Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli

Let -1\leq B<A\leq 1. Condition on \beta, is determined so that 1+\beta zp'(z)/p^k(z)\prec(1+Az)/(1+Bz)\;(-1<k\leq3) implies p(z)\prec \sqrt{1+z}. Similarly, condition on \beta is determined so that 1+\beta zp'(z)/p^n(z) or p(z)+\beta zp'(z)/p^n(z)\prec\sqrt{1+z}\;(n=0, 1, 2) implies p(z)\prec(1+Az)/(1+Bz) or \sqrt{1+z}. In addition to that condition on \beta is derived so that p(z)\prec(1+Az)/(1+Bz) when p(z)+\beta zp'(z)/p(z)\prec\sqrt{1+z}. Few more problems of the similar flavor are also considered

Theory of stripes in quasi two dimensional rare-earth tritellurides

Even though the rare-earth tritellurides are tetragonal materials with a quasi two dimensional (2D) band structure, they have a "hidden" 1D character. The resultant near-perfect nesting of the Fermi surface leads to the formation of a charge density wave (CDW) state. We show that for this band structure, there are two possible ordered phases: A bidirectional "checkerboard" state would occur if the CDW transition temperature were sufficiently low, whereas a unidirectional "striped" state, consistent with what is observed in experiment, is favored when the transition temperature is higher. This result may also give some insight into why, in more strongly correlated systems, such as the cuprates and nickelates, the observed charge ordered states are generally stripes as opposed to checkerboards.Comment: Added contents and references, changed title and figures. Accepted to PR

Rapid evolution of protein kinase PKR alters sensitivity to viral inhibitors.

Protein kinase PKR (also known as EIF2AK2) is activated during viral infection and phosphorylates the alpha subunit of eukaryotic translation initiation factor 2 (eIF2), leading to inhibition of translation and viral replication. We report fast evolution of the PKR kinase domain in vertebrates, coupled with positive selection of specific sites. Substitution of positively selected residues in human PKR with residues found in related species altered sensitivity to PKR inhibitors from different poxviruses. Species-specific differences in sensitivity to poxviral pseudosubstrate inhibitors were identified between human and mouse PKR, and these differences were traced to positively selected residues near the eIF2alpha binding site. Our findings indicate how an antiviral protein evolved to evade viral inhibition while maintaining its primary function. Moreover, the identified species-specific differences in the susceptibility to viral inhibitors have important implications for studying human infections in nonhuman model systems

Topology of Luminous Red Galaxies from the Sloan Digital Sky Survey

We present measurements of the genus topology of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) Data Release 7 catalog, with unprecedented statistical significance. To estimate the uncertainties in the measured genus, we construct 81 mock SDSS LRG surveys along the past light cone from the Horizon Run 3, one of the largest N-body simulations to date that evolved 7210^3 particles in a 10815 Mpc/h size box. After carefully modeling and removing all known systematic effects due to finite pixel size, survey boundary, radial and angular selection functions, shot noise and galaxy biasing, we find the observed genus amplitude to reach 272 at 22 Mpc/h smoothing scale with an uncertainty of 4.2%; the estimated error fully incorporates cosmic variance. This is the most accurate constraint of the genus amplitude to date, which significantly improves on our previous results. In particular, the shape of the genus curve agrees very well with the mean topology of the SDSS LRG mock surveys in the LCDM universe. However, comparison with simulations also shows small deviations of the observed genus curve from the theoretical expectation for Gaussian initial conditions. While these discrepancies are mainly driven by known systematic effects such as those of shot noise and redshift-space distortions, they do contain important cosmological information on the physical effects connected with galaxy formation, gravitational evolution and primordial non-Gaussianity. We address here the key role played by systematics on the genus curve, and show how to accurately correct for their effects to recover the topology of the underlying matter. In a forthcoming paper, we provide an interpretation of those deviations in the context of the local model of non-Gaussianity.Comment: 23 pages, 18 figures. APJ Supplement Series 201

Two-Photon Beatings Using Biphotons Generated from a Two-Level System

We propose a two-photon beating experiment based upon biphotons generated from a resonant pumping two-level system operating in a backward geometry. On the one hand, the linear optical-response leads biphotons produced from two sidebands in the Mollow triplet to propagate with tunable refractive indices, while the central-component propagates with unity refractive index. The relative phase difference due to different refractive indices is analogous to the pathway-length difference between long-long and short-short in the original Franson interferometer. By subtracting the linear Rayleigh scattering of the pump, the visibility in the center part of the two-photon beating interference can be ideally manipulated among [0, 100%] by varying the pump power, the material length, and the atomic density, which indicates a Bell-type inequality violation. On the other hand, the proposed experiment may be an interesting way of probing the quantum nature of the detection process. The interference will disappear when the separation of the Mollow peaks approaches the fundamental timescales for photon absorption in the detector.Comment: to appear in Phys. Rev. A (2008

Differences in hearing acuity among “normal-hearing” young adults modulate the neural basis for speech comprehension

AbstractIn this paper, we investigate how subtle differences in hearing acuity affect the neural systems supporting speech processing in young adults. Auditory sentence comprehension requires perceiving a complex acoustic signal and performing linguistic operations to extract the correct meaning. We used functional MRI to monitor human brain activity while adults aged 18–41 years listened to spoken sentences. The sentences varied in their level of syntactic processing demands, containing either a subject-relative or object-relative center-embedded clause. All participants self-reported normal hearing, confirmed by audiometric testing, with some variation within a clinically normal range. We found that participants showed activity related to sentence processing in a left-lateralized frontotemporal network. Although accuracy was generally high, participants still made some errors, which were associated with increased activity in bilateral cingulo-opercular and frontoparietal attention networks. A whole-brain regression analysis revealed that activity in a right anterior middle frontal gyrus (aMFG) component of the frontoparietal attention network was related to individual differences in hearing acuity, such that listeners with poorer hearing showed greater recruitment of this region when successfully understanding a sentence. The activity in right aMFGs for listeners with poor hearing did not differ as a function of sentence type, suggesting a general mechanism that is independent of linguistic processing demands. Our results suggest that even modest variations in hearing ability impact the systems supporting auditory speech comprehension, and that auditory sentence comprehension entails the coordination of a left perisylvian network that is sensitive to linguistic variation with an executive attention network that responds to acoustic challenge.</jats:p

Rapid Assessment of Reward-Related Eating: The RED-X5.

OBJECTIVE:The prevalence of obesity has created a plethora of questionnaires characterizing psychological aspects of eating behavior, such as reward-related eating (RRE). The Reward-based Eating Drive questionnaires (RED-9, RED-13) broadly and deeply assess the RRE construct. However, large-sample research designs require shorter questionnaires that capture RRE quickly and precisely. This study sought to develop a brief, reliable, and valid version of the RED questionnaire. METHODS:All-subset correlation was used to find a subset that maximally associated with the full RED-13 in two separate samples. Results were validated in a third independent sample. Internal consistency, test-retest reliability, and ability to explain variance in external outcomes were also assessed. RESULTS:A five-item questionnaire (RED-X5) correlated strongly with RED-13 in the independent sample (r = 0.95). RED-X5 demonstrated high internal consistency (omega total ≥ 0.80) and 6-month test-retest reliability (r = 0.72). RED-X5 accurately reproduced known associations between RED-13 and BMI, diabetes status, and craving for sweet and savory foods. As a novel finding, RED questionnaires predicted laboratory intake of chips. CONCLUSIONS:RED-X5 is a short, reliable, and valid measure of the RRE construct and can be readily implemented in large-sample research designs in which questionnaire space is limited

Quantum oscillations in YBa2Cu3O6+δ\mathrm{YBa_{2}Cu_{3}O_{6+\delta}} from an incommensurate dd-density wave order

We consider quantum oscillation experiments in $\mathrm{YBa_{2}Cu_{3}O_{6+\delta}}$ from the perspective of an incommensurate Fermi surface reconstruction using an exact transfer matrix method and the Pichard-Landauer formula for the conductivity. The specific density wave order considered is a period-8 $d$-density wave in which the current density is unidirectionally modulated. The current modulation is also naturally accompanied by a period-4 site charge modulation in the same direction, which is consistent with recent magnetic resonance measurements. In principle Landau theory also allows for a period-4 bond charge modulation, which is not discussed, but should be simple to incorporate in the future. This scenario leads to a natural, but not a unique, explanation of why only oscillations from a single electron pocket is observed, and a hole pocket of roughly twice the frequency as dictated by two-fold commensurate order, and the corresponding Luttinger sum rule, is not observed. However, it is possible that even higher magnetic fields will reveal a hole pocket of half the frequency of the electron pocket or smaller. This may be at the borderline of achievable high field measurements because at least a few complete oscillations have to be clearly resolved.Comment: 8 pages, 7 figure