously thought. ... More

Hungaria Asteroid Family as the Source of Aubrite MeteoritesJun 03 2014The Hungaria asteroids are interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Small asteroids in the Hungaria region are dominated by a collisional family associated with ... More

Titan-Hyperion Resonance and the Tidal Q of SaturnNov 26 2013Lainey et al. (2012), by re-analyzing long-baseline astrometry of Saturn's moons, have found that the moons' tidal evolution is much faster than previously thought, implying an order of magnitude stronger tidal dissipation within Saturn. This result is ... More

Ruin under stochastic dependence between premium and claim arrivalsFeb 15 2016We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their intensities, the two mixed Poisson processes governing the arrival times of ... More

First passage upwards for state dependent-killed spectrally negative Lévy processesMar 13 2018Apr 14 2018For a spectrally negative L\'evy process (snLp) $X$, killed according to a rate that is a function $\omega$ of its position, we analyse the exit probability of the one-sided upwards-passage problem. When $\omega$ is strictly positive, this problem is ... More

Long-Term Stability of Horseshoe OrbitsJun 08 2012Aug 24 2012Unlike Trojans, horseshoe coorbitals are not generally considered to be long-term stable (Dermott and Murray, 1981; Murray and Dermott, 1999). As the lifetime of Earth's and Venus's horseshoe coorbitals is expected to be about a Gyr, we investigated the ... More

Yarkovsky-Driven Spreading of the Eureka Family of Mars TrojansDec 04 2014Out of nine known stable Mars Trojans, seven appear to be members of an orbital grouping including the largest Trojan, Eureka. In order to test if this could be a genetic family, we simulated the long term evolution of a tight orbital cluster centered ... More

Observing a Lévy process up to a stopping timeDec 12 2018It is proved that the law of a possibly killed L\'evy process $X$, seen up to and including (resp. up to strictly before) a stopping time, determines already the law of $X$ (resp. up to a compound Poisson component and killing).

On the existence of a minimal generating set for $σ$-algebrasJun 03 2014Does there exist for any $\sigma$-algebra a minimal (with respect to inclusion) generating set? We formulate this problem and answer it in the very special instance of partition generated and standard measurable spaces, the general case remaining open. ... More

Arithmetic of (independent) sigma-fields on probability spacesSep 14 2018This note gathers what is known about, and provides some new results concerning the operations of intersection, of "generated $\sigma$-field", and of "complementation" for (independent) complete $\sigma$-fields on probability spaces.

A temporal factorization at the maximum for spectrally negative positive self-similar Markov processesMay 10 2018May 15 2018For a spectrally negative positive self-similar Markov process with an a.s. finite overall supremum we provide, in tractable detail, a kind of conditional Wiener-Hopf factorization at the maximum of the absorption time at zero, the conditioning being ... More

Exit problems for positive self-similar Markov processes with one-sided jumpsJul 02 2018A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided L\'evy processes ... More

Independence times for iid sequences, random walks and Lévy processesApr 20 2017Sep 28 2018For a sequence in discrete time having stationary independent values (respectively, random walk) $X$, those random times $R$ of $X$ are characterized set-theoretically, for which the strict post-$R$ sequence (respectively, the process of the increments ... More

Inferring Algebraic EffectsDec 09 2013Sep 11 2014We present a complete polymorphic effect inference algorithm for an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references and many others. Our main aim is to offer the programmer ... More

Proper two-sided exits of a Lévy processNov 24 2015It is proved that the two-sided exits of a Levy process are proper, i.e. not a.s. equal to their one-sided counterparts, if and only if said process is not a subordinator or the negative of a subordinator. Furthermore, Levy processes are characterized, ... More

A couple of remarks on the convergence of $σ$-fields on probability spacesJun 09 2016The following modes of convergence of sub-$\sigma$-fields on a given probability space have been studied in the literature: weak convergence, strong convergence, convergence with respect to the Hausdorff metric, almost-sure convergence, set-theoretic ... More

Another characterization of homogeneous Poisson processesOct 23 2016For a general renewal process $N$ (with delay and defect) the independence of the first renewal epochs of the marked processes got from $N$ by Bernoulli $0$/$1$ thinning is characterized. By way of corollary we obtain a related characterization of homogeneous ... More

Non-random overshoots of Lévy processesJan 18 2013Sep 23 2013The class of Levy processes for which overshoots are almost surely constant quantities is precisely characterized.

Excursions of a spectrally negative Lévy process from a two-point setSep 03 2018Let $a\in (0,\infty)$. For a spectrally negative L\'evy process $X$ with infinite variation paths the resolvent of the process killed on hitting the two-point set $V=\{-a,a\}$ is identified. When further $X$ has no diffusion component the Laplace transforms ... More

A note on the times of first passage for `nearly right-continuous' random walksOct 24 2013Aug 12 2014A natural extension of a right-continuous integer-valued random walk is one which can jump to the right by one or two units. First passage times above a given fixed level then admit a tractable Laplace transform (probability generating function). Explicit ... More

Fluctuation theory for upwards skip-free Lévy chainsSep 20 2013May 18 2015A fluctuation theory and, in particular, a theory of scale functions is developed for upwards skip-free L\'evy chains, i.e. for right-continuous random walks embedded into continuous time as compound Poisson processes. This is done by analogy to the spectrally ... More

Homology of dendroidal setsSep 02 2015We define for every dendroidal set X a chain complex and show that this assignment determines a left Quillen functor. Then we define the homology groups $H_n(X)$ as the homology groups of this chain complex. This generalizes the homology of simplicial ... More

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum EarthFeb 09 2018In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however the current lunar orbital inclination of 5 degrees requires a subsequent dynamical process that is still debated. In addition, the giant ... More

Dendroidal sets as models for connective spectraMar 30 2012May 19 2014Dendroidal sets have been introduced as a combinatorial model for homotopy coherent operads. We introduce the notion of fully Kan dendroidal sets and show that there is a model structure on the category of dendroidal sets with fibrant objects given by ... More

Copulas for maxmin systemsDec 30 2015Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$ and the mentioned ... More

Diophantine m-tuples in finite fields and modular formsSep 29 2016For a prime p, a Diophantine m-tuple in $\mathbb{F}_p$ is a set of m nonzero elements of $\mathbb{F}_p$ with the property that the product of any two of its distinct elements is one less than a square. In this paper, we present formulas for the number ... More

More on Diophantine sextuplesSep 22 2016A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely ... More

An Effect System for Algebraic Effects and HandlersJun 26 2013Dec 09 2014We present an effect system for core Eff, a simplified variant of Eff, which is an ML-style programming language with first-class algebraic effects and handlers. We define an expressive effect system and prove safety of operational semantics with respect ... More

Programming with Algebraic Effects and HandlersMar 07 2012Eff is a programming language based on the algebraic approach to computational effects, in which effects are viewed as algebraic operations and effect handlers as homomorphisms from free algebras. Eff supports first-class effects and handlers through ... More

On a special case of Watkins' conjectureNov 17 2016Watkins' conjecture asserts that for a rational elliptic curve $E$ the degree of the modular parametrization is divisible by $2^r$, where $r$ is the rank of $E$. In this paper we prove that if the modular degree is odd then $E$ has rank $0$. Moreover, ... More

SW# - GPU enabled exact alignments on genome scaleApr 22 2013Sequence alignment is one of the oldest and the most famous problems in bioinformatics. Even after 45 years, for one reason or another, this problem is still actual; current solutions are trade-offs between execution time, memory consumption and accuracy. ... More

No value restriction is needed for algebraic effects and handlersMay 23 2016We present a straightforward, sound Hindley-Milner polymorphic type system for algebraic effects and handlers in a call-by-value calculus, which allows type variable generalisation of arbitrary computations, not just values. This result is surprising. ... More

On the informational structure in optimal dynamic stochastic controlMar 09 2015Sep 20 2016We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated and proved. In ... More

Supersingular zeros of divisor polynomials of elliptic curves of prime conductorNov 17 2016For a prime number $p$ we study the zeros modulo $p$ of divisor polynomials of rational elliptic curves $E$ of conductor $p$. Ono made the observation that these zeros of are often $j$-invariants of supersingular elliptic curves over $\overline{\mathbb{F}_p}$. ... More

First passage problems for upwards skip-free random walks via the $Φ,W,Z$ paradigmAug 21 2017Apr 14 2018We develop the theory of the $W$ and $Z$ scale functions for right-continuous (upwards skip-free) discrete-time discrete-space random walks, along the lines of the analogue theory for spectrally negative L\'evy processes. Notably, we introduce for the ... More

On the informational structure in optimal dynamic stochastic controlMar 09 2015May 15 2018We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated and proved. In ... More

Modular forms, de Rham cohomology and congruencesJan 24 2013Apr 22 2013In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold for weakly modular forms (modular forms that are permitted to have poles at cusps). Unlike the case of original congruences for cusp forms, these congruences are nontrivial ... More

On the Secular Behavior of Irregular SatellitesAug 05 2004Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because ... More

Handling Algebraic EffectsDec 05 2013Dec 16 2013Algebraic effects are computational effects that can be represented by an equational theory whose operations produce the effects at hand. The free model of this theory induces the expected computational monad for the corresponding effect. Algebraic effects ... More

Constraints on the Orbital Evolution of TritonMay 11 2005We present simulations of Triton's post-capture orbit that confirm the importance of Kozai-type oscillations in its orbital elements. In the context of the tidal orbital evolution model, these variations require average pericenter distances much higher ... More

Modular parametrizations of certain elliptic curvesDec 26 2012Kaneko and Sakai recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre ... More

Simulating the Phases of the Moon Shortly After Its FormationMar 10 2015The leading theory for the origin of the Moon is the giant impact hypothesis, in which the Moon was formed out of the debris left over from the collision of a Mars-sized body with the Earth. Soon after its formation, the orbit of the Moon may have been ... More

The Complemented System Approach: A Novel Method for Calculating the X-ray Scattering from Computer SimulationsNov 09 2010In this paper, we review the main problem concerning the calculation of X-ray scattering of simulated model systems, namely their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows sidestepping this issue ... More

Multicolour bipartite Ramsey number of pathsJan 17 2019The $k$-colour bipartite Ramsey number of a bipartite graph $H$ is the least integer $N$ for which every $k$-edge-coloured complete bipartite graph $K_{N,N}$ contains a monochromatic copy of $H$. The study of bipartite Ramsey numbers was initiated over ... More

The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddabilityApr 19 2008Aug 17 2010We define a quadratic form which gives an obstruction to embedding $N^{4k+2} \subset \R^{6k+4}$ of a smooth highly connected manifold into Euclidean space, with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove ... More

Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019Feb 19 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More

Max-min measures on ultrametric spacesFeb 26 2013The ultrametrization of the set of all probability measures of compact support on the ultrametric spaces was first defined by Hartog and de Vink. In this paper we consider a similar construction for the so called max-min measures on the ultrametric spaces. ... More

Markov chain approximations to scale functions of Lévy processesOct 07 2013Apr 20 2015We introduce a general algorithm for the computation of the scale functions of a spectrally negative L\'evy process $X$, based on a natural weak approximation of $X$ via upwards skip-free continuous-time Markov chains with stationary independent increments. ... More

Rigidity of the Minimal Grope GroupAug 04 2006We give a systematic definition of the fundamental groups of gropes, which we call grope groups. We show that there exists a nontrivial homomorphism from the minimal grope group M to another grope group G only if G is the free product of M with another ... More

Multiple perturbations of a singular eigenvalue problemFeb 22 2016We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle ... More

Markov chain approximations for transition densities of Lévy processesNov 02 2012Jun 26 2013We consider the convergence of a continuous-time Markov chain approximation X^h, h>0, to an R^d-valued Levy process X. The state space of X^h is an equidistant lattice and its Q-matrix is chosen to approximate the generator of X. In dimension one (d=1), ... More

On structure sets of manifold pairsAug 10 2009In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with ... More

Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More

A short proof of the Twelve points theoremAug 08 2008We present a short elementary proof of the following Twelve Points Theorem: Let M be a convex polygon with vertices at the lattice points, containing a single lattice point in its interior. Denote by m (resp. m*) the number of lattice points in the boundary ... More

There are infinitely many rational Diophantine sextuplesJul 02 2015Nov 30 2015A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely ... More

Generating Entangled Spin States for Quantum Metrology by Single-Photon DetectionAug 28 2013We propose and analyze a probabilistic but heralded scheme to generate pure, entangled, non-Gaussian states of collective spin in large atomic ensembles by means of single-photon detection. One photon announces the preparation of a Dicke state, while ... More

Inelastic photon scattering via the intracavity Rydberg blockadeApr 21 2016Electromagnetically induced transparency (EIT) in a ladder system involving a Rydberg level is known to yield giant optical nonlinearities for the probe field, even in the few-photon regime. This enhancement is due to the strong dipole-dipole interactions ... More

Coarse classification of abelian groups and amenable shift-homogeneous metric spacesDec 13 2014In this paper we classify countable locally finite-by-abelian groups up to coarse isomorphism. This classification is derived from a coarse classification of amenable shift-homogeneous metric spaces.

Coupled channel analysis of the rho meson decay in lattice QCDMay 27 2011Apr 18 2014We employ a variational basis with a number of $\bar{q}q$ and $\pi\pi$ lattice interpolating fields with quantum numbers of the $\rho$ resonance to extract the discrete energy spectrum in a finite volume. In the elastic region, this spectrum is related ... More

Double phase problems with variable growthOct 18 2018We consider a class of double phase variational integrals driven by nonhomogeneous potentials. We study the associated Euler equation and we highlight the existence of two different Rayleigh quotients. One of them is in relationship with the existence ... More

Constraints on the Source of Lunar Cataclysm ImpactorsDec 10 2009Multiple impact basins formed on the Moon about 3.8 Gyr ago in what is known as the lunar cataclysm or late heavy bombardment. Many workers currently interpret the lunar cataclysm as an impact spike primarily caused by main-belt asteroids destabilized ... More

Characterizing compact Clifford semigroups that embed into convolution and functor-semigroupsNov 06 2008Aug 02 2011We study algebraic and topological properties of the convolution semigroups of probability measures on a topological groups and show that a compact Clifford topological semigroup $S$ embeds into the convolution semigroup $P(G)$ over some topological group ... More

On the Expressive Power of User-Defined Effects: Effect Handlers, Monadic Reflection, Delimited ControlOct 28 2016We compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers, Filinski's monadic reflection, and delimited control. This comparison allows a precise discussion about the ... More

Minimum saturated families of setsJan 16 2018Apr 24 2018We call a family $\mathcal{F}$ of subsets of $[n]$ $s$-saturated if it contains no $s$ pairwise disjoint sets, and moreover no set can be added to $\mathcal{F}$ while preserving this property (here $[n] = \{1,\ldots,n\}$). More than 40 years ago, Erd\H{o}s ... More

Edgeless and Purely Gate-Defined Nanostructures in InAs Quantum WellsSep 07 2018Nanostructures in InAs quantum wells have so far remained outside of the scope of traditional microfabrication techniques based on etching. This is due to parasitic parallel conduction arising from charge carrier accumulation at the physical edges of ... More

Collective state measurement of mesoscopic ensembles with single-atom resolutionMar 14 2012Sep 28 2012For mesoscopic ensembles containing 100 or more atoms we measure the total atom number and the number of atoms in a specific hyperfine state with single-atom resolution. The measurement detects the atom-induced shift of the resonance frequency of an optical ... More

Modeling peer and external influence in online social networksOct 26 2016Opinion polls mediated through a social network can give us, in addition to usual demographics data like age, gender and geographic location, a friendship structure between voters and the temporal dynamics of their activity during the voting process. ... More

News Cohesiveness: an Indicator of Systemic Risk in Financial MarketsFeb 14 2014Motivated by recent financial crises significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said about influence of financial news on financial markets. We propose a novel ... More

The Hall effect in the organic conductor TTF-TCNQ: Choice of geometry for accurate measurements of highly anisotropic systemJan 25 2011Jan 24 2012We have measured the Hall effect on recently synthesized single crystals of quasi-one-dimensional organic conductor TTF-TCNQ, a well known charge transfer complex that has two kinds of conductive stacks: the donor (TTF) and the acceptor (TCNQ) chains. ... More

Gate-tunable Electronic Transport in p-type GaSb Quantum WellsJan 30 2019We investigate two-dimensional hole transport in GaSb quantum wells at cryogenic temperatures using gate-tunable devices. Measurements probing the valence band structure of GaSb unveil a significant spin splitting of the ground subband induced by spin-orbit ... More

Non-local transport via edge-states in InAs/GaSb coupled quantum wellsApr 27 2015We have investigated low-temperature electronic transport on InAs/GaSb double quantum wells, a system which promises to be electrically tunable from a normal to a topological insulator. Hall bars of $50\,\mu$m in length down to a few $\mu$m gradually ... More

Transport Spectroscopy of a Spin-Coherent Dot-Cavity SystemMar 10 2015Sep 01 2015Quantum engineering requires controllable artificial systems with quantum coherence exceeding the device size and operation time. This can be achieved with geometrically confined low-dimensional electronic structures embedded within ultraclean materials, ... More

Experimental Evidence for the Topological Insulator Phase in InAs/GaSb Coupled Quantum WellsJun 11 2016Transport measurements are performed on InAs/GaSb double quantum wells at zero and finite magnetic fields applied parallel and perpendicular to the quantum wells. We investigate a sample in the inverted regime where electrons and holes coexist, and compare ... More

Design, Construction and Commissioning of the Digital Hadron Calorimeter - DHCALMar 04 2016A novel hadron calorimeter is being developed for future lepton colliding beam detectors. The calorimeter is optimized for the application of Particle Flow Algorithms (PFAs) to the measurement of hadronic jets and features a very finely segmented readout ... More