Moderate deviations for longest increasing subsequences : the lower tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity

Atomic Zitterbewegung

Ultra-cold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels.Comment: 6 pages, 4 figure

Time Evolution of the External Field Problem in QED

We construct the time-evolution for the second quantized Dirac equation subject to a smooth, compactly supported, time dependent electromagnetic potential and identify the degrees of freedom involved. Earlier works on this (e.g. Ruijsenaars) observed the Shale-Stinespring condition and showed that the one-particle time-evolution can be lifted to Fock space if and only if the external field had zero magnetic components. We scrutinize the idea, observed earlier by Fierz and Scharf, that the time-evolution can be implemented between time varying Fock spaces. In order to define these Fock spaces we are led to consider classes of reference vacua and polarizations. We show that this implementation is up to a phase independent of the chosen reference vacuum or polarization and that all induced transition probabilities are well-defined and unique.Comment: 60 pages, 1 figure, revised introduction, summary of results added, typos correcte

Spatially resolved spectroscopy of Coma cluster early-type galaxies - II:the minor axis dataset

We present minor axis, off set major axis and one diagonal long slit spectra for 10 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. We derive rotation curves, velocity dispersion profiles and the H-3 and H-4 coefficients of the Hermite decomposition of the line of sight velocity distribution. Moreover, we derive the line index profiles of Mg, Fe and Hbeta line indices and assess their errors. The data will be used to construct dynamical models of the galaxies and study their stellar populations

True bugs and beetles new to Montenegro and Bulgaria (Insecta: Heteroptera, Coleoptera)

From Montenegro, one species of Heteroptera, Lethocerus patruelis, and eight species of Coleoptera, Ampedus cardinalis, Cardiophorus anticus (Elateridae), Diaperis boleti, Iphthiminus italicus croaticus, Opatrum verrucosum, Pedinus helopioides (Tenebrionidae), Prostomis mandibularis (Prostomidae), Camptorhinus simplex (Curculionidae) are recorded for the first time. Pytho depressus (Pythidae) is recorded for the first time from Bulgaria

Chiral confinement in quasirelativistic Bose-Einstein condensates

In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coupling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multi-dimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.Comment: 4 page

From Anderson to anomalous localization in cold atomic gases with effective spin-orbit coupling

We study the dynamics of a one-dimensional spin-orbit coupled Schrodinger particle with two internal components moving in a random potential. We show that this model can be implemented by the interaction of cold atoms with external lasers and additional Zeeman and Stark shifts. By direct numerical simulations a crossover from an exponential Anderson-type localization to an anomalous power-law behavior of the intensity correlation is found when the spin-orbit coupling becomes large. The power-law behavior is connected to a Dyson singularity in the density of states emerging at zero energy when the system approaches the quasi-relativistic limit of the random mass Dirac model. We discuss conditions under which the crossover is observable in an experiment with ultracold atoms and construct explicitly the zero-energy state, thus proving its existence under proper conditions.Comment: 4 pages and 4 figure

A computational approach to managing coupled human–environmental systems: the POSEIDON model of ocean fisheries

Sustainable management of complex human–environment systems, and the essential services they provide, remains a major challenge, felt from local to global scales. These systems are typically highly dynamic and hard to predict, particularly in the context of rapid environmental change, where novel sets of conditions drive coupled socio-economic-environmental responses. Faced with these challenges, our tools for policy development, while informed by the past experience, must not be unduly constrained; they must allow equally for both the fine-tuning of successful existing approaches and the generation of novel ones in unbiased ways. We study ocean fisheries as an example class of complex human–environmental systems, and present a new model (POSEIDON) and computational approach to policy design. The model includes an adaptive agent-based representation of a fishing fleet, coupled to a simplified ocean ecology model. The agents (fishing boats) do not have programmed responses based on empirical data, but respond adaptively, as a group, to their environment (including policy constraints). This conceptual model captures qualitatively a wide range of empirically observed fleet behaviour, in response to a broad set of policies. Within this framework, we define policy objectives (of arbitrary complexity) and use Bayesian optimization over multiple model runs to find policy parameters that best meet the goals. The trade-offs inherent in this approach are explored explicitly. Taking this further, optimization is used to generate novel hybrid policies. We illustrate this approach using simulated examples, in which policy prescriptions generated by our computational methods are counterintuitive and thus unlikely to be identified by conventional frameworks

Identification and characterization of two novel primate-specific histone H3 variants, H3.X and H3.Y

The expression of a new histone variant H3.Y increases during cellular stress to regulate cell cycle progression and gene expression