Abstract:
We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in in-situ. We calculate the correlations of these fluctuations both in real space and in momentum space, and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasi-condensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasi-condensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.

Abstract:
Oral controlled release delivery systems are programmed to deliver the drug in predictable time frame that will increase the efficacy and minimize the adverse effects and increase the bioavailability of drugs. Oral route is considered mostnatural, uncomplicated, convenient and safe due to its ease of administration, patient acceptance, and cost-effective manufacturing process.Floating Drug delivery system are designed to prolong the gastric residence time after oral administration, at particular site and controlling the release of drug especially useful for achieving controlled plasma level a swell as improving bioavailability Several approaches are currently being used to prolong the GRT, including floating drug delivery systems (FDDS), also known as hydrodynamically balanced systems (HBS), swelling and expanding systems, high-density systems, and other delayed gastric emptying devices.

Abstract:
There are two very common sayings about corpse (dead body). The first common saying is that “the corpse is a silent witness who never lies” and the other common saying is that “the dead body is extremely eloquent and honestly informative, if one exercises patience in listening to it.” Both these sayings were proved in one of our cases. In the present case, decomposed body of an unidentified female individual aged about 25 - 26 years was recovered from the bank of western Yamuna canal in Haryana. The police made the efforts for establishing the identity of the deceased but could not succeed. The body was forwarded to the district hospital for autopsy along with the inquest report. However, the body being in advanced stage of decomposition so it was referred from the district hospital to the department of Forensic Medicine, PGIMS, Rohtak (Haryana) for the examination and the expert opinion regarding the cause of death. The findings observed on examination of the body helped to deduce the cause, time and manner of death whereas certain important objective features of identification were also observed and ultimately proper identity of the deceased could be established beyond the reasonable doubt by DNA profile of the samples preserved at autopsy. The autopsy findings, DNA profile and the results of examination of other materials (exhibits) taken from the body not only revealed the truth from the silent witness—the corpse, but also provided objective and scientific evidence to establish the corpus delicti in this case.

Abstract:
We consider a system of m linear equations in n variables Ax=b where A is a given m x n matrix and b is a given m-vector known to be equal to Ax' for some unknown solution x' that is integer and k-sparse: x' in {0,1}^n and exactly k entries of x' are 1. We give necessary and sufficient conditions for recovering the solution x exactly using an LP relaxation that minimizes l1 norm of x. When A is drawn from a distribution that has exchangeable columns, we show an interesting connection between the recovery probability and a well known problem in geometry, namely the k-set problem. To the best of our knowledge, this connection appears to be new in the compressive sensing literature. We empirically show that for large n if the elements of A are drawn i.i.d. from the normal distribution then the performance of the recovery LP exhibits a phase transition, i.e., for each k there exists a value m' of m such that the recovery always succeeds if m > m' and always fails if m < m'. Using the empirical data we conjecture that m' = nH(k/n)/2 where H(x) = -(x)log_2(x) - (1-x)log_2(1-x) is the binary entropy function.

Abstract:
In this paper, we prove that most of the boolean functions, $f : \{-1,1\}^n \rightarrow \{-1,1\}$ satisfy the Fourier Entropy Influence (FEI) Conjecture due to Friedgut and Kalai (Proc. AMS'96). The conjecture says that the Entropy of a boolean function is at most a constant times the Influence of the function. The conjecture has been proven for families of functions of smaller sizes. O'donnell, Wright and Zhou (ICALP'11) verified the conjecture for the family of symmetric functions, whose size is $2^{n+1}$. They are in fact able to prove the conjecture for the family of $d$-part symmetric functions for constant $d$, the size of whose is $2^{O(n^d)}$. Also it is known that the conjecture is true for a large fraction of polynomial sized DNFs (COLT'10). Using elementary methods we prove that a random function with high probability satisfies the conjecture with the constant as $(2 + \delta)$, for any constant $\delta > 0$.

Abstract:
Research Question: What is the trend of malaria and proportion of Plasmodium falciparum infections amongst troops of the Army units deployed in Assam over the last 5 years? Study Design: Retrospective cross -sectional descriptive study. Setting: Army units deployed in the state of Assam over the last 5 years. Participants: Population of army units deployed in the state of Assam over the last 5 years. Statistical Analysis: Percentage, Chi square. Results: Malaria contributed to 3.60% to 7% of all hospital admissions over the period of 5 years. The overall malaria incidence showed a significantly increasing trend during the study period. (Chi square for linear trend = 5.19; P = 0.023). Out of these, P falciparum contributed 86% to 98%. The proportion of P falciparum infections showed a significantly increasing trend from 2005 to 2006. (Yate′s corrected Chi square = 7.123; P = 0.008).

Abstract:
Hemangioma is the most common benign tumor of liver and is often asymptomatic. Spontaneous rupture is rare but has a catastrophic outcome if not promptly managed. Emergent hepatic resection has been the treatment of choice but has high operative mortality. Preoperative transcatheter arterial embolization (TAE) can significantly improve outcome in such patients. We report a case of spontaneous rupture of giant hepatic hemangioma that presented with abdominal pain and shock due to hemoperitoneum. Patient was successfully managed by TAE, followed by tumor resection. TAE is an effective procedure in symptomatic hemangiomas, and should be considered in such high risk patients prior to surgery.

Abstract:
Siddha system of medicine (SSM) is one of the oldest traditional systems of medicine, which hasbeen originated from India and is practiced mostly in the southern part of this country for treating variousdiseases including even chronic conditions. However, it is relatively veiled to the scientific community ascompared to other traditional systems such as Ayurveda (a popular Indian medicine), TCM (traditionalChinese medicine) and Kampo (traditional Japanese medicine). Respiratory diseases such as asthma andchronic obstructive pulmonary disease (COPD) are a serious health problem, which are increasing rapidlyworldwide. The current therapy has its own shortcomings and notable adverse effects. There is an intenseneed to search some safer alternative therapy for treating these epidemic diseases. The objectives of thisarticle is, first, to increase the awareness about SSM to the scientific community, thus inviting more scientificstudies on this system, and secondly, to list certain medicinal plants of this system which are commonlyused for treating respiratory diseases. To explore the possibility for obtaining potential drugs from theseplants, certain future perspectives have also been discussed.