Harmonically Trapped Quantum Gases

We solve the problem of a Bose or Fermi gas in $d$-dimensions trapped by $\delta \leq d$ mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature $T_{c}$ if and only if $d+\delta >2$, and a jump in the specific heat at $T_{c}$ if and only if $d+\delta >4$. Specific heats for both gas types precisely coincide as functions of temperature when $d+\delta =2$. The trapped system behaves like an ideal free quantum gas in $d+\delta$ dimensions. For $\delta =0$ we recover all known thermodynamic properties of ideal quantum gases in $d$ dimensions, while in 3D for $\delta =$ 1, 2 and 3 one simulates behavior reminiscent of quantum {\it wells, wires}and{\it dots}, respectively.Comment: 14 pages including 3 figures and 3 table

Node Sampling using Random Centrifugal Walks

Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the \emph{source}, with a given probability distribution. All these algorithms are based on a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW is a random walk that starts at the source and always moves away from it. Firstly, an algorithm to sample any connected network using RCW is proposed. The algorithm assumes that each node has a weight, so that the sampling process must select a node with a probability proportional to its weight. This algorithm requires a preprocessing phase before the sampling of nodes. In particular, a minimum diameter spanning tree (MDST) is created in the network, and then nodes' weights are efficiently aggregated using the tree. The good news are that the preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. After that, every sample is done with a RCW whose length is bounded by the network diameter. Secondly, RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source. The key features of the RCW algorithms (unlike previous Markovian approaches) are that (1) they do not need to warm-up (stabilize), (2) the sampling always finishes in a number of hops bounded by the network diameter, and (3) it selects a node with the exact probability distribution

Cooper pairs as bosons

Although BCS pairs of fermions are known not to obey Bose-Einstein (BE) commutation relations nor BE statistics, we show how Cooper pairs (CPs), whether the simple original ones or the CPs recently generalized in a many-body Bethe-Salpeter approach, being clearly distinct from BCS pairs at least obey BE statistics. Hence, contrary to widespread popular belief, CPs can undergo BE condensation to account for superconductivity if charged, as well as for neutral-atom fermion superfluidity where CPs, but uncharged, are also expected to form.Comment: 8 pages, 2 figures, full biblio info adde

Multi-filter transit observations of WASP-39b and WASP-43b with three San Pedro M\'artir telescopes

Three optical telescopes located at the San Pedro M\'artir National Observatory were used for the first time to obtain multi-filter defocused photometry of the transiting extrasolar planets WASP-39b and WASP-43b. We observed WASP-39b with the 2.12m telescope in the U filter for the first time, and additional observations were carried out in the R and I filters using the 0.84m telescope. WASP-43b was observed in VRI with the same instrument, and in the i filter with the robotic 1.50m telescope. We reduced the data using different pipelines and performed aperture photometry with the help of custom routines, in order to obtain the light curves. The fit of the light curves (1.5--2.5mmag rms), and of the period analysis, allowed a revision of the orbital and physical parameters, revealing for WASP-39b a period ($4.0552947 \pm 9.65 \times 10^{-7}$ days) which is $3.084 \pm 0.774$ seconds larger than previously reported. Moreover, we find for WASP-43b a planet/star radius ($0.1738 \pm 0.0033$) which is $0.01637 \pm 0.00371$ larger in the i filter with respect to previous works, and that should be confirmed with additional observations. Finally, we confirm no evidence of constant period variations in WASP-43b.Comment: 13 pages, 7 figures, accepted in PASP, scheduled for the February 1, 2015 issu

Redox-based transcriptional regulation in prokaryotes: revisiting model mechanisms

Significance: The successful adaptation of microorganisms to ever-changing environments depends, to a great extent, on their ability to maintain redox homeostasis. To effectively maintain the redox balance, cells have developed a variety of strategies mainly coordinated by a battery of transcriptional regulators through diverse mechanisms. Recent Advances: This comprehensive review focuses on the main mechanisms used by major redox-responsive regulators in prokaryotes and their relationship with the different redox signals received by the cell. An overview of the corresponding regulons is also provided. Critical Issues: Some regulators are difficult to classify since they may contain several sensing domains and respond to more than one signal. We propose a classification of redox-sensing regulators into three major groups. The first group contains one-component or direct regulators, whose sensing and regulatory domains are in the same protein. The second group comprises the classical two-component systems involving a sensor kinase that transduces the redox signal to its DNA-binding partner. The third group encompasses a heterogeneous group of flavin-based photosensors whose mechanisms are not always fully understood and are often involved in more complex regulatory networks. Future Directions: Redox-responsive transcriptional regulation is an intricate process as identical signals may be sensed and transduced by different transcription factors, which often interplay with other DNA-binding proteins with or without regulatory activity. Although there is much information about some key regulators, many others remain to be fully characterized due to the instability of their clusters under oxygen. Understanding the mechanisms and the regulatory networks operated by these regulators is essential for the development of future applications in biotechnology and medicine