Linear forms and quadratic uniformity for functions on ZN\mathbb{Z}_N

A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that quasirandomness can often be measured by means of certain easily described norms, known as uniformity norms. However, determining which uniformity norms work for which structures turns out to be a surprisingly hard question. In [GW09a] and [GW09b, GW09c] we gave a complete answer to this question for groups of the form $G=\mathbb{F}_p^n$, provided $p$ is not too small. In $\mathbb{Z}_N$, substantial extra difficulties arise, of which the most important is that an "inverse theorem" even for the uniformity norm $\|.\|_{U^3}$ requires a more sophisticated (local) formulation. When $N$ is prime, $\mathbb{Z}_N$ is not rich in subgroups, so one must use regular Bohr neighbourhoods instead. In this paper, we prove the first non-trivial case of the main conjecture from [GW09a].Comment: 66 page

A Uniform Min-Max Theorem with Applications in Cryptography

We present a new, more constructive proof of von Neumann’s Min-Max Theorem for two-player zero-sum game — specifically, an algorithm that builds a near-optimal mixed strategy for the second player from several best-responses of the second player to mixed strategies of the first player. The algorithm extends previous work of Freund and Schapire (Games and Economic Behavior ’99) with the advantage that the algorithm runs in poly(n) time even when a pure strategy for the first player is a distribution chosen from a set of distributions over {0, 1}$^n$ . This extension enables a number of additional applications in cryptography and complexity theory, often yielding uniform security versions of results that were previously only proved for nonuniform security (due to use of the non-constructive Min-Max Theorem). We describe several applications, including a more modular and improved uniform version of Impagliazzo’s Hardcore Theorem (FOCS ’95), showing impossibility of constructing succinct non-interactive arguments (SNARGs) via black-box reductions under uniform hardness assumptions (using techniques from Gentry and Wichs (STOC ’11) for the nonuniform setting), and efficiently simulating high entropy distributions within any sufficiently nice convex set (extending a result of Trevisan, Tulsiani and Vadhan (CCC ’09)).Engineering and Applied Science

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

On certain other sets of integers

We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).Comment: 29 pp. Corrected typos. Added definitions for some non-standard notation and remarks on lower bound

Pressure effects on the electron-doped high Tc superconductor BaFe(2-x)Co(x)As(2)

Application of pressures or electron-doping through Co substitution into Fe sites transforms the itinerant antiferromagnet BaFe(2)As(2) into a superconductor with the Tc exceeding 20K. We carried out systematic transport measurements of BaFe(2-x)Co(x)As(2) superconductors in pressures up to 2.5GPa, and elucidate the interplay between the effects of electron-doping and pressures. For the underdoped sample with nominal composition x = 0.08, application of pressure strongly suppresses a magnetic instability while enhancing Tc by nearly a factor of two from 11K to 21K. In contrast, the optimally doped x=0.20 sample shows very little enhancement of Tc=22K under applied pressure. Our results strongly suggest that the proximity to a magnetic instability is the key to the mechanism of superconductivity in iron-pnictides.Comment: 5 figure

The Sloan Digital Sky Survey Reverberation Mapping Project: Rapid CIV Broad Absorption Line Variability

We report the discovery of rapid variations of a high-velocity CIV broad absorption line trough in the quasar SDSS J141007.74+541203.3. This object was intensively observed in 2014 as a part of the Sloan Digital Sky Survey Reverberation Mapping Project, during which 32 epochs of spectroscopy were obtained with the Baryon Oscillation Spectroscopic Survey spectrograph. We observe significant (>4sigma) variability in the equivalent width of the broad (~4000 km/s wide) CIV trough on rest-frame timescales as short as 1.20 days (~29 hours), the shortest broad absorption line variability timescale yet reported. The equivalent width varied by ~10% on these short timescales, and by about a factor of two over the duration of the campaign. We evaluate several potential causes of the variability, concluding that the most likely cause is a rapid response to changes in the incident ionizing continuum. If the outflow is at a radius where the recombination rate is higher than the ionization rate, the timescale of variability places a lower limit on the density of the absorbing gas of n_e > 3.9 x 10^5 cm^-3. The broad absorption line variability characteristics of this quasar are consistent with those observed in previous studies of quasars, indicating that such short-term variability may in fact be common and thus can be used to learn about outflow characteristics and contributions to quasar/host-galaxy feedback scenarios.Comment: 15 pages, 14 figures. Accepted for publication in the Astrophysical Journa

Oblique Parameter Constraints on Large Extra Dimensions

We consider the Kaluza-Klein scenario in which gravity propagates in the $4+n$ dimensional bulk of spacetime and the Standard Model particles are confined to a 3-brane. We calculate the gauge boson self-energy corrections arising from the exchange of virtual gravitons and present our results in the $STU$-formalism. We find that the new physics contributions to $S$, $T$ and $U$ decouple in the limit that the string scale $M_S$ goes to infinity. The oblique parameters constrain the lower limit on $M_S$. Taking the quantum gravity cutoff to be $M_S$, $S$-parameter constraints impose $M_S>1.55$ TeV for $n=2$ at the 1$\sigma$ level. $T$-parameter constraints impose $M_S>1.25 (0.75)$ TeV for $n=3 (6)$.Comment: Version to appear in PR

Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes

We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re

The Sloan Digital Sky Survey Reverberation Mapping Project: Technical Overview

The Sloan Digital Sky Survey Reverberation Mapping project (SDSS-RM) is a dedicated multi-object RM experiment that has spectroscopically monitored a sample of 849 broad-line quasars in a single 7 deg$^2$ field with the SDSS-III BOSS spectrograph. The RM quasar sample is flux-limited to i_psf=21.7 mag, and covers a redshift range of 0.1<z<4.5. Optical spectroscopy was performed during 2014 Jan-Jul dark/grey time, with an average cadence of ~4 days, totaling more than 30 epochs. Supporting photometric monitoring in the g and i bands was conducted at multiple facilities including the CFHT and the Steward Observatory Bok telescopes in 2014, with a cadence of ~2 days and covering all lunar phases. The RM field (RA, DEC=14:14:49.00, +53:05:00.0) lies within the CFHT-LS W3 field, and coincides with the Pan-STARRS 1 (PS1) Medium Deep Field MD07, with three prior years of multi-band PS1 light curves. The SDSS-RM 6-month baseline program aims to detect time lags between the quasar continuum and broad line region (BLR) variability on timescales of up to several months (in the observed frame) for ~10% of the sample, and to anchor the time baseline for continued monitoring in the future to detect lags on longer timescales and at higher redshift. SDSS-RM is the first major program to systematically explore the potential of RM for broad-line quasars at z>0.3, and will investigate the prospects of RM with all major broad lines covered in optical spectroscopy. SDSS-RM will provide guidance on future multi-object RM campaigns on larger scales, and is aiming to deliver more than tens of BLR lag detections for a homogeneous sample of quasars. We describe the motivation, design and implementation of this program, and outline the science impact expected from the resulting data for RM and general quasar science.Comment: 25 pages, submitted to ApJS; project website at http://www.sdssrm.or

Yang-Mills instantons and dyons on homogeneous G_2-manifolds

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S^1 x G/H and dyons on iR x G/H are also given.Comment: 1+26 pages, 14 figures, 6 miniplot