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For a sample of star forming galaxies in the redshift interval 0.15$<$z$<$0.3, we study how both the relative strength of the AGN infra-red emission, compared to that due to the star formation (SF), and the numerical fraction of AGNs, change as a function of the total stellar mass of the hosting galaxy group (M$^{*}_{\mathrm{group}}$), between $10^{10.25}$ and $10^{11.9}$M$_{\odot}$. Using a multi-component SED fitting analysis, we separate the contribution of stars, AGN torus and star formation to the total emission at different wavelengths. This technique is applied to a new multi-wavelength data-set in the SIMES field (23 not redundant photometric bands), spanning the wavelength range from the UV (GALEX) to the far-IR (Herschel) and including crucial AKARI and WISE mid-IR observations (4.5 \mu m$<\lambda<$24 \mu m), where the BH thermal emission is stronger. This new photometric catalog, that includes our best photo-z estimates, is released through the NASA/IPAC Infrared Science Archive (IRSA). Groups are identified through a friends of friends algorithm ($\sim$62% purity, $\sim$51% completeness). We identified a total of 45 galaxies requiring an AGN emission component, 35 of which in groups and 10 in the field. We find BHAR$\propto ($M$^{*}_{\mathrm{group}})^{1.21\pm0.27}$ and (BHAR/SFR)$\propto ($M$^{*}_{\mathrm{group}})^{1.04\pm0.24}$ while, in the same range of M$^{*}_{\mathrm{group}}$, we do not observe any sensible change in the numerical fraction of AGNs. Our results indicate that the nuclear activity (i.e. the BHAR and the BHAR/SFR ratio) is enhanced when galaxies are located in more massive and richer groups. Comment: 31 pages, 23 figures

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) \sim w^{-\gamma}$ for small weight $w$. We obtain the exponent $\gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare. Comment: 8 pages, 8 figures

Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schr\"{o}dinger equations linearly coupled at the single site. Symmetric, antisymmetric and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones. Comment: 9 figures

We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class by the Schwartz and Cauchy integrals. These conditions extend a previous result of Aleksandrov. 10 pages, to appear in Mat. fizika, analiz, geometriya (Kharkov)

We show there exists a constant $0

We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Cech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value. 32 pages, including 9 embedded figures

Abstract In the Split to Block Vertex Deletion and Split to Threshold Vertex Deletion problems the input is a split graph G and an integer k, and the goal is to decide whether there is a set S of vertices of size at most k such that G − S is a block graph and G − S is a threshold graph, respectively. In this paper we give algorithms for these problems whose running times are O ⁎ ( 2.076 k ) and O ⁎ ( 1.619 k ) , respectively.

We compute the Welschinger invariants of blowups of the projective plane at an arbitrary conjugation invariant configuration of points. Specifically, open analogues of the WDVV equation and Kontsevich-Manin axioms lead to a recursive algorithm that reconstructs all the invariants from a small set of known invariants. Example computations are given, including the non-del Pezzo case. 34 pages

We consider the problem of distributed source simulation with no communication, in which Alice and Bob observe sequences $U^{n}$ and $V^{n}$ respectively, drawn from a joint distribution $p_{UV}^ {\otimes n}$ , and wish to locally generate sequences $X^{n}$ and $Y^{n}$ respectively with a joint distribution that is close (in KL divergence) to $p_{XY}^ {\otimes n}$ . We provide a single-letter condition under which such a simulation is asymptotically possible with a vanishing KL divergence. Our condition is nontrivial only in the case where the Gacs-Korner (GK) common information between $U$ and $V$ is nonzero, and we conjecture that only scalar Markov chains $X-U-V-Y$ can be simulated otherwise. Motivated by this conjecture, we further examine the case where both $p_{UV}$ and $p_{XY}$ are doubly symmetric binary sources with parameters $p,q\leq 1/2$ respectively. While it is trivial that in this case $p\leq q$ is both necessary and sufficient, we use Fourier analytic tools to show that when $p$ is close to $q$ then any successful simulation is close to being scalar in the total variation sense.

We propose a combinatorial approach to the following strengthening of Gal's conjecture: $\gamma(\Delta)\ge \gamma(E)$ coefficientwise, where $\Delta$ is a flag homology sphere and $E\subseteq \Delta$ an induced homology sphere of codimension $1$. We provide partial evidence in favor of this approach, and prove a nontrivial nonlinear inequality that follows from the above conjecture, for boundary complexes of flag $d$-polytopes: $h_1(\Delta) h_i(\Delta) \ge (d-i+1)h_{i-1}(\Delta) + (i+1) h_{i+1}(\Delta)$ for all $0\le i\le d$. Comment: 12 pages