Statistical analysis of bound companions in the Coma cluster

The rich and nearby Coma cluster of galaxies is known to have substructure. We aim to create a more detailed picture of this substructure by searching directly for bound companions around individual giant members. We have used two catalogs of Coma galaxies, one covering the cluster core for a detailed morphological analysis, another covering the outskirts. The separation limit between possible companions (secondaries) and giants (primaries) is chosen as M_B = -19 and M_R = -20, respectively for the two catalogs. We have created pseudo-clusters by shuffling positions or velocities of the primaries and search for significant over-densities of possible companions around giants by comparison with the data. This method was developed and applied first to the Virgo cluster by Ferguson (1992). In a second approach we introduced a modified nearest neighbor analysis using several interaction parameters for all galaxies. We find evidence for some excesses due to possible companions for both catalogs. Satellites are typically found among the faintest dwarfs (M_B < -16) around high-luminosity primaries. The most significant excesses are found around very luminous late-type giants (spirals) in the outskirts, which is expected in an infall scenario of cluster evolution. A rough estimate for an upper limit of bound galaxies within Coma is 2 - 4 percent, to be compared with ca. 7 percent for Virgo. The results agree well with the expected low frequency of bound companions in a regular cluster such as Coma.Comment: Astronomy & Astrophysics, in press; 17 pages, 13 figure

On the non-vanishing of certain Dirichlet series

Given $k\in\mathbb N$, we study the vanishing of the Dirichlet series $$D_k(s,f):=\sum_{n\geq1} d_k(n)f(n)n^{-s}$$ at the point $s=1$, where $f$ is a periodic function modulo a prime $p$. We show that if $(k,p-1)=1$ or $(k,p-1)=2$ and $p\equiv 3\mod 4$, then there are no odd rational-valued functions $f\not\equiv 0$ such that $D_k(1,f)=0$, whereas in all other cases there are examples of odd functions $f$ such that $D_k(1,f)=0$. As a consequence, we obtain, for example, that the set of values $L(1,\chi)^2$, where $\chi$ ranges over odd characters mod $p$, are linearly independent over $\mathbb Q$.Comment: 16 page

On the Smoothness of Value Functions

We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice continuously differentiable, as long as the control space is compact and the volatility is uniformly bounded below, away from zero. Under similar conditions, the value function of any optimal stopping problem is continuously differentiable. For the first problem, we provide sufficient conditions for the existence of an optimal control, which is also shown to be Markov. These conditions are based on the theory of monotone comparative statics.Super Contact; Smooth Pasting; HJB Equation; Optimal Control; Markov Control; Comparative Statics; Supermodularity; Single-Crossing; Interval Dominance Order

Multiplier phenomenology in random multiplicative cascade processes

We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into account, all reported properties of both unconditioned and conditioned multiplier distributions can be reproduced by cascade models with uncorrelated random weights if their bivariate splitting function is non-energy conserving. For the alpha-model we show that the simulated multiplier distributions converge to a limiting form, which is very close to the experimentally observed one. If random translations of the observation window are accounted for, also the subtle effects found in conditioned multiplier distributions are precisely reproduced.Comment: 4 pages, 3 figure

On the centralizer of vector fields: criteria of triviality and genericity results

In this paper, we investigate the question of whether a typical vector field on a compact connected Riemannian manifold $M^d$ has a `small' centralizer. In the $C^1$ case, we give two criteria, one of which is $C^1$-generic, which guarantees that the centralizer of a $C^1$-generic vector field is indeed small, namely \textit{collinear}. The other criterion states that a $C^1$ \textit{separating} flow has a collinear $C^1$-centralizer. When all the singularities are hyperbolic, we prove that the collinearity property can actually be promoted to a stronger one, refered as \textit{quasi-triviality}. In particular, the $C^1$-centralizer of a $C^1$-generic vector field is quasi-trivial. In certain cases, we obtain the triviality of the centralizer of a $C^1$-generic vector field, which includes $C^1$-generic Axiom A (or sectional Axiom A) vector fields and $C^1$-generic vector fields with countably many chain recurrent classes. For sufficiently regular vector fields, we also obtain various criteria which ensure that the centralizer is \textit{trivial} (as small as it can be), and we show that in higher regularity, collinearity and triviality of the $C^d$-centralizer are equivalent properties for a generic vector field in the $C^d$ topology. We also obtain that in the non-uniformly hyperbolic scenario, with regularity $C^2$, the $C^1$-centralizer is trivial.Comment: This is the final version, accepted in Mathematische Zeitschrift. New introduction and some proofs where rewritten and/or expanded, according to referee's suggestion. Also, a new appendix was adde

On Algorithms and Complexity for Sets with Cardinality Constraints

Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate properties: relationships between the typestates of objects can be expressed as subset and disjointness relations on sets, and elements of sets can be represented as sets of cardinality one. Motivated by these applications, this paper presents new algorithms and new complexity results for constraints on sets and their cardinalities. We study several classes of constraints and demonstrate a trade-off between their expressive power and their complexity. Our first result concerns a quantifier-free fragment of Boolean Algebra with Presburger Arithmetic. We give a nondeterministic polynomial-time algorithm for reducing the satisfiability of sets with symbolic cardinalities to constraints on constant cardinalities, and give a polynomial-space algorithm for the resulting problem. In a quest for more efficient fragments, we identify several subclasses of sets with cardinality constraints whose satisfiability is NP-hard. Finally, we identify a class of constraints that has polynomial-time satisfiability and entailment problems and can serve as a foundation for efficient program analysis.Comment: 20 pages. 12 figure

Pulsed source of spectrally uncorrelated and indistinguishable photons at telecom wavelengths

We report on the generation of indistinguishable photon pairs at telecom wavelengths based on a type-II parametric down conversion process in a periodically poled potassium titanyl phosphate (PPKTP) crystal. The phase matching, pump laser characteristics and coupling geometry are optimised to obtain spectrally uncorrelated photons with high coupling efficiencies. Four photons are generated by a counter- propagating pump in the same crystal and anlysed via two photon interference experiments between photons from each pair source as well as joint spectral and g^(2) measurements. We obtain a spectral purity of 0.91 and coupling efficiencies around 90% for all four photons without any filtering. These pure indistinguishable photon sources at telecom wavelengths are perfectly adapted for quantum network demonstrations and other multi-photon protocols