Revisiting the Problem of Searching on a Line

We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the first tight bounds on the exact optimal competitive ratio achievable, parameterized in terms of the given bounds on D, along with an optimal search strategy that achieves this competitive ratio. We prove that this optimal strategy is unique. We characterize the conditions under which an optimal strategy can be computed exactly and, when it cannot, we explain how numerical methods can be used efficiently. In addition, we answer several related open questions, including the maximal reach problem, and we discuss how to generalize these results to m rays, for any m >= 2

Extended WKB method, resonances and supersymmetric radial barriers

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.Comment: 12 pages, 4 figures, 3 table

A self-consistent model of Galactic stellar and dust infrared emission and the abundance of polycyclic aromatic hydrocarbons

We present a self-consistent three-dimensional Monte-Carlo radiative transfer model of the stellar and dust emission in the Milky-Way, and have computed synthetic observations of the 3.6 to 100 microns emission in the Galactic mid-plane. In order to compare the model to observations, we use the GLIMPSE, MIPSGAL, and IRAS surveys to construct total emission spectra, as well as longitude and latitude profiles for the emission. The distribution of stars and dust is taken from the SKY model, and the dust emissivities includes an approximation of the emission from polycyclic aromatic hydrocarbons in addition to thermal emission. The model emission is in broad agreement with the observations, but a few modifications are needed to obtain a good fit. Firstly, by adjusting the model to include two major and two minor spiral arms rather than four equal spiral arms, the fit to the longitude profiles for |l|>30 degrees can be improved. Secondly, introducing a deficit in the dust distribution in the inner Galaxy results in a better fit to the shape of the IRAS longitude profiles at 60 and 100 microns. With these modifications, the model fits the observed profiles well, although it systematically under-estimates the 5.8 and 8.0 microns fluxes. One way to resolve this discrepancy is to increase the abundance of PAH molecules by 50% compared to the original model, although we note that changes to the dust distribution or radiation field may provide alternative solutions. Finally, we use the model to quantify which stellar populations contribute the most to the heating of different dust types, and which stellar populations and dust types contribute the most to the emission at different wavelengths.Comment: Published in A&A. This version has been revised (compared to the published version) to include additional references to previous work. Scripts to reproduce the results in this paper can be found as supplementary material on the A&A site, or at https://github.com/hyperion-rt/paper-galaxy-rt-mode

Preferred growth direction by PbS nanoplatelets preserves perovskite infrared light harvesting for stable, reproducible, and efficient solar cells

Formamidinium-based perovskite solar cells (PSCs) present the maximum theoretical efficiency of the lead perovskite family. However, formamidinium perovskite exhibits significant degradation in air. The surface chemistry of PbS has been used to improve the formamidinium black phase stability. Here, the use of PbS nanoplatelets with (100) preferential crystal orientation is reported, to potentiate the repercussion on the crystal growth of perovskite grains and to improve the stability of the material and consequently of the solar cells. As a result, a vertical growth of perovskite grains, a stable current density of 23 mA cm(-2), and a stable incident photon to current efficiency in the infrared region of the spectrum for 4 months is obtained, one of the best stability achievements for planar PSCs. Moreover, a better reproducibility than the control device, by optimizing the PbS concentration in the perovskite matrix, is achieved. These outcomes validate the synergistic use of PbS nanoplatelets to improve formamidinium long-term stability and performance reproducibility, and pave the way for using metastable perovskite active phases preserving their light harvesting capability

A squalene-hopene cyclase in Schizosaccharomyces japonicus represents a eukaryotic adaptation to sterol-limited anaerobic environments

Biosynthesis of sterols, which are key constituents of canonical eukaryotic membranes, requires molecular oxygen. Anaerobic protists and deep-branching anaerobic fungi are the only eukaryotes in which a mechanism for sterol-independent growth has been elucidated. In these organisms, tetrahymanol, formed through oxygen-independent cyclization of squalene by a squalene-tetrahymanol cyclase, acts as a sterol surrogate. This study confirms an early report [C. J. E. A. Bulder, Antonie Van Leeuwenhoek, 37, 353-358 (1971)] that Schizosaccharomyces japonicus is exceptional among yeasts in growing anaerobically on synthetic media lacking sterols and unsaturated fatty acids. Mass spectrometry of lipid fractions of anaerobically grown Sch. japonicus showed the presence of hopanoids, a class of cyclic triterpenoids not previously detected in yeasts, including hop-22(29)-ene, hop17(21)-ene, hop-21(22)-ene, and hopan-22-ol. A putative gene in Sch. japonicus showed high similarity to bacterial squalene-hopene cyclase (SHC) genes and in particular to those of Acetobacter species. No orthologs of the putative Sch. japonicus SHC were found in other yeast species. Expression of the Sch. japonicus SHC gene (Sjshc1) in Saccharomyces cerevisiae enabled hopanoid synthesis and stimulated anaerobic growth in sterol-free media, thus indicating that one or more of the hopanoids produced by SjShc1 could at least partially replace sterols. Use of hopanoids as sterol surrogates represents a previously unknown adaptation of eukaryotic cells to anaerobic growth. The fast anaerobic growth of Sch. japonicus in sterol-free media is an interesting trait for developing robust fungal cell factories for application in anaerobic industrial processes.Proteomic

The long-time dynamics of two hydrodynamically-coupled swimming cells

Swimming micro-organisms such as bacteria or spermatozoa are typically found in dense suspensions, and exhibit collective modes of locomotion qualitatively different from that displayed by isolated cells. In the dilute limit where fluid-mediated interactions can be treated rigorously, the long-time hydrodynamics of a collection of cells result from interactions with many other cells, and as such typically eludes an analytical approach. Here we consider the only case where such problem can be treated rigorously analytically, namely when the cells have spatially confined trajectories, such as the spermatozoa of some marine invertebrates. We consider two spherical cells swimming, when isolated, with arbitrary circular trajectories, and derive the long-time kinematics of their relative locomotion. We show that in the dilute limit where the cells are much further away than their size, and the size of their circular motion, a separation of time scale occurs between a fast (intrinsic) swimming time, and a slow time where hydrodynamic interactions lead to change in the relative position and orientation of the swimmers. We perform a multiple-scale analysis and derive the effective dynamical system - of dimension two - describing the long-time behavior of the pair of cells. We show that the system displays one type of equilibrium, and two types of rotational equilibrium, all of which are found to be unstable. A detailed mathematical analysis of the dynamical systems further allows us to show that only two cell-cell behaviors are possible in the limit of $t\to\infty$, either the cells are attracted to each other (possibly monotonically), or they are repelled (possibly monotonically as well), which we confirm with numerical computations

Periodic and Quasiperiodic Motion of an Elongated Microswimmer in Poiseuille Flow

We study the dynamics of a prolate spheroidal microswimmer in Poiseuille flow for different flow geometries. When moving between two parallel plates or in a cylindrical microchannel, the swimmer performs either periodic swinging or periodic tumbling motion. Although the trajectories of spherical and elongated swimmers are qualitatively similar, the swinging and tumbling frequency strongly depends on the aspect ratio of the swimmer. In channels with reduced symmetry the swimmers perform quasiperiodic motion which we demonstrate explicitely for swimming in a channel with elliptical cross section

Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point

We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of the asymptotics of the transition probability when the tuning parameter slowly changes in the finite range. Then we apply this perturbation theory to many-particle systems with low energy spectrum characterized by quasiparticle excitations. Within this approach we derive the scaling of various quantities such as the density of generated defects, entropy and energy. We discuss the applications of this approach to a specific situation where the system crosses a quantum critical point. We also show the connection between adiabatic and sudden quenches near a quantum phase transitions and discuss the effects of quasiparticle statistics on slow and sudden quenches at finite temperatures.Comment: 20 pages, 3 figures, contribution to "Quantum Quenching, Annealing and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes in Phys., Springer, Heidelberg (2009, to be published), reference correcte

The forkhead transcription factor FOXL2 is expressed in somatic cells of the human ovary prior to follicle formation

Interactions between germ cells and surrounding somatic cells are central to ovarian development as well as later function. Disruption of these interactions arising from abnormalities in either cell type can lead to premature ovarian failure (POF). The forkhead transcription factor FOXL2 is a candidate POF factor, and mutations in the FOXL2 gene are associated with syndromic and non-syndromic ovarian failure. Foxl2-deficient mice display major defects in primordial follicle activation with consequent follicle loss, and earlier roles in gonadal development and sex determination have also been suggested. However, despite its importance no data presently exist on its expression in the developing human ovary. Expression of FOXL2 mRNA was demonstrated in the human fetal ovary between 8 and 19 weeks gestation, thus from soon after sex determination to primordial follicle development. Expression in the ovary was higher after 14 weeks than at earlier gestation weeks and was very low in the fetal testis at all ages examined. Immunolocalization revealed FOXL2 expression to be confined to somatic cells, both adjacent to germ cells and those located in the developing ovarian stroma. These cells are the site of action of oocyte-derived activin signalling, but in vitro treatment of human fetal ovaries with activin failed to reveal any regulation of FOXL2 transcription by this pathway. In summary, the expression of FOXL2 in somatic cells of the developing human ovary before and during follicle formation supports a conserved and continuing role for this factor in somatic/germ cell interactions from the earliest stages of human ovarian development