Results for "Matija Ćuk"
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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 Chronology and Sources of Lunar Impact BombardmentNov 30 2011The Moon has suffered intense impact bombardment ending at 3.9 Gyr ago, and this bombardment probably affected all of the inner Solar System. Basin magnetization signatures and lunar crater size-distributions indicate that the last episode of bombardment ... 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 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 Planetary Chaos and the (In)stability of Hungaria AsteroidsApr 18 2017The Hungaria asteroid group is located interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Recently, it has been proposed that Hungaria asteroids are a secularly declining ... More 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 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 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). 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 On laws exhibiting universal ordering under stochastic restartApr 23 2019For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible ... 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 Another characterization of homogeneous Poisson processesOct 23 2016Aug 13 2017For a general renewal process $N$ (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from $N$ by Bernoulli $0$/$1$ thinning is characterized. This independence is well-known ... 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 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 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 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 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 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 The origin of the Moon within a terrestrial synestiaFeb 28 2018The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum ... 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 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 Disentangling sources of influence in online social networksNov 26 2018Nov 27 2018Information propagation in online social networks is facilitated by two types of influence - endogenous (peer) influence that is dependent on the network structure and current state of each user and exogenous (external) which is independent of these. ... More Monochromatic paths in random tournamentsMar 30 2017Dec 09 2017We prove that, with high probability, any $2$-edge-colouring of a random tournament on $n$ vertices contains a monochromatic path of length $\Omega(n / \sqrt{\log n})$. This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly ... More Three colour bipartite Ramsey number of cycles and pathsMar 09 2018The $k$-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 Disentangling sources of influence in online social networksNov 26 2018Mar 27 2019Information propagation in online social networks is facilitated by two types of influence - endogenous (peer) influence that acts between users of the social network and exogenous (external) that corresponds to various external mediators such as online ... 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 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 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 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 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 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 An improved bound for disjoint directed cyclesJan 23 2017Apr 24 2018We show that every directed graph with minimum out-degree at least $18k$ contains at least $k$ vertex disjoint cycles. This is an improvement over the result of Alon who showed this result for digraphs of minimum out-degree at least $64k$. The main benefit ... More Modular forms, hypergeometric functions and congruencesJan 15 2013Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \sum \binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in N, and the summation is over the integers i_1, i_2, ...i_k >= 0 such that ... More On Kahn's basis conjectureOct 17 2018In 1991, Kahn made the following conjecture. For any $n$-dimensional vector space $V$ and any $n\times n$ array of $n^2$ bases of $V$, it is possible to choose a representative vector from each of these bases in such a way that the representatives from ... More Partition problems in high dimensional boxesMay 29 2018Jun 30 2018Alon, Bohman, Holzman and Kleitman proved that any partition of a $d$-dimensional discrete box into proper sub-boxes must consist of at least $2^d$ sub-boxes. Recently, Leader, Mili\'{c}evi\'{c} and Tan considered the question of how many odd-sized proper ... More 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 On the existence of a minimal generating set for $σ$-algebrasJun 03 2014May 16 2018Does 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 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 Monochromatic trees in random tournamentsSep 19 2018We prove that, with high probability, in every $2$-edge-colouring of the random tournament on $n$ vertices there is a monochromatic copy of every oriented tree of order $O (n / \sqrt{\log n})$. This generalises a result of the first, third and forth authors ... More On the Alexandroff-Borsuk problemMar 03 2017We investigate the classical Alexandroff-Borsuk problem in the category of non-triangulable manifolds: Given an $n$-dimensional compact non-triangulable manifold $M^n$ and $\varepsilon > 0$, does there exist an $\varepsilon$-map of $M^n$ onto an $n$-dimensional ... More Double hypergeometric Lévy processes and self-similarityApr 12 2019Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of L\'evy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation ... More Diophantine m-tuples in finite fields and modular formsSep 29 2016Jan 31 2018For 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 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 Lateral p-n Junction in an Inverted InAs/GaSb Double Quantum WellMar 24 2017May 21 2017We present transport measurements on a lateral p-n junction in an inverted InAs/GaSb double quantum well at zero and nonzero perpendicular magnetic fields. At a zero magnetic field, the junction exhibits diodelike behavior in accordance with the presence ... More Design and Implementation of the Andromeda Proof AssistantFeb 17 2018Andromeda is an LCF-style proof assistant where the user builds derivable judgments by writing code in a meta-level programming language AML. The only trusted component of Andromeda is a minimalist nucleus (an implementation of the inference rules of ... 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 Nearly-linear monotone paths in edge-ordered graphsSep 05 2018May 02 2019How long a monotone path can one always find in any edge-ordering of the complete graph $K_n$? This appealing question was first asked by Chv\'atal and Koml\'os in 1971, and has since attracted the attention of many researchers, inspiring a variety of ... More Nearly-linear monotone paths in edge-ordered graphsSep 05 2018How long a monotone path can one always find in any edge-ordering of the complete graph $K_n$? This appealing question was first asked by Chv\'atal and Koml\'os in 1971, and has since attracted the attention of many researchers, inspiring a variety of ... 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 Satisfiability Thresholds for Regular Occupation ProblemsNov 02 2018Apr 27 2019In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the rigorous and ... More