On Optimal Mechanisms in the Two-Item Single-Buyer Unit-Demand Setting

We consider the problem of designing a revenue-optimal mechanism in the two-item, single-buyer, unit-demand setting when the buyer's valuations, $(z_1, z_2)$, are uniformly distributed in an arbitrary rectangle $[c,c+b_1]\times[c,c+b_2]$ in the positive quadrant. We provide a complete and explicit solution for arbitrary nonnegative values of $(c,b_1,b_2)$. We identify five simple structures, each with at most five (possibly stochastic) menu items, and prove that the optimal mechanism has one of the five structures. We also characterize the optimal mechanism as a function of $b_1, b_2$, and $c$. When $c$ is low, the optimal mechanism is a posted price mechanism with an exclusion region; when $c$ is high, it is a posted price mechanism without an exclusion region. Our results are the first to show the existence of optimal mechanisms with no exclusion region, to the best of our knowledge

General relativistic treatment of LISA optical links

LISA is a joint space mission of the NASA and the ESA for detecting low frequency gravitational waves in the band $10^{-5} - 1$ Hz. In order to attain the requisite sensitivity for LISA, the laser frequency noise must be suppressed below the other secondary noises such as the optical path noise, acceleration noise etc. This is achieved by combining time-delayed data for which precise knowledge of time-delays is required. The gravitational field, mainly that of the Sun and the motion of LISA affect the time-delays and the optical links. Further, the effect of the gravitational field of the Earth on the orbits of spacecraft is included. This leads to additional flexing over and above that of the Sun. We have written a numerical code which computes the optical links, that is, the time-delays with great accuracy $\sim 10^{-2}$ metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with sufficient accuracy within $\sim 10$ metres for an integrated time window of about six days, when one of the arms tends to be tangent to the orbit. Our analysis of the optical links is fully general relativistic and the numerical code takes into account effects such as the Sagnac, Shapiro delay, etc.. We show that with the deemed parameters in the design of LISA, there are symmetries inherent in the configuration of LISA and in the physics, which may be used effectively to suppress the residual laser noise in the modified first generation TDI. We demonstrate our results for some important TDI variables

Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda_c and annihilation at rate lambda_a. The test particle dies at rate lambda' on coming into contact with the other particles. The survival probability decays algebraically with time as t^{-theta}. The exponent theta in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d. It is shown to be universal, independent of lambda', and to depend only on delta, the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda_a/lambda_c. In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the log corrections are non-universal. The one loop answer for theta in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda_a/lambda_c. The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.Comment: 8 pages, 8 figure

Optimising the directional sensitivity of LISA

It was shown in a previous work that the data combinations canceling laser frequency noise constitute a module - the module of syzygies. The cancellation of laser frequency noise is crucial for obtaining the requisite sensitivity for LISA. In this work we show how the sensitivity of LISA can be optimised for a monochromatic source - a compact binary - whose direction is known, by using appropriate data combinations in the module. A stationary source in the barycentric frame appears to move in the LISA frame and our strategy consists of "coherently tracking" the source by appropriately "switching" the data combinations so that they remain optimal at all times. Assuming that the polarisation of the source is not known, we average the signal over the polarisations. We find that the best statistic is the `network' statistic, in which case LISA can be construed of as two independent detectors. We compare our results with the Michelson combination, which has been used for obtaining the standard sensitivity curve for LISA, and with the observable obtained by optimally switching the three Michelson combinations. We find that for sources lying in the ecliptic plane the improvement in SNR increases from 34% at low frequencies to nearly 90% at around 20 mHz. Finally we present the signal-to-noise ratios for some known binaries in our galaxy. We also show that, if at low frequencies SNRs of both polarisations can be measured, the inclination angle of the plane of the orbit of the binary can be estimated.Comment: 16 pages, 8 figures, submitted to Phys Rev

DEVELOPMENT AND EVALUATION OF ANTIDIABETIC POLYHERBAL TABLET USING MEDICINAL PLANTS OF TRADITIONAL USE

Objective: The aim of the present study is to develop and evaluate poly herbal tablet prepared for management of diabetes with enhanced disintegration time. Methods: The polyherbal extract prepared using methanolic extract of selected traditionally used medicinal plants such as Adenanthera pavonina, Kigelia africana, Parkia biglandulosa and Syzygium jambose (1:1:1:2) was evaluated in the alloxan monohydrate induced diabetic rat model. The polyherbal tablets were prepared by wet granulation method with excipients microcrystalline cellulose, dicalcium phosphate dehydrate and sodium starch glycolate. After preformulation studies tablets were evaluated by using weight variation, hardness, friability and disintegration time. The diabetic rats treated with polyherbal extract were compared with the diabetic control rats group. Results: Positive results were obtained in the observed parameters, thus favoring the use of the plants. Pre-formulation study revealed that all the evaluated parameters were found to be within the acceptable limits. The weight variation of the formulated tablets was 1.43 % RSD. The disintegration time of the formulations was found to be 9.50 minutes. The tablets also underwent accelerated stability over the period of three months. No marked changes were observed in all the parameters evaluated during three months of accelerated stability study. Conclusion: Laboratory-scale preparation of polyherbal tablet can lead to new powerful and stable oral dosage formulations for diabetes mellitus and lighten the synergistic area of ​​action of herbs

Percolation of Immobile Domains in Supercooled Thin Polymeric Films

We present an analysis of heterogeneous dynamics in molecular dynamics simulations of a thin polymeric film, supported by an absorbing structured surface. Near the glass transition "immobile" domains occur throughout the film, yet the probability of their occurrence decreasing with larger distance from the surface. Still, enough immobile domains are located near the free surface to cause them to percolate in the direction perpendicular to surface, at a temperature near the glass transition temperature. This result is in agreement with a recent theoretical model of glass transition

Substance Classification By Legend Rooted Vector Gap

Unlike tree indexes adopted in current business, our index is less receptive to scaling up dimensions and scales well with multi-dimensional data. Unsolicited candidates are cut according to distances between MBR points or keywords and also with the best diameter found. NKS queries are useful for many applications, for example, discussing images in social systems, searching for graphic patterns, searching for geolocation in GIS systems, etc. We produce accurate shape as well as approx shape of formula. In this paper, we consider keyword-bearing objects thus baked into a vector space. Keyword-based searches in text-rich multi-dimensional datasets facilitate many new applications and tools. From these datasets, we study queries that require the smallest point categories that satisfy the set of proven keywords. Our experimental results on real and synthetic datasets show that ProMiSH has up to 60 chances of acceleration compared to modern column-based technologies. We recommend a unique method known as ProMiSH, which uses random projection and hash-based index structures and delivers high scalability and acceleration. We are conducting extensive pilot studies to demonstrate the performance of the proposed technologies

Maternal and perinatal outcome associated with pregnancy induced hypertension

Background: Pregnancy Induced hypertension continues to be rampant globally and is associated with high perinatal and maternal mortality and morbidity.Methods: All patients beyond 20 weeks of pregnancy with pregnancy induced hypertension admitted in Kamineni Institute of Medical Sciences during the one year study period were enrolled in the study. The objective of the study was to analyse the cases of gestational hypertension, pre-eclampsia and eclampsia and their maternal outcome in terms of mode of delivery and complications. Perinatal outcome in relation to birth weight, APGAR and complications was also studied. The mean and standard deviation for socio-demographic variables, risk factors and symptomatology variables were analysed.Results: Total hypertensive cases accounted for 234 (7.9%) of the total deliveries; out of which gestational hypertension were 63 cases, preeclampsia 146 and eclampsia 25 cases, accounting for ( 2.1%), (4.9%) and (0.9%)  of all deliveries. Commonest maternal complication was HELLP syndrome 8 cases (3.4%) and there was no maternal mortality in our study. Total number of preterm deliveries were 74 (3.47%). Perinatal mortality was seen in 54 cases (23%).  IUGR was the commonest foetal complication 78 cases (33.4%).Conclusions: Though the incidence of pre-eclampsia and eclampsia is on the decline, still it remains the major contributor to poor maternal and fetal outcome. Regular antenatal check-ups, early diagnosis, prompt multidisciplinary treatment, optimum timing of delivery reduces the incidence of complications and the maternal mortality. Early referral to and management of these cases at centers with advanced neonatal facilities will reduce the perinatal mortality