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

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

Paper 6: A Mathematics Teacher’s Journey of Identity Construction and Change

Despite some gains, improving mathematics instruction remains an area of concern in the United States. The implementation of the Common Core Standards and the challenge of teaching the 21st Century student require mathematics teachers to examine their pedagogy to determine if they need to change or improve their practices. This paper provides a personal account of my journey when determining my identity as a mathematics teacher and how constructing my identity helped in changing and improving my practices as a mathematics teacher. The study was done using autoethnography, a burgeoning research method, and identity theory. This study has the goals of giving “voice” to the classroom teacher and providing a practical method for improving instruction. The findings indicate that my identity is composed of many facets, and my identity is a key factor underlying who I am as a mathematics teacher. The findings also resulted in the development of the Math Madness Model (M3) Instrument, which can facilitate self-studies by other mathematics classroom teachers and educators with the purpose of improving their practices

An Autoethnography:A Mathematics Teacher\u27s Journey of Identity Construction and Change

Despite some gains, improving secondary mathematics instruction remains an area of concern of the National Council of Teachers of Mathematics (NCTM). Recitation, also known as lecturing, prevails as the practice of choice of mathematics teachers in the United States. However, the report of the NCTM Research Advisory Committee 2000 indicates that the mathematical proficiency of students increases when the practice of choice includes more than recitation. Therefore, changes in instruction in the mathematics classroom should occur to improve student learning. The purpose of this dissertation is to provide a personalized account of one mathematics teacher’s use of reflective teaching as an agent of change. This dissertation is about a journey of change in instruction fostered by a change of identity as a mathematics teacher. This dissertation chronicles the identity construction of the teacher. This study has relevance because the process utilized by the teacher provides a method of self-examination and identity construction for other mathematics classroom teachers who want to improve their practices. This study also has relevance because it describes the process of how a classroom teacher takes ownership of self-improvement. This qualitative dissertation uses autoethnography as the methodology. Autoethnography is research, writing and story where the researcher is the subject and the researcher’s experiences are the data (Ellis and Bochner 2000). The theoretical frame for this autoethnography is identity theory as it relates to teacher identity construction. Memory, videotaped lessons, student commentary and a reflective journal serve as supporting data sources to render narratives detailing the findings. The research question guiding this dissertation is: In what ways does a teacher’s reflection on mathematics practice facilitate teacher identity construction and change of practice? The findings show that a teacher’s identity can be interwoven by many characteristics that at times work simultaneously. The findings also indicate that changing one’s practices is an arduous process but can be accomplished and the process given “voice.

NIRA to NESRA

Article traces the development of employee services and its rapid growth into a major force in the field of personnel administration

A Mathematics Teacher’s Journey of Identity Construction and Change

Despite some gains, improving mathematics instruction remains an area of concern in the United States. The implementation of the Common Core Standards and the challenge of teaching the 21st Century student require mathematics teachers to examine their pedagogy to determine if they need to change or improve their practices. This paper provides a personal account of my journey when determining my identity as a mathematics teacher and how constructing my identity helped in changing and improving my practices as a mathematics teacher. The study was done using autoethnography, a burgeoning research method, and identity theory. This study has the goals of giving “voice” to the classroom teacher and providing a practical method for improving instruction. The findings indicate that my identity is composed of many facets, and my identity is a key factor underlying who I am as a mathematics teacher. The findings also resulted in the development of the Math Madness Model (M3) Instrument, which can facilitate self-studies by other mathematics classroom teachers and educators with the purpose of improving their practices

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