Random polytopes obtained by matrices with heavy tailed entries

Let $\Gamma$ be an $N\times n$ random matrix with independent entries and such that in each row entries are i.i.d. Assume also that the entries are symmetric, have unit variances, and satisfy a small ball probabilistic estimate uniformly. We investigate properties of the corresponding random polytope $\Gamma^* B_1^N$ in $\mathbb{R}$ (the absolute convex hull of rows of $\Gamma$). In particular, we show that $$\Gamma B_1^N \supset b^{-1} \left( B_{\infty}^n \cap \sqrt{\ln (N/n)}\, B_2^n \right).$$ where $b$ depends only on parameters in small ball inequality. This extends results of \cite{LPRT} and recent results of \cite{KKR}. This inclusion is equivalent to so-called $\ell_1$-quotient property and plays an important role in compressive sensing (see \cite{KKR} and references therein).Comment: Last version, to appear in Communications in Contemporary Mathematic

Random polytopes obtained by matrices with heavy tailed entries

Let $\Gamma$ be an $N\times n$ random matrix with independent entries and such that in each row entries are i.i.d. Assume also that the entries are symmetric, have unit variances, and satisfy a small ball probabilistic estimate uniformly. We investigate properties of the corresponding random polytope $\Gamma^* B_1^N$ in $\mathbb{R}$ (the absolute convex hull of rows of $\Gamma$). In particular, we show that $$\Gamma B_1^N \supset b^{-1} \left( B_{\infty}^n \cap \sqrt{\ln (N/n)}\, B_2^n \right).$$ where $b$ depends only on parameters in small ball inequality. This extends results of \cite{LPRT} and recent results of \cite{KKR}. This inclusion is equivalent to so-called $\ell_1$-quotient property and plays an important role in compressive sensing (see \cite{KKR} and references therein).Comment: Last version, to appear in Communications in Contemporary Mathematic

Decoherence suppression via environment preparation

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For models in which a two-state system interacts with a dynamical environment, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.Comment: 4 pages, 2 figure

Temperature in nonequilibrium systems with conserved energy

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.Comment: 4 pages, 1 figure, final versio

The Origin of Nitrogen on Jupiter and Saturn from the 15^{15}N/14^{14}N Ratio

The Texas Echelon cross Echelle Spectrograph (TEXES), mounted on NASA's Infrared Telescope Facility (IRTF), was used to map mid-infrared ammonia absorption features on both Jupiter and Saturn in February 2013. Ammonia is the principle reservoir of nitrogen on the giant planets, and the ratio of isotopologues ($^{15}$N/$^{14}$N) can reveal insights into the molecular carrier (e.g., as N$_2$ or NH$_3$) of nitrogen to the forming protoplanets, and hence the source reservoirs from which these worlds accreted. We targeted two spectral intervals (900 and 960 cm$^{-1}$) that were relatively clear of terrestrial atmospheric contamination and contained close features of $^{14}$NH$_3$ and $^{15}$NH$_3$, allowing us to derive the ratio from a single spectrum without ambiguity due to radiometric calibration (the primary source of uncertainty in this study). We present the first ground-based determination of Jupiter's $^{15}$N/$^{14}$N ratio (in the range from $1.4\times10^{-3}$ to $2.5\times10^{-3}$), which is consistent with both previous space-based studies and with the primordial value of the protosolar nebula. On Saturn, we present the first upper limit on the $^{15}$N/$^{14}$N ratio of no larger than $2.0\times10^{-3}$ for the 900-cm$^{-1}$ channel and a less stringent requirement that the ratio be no larger than $2.8\times10^{-3}$ for the 960-cm$^{-1}$ channel ($1\sigma$ confidence). Specifically, the data rule out strong $^{15}$N-enrichments such as those observed in Titan's atmosphere and in cometary nitrogen compounds. To the extent possible with ground-based radiometric uncertainties, the saturnian and jovian $^{15}$N/$^{14}$N ratios appear indistinguishable, implying that $^{15}$N-enriched ammonia ices could not have been a substantial contributor to the bulk nitrogen inventory of either planet, favouring the accretion of primordial N$_2$ from the gas phase or as low-temperature ices.Comment: 33 pages, 19 figures, manuscript accepted for publication in Icaru

Being an Early-Career CMS Academic in the Context of Insecurity and ‘Excellence’: The Dialectics of Resistance and Compliance

Drawing on a dialectical approach to resistance, we conceptualise the latter as a multifaceted, pervasive and contradictory phenomenon. This enables us to examine the predicament in which early-career Critical Management Studies academics find themselves in the current times of academic insecurity and ‘excellence’, as gleaned through this group’s understandings of themselves as resisters and participants in the complex and contradictory forces constituting their field. We draw on 24 semi-structured interviews to map our participants’ accounts of themselves as resisters in terms of different approaches to tensions and contradictions between, on the one hand, the interviewees’ Critical Management Studies alignment and, on the other, the ethos of business school neoliberalism. Emerging from this analysis are three contingent and interlinked narratives of resistance and identity – diplomatic, combative and idealistic – each of which encapsulates a particular mode (negotiation, struggle, and laying one’s own path) of engaging with the relationship between Critical Management Studies and the business school ethos. The three narratives show how early-career Critical Management Studies academics not only use existing tensions, contradictions, overlaps and alliances between these positions to resist and comply with selected forces within each, but also contribute to the (re-)making of such overlaps, alliances, tensions and contradictions. Through this reworking of what it means to be both Critical Management Studies scholars and business school academics, we argue, early-career Critical Management Studies academics can be seen as active resisters and re-constituters of their complex field

The Canada-UK Deep Sub-Millimeter Survey II: First identifications, redshifts and implications for galaxy evolution

Identifications are sought for 12 sub-mm sources detected by Eales et al (1998). Six are securely identified, two have probable identifications and four remain unidentified with I_AB > 25. Spectroscopic and estimated photometric redshifts indicate that four of the sources have z < 1, and four have 1 < z < 3, with the remaining four empty field sources probably lying at z > 3. The spectral energy distributions of the identifications are consistent with those of high extinction starbursts such as Arp 220. The far-IR luminosities of the sources at z > 0.5 are of order 3 x 10^12 h_50^-2 L_sun, i.e. slightly larger than that of Arp 220. Based on this small sample, the cumulative bolometric luminosity function shows strong evolution to z ~ 1, but weaker or possibly even negative evolution beyond. The redshift dependence of the far-IR luminosity density does not appear, at this early stage, to be inconsistent with that seen in the ultraviolet luminosity density. Assuming that the energy source in the far-IR is massive stars, the total luminous output from star-formation in the Universe is probably dominated by the far-IR emission. The detected systems have individual star-formation rates (exceeding 300 h_50^-2 M_O yr^-1) that are much higher than seen in the ultraviolet selected samples, and which are sufficient to form substantial stellar populations on dynamical timescales of 10^8 yr. The association with merger-like morphologies and the obvious presence of dust makes it attractive to identify these systems as forming the metal-rich spheroid population, in which case we would infer that much of this activity has occurred relatively recently, at z ~ 2.Comment: 17 pages text + 14 figures. Accepted for publication in the Astrophysical Journal. Gzipped tar file contains one text.ps file for text and tables, one Fig2.jpg file for Fig 2, and 13 Fig*.ps files for the remaining figure

Self healing slip pulses along a gel/glass interface

We present an experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity : steady sliding at high velocity (> Vc = 100-125 \mu m/s), caracterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a ``healing instability'' occuring when the local sliding velocity reaches the macroscopic transition velocity Vc. At driving velocities close below Vc, the system exhibits complex spatio-temporal behavior.Comment: 4 pages, 6 figure