Flavoured co-annihilation

In minimal supergravity (mSUGRA) or CMSSM, one of the main co-annihilating partners of the neutralino is the lightest stau, (tau) over tilde (1). In the presence of flavour violation in the right-handed sector, the co-annihilating partner would be a flavour mixed state. The flavour effect is two-fold: (a) It changes the mass of (tau) over tilde (1) thus modifying the parameter space of the co-annihilation and (b) flavour violating scatterings could now contribute to the cross-sections in the early Universe. In fact, it is shown that for large enough delta similar to 0.2, these processes would constitute the dominant channels in co-annihilation regions. The amount of flavour mixing permissible is constrained by flavour violating tau -> mu or tau -> e processes. For Delta(RR) mass insertions, the constraints from flavour violation are not strong enough in some regions of the parameter space due to partial cancellations in the amplitudes. In mSUGRA, the regions with cancelations within LFV amplitudes do not overlap with the regions of co-annihilations. In non-universal Higgs model (NUHM), however, these regions do overlap leading to significant flavoured co-annihilations. At the LHC and other colliders, these regions can constitute for interesting signals.

New Mass Limit for White Dwarfs: Super-Chandrasekhar Type Ia Supernova as a New Standard Candle

Type Ia supernovae, sparked off by exploding white dwarfs of mass close to the Chandrasekhar limit, play the key role in understanding the expansion rate of the Universe. However, recent observations of several peculiar type Ia supernovae argue for its progenitor mass to be significantly super-Chandrasekhar. We show that strongly magnetized white dwarfs not only can violate the Chandrasekhar mass limit significantly, but exhibit a different mass limit. We establish from a foundational level that the generic mass limit of white dwarfs is 2.58 solar mass. This explains the origin of overluminous peculiar type Ia supernovae. Our finding further argues for a possible second standard candle, which has many far reaching implications, including a possible reconsideration of the expansion history of the Universe. DOI: 10.1103/PhysRevLett.110.071102

Give-and-take based peer-to-peer content distribution networks

Content Distribution Networks (CDNs) are widely used to distribute data to large number of users. Traditionally, content is being replicated among a number of surrogate servers, leading to high operational costs. In this context, Peer-to-Peer (P2P) CDNs have emerged as a viable alternative. An issue of concern in P2P networks is that of free riders, i.e., selfish peers who download files and leave without uploading anything in return. Free riding must be discouraged. In this paper, we propose a criterion, the Give-and-Take (G&T) criterion, that disallows free riders. Incorporating the G&T criterion in our model, we study a problem that arises naturally when a new peer enters the system: viz., the problem of downloading a `universe' of segments, scattered among other peers, at low cost. We analyse this hard problem, and characterize the optimal download cost under the G&T criterion. We propose an optimal algorithm, and provide a sub-optimal algorithm that is nearly optimal, but runs much more quickly; this provides an attractive balance between running time and performance. Finally, we compare the performance of our algorithms with that of a few existing P2P downloading strategies in use. We also study the computation time for prescribing the strategy for initial segment and peer selection for the newly arrived peer for various existing and proposed algorithms, and quantify cost-computation time trade-offs.

Modified Einstein's gravity as a possible missing link between sub- and super-Chandrasekhar type Ia supernovae

We explore the effect of modification to Einstein's gravity in white dwarfs for the first time in the literature, to the best of our knowledge. This leads to significantly sub- and super-Chandrasekhar limiting masses of white dwarfs, determined by a single model parameter. On the other hand, type Ia supernovae (SNeIa), a key to unravel the evolutionary history of the universe, are believed to be triggered in white dwarfs having mass close to the Chandrasekhar limit. However, observations of several peculiar, under- and over-luminous SNeIa argue for exploding masses widely different from this limit. We argue that explosions of the modified gravity induced sub- and super-Chandrasekhar limiting mass white dwarfs result in under- and over-luminous SNeIa respectively, thus unifying these two apparently disjoint sub-classes and, hence, serving as a missing link. Our discovery raises two fundamental questions. Is the Chandrasekhar limit unique? Is Einstein's gravity the ultimate theory for understanding astronomical phenomena? Both the answers appear to be no!

Narrow escape: how ionizing photons escape from disc galaxies

In this paper we calculate the escape fraction (f(esc)) of ionizing photons from starburst galaxies. Using 2D axisymmetric hydrodynamic simulations, we study superbubbles created by overlapping supernovae in OB associations. We calculate the escape fraction of ionizing photons from the centre of the disc along different angles through the superbubble and the gas disc. After convolving with the luminosity function of OB associations, we show that the ionizing photons escape within a cone of similar to 40 degrees, consistent with observations of nearby galaxies. The evolution of the escape fraction with time shows that it falls initially as cold gas is accumulated in a dense shell. After the shell crosses a few scaleheights and fragments, the escape fraction through the polar regions rises again. The angle-averaged escape fraction cannot exceed similar to1 - cos (1 rad)] = 0.5 from geometrical considerations (using the emission cone opening angle). We calculate the dependence of the time-and angle-averaged escape fraction on the mid-plane disc gas density (in the range n(0) = 0.15-50 cm(-3)) and the disc scaleheight (between z(0) = 10 and 600 pc). We find that the escape fraction is related to the disc parameters (the mid-plane disc density and scaleheight) roughly so that f(esc)(alpha)n(0)(2)z(0)(3) (with alpha approximate to 2.2) is a constant. For discs with a given warm neutral medium temperature, massive discs have lower escape fraction than low-mass galaxies. For Milky Way ISM parameters, we find f(esc) similar to 5 per cent, and it increases to approximate to 10 per cent for a galaxy 10 times less massive. We discuss the possible effects of clumpiness of the ISM on the estimate of the escape fraction and the implications of our results for the reionization of the Universe.

Parameterized Algorithms and Kernels for 3-Hitting Set with Parity Constraints

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U. The goal is to find a subset of U of the smallest possible size that intersects every set in F. The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the intersections of S with each set in the family F. In particular, an odd (even) set is a hitting set that hits every set at either one or three (two) elements, and a perfect code is a hitting set that intersects every set at exactly one element. These questions are of fundamental interest in many contexts for general set systems. Just as for Hitting Set, we find these questions to be interesting for the case of families consisting of sets of size at most three. In this work, we initiate an algorithmic study of these problems in this special case, focusing on a parameterized analysis. We show, for each problem, efficient fixed-parameter tractable algorithms using search trees that are tailor-made to the constraints in question, and also polynomial kernels using sunflower-like arguments in a manner that accounts for equivalence under the additional parity constraints.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.

Imprint of modified Einstein's gravity on white dwarfs: Unifying Type Ia supernovae

We establish the importance of modified Einstein's gravity (MG) in white dwarfs (WDs) for the first time in the literature. We show that MG leads to significantly sub- and super-Chandrasekhar limiting mass WDs, depending on a single model parameter. However, conventional WDs on approaching Chandrasekhar's limit are expected to trigger Type Ia supernovae (SNeIa), a key to unravel the evolutionary history of the universe. Nevertheless, observations of several peculiar, under-and over-luminous SNeIa argue for the limiting mass widely different from Chandrasekhar's limit. Explosions of MG induced sub-and super-Chandrasekhar limiting mass WDs explain under-and over-luminous SNeIa respectively, thus unifying these two apparently disjoint sub-classes. Our discovery questions both the global validity of Einstein's gravity and the uniqueness of Chandrasekhar's limit.

DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

Social optimum in social groups with give-and-take criterion

We consider a Social Group' of networked nodes, seeking a universe' of segments. Each node has a subset of the universe and access to an expensive resource for downloading data. Nodes can also acquire the universe by exchanging copies of segments among themselves, at low cost, using inter-node links. While exchanges over inter-node links ensure minimum cost, some nodes in the group try to exploit the system. We term such nodes as non-reciprocating nodes' and prohibit such behavior by proposing the give-and-take' criterion, where exchange is allowed if each node has segments unavailable with the other. Under this criterion, we consider the problem of maximizing the number of nodes with the universe at the end of local exchanges. First, we present a randomized algorithm that is shown to be optimal in the asymptotic regime. Then, we present greedy links algorithm, which performs well for most of the scenarios and yields an optimal result when the number of nodes is four. The polygon algorithm is proposed, which yields an optimal result when each of the nodes has a unique segment. After presenting some intuitive algorithms (e.g., greedy incremental algorithm and rarest first algorithm), we compare the performances of all proposed algorithms with the optimal. Copyright (c) 2015 John Wiley & Sons, Ltd.

Infrared Magnitude-Redshift Relations for Luminous Radio Galaxies

Infrared magnitude-redshift relations for the 3CR and 6C samples of radio galaxies are presented for a wide range of plausible cosmological models, including those with non-zero cosmological constant OmegaLambda. Variations in the galaxy formation redshift, metallicity and star formation history are also considered. The results of the modelling are displayed in terms of magnitude differences between the models and no-evolution tracks, illustrating the amount of K-band evolution necessary to account for the observational data. Given a number of plausible assumptions, the results of these analyses suggest that: (i) cosmologies which predict T_0xH_0>1 (where T_0 denotes the current age of the universe) can be excluded; (ii) the star formation redshift should lie in the redshift interval 5

La teología ante la física moderna : cuestiones fundamentales para un diálogo posible : 2ª parte: la teología de la creación ante la cosmología científica

Resumen: El descubrimiento de la verdadera naturaleza evolutiva y mutable de este universo en que vivimos ha dado origen a la moderna cosmología científica, que con sus modelos del nacimiento y evolución del cosmos plantea estimulantes cuestiones teológicas como la relación entre creación e inicio del universo, la acción divina en el mundo o la teleología y finalidad última de la Creación.

Justino presenta la divinidad de Cristo ante judíos y paganos

Resumen: El autor nos ofrece una rápida visión de la Trinidad en Justino, fruto de una larga investigación. Resume primero el camino del Diálogo, donde Justino atribuye las teofanías del Antiguo Testamento al Logos. Este Dios es numéricamente distinto del Padre Creador del universo, pero está por debajo de él. En las Apologías, en cambio, se confronta con el paganismo y el platonismo: ubica al Logos en el segundo lugar, y al Espíritu en el Tercero. El Hijo, unigénito, es engendrado por el Padre antes de las creaturas, sin dividirlo, sino como un fuego enciende a otro fuego. El Padre todo lo hace por medio de él. Poco alude a la actividad propia del Espíritu profético. Estos dos caminos confluyen en una cierta inferioridad del Hijo respecto al Padre, la que es típica de diversos Padres prenicenos. Los perversos demonios han perseguido a todos los que, como Sócrates, han vivido según el Logos. Platón copió a Moisés sin entenderlo del todo. La cruz del Hijo es cósmica. Jesús es el maestro crucificado

Amadís de Gaula humanizado : vejez y melancolía en la obra de Feliciano de Silva

Integran este número de la revista ponencias presentadas en Studia Hispanica Medievalia VIII: Actas de las IX Jornadas Internacionales de Literatura Española Medieval, 2008, y de Homenaje al Quinto Centenario de Amadis de Gaula