Combinatorial batch codes

In this paper, we study batch codes, which were introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4]. A batch code specifies a method to distribute a database of [n] items among [m] devices (servers) in such a way that any [k] items can be retrieved by reading at most [t] items from each of the servers. It is of interest to devise batch codes that minimize the total storage, denoted by [N] , over all [m] servers. We restrict out attention to batch codes in which every server stores a subset of the items. This is purely a combinatorial problem, so we call this kind of batch code a ''combinatorial batch code''. We only study the special case [t=1] , where, for various parameter situations, we are able to present batch codes that are optimal with respect to the storage requirement, [N] . We also study uniform codes, where every item is stored in precisely [c] of the [m] servers (such a code is said to have rate [1/c] ). Interesting new results are presented in the cases [c = 2, k-2] and [k-1] . In addition, we obtain improved existence results for arbitrary fixed [c] using the probabilistic method

Hierarchical formation of bulgeless galaxies II: Redistribution of angular momentum via galactic fountains

Within a fully cosmological hydrodynamical simulation, we form a galaxy which rotates at 140 km/s, and is characterised by two loose spiral arms and a bar, indicative of a Hubble Type SBc/d galaxy. We show that our simulated galaxy has no classical bulge, with a pure disc profile at z=1, well after the major merging activity has ended. A long-lived bar subsequently forms, resulting in the formation of a secularly-formed "pseudo" bulge, with the final bulge-to-total light ratio B/T=0.21. We show that the majority of gas which loses angular momentum and falls to the central region of the galaxy during the merging epoch is blown back into the hot halo, with much of it returning later to form stars in the disc. We propose that this mechanism of redistribution of angular momentum via a galactic fountain, when coupled with the results from our previous study which showed why gas outflows are biased to have low angular momentum, can solve the angular momentum/bulgeless disc problem of the cold dark matter paradigm.Comment: 9 Pages, 10 Figures, accepted MNRAS version. Comments welcom

The role of feedback in shaping the structure of the interstellar medium

We present an analysis of the role of feedback in shaping the neutral hydrogen (H I) content of simulated disc galaxies. For our analysis, we have used two realizations of two separate Milky Way-like (similar to L star) discs - one employing a conservative feedback scheme (McMaster Unbiased Galaxy Survey), the other significantly more energetic [Making Galaxies In a Cosmological Context (MaGICC)]. To quantify the impact of these schemes, we generate zeroth moment (surface density) maps of the inferred H I distribution; construct power spectra associated with the underlying structure of the simulated cold interstellar medium, in addition to their radial surface density and velocity dispersion profiles. Our results are compared with a parallel, self-consistent, analysis of empirical data from The H I Nearby Galaxy Survey (THINGS). Single power-law fits (P proportional to k(gamma)) to the power spectra of the stronger feedback (MaGICC) runs (over spatial scales corresponding to similar to 0.5 to similar to 20 kpc) result in slopes consistent with those seen in the THINGS sample (gamma similar to -2.5). The weaker feedback (MUGS) runs exhibit shallower power-law slopes (gamma similar to -1.2). The power spectra of the MaGICC simulations are more consistent though with a two-component fit, with a flatter distribution of power on larger scales (i.e. gamma similar to -1.4 for scales in excess of similar to 2 kpc) and a steeper slope on scales below similar to 1 kpc (gamma similar to -5), qualitatively consistent with empirical claims, as well as our earlier work on dwarf discs. The radial H I surface density profiles of the MaGICC discs show a clear exponential behaviour, while those of the MUGS suite are essentially flat; both behaviours are encountered in nature, although the THINGS sample is more consistent with our stronger (MaGICC) feedback runs

Optimal constructions for ID-based one-way-function key predistribution schemes realizing specified communication graphs

We study a method for key predistribution in a network of n users where pairwise keys are computed by hashing users’ IDs along with secret information that has been (pre)distributed to the network users by a trusted entity. A communication graph G can be specified to indicate which pairs of users should be able to compute keys. We determine necessary and sufficient conditions for schemes of this type to be secure. We also consider the problem of minimizing the storage requirements of such a scheme; we are interested in the total storage as well as the maximum storage required by any user. Minimizing the total storage is NP-hard, whereas minimizing the maximum storage required by a user can be computed in polynomial time

Properties of simulated Milky Way-mass galaxies in loose group and field environments

We test the validity of comparing simulated field disk galaxies with the empirical properties of systems situated within environments more comparable to loose groups, including the Milky Way's Local Group. Cosmological simulations of Milky Way-mass galaxies have been realised in two different environment samples: in the field and in environments with similar properties to the Local Group. Apart from the environments of the galaxies, the samples are kept as homogeneous as possible with equivalent ranges in last major merger time, halo mass and halo spin. Comparison of these two samples allow for systematic differences in the simulations to be identified. Metallicity gradients, disk scale lengths, colours, magnitudes and age-velocity dispersion relations are studied for each galaxy in the suite and the strength of the link between these and environment of the galaxies is studied. The bulge-to-disk ratio of the galaxies show that these galaxies are less spheroid dominated than many other simulated galaxies in literature with the majority of both samples being disk dominated. We find that secular evolution and mergers dominate the spread of morphologies and metallicity gradients with no visible differences between the two environment samples. In contrast with this consistency in the two samples there is tentative evidence for a systematic difference in the velocity dispersion-age relations of galaxies in the different environments. Loose group galaxies appear to have more discrete steps in their velocity dispersion-age relations. We conclude that at the current resolution of cosmological galaxy simulations field environment galaxies are sufficiently similar to those in loose groups to be acceptable proxies for comparison with the Milky Way provided that a similar assembly history is considered.Comment: 16 pages, 11 figures, abstract abridged for arXiv. Accepted for publication in Astronomy & Astrophysic

Constraining sub-grid physics with high-redshift spatially-resolved metallicity distributions

Aims. We examine the role of energy feedback in shaping the distribution of metals within cosmological hydrodynamical simulations of L* disc galaxies. While negative abundance gradients today provide a boundary condition for galaxy evolution models, in support of inside-out disc growth, empirical evidence as to whether abundance gradients steepen or flatten with time remains highly contradictory. Methods. We made use of a suite of L* discs, realised with and without "enhanced" feedback. All the simulations were produced using the smoothed particle hydrodynamics code Gasoline, and their in situ gas-phase metallicity gradients traced from redshift z similar to 2 to the present-day. Present-day age-metallicity relations and metallicity distribution functions were derived for each system. Results. The "enhanced" feedback models, which have been shown to be in agreement with a broad range of empirical scaling relations, distribute energy and re-cycled ISM material over large scales and predict the existence of relatively "flat" and temporally invariant abundance gradients. Enhanced feedback schemes reduce significantly the scatter in the local stellar age-metallicity relation and, especially, the [O/Fe]-[Fe/H] relation. The local [O/Fe] distribution functions for our L* discs show clear bimodality, with peaks at [O/Fe] = -0.05 and +0.05 (for stars with [Fe/H] > -1), consistent with our earlier work on dwarf discs. Conclusions. Our results with "enhanced" feedback are inconsistent with our earlier generation of simulations realised with "conservative" feedback. We conclude that spatially-resolved metallicity distributions, particularly at high-redshift, offer a unique and under-utilised constraint on the uncertain nature of stellar feedback processes

A coding theory foundation for the analysis of general unconditionally secure proof-of-retrievability schemes for cloud storage

There has been considerable recent interest in “cloud storage” wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover or retrieve the file given any “proving algorithm” that has a sufficiently high success probability. This paper treats proof-of-retrievability schemes in the model of unconditional security, where an adversary has unlimited computational power. In this case retrievability of the file can be modelled as error-correction in a certain code. We provide a general analytical framework for such schemes that yields exact (non-asymptotic) reductions that precisely quantify conditions for extraction to succeed as a function of the success probability of a proving algorithm, and we apply this analysis to several archetypal schemes. In addition, we provide a new methodology for the analysis of keyed POR schemes in an unconditionally secure setting, and use it to prove the security of a modified version of a scheme due to Shacham and Waters [Lecture Notes in Comput. Sci. 5350, Springer (2008), 90–107] under a slightly restricted attack model, thus providing the first example of a keyed POR scheme with unconditional security. We also show how classical statistical techniques can be used to evaluate whether the responses of the prover are accurate enough to permit successful extraction. Finally, we prove a new lower bound on storage and communication complexity of POR schemes. This paper treats proof-of-retrievability schemes in the model of unconditional security, where an adversary has unlimited computational power. In this case retrievability of the file can be modelled as error-correction in a certain code. We provide a general analytical framework for such schemes that yields exact (non-asymptotic) reductions that precisely quantify conditions for extraction to succeed as a function of the success probability of a proving algorithm, and we apply this analysis to several archetypal schemes. In addition, we provide a new methodology for the analysis of keyed POR schemes in an unconditionally secure setting, and use it to prove the security of a modified version of a scheme due to Shacham and Waters under a slightly restricted attack model, thus providing the first example of a keyed POR scheme with unconditional security. We also show how classical statistical techniques can be used to evaluate whether the responses of the prover are accurate enough to permit successful extraction. Finally, we prove a new lower bound on storage and communication complexity of POR schemes

Forming Disk Galaxies in Lambda CDM Simulations

We used fully cosmological, high resolution N-body + SPH simulations to follow the formation of disk galaxies with rotational velocities between 135 and 270 km/sec in a Lambda CDM universe. The simulations include gas cooling, star formation, the effects of a uniform UV background and a physically motivated description of feedback from supernovae. The host dark matter halos have a spin and last major merger redshift typical of galaxy sized halos as measured in recent large scale N--Body simulations. The simulated galaxies form rotationally supported disks with realistic exponential scale lengths and fall on both the I-band and baryonic Tully Fisher relations. An extended stellar disk forms inside the Milky Way sized halo immediately after the last major merger. The combination of UV background and SN feedback drastically reduces the number of visible satellites orbiting inside a Milky Way sized halo, bringing it in fair agreement with observations. Our simulations predict that the average age of a primary galaxy's stellar population decreases with mass, because feedback delays star formation in less massive galaxies. Galaxies have stellar masses and current star formation rates as a function of total mass that are in good agreement with observational data. We discuss how both high mass and force resolution and a realistic description of star formation and feedback are important ingredients to match the observed properties of galaxies.Comment: Revised version after the referee's comments. Conclusions unchanged. 2 new plots. MNRAS in press. 20 plots. 21 page