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

Sudden Cardiac Death in Young Adults with Long-Chain 3-Hydroxyacyl CoA Dehydrogenase Deficiency (LCHADD)

Long-chain 3-Hydroxyacyl CoA Dehydrogenase Deficiency (LCHADD) is an autosomal recessive defect in fatty acid oxidation that presents with hypoketotic hypoglycemia and/or hypertrophic cardiomyopathy in infancy, and recurrent rhabdomyolysis in adolescence, however, sudden cardiac death has not been a previously reported complication of LCHADD. We have conducted a case review study comparing young adult LCHADD patients who have experienced sudden cardiac arrest events (n=5) to similar patients who have not (n=5) for the purpose of evaluating associated cardiac risk factors. We reviewed medical records from ECG tests, hospitalization reports, acylcarnitine, and complete metabolic panels, clinic notes, and autopsy reports. Retrospective chart review has led to no certain etiology however, electrolyte derangements, low free carnitine and elevated total to free carnitine ratio have been noted upon hospitalization in sudden cardiac arrest cases. At the time of the sudden cardiac death event, only one subject was in a metabolic crisis with elevated creatine phosphokinase levels. Life-threatening ventricular arrhythmias appear to be a newly recognized life-threatening complication in the adolescent and young adult age groups of LCHADD patients. The exact mechanism underlying the sudden death events is not understood and there are no current therapies. Understanding the pathophysiology of inherited arrhythmias can be challenging due to the complexity of both the heart and LCHAD deficiency along with the lack of appropriate cellular and in vivo models. Recent advances in human-induced pluripotent stem cell (hiPSC) technology have provided extraordinary progress in understanding the mechanisms in generating human-induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs). Future directions of this study seek to generate LCHAD deficient patient-derived iPSC-CMs in order to assess mitochondrial function, force of contraction, oxygen consumption rates, impacts of analytes, and calcium regulation. In a paper published in the Nature Methods Journal, Burridge and colleagues establish an easily reproducible protocol for the chemically defined generation of human cardiomyocytes (Burridge, Matsa, & Shukla, 2014) from skin fibroblast-derived induced pluripotent stem cells. Our research lab will establish this method which utilizes three crucial components of a chemically defined medium consisting of the basal medium RPMI 1640, L-ascorbic acid 2-phosphate along with recombinant human albumin to generate cardiomyocytes with an immature phenotype. This chemically defined medium will provide reproducible, scalable methods for deriving cardiomyocytes from iPSCs however, they do remain immature in nature and future directions of the study seek to adapt newly engineered maturation protocols. Assessing the disruption of bioenergetics and mitochondrial function in hiPSC-CMs will provide a meaningful in vitro model to examine the potential pathways and biochemical mechanisms that contribute to cardiac arrhythmias observed in affected LCHADD patients who have experienced sudden cardiac death events. Ultimately, clinical trials will be needed to further characterize the pathophysiology of these severe cardiac manifestations in young adult LHCADD populations

Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and \LL(k) (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $\epsilon < 1/2$ must use $\Omega(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems

Lymphoma of the thyroid gland: a clinicopathologic study over a period of five years in a tertiary care center

Background: Primary Thyroid Lymphoma (PTL) is uncommon, accounting for only 5% of thyroid neoplasmsand less than 2.5 to 7% of extranodal lymphomas. The study aims to analyze the histopathological findings and to correlate it with clinical features.Methods: This study includes cases of PTL received in the department of pathology in a tertiary care center, Kerala, south India over a period of 5 years. Patient details and follow up data were obtained by communication with treating doctors and reviewing the hospital records. All cases had a minimum follow up of 6 months.Results: 15 cases of PTL were diagnosed over the five year period. In total 72 cases of extranodal lymphomas were diagnosed, thus forming 20.83% of extra nodal lymphomas. Lymphocytic thyroiditis was present in 93.3%. Most of the cases were Extranodal Marginal Zone B Cell Lymphoma (EMZBCL) and Diffuse Large B Cell Lymphoma (DLBCL).Conclusion: It is important to consider the diagnosis of primary thyroid lymphoma in patients presenting with an enlarging neck mass especially with the history of Hashimoto’s thyroiditis. Random microscopic foci of DLBCL or small areas of MZBL could be overlooked examination or missed with limited sampling. The distinction between MZBL and DLBCL in the thyroid is clinically significant.

Study of diagnosis and management of ectopic pregnancy

Background: Diagnosis of ectopic pregnancy was frequently missed. Aim of the study was to determine the clinical presentation, and treatment associated with ectopic pregnancy.Methods: This is a prospective study which was carried out at Obstetrics and Gynaecology department, GMERS SOLA civil hospital from August 2017 to October 2018. Total 416 patients were admitted during study period out of them 50 patients diagnosed with ectopic pregnancy were enrolled in the study and information was collected and analysed.Results: 80% patients were between the age group of 21-30 years. 56% patients were nulliparous. Amenorrhea (92%) with lower abdominal pain (94%) is the most common presenting symptom. 26% of patients show typical triad of amenorrhea, abdominal pain and bleeding per vagina. UPT and USG were most commonly performed investigations. 96% cases showed UPT positive. 100% USG showed adnexal pathology. Serum beta-hCG was done in 37 patients as an aid for diagnosis and to decide the line of management. Conservative medical management with Injection MTX was done in 4 patients of which 1 patients required laparotomy later on. Surgical management was done in 90% of patients. Laparoscopic management was done in 54% of cases.Conclusions: Early diagnosis and timely intervention in the form of conservative or surgical treatment will help in reducing the morbidity and mortality associated with ectopic pregnancy

A study of the effect of neoadjuvant chemotherapy with FAC regime in locally advanced breast carcinoma

Background: Cases of carcinoma breast with TNM stage 3 are considered as locally advanced breast cancer. This study was done to demonstrate the effect of neoadjuvant chemotherapy in cases of stage 3 technically inoperable breast cancers. As neoadjuvant chemotherapy is an already established form of treatment, its effect on ‘complete clinical response and pathological response’ were studied.Methods: This prospective study was carried out in department of general surgery of Medical college, Thiruvananthapuram after obtaining approval from research ethical committee. Relevant data of chemotherapy was collected from department of Radiotherapy and Histopathological data was collected from department of Pathology. 25 cases of locally advanced breast carcinoma were studied. These patients were started on treatment with FAC regime and the response was assessed.Results: In this study 20% of patients had complete clinical response at the completion of 3 cycles of chemotherapy with FAC regime. 48% had partial response. In 32% of patients, stasis was observed. None showed increase in tumor size during treatment.Conclusion: The study demonstrated the effectiveness of neoadjuvant chemotherapy in downstaging the tumor enabling definitive surgery with less morbidity. It also showed a complete clinical and pathological response in a significant number of patients.

A comparative study of non-descent vaginal hysterectomy and total laparoscopic hysterectomy

Background: Hysterectomy is the second most common operation performed by the gynecologists, next only to caesarean section. Objective of the study was to compare fall in blood haemoglobin level, duration of operation, intra- and post-op complications between non-descent vaginal hysterectomy and total laparoscopic hysterectomy and establish the better method for hysterectomy in non-descent uterus.Methods: A retrospective comparative study of 90 hysterectomies was done from a period of May 2018 - April 2019 at GMERS Medical College and Hospital Sola, with 45 cases in group of non-descent vaginal hysterectomy (NDVH) and 45 in group of total laparoscopic hysterectomy (TLH). Demographic characteristics, co-morbid conditions, indications for surgery, operative time, intra- operative blood loss, post-operative analgesia requirements, post-operative hospital stay and post-operative complications were compared between both groups. Those patients having malignancy as diagnosed by Pap smear or by D and C were excluded from the studyResults: The most common age in both groups was 41-50 years. Adenomyotic uterus was the most common indication for surgery in both groups. The mean operative time in NDVH group was 45 min while it was 80 min in TLH group. p<0.001 suggested significant difference when operative time were compared between both groups. Both groups were similar in post-operative analgesia requirement and post-operative hospital stay. Post-operative complications were similar in both groups.Conclusions: In which way to approach the uterus shall depend upon skill of the surgeon, size and pathological nature of uterus, technology available in the hospital and preference of patient as well as surgeon

Incidence of maternal near-miss events in a tertiary care hospital of Gujarat, India

Background: Maternal near miss is said to have occurred when women presented with life threatening complication during pregnancy, child birth and within 42 days after delivery, but survive by chance or good institutional care. For identifying near-miss cases five-factor scoring system was used. In 2009 WHO working group has standardized the criteria for selecting these cases. Because maternal mortality is a rare event, it is important to study maternal near-miss as a complement to evaluate and improve the quality of obstetric care. Thus, the study was conducted with the aim of assessing the incidence and causes of maternal near-miss.Methods: A facility-based cross-sectional study was conducted in the department of obstetrics and gynecology in GMERS medical college and hospital, Sola, Ahmedabad from January 1, 2019 to August 31, 2019. All maternal near-miss cases admitted to the hospital during the study period were recruited. World Health Organization criteria were used to identify maternal near-miss cases. The number of maternal near-miss cases over one year per 1000 live births occurring during the same year was calculated to determine the incidence of maternal near-miss. Underlying and contributing causes of maternal near-miss were documented from each participant’s record.Results: During the period of study, 3235 deliveries were done at the institution while 16 cases of near-miss were identified. The prevalence of near-miss case in this study was 0.5%. Near-miss per 1000 delivery was 5%. Maternal death to near miss ratio was 1:2.67. The leading causes of maternal near miss were hypertensive disorders (62%) and haemorrhage (32%) The morbidity was high in un-booked cases.Conclusions: Maternal near miss is good alternative indicator of health care system. Efforts made toward improvement in the management of life-threatening obstetric complications could reduce the occurrence of maternal near-miss problems that occur during hospitalization