Thermal robustness of multipartite entanglement of the 1-D spin 1/2 XY model

We study the robustness of multipartite entanglement of the ground state of the one-dimensional spin 1/2 XY model with a transverse magnetic field in the presence of thermal excitations, by investigating a threshold temperature, below which the thermal state is guaranteed to be entangled. We obtain the threshold temperature based on the geometric measure of entanglement of the ground state. The threshold temperature reflects three characteristic lines in the phase diagram of the correlation function. Our approach reveals a region where multipartite entanglement at zero temperature is high but is thermally fragile, and another region where multipartite entanglement at zero temperature is low but is thermally robust.Comment: Revised, 11 pages, 7 figure

Stability analysis of multi-compartment models for cell production systems

We study two-and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result

Global dynamics of two-compartment models for cell production systems with regulatory mechanisms

We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system. Using global stability analysis, we compare different regulatory mechanisms. For both models, we show that there exists a unique positive equilibrium that is globally asymptotically stable if and only if the respective reproduction numbers exceed one. The proof is based on constructing Lyapunov functions, which are appropriate to handle the specific nonlinearities of the model. Additionally, we propose a new model to test biological hypothesis on the regulation of the fraction of differentiating cells. We show that such regulatory mechanism is incapable of maintaining homeostasis and leads to unbounded cell growth. Potential biological implications are discussed

Early-type Galaxies at z ~ 1.3. II. Masses and Ages of Early-type Galaxies in Different Environments and Their Dependence on Stellar Population Model Assumptions

We have derived masses and ages for 79 early-type galaxies (ETGs) in different environments at z ~ 1.3 in the Lynx supercluster and in the GOODS/CDF-S field using multi-wavelength (0.6-4.5 μm; KPNO, Palomar, Keck, Hubble Space Telescope, Spitzer) data sets. At this redshift the contribution of the thermally pulsing asymptotic giant branch (TP-AGB) phase is important for ETGs, and the mass and age estimates depend on the choice of the stellar population model used in the spectral energy distribution fits. We describe in detail the differences among model predictions for a large range of galaxy ages, showing the dependence of these differences on age. Current models still yield large uncertainties. While recent models from Maraston and Charlot & Bruzual offer better modeling of the TP-AGB phase with respect to less recent Bruzual & Charlot models, their predictions do not often match. The modeling of this TP-AGB phase has a significant impact on the derived parameters for galaxies observed at high redshift. Some of our results do not depend on the choice of the model: for all models, the most massive galaxies are the oldest ones, independent of the environment. When using the Maraston and Charlot & Bruzual models, the mass distribution is similar in the clusters and in the groups, whereas in our field sample there is a deficit of massive (M ≳ 10^(11) M_☉) ETGs. According to those last models, ETGs belonging to the cluster environment host on average older stars with respect to group and field populations. This difference is less significant than the age difference in galaxies of different masses

The Power of Two Choices in Distributed Voting

Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion. On many graph classes including regular graphs, pull voting requires $\Theta(n)$ expected steps to complete, even if initially there are only two distinct opinions. In this paper we consider a related process which we call two-sample voting: every vertex chooses two random neighbours in each step. If the opinions of these neighbours coincide, then the vertex revises its opinion according to the chosen sample. Otherwise, it keeps its own opinion. We consider the performance of this process in the case where two different opinions reside on vertices of some (arbitrary) sets $A$ and $B$, respectively. Here, $|A| + |B| = n$ is the number of vertices of the graph. We show that there is a constant $K$ such that if the initial imbalance between the two opinions is ?$\nu_0 = (|A| - |B|)/n \geq K \sqrt{(1/d) + (d/n)}$, then with high probability two sample voting completes in a random $d$ regular graph in $O(\log n)$ steps and the initial majority opinion wins. We also show the same performance for any regular graph, if $\nu_0 \geq K \lambda_2$ where $\lambda_2$ is the second largest eigenvalue of the transition matrix. In the graphs we consider, standard pull voting requires $\Omega(n)$ steps, and the minority can still win with probability $|B|/n$.Comment: 22 page

Crystal structure of mixed fluorites Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) and luminescence of Eu(2+) in the crystals

Within the framework of the virtual crystal method implemented in the shell model and pair potential approximation the crystal structure of mixed fluorites Ca(1-x)Sr(x)F(2) and Sr(1-x)Ba(x)F(2) has been calculated. The impurity center Eu(2+) and the distance Eu(2+)-F in this crystals have been also calculated. The low level position of excited 4f65d configuration of the Eu(2+) ion has been expressed using phenomenological dependence on distance E(2+)-F. The dependences of Stokes shift and Huang-Rhys factor on concentration x have been received for yellow luminescence in Sr(1-x)Ba(x)F(2):Eu(2+). The value x, for which the eg -level of Eu(2+) ion will be in conduction band in Sr(1-x)Ba(x)F(2):Eu(2+) has been calculated.Comment: 8 pages, 3 figures. The manuscript is sent to journal 'Physics of the solid state'. The results will be submitted on inernational conference SCINTMAT'2002 in oral session (june,20-22,2002,Ekaterinburg,Russia). Corresponding author e-mail: [email protected]

Scaling and Crossover to Tricriticality in Polymer Solutions

We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the "ideal-gas" limit for the pure-solvent phase, and the tricritical limit for the polymer-rich phase asymptotically close to the theta point. We have also developed a phenomenological crossover theory based on the near-tricritical-point Landau expansion renormalized by fluctuations. This theory validates the proposed scaled representation of experimental data and crossover to tricriticality.Comment: 4 pages, 3 figure

Early-type Galaxies at z ~ 1.3. III. On the Dependence of Formation Epochs and Star Formation Histories on Stellar Mass and Environment

We study the environmental dependence of stellar population properties at z ~ 1.3. We derive galaxy properties (stellar masses, ages, and star formation histories) for samples of massive, red, passive early-type galaxies (ETGs) in two high-redshift clusters, RXJ0849+4452 and RXJ0848+4453 (with redshifts of z = 1.26 and 1.27, respectively), and compare them with those measured for the RDCS1252.9–2927 cluster at z = 1.24 and with those measured for a similarly mass-selected sample of field contemporaries drawn from the GOODS-South field. Robust estimates of the aforementioned parameters have been obtained by comparing a large grid of composite stellar population models with extensive 8- to 10-band photometric coverage, from the rest-frame far-ultraviolet to the infrared. We find no variations of the overall stellar population properties among the different samples of cluster ETGs. However, when comparing cluster versus field stellar population properties we find that, even if the ages are similar and depend only on galaxy mass, the ones in the field do employ longer timescales to assemble their final mass. We find that, approximately 1 Gyr after the onset of star formation, the majority (75%) of cluster galaxies have already assembled most (>80%) of their final mass, while, by the same time, fewer (35%) field ETGs have. Thus, we conclude that while galaxy mass regulates the timing of galaxy formation, the environment regulates the timescale of their star formation histories

Functional Big-step Semantics

When doing an interactive proof about a piece of software, it is important that the underlying programming language’s semantics does not make the proof unnecessarily difficult or unwieldy. Both smallstep and big-step semantics are commonly used, and the latter is typically given by an inductively defined relation. In this paper, we consider an alternative: using a recursive function akin to an interpreter for the language. The advantages include a better induction theorem, less duplication, accessibility to ordinary functional programmers, and the ease of doing symbolic simulation in proofs via rewriting. We believe that this style of semantics is well suited for compiler verification, including proofs of divergence preservation. We do not claim the invention of this style of semantics: our contribution here is to clarify its value, and to explain how it supports several language features that might appear to require a relational or small-step approach. We illustrate the technique on a simple imperative language with C-like for-loops and a break statement, and compare it to a variety of other approaches. We also provide ML and lambda-calculus based examples to illustrate its generality