New Nonexistence Results on Circulant Weighing Matrices

A circulant weighing matrix $W = (w_{i,j})$ is a square matrix of order $n$ and entries $w_{i,j}$ in $\{0, \pm 1\}$ such that $WW^T=kI_n$. In his thesis, Strassler gave a table of existence results for such matrices with $n \leq 200$ and $k \leq 100$. In the latest version of Strassler's table given by Tan \cite{arXiv:1610.01914} there are 34 open cases remaining. In this paper we give nonexistence proofs for 12 of these cases, report on preliminary searches outside Strassler's table, and characterize the known proper circulant weighing matrices.Comment: 15 page

A Nonexistence Result for Abelian Menon Difference Sets Using Perfect Binary Arrays

A Menon difference set has the parameters (4N2, 2N2-N, N2-N). In the abelian case it is equivalent to a perfect binary array, which is a multi-dimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. Suppose that the abelian group H×K×Zpα contains a Menon difference set, where p is an odd prime, |K|=pα, and pj≡−1 (mod exp (H)) for some j. Using the viewpoint of perfect binary arrays we prove that K must be cyclic. A corollary is that there exists a Menon difference set in the abelian group H×K×Z3α, where exp (H)=2 or 4 and |K|=3α, if and only if K is cyclic

Clinical and radiological correlation of severity of acute pancreatitis

BACKGROUND: Acute pancreatitis is a disease with wide clinical variation, which makes its diagnosis complex. Serum / urinary amylase measurement is a standard diagnostic method, although it was shown to be unable to recognize one fifth of AP patients. The severity of AP forms a continuum, and the average mortality rate approaches 2-10%. Most of the cases are mild and conservative treatment results in a rapid recovery in most of them. However, severe AP constitutes 15–20% of all cases. In recent decades, mortality rate of severe AP has decreased from 30-80% to 15-20%. CT scanning has increased the identification of pancreatitis. The care of a pancreatitis patient is demanding and requires dedication, diligence and efficiency. In view of the hazardous nature of severe pancreatitis and its high mortality rate this dissertation is chosen to study the co relation of CT scoring and Clinical scoring of Pancreatitis so that CT scans can be used as a reliable marker of severe acute pancreatitis and diagnose it in the early stages and treated accordingly. OBJECTIVES : 1. To analyse and compare the various clinical presentations of acute pancreatitis. 2. To correlate the severity of acute pancreatitis with regard to available biochemical parameters. 3. To assess the severity in relation to computerized tomography of abdomen. 4. To predict the outcome of acute pancreatitis with regard to CT abdomen. 5. To prognosticate the disease. 6. To decide the further management with CT abdomen and to decide when to intervene. Duration of Study: 1 year (2017). Population to be studied: Minimum of 50 cases. Study Group: 15 to 75 Yrs age group. Study setting: Department of General Surgery, Chengalpattu Medical College and Hospital, Chengalpattu. DIAGNOSTIC CRITERIA FOR ACUTE PANCREATITIS: Acute pancreatitis was diagnosed if there were findings consistent with acute pancreatitis and a raised serum amylase above the upper reference limit (URL). This diagnosis was further complemented with transabdominal USG and CE-CT. Exclusion of acute pancreatitis in patients with acute abdominal pain was based on clinical, radiographic, endoscopic and surgical findings. SEVERITY ASSESSMENT OF ACUTE PANCREATITIS: Assessment of severity based on clinical presentations. Assessment of severity was also based on CT abdomen. A correlation was obtained between clinical severity and that based on CT abdomen. SCORING SYSTEMS: 1. CLINICAL SCORING: In AP patients appropriate laboratory and physiological data were recorded on day 1 and 48 hours after admission to calculate the ranson criteria. MODS score provides a means to grade the intensity of dysfunction of six organ systems: the respiratory (spo2), renal (serum creatinine), hepatic (serum bilirubin), nervous system (GCS), cardiovascular (pulse rate) and the hematological system (platelet count). CT SCORING (Balthazar): GRADE APPEARANCE SCORE: Grade A - Normal appearance 0, Grade B - Focal or diffuse enlargement of pancreas - One, Grade C - Peripancreatic inflammation - Two, Grade D - Intra/ extrapancreatic fluid collection - Three, Grade E - Two or more fluid collection or gas in pancreas or retroperitoneum – Four. CT SEVERITY INDEX: Necrosis score based on CE-CT. 0% OF NECROSED PANCREAS 0, <33% OF NECROSED PANCREAS 2, 33 – 50% OF NECROSED PANCREAS 4, >50% OF NECROSED PANCREAS 6, CT severity index = unenhanced CT score + necrosis score, >5 score indicates an 8 fold higher mortality. CONCLUSION: The above study gives a comprehensive and detailed analysis of the pattern of acute pancreatitis with emphasis on early recognition severe pancreatitis with CT Abdomen

Some Non-Existence Results on Divisible Difference Sets

In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches: (i) character sum arguments similar to the work of Turyn [25] for ordinary difference sets, (ii) involution arguments, and (iii) multipliers in conjunction with results on ordinary difference sets. Among other results, we show that an abelian affine difference set of odd order s (s not a perfect square) in G can exist only if the Sylow 2-subgroup of G is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd order n

A Note on Intersection Numbers of Difference Sets

We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets

A Note on Intersection Numbers of Difference Sets

We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets

On circulant and two-circulant weighing matrices

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W(148, 144), W(152, 144), W(156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer “YES”, by constructing a circulant weighing matrix of order 142 with weight 100

New Constructions of Menon Difference Sets

Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays

Investigating hookworm genomes by comparative analysis of two Ancylostoma species

Background Hookworms, infecting over one billion people, are the mostly closely related major human parasites to the model nematode Caenorhabditis elegans. Applying genomics techniques to these species, we analyzed 3,840 and 3,149 genes from Ancylostoma caninum and A. ceylanicum. Results Transcripts originated from libraries representing infective L3 larva, stimulated L3, arrested L3, and adults. Most genes are represented in single stages including abundant transcripts like hsp-20 in infective L3 and vit-3 in adults. Over 80% of the genes have homologs in C. elegans, and nearly 30% of these were with observable RNA interference phenotypes. Homologies were identified to nematode-specific and clade V specific gene families. To study the evolution of hookworm genes, 574 A. caninum / A. ceylanicum orthologs were identified, all of which were found to be under purifying selection with distribution ratios of nonsynonymous to synonymous amino acid substitutions similar to that reported for C. elegans / C. briggsae orthologs. The phylogenetic distance between A. caninum and A. ceylanicum is almost identical to that for C. elegans / C. briggsae. Conclusion The genes discovered should substantially accelerate research toward better understanding of the parasites' basic biology as well as new therapies including vaccines and novel anthelmintics