PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold

The $PT$ symmetric potential $V_0[\cos(2\pi x/a)+i\lambda\sin(2\pi x/a)]$ has a completely real spectrum for $\lambda\le 1$, and begins to develop complex eigenvalues for $\lambda>1$. At the symmetry-breaking threshold $\lambda=1$ some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to result in a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for a broad initial wave packet this growth is suppressed, and instead a saturation leading to a constant maximum amplitude is observed. We revisit this problem by explicitly constructing the Bloch wave-functions and the associated Jordan functions and using the method of stationary states to find the dependence on the longitudinal distance $z$ for a variety of different initial wave packets. This allows us to show in detail how the saturation of the linear growth arises from the close connection between the contributions of the Jordan functions and those of the neighbouring Bloch waves.Comment: 15 pages, 7 figures Minor corrections, additional reference

Sub-Optimal Allocation of Time in Sequential Movements

The allocation of limited resources such as time or energy is a core problem that organisms face when planning complex actions. Most previous research concerning planning of movement has focused on the planning of single, isolated movements. Here we investigated the allocation of time in a pointing task where human subjects attempted to touch two targets in a specified order to earn monetary rewards. Subjects were required to complete both movements within a limited time but could freely allocate the available time between the movements. The time constraint presents an allocation problem to the subjects: the more time spent on one movement, the less time is available for the other. In different conditions we assigned different rewards to the two tokens. How the subject allocated time between movements affected their expected gain on each trial. We also varied the angle between the first and second movements and the length of the second movement. Based on our results, we developed and tested a model of speed-accuracy tradeoff for sequential movements. Using this model we could predict the time allocation that would maximize the expected gain of each subject in each experimental condition. We compared human performance with predicted optimal performance. We found that all subjects allocated time sub-optimally, spending more time than they should on the first movement even when the reward of the second target was five times larger than the first. We conclude that the movement planning system fails to maximize expected reward in planning sequences of as few as two movements and discuss possible interpretations drawn from economic theory

Reactivity of pi-complexes of Ti, V, and Nb towards dithioacetic acid: Synthesis and structure of novel metal sulfur-containing complexes

In order to use sulfur-containing resources economically and with minimal environmental damage, it is important to understand the desulfurization processes. Hydrodesulfurization, for example, is carried out on the surface of a heterogeneous metal sulfide catalyst. Studies of simple, soluble inorganic systems provide information regarding the structure and reactivity of sulfur-containing compounds with metal complexes. Further, consistent with recent trends in materials chemistry, many model compounds warrant further study as catalyst precursors. The reactivity of low-valent organometallic sandwich pi-complexes toward dithiocarboxylic acids is described. For example, treatment of bisbenzene vanadium with CH3CSSH affords a divanadium tetrakis(dithioacetate) complex. The crystallographically determined V-V bond distance, 2.800(2), is nearly the same as the V-V bond distance in a V(mu-nu squared-S2)2V' unit in the mineral patonite (VS4)n. The stability of the V2S4 core in the dimer is demonstrated by evidence of V2S4(+) in the mass spectrum (70 eV, solid probe) of the vanadium dimer. Several other systems relevant to HDS catalysis are also discussed

Symmetries of Two Higgs Doublet Model and CP violation

We use the invariance of physical picture under a change of Lagrangian, the reparametrization invariance in the space of Lagrangians and its particular case -- the rephrasing invariance, for analysis of the two-Higgs-doublet extension of the SM. We found that some parameters of theory like tan beta are reparametrization dependent and therefore cannot be fundamental. We use the Z2-symmetry of the Lagrangian, which prevents a phi_1 phi_2 transitions, and the different levels of its violation, soft and hard, to describe a physical content of the model. In general, the broken Z2-symmetry allows for a CP violation in the physical Higgs sector. We argue that the 2HDM with a soft breaking of Z2-symmetry is a natural model in the description of EWSB. To simplify an analysis we choose among different forms of Lagrangian describing the same physical reality a specific one, in which the vacuum expectation values of both Higgs fields are real. A possible CP violation in the Higgs sector is described by using a two-step procedure with the first step identical to a diagonalization of mass matrix for CP-even fields in the CP conserved case. We find very simple necessary and sufficient condition for a CP violation in the Higgs sector. We determine the range of parameters for which CP violation and Flavor Changing Neutral Current effects are naturally small,what corresponds to a small dimensionless mass parameter nu= Re m_{12}^2/(2v1v2). We discuss how for small nu some Higgs bosons can be heavy, with mass up to about 0.6 TeV, without violating of the unitarity constraints. We discuss main features of the large nu case, which corresponds for nu -> infty to a decoupling of heavy Higgs bosons.Comment: 27 pages, extended discussion, references added, one figure, Revtex

Foeniculum vulgare Essential Oils: Chemical Composition, Antioxidant and Antimicrobial Activities

The essential oils from Foeniculum vulgare commercial aerial parts and fruits were isolated by hydrodistillation, with different distillation times (30 min, I h, 2 h and 3 h), and analyzed by GC and GC-MS. The antioxidant ability was estimated using four distinct methods. Antibacterial activity was determined by the agar diffusion method. Remarkable differences, and worrying from the quality and safety point of view, were detected in the essential oils. trans-Anethole (31-36%), alpha-pinene (14-20%) and limonene (11-13%) were the main components of the essentials oil isolated from F. vulgare dried aerial parts, whereas methyl chavicol (= estragole) (79-88%) was dominant in the fruit oils. With the DPPH method the plant oils showed better antioxidant activity than the fruits oils. With the TBARS method and at higher concentrations, fennel essential oils showed a pro-oxidant activity. None of the oils showed a hydroxyl radical scavenging capacity >50%, but they showed an ability to inhibit 5-lipoxygenase. The essential oils showed a very low antimicrobial activity. In general, the essential oils isolated during 2 h were as effective, from the biological activity point of view, as those isolated during 3 h.info:eu-repo/semantics/publishedVersio

Diatom Proteomics Reveals Unique Acclimation Strategies to Mitigate Fe Limitation

Phytoplankton growth rates are limited by the supply of iron (Fe) in approximately one third of the open ocean, with major implications for carbon dioxide sequestration and carbon (C) biogeochemistry. To date, understanding how alteration of Fe supply changes phytoplankton physiology has focused on traditional metrics such as growth rate, elemental composition, and biophysical measurements such as photosynthetic competence (Fv/Fm). Researchers have subsequently employed transcriptomics to probe relationships between changes in Fe supply and phytoplankton physiology. Recently, studies have investigated longer-term (i.e. following acclimation) responses of phytoplankton to various Fe conditions. In the present study, the coastal diatom, Thalassiosira pseudonana, was acclimated (10 generations) to either low or high Fe conditions, i.e. Fe-limiting and Fe-replete. Quantitative proteomics and a newly developed proteomic profiling technique that identifies low abundance proteins were employed to examine the full complement of expressed proteins and consequently the metabolic pathways utilized by the diatom under the two Fe conditions. A total of 1850 proteins were confidently identified, nearly tripling previous identifications made from differential expression in diatoms. Given sufficient time to acclimate to Fe limitation, T. pseudonana up-regulates proteins involved in pathways associated with intracellular protein recycling, thereby decreasing dependence on extracellular nitrogen (N), C and Fe. The relative increase in the abundance of photorespiration and pentose phosphate pathway proteins reveal novel metabolic shifts, which create substrates that could support other well-established physiological responses, such as heavily silicified frustules observed for Fe-limited diatoms. Here, we discovered that proteins and hence pathways observed to be down-regulated in short-term Fe starvation studies are constitutively expressed when T. pseudonana is acclimated (i.e., nitrate and nitrite transporters, Photosystem II and Photosystem I complexes). Acclimation of the diatom to the desired Fe conditions and the comprehensive proteomic approach provides a more robust interpretation of this dynamic proteome than previous studies.This work was supported by National Science Foundation grants OCE1233014 (BLN) and the Office of Polar Programs Postdoctoral Fellowship grant 0444148 (BLN). DRG was supported by National Institutes of Health 5P30ES007033-10. AH and MTM were supported by Natural Sciences and Engineering Research Council of Canada. RFS and PWB were supported by the New Zealand Royal Society Marsden Fund and the Ministry of Science. This work is supported in part by the University of Washington's Proteomics Computer Resource Centre (UWPR95794). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript