An entropy based proof of the Moore bound for irregular graphs

We provide proofs of the following theorems by considering the entropy of random walks: Theorem 1.(Alon, Hoory and Linial) Let G be an undirected simple graph with n vertices, girth g, minimum degree at least 2 and average degree d: Odd girth: If g=2r+1,then n \geq 1 + d*(\Sum_{i=0}^{r-1}(d-1)^i) Even girth: If g=2r,then n \geq 2*(\Sum_{i=0}^{r-1} (d-1)^i) Theorem 2.(Hoory) Let G = (V_L,V_R,E) be a bipartite graph of girth g = 2r, with n_L = |V_L| and n_R = |V_R|, minimum degree at least 2 and the left and right average degrees d_L and d_R. Then, n_L \geq \Sum_{i=0}^{r-1}(d_R-1)^{i/2}(d_L-1)^{i/2} n_R \geq \Sum_{i=0}^{r-1}(d_L-1)^{i/2}(d_R-1)^{i/2}Comment: 6 page

The Quantum Complexity of Set Membership

We study the quantum complexity of the static set membership problem: given a subset S (|S| \leq n) of a universe of size m (m \gg n), store it as a table of bits so that queries of the form `Is x \in S?' can be answered. The goal is to use a small table and yet answer queries using few bitprobes. This problem was considered recently by Buhrman, Miltersen, Radhakrishnan and Venkatesh, where lower and upper bounds were shown for this problem in the classical deterministic and randomized models. In this paper, we formulate this problem in the "quantum bitprobe model" and show tradeoff results between space and time.In this model, the storage scheme is classical but the query scheme is quantum.We show, roughly speaking, that similar lower bounds hold in the quantum model as in the classical model, which imply that the classical upper bounds are more or less tight even in the quantum case. Our lower bounds are proved using linear algebraic techniques.Comment: 19 pages, a preliminary version appeared in FOCS 2000. This is the journal version, which will appear in Algorithmica (Special issue on Quantum Computation and Quantum Cryptography). This version corrects some bugs in the parameters of some theorem

Bacterial Flora of Sputum, Its Antibiogram and Its relationship with Severity of COPD in patients with Acute Exacerbation: A Hospital Based study in a Tertiary Care Hospital

BACKGROUND: Chronic obstructive pulmonary disease (COPD) is a common disease characterized by persistent airflow obstruction with an enhanced chronic inflammatory response in the airways and the lung to noxious particles or gases. The aim of the present study was to obtain comprehensive insight into the bacteriological profile and antibiotic sensitivity pattern in sputum culture of AECOPD patients and its relationship with severity of COPD. Knowledge of common bacterial pathogens and their sensitivity pattern to antibiotics will help in early proper institution of appropriate antibiotic therapy in AECOPD. METHODS: A retrospective observational study was carried out at Madurai Medical College and Govt. Rajaji Hospital, Madurai which comprised of 100 patients diagnosed with chronic obstructive pulmonary disease from November 2015 to April 2016.Sputum culture and sensitivity reports were retrospectively analysed for the bacteriological profile and their antimicrobial sensitivity pattern. COPD severity was assessed by FEV1 and FEV1/FVC. RESULTS: Hundred patients diagnosed with COPD included with the age group comprising from 40 to 70 years of age, most common pathogenic bacteria isolated was Klebsiella pneumonia (52%), followed by Pseudomonas aerogionsa (27%), Klebsiella oxytoca (10%), Coagulase negative staphylococcus aureus (10%), Enterococcus (1%) .In patients with FEV1 <50% Pseudomonas was isolated more frequently. So there is significant association between COPD severity and organism. Klebsiella pneumonia, Pseudomonas, Klebsiella oxytoca, CONS were 100% sensitive to Cefeperazone sulbactum, Klebsiella pneumonia was 90.3% sensitive to Amikacin and Gentamycin, 73% sensitive to ciprofloxacin and 100% resistant to Ceftriaxone and cefatoxime. Pseudomonas was92.5% sensitive to Amikacin and Gentamycin, 89% sensitive to Ciprofloxacin. CONCLUSIONS: Klebsiella pneumoniae was the most common pathogen followed by Pseudomonas in AECOPD patients, and Cefeperazone sulbactum was most effective antibiotic against the most of the organism. Cefeperazone sulbactum should be the first line empirical antibiotic

Impact of Tandem Repeats on the Scaling of Nucleotide Sequences

Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in nucleotide sequences can prevent reliable estimation of possible long-range correlations. Therefore, it is important to investigate the presence of tandem repeats prior to scaling exponent estimation.Comment: 14 Pages, 3 Figure

Symptomatic giant left atrial aneurysm in a child : a rare entity

Isolated left atrial aneurysms are rare entities in clinical practice. Usually the condition is diagnosed in the second to fourth decades of life. The presence of such lesions in the pediatric age group is scantily described. We present a 2 year boy who presented with complaints of excessive irritability, respiratory distress and swelling of the feet. On examination, child was tachypnoeic with irregularly irregular rhythm. Echo showed a huge aneurysmal LA appendage with severe left ventricle dysfunction. The child underwent surgical resection for same. Findings were confirmed intraoperatively but he continued to have low cardiac output state after the surgery, with frequent arrhythmias and expired on day 7 of surgery. The case is reviewed and compared with the available English literature.peer-reviewe

Length-weight relationship and certain biological aspects of the Indian white shrimp Fenneropenaeus indicus (H. Milne Edwards, 1837) exploited by trawls in the Arabian Sea off Kerala coast, India

Length-weight relationship (LWR), sex ratio and maturity of Fenneropenaeus indicus (H. Milne Edwards, 1837), was analysed based on samplings from coastal trawl fishing grounds in the Arabian Sea off Kerala coast, India. The male to female ratio (1:1.27) did not vary significantly from the hypothetical 1:1 ratio. Length at maturity (Lm50) was estimated at 122 mm total length for females. The LWR did not differ significantly between male and female shrimps. The information generated from this study will enhance knowledge on the biology of the species and assist in assessment and management of its stock

Failure of Aileron Control Cable in Ajeet Aircraft MK-E-2015

The Aileron control cable of an Ajeet aircraft was found snapped . On ootical and scanning electron microscopic examination, it was found that the majority of the strands of the cable had thinned due to excessive contact wear with a oulley and subsequently failed in tension

Interactive Proof Systems

The report is a compilation of lecture notes that were prepared during the course ``Interactive Proof Systems'' given by the authors at Tata Institute of Fundamental Research, Bombay. These notes were also used for a short course ``Interactive Proof Systems'' given by the second author at MPI, Saarbruecken. The objective of the course was to study the recent developments in complexity theory about interactive proof systems, which led to some surprising consequences on nonapproximability of NP hard problems. We start the course with an introduction to complexity theory and covered some classical results related with circuit complexity, randomizations and counting classes, notions which are either part of the definitions of interactive proof systems or are used in proving the above results. We define arthur merlin games and interactive proof systems, which are equivalent formulations of the notion of interactive proofs and show their equivalence to each other and to the complexity class PSPACE. We introduce probabilistically checkable proofs, which are special forms of interactive proofs and show through sequence of intermediate results that the class NP has probabilistically checkable proofs of very special form and very small complexity. Using this we conclude that several NP hard problems are not even weakly approximable in polynomial time unless P = NP