Dihedral Sieving Phenomena

Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions and representations of the cyclic group. We propose a definition of sieving for an arbitrary group $G$ and study it for the dihedral group $I_2(n)$ of order $2n$. This requires understanding the generators of the representation ring of the dihedral group. For $n$ odd, we exhibit several instances of dihedral sieving which involve the generalized Fibonomial coefficients, recently studied by Amdeberhan, Chen, Moll, and Sagan. We also exhibit an instance of dihedral sieving involving Garsia and Haiman's $(q,t)$-Catalan numbers.Comment: 10 page

Analysis of sum-of-squares relaxations for the quantum rotor model

The noncommutative sum-of-squares (ncSoS) hierarchy was introduced by Navascu\'{e}s-Pironio-Ac\'{i}n as a sequence of semidefinite programming relaxations for approximating values of noncommutative polynomial optimization problems, which were originally intended to generalize quantum values of nonlocal games. Recent work has started to analyze the hierarchy for approximating ground energies of local Hamiltonians, initially through rounding algorithms which output product states for degree-2 ncSoS applied to Quantum Max-Cut. Some rounding methods are known which output entangled states, but they use degree-4 ncSoS. Based on this, Hwang-Neeman-Parekh-Thompson-Wright conjectured that degree-2 ncSoS cannot beat product state approximations for Quantum Max-Cut and gave a partial proof relying on a conjectural generalization of Borrell's inequality. In this work we consider a family of Hamiltonians (called the quantum rotor model in condensed matter literature or lattice $O(k)$ vector model in quantum field theory) with infinite-dimensional local Hilbert space $L^{2}(S^{k - 1})$, and show that a degree-2 ncSoS relaxation approximates the ground state energy better than any product state.Comment: 28 pages, submitted to QIP 202

Generalized inverse of a matrix and its applications

This article does not have an abstract

Chow Rings of Vector Space Matroids

The Chow ring of a matroid (or more generally, atomic latice) is an invariant whose importance was demonstrated by Adiprasito, Huh and Katz, who used it to resolve the long-standing Heron-Rota-Welsh conjecture. Here, we make a detailed study of the Chow rings of uniform matroids and of matroids of finite vector spaces. In particular, we express the Hilbert series of such matroids in terms of permutation statistics; in the full rank case, our formula yields the maj-exc $q$-Eulerian polynomials of Shareshian and Wachs. We also provide a formula for the Charney-Davis quantities of such matroids, which can be expressed in terms of either determinants or $q$-secant numbers

Conditions for optimality and validity of simple least squares theory

This article does not have an abstract

Quantitative and qualitative assessment of exploitation of juvenile cephalopods from the Arabian Sea and Bay of Bengal and determination of minimum legal sizes

Using the minimum size at maturity (MSM) as a biological reference point and relatively low reproductive loads and generation times of the studied animals, the minimum legal sizes (MLS) for the Indian squid Loligo duvauceli, the pharaoh cuttlefish Sepia pharaonis and for the webfoot octopus Octopus membranaceous was fixed at 80, 115 and 45 mm Dorsal Mantle Length (DML) respectively with corresponding minimum legal weights at 25, 150 and 15 g. For L. duvauceli, during 1997-2001, 12.8% of the average catch was constituted by juveniles, the proportion being higher along the west coast. In 2002-05, the proportion of juveniles was lower at 5.3% and the total weights were also much less (1817 t as compared to 5354 t). In the case of S. pharaonis, 6.9% (2281 t) of the catch was constituted by juveniles, but the proportion was very high (22.4%) along the east coast. In O. membranaceous during 2002-04, an estimated 527 t (5.9%) of the total catch comprised of juveniles. The present Lmean in the fishery is lower than the Lopt and their difference is considerably high at 60 mm for L. duvauceli. However, in the case of S. pharaonis this difference is only 10 mm and in the case of O. membranaceous the Lmean is higher than the Lopt. If the juveniles are permitted to grow to Lmean by implementing the MLS, the estimated economic gain is to the tune of Rs. 426 crores per annum. The present study shows that harvest weights can be improved by up to 34 times and would result in higher incomes to trawl fishers

Production of galactitol from galactose by the oleaginous yeast Rhodosporidium toruloides IFO0880

Background Sugar alcohols are commonly used as low-calorie sweeteners and can serve as potential building blocks for bio-based chemicals. Previous work has shown that the oleaginous yeast Rhodosporidium toruloides IFO0880 can natively produce arabitol from xylose at relatively high titers, suggesting that it may be a useful host for sugar alcohol production. In this work, we explored whether R. toruloides can produce additional sugar alcohols. Results Rhodosporidium toruloides is able to produce galactitol from galactose. During growth in nitrogen-rich medium, R. toruloides produced 3.2 ± 0.6 g/L, and 8.4 ± 0.8 g/L galactitol from 20 to 40 g/L galactose, respectively. In addition, R. toruloides was able to produce galactitol from galactose at reduced titers during growth in nitrogen-poor medium, which also induces lipid production. These results suggest that R. toruloides can potentially be used for the co-production of lipids and galactitol from galactose. We further characterized the mechanism for galactitol production, including identifying and biochemically characterizing the critical aldose reductase. Intracellular metabolite analysis was also performed to further understand galactose metabolism. Conclusions Rhodosporidium toruloides has traditionally been used for the production of lipids and lipid-based chemicals. Our work demonstrates that R. toruloides can also produce galactitol, which can be used to produce polymers with applications in medicine and as a precursor for anti-cancer drugs. Collectively, our results further establish that R. toruloides can produce multiple value-added chemicals from a wide range of sugars.Ope

Scope of Real Time Fluorescence Imaging in Esophagectomy

Esophagectomy is a challenging surgery that is known to be associated with high rates of morbidity. Anastomotic leaks, pneumonia, conduit necrosis and chyle leaks are the commonly reported complications. Perfusion assessment and tissue injection based fluorescence guided surgery (FGS) are the newer clinical applications of fluorescent dyes. With the advent and integration of real time fluorescence imaging with the existing minimal access platforms, the esophageal surgeon can employ these techniques to potentially improve outcomes. During thoracic dissection, thoracic duct lymphography, fluorescence guided airway visualization, tracheal perfusion assessment and sentinel lymph node biopsy/dissection are the reported clinical applications. In the abdominal dissection, gastroepiploic arcade identification, gastric conduit perfusion assessment and proximal esophagus perfusion assessment have been described. Using the different routes of administration, the same dye can be used for different uses at separate points in a single esophagectomy surgery. The principles and evidence pertaining to these applications have been outlined

yuDetecting the percent of peripheral blood mononuclear cells displaying p-STAT-3 in malignant glioma patients

<p>Abstract</p> <p>Background</p> <p>The signal transducer and activator of transcription 3 (STAT-3) is frequently overexpressed in cancer cells, propagates tumorigenesis, and is a key regulator of immune suppression in cancer patients. The presence of phosphorylated STAT-3 (p-STAT-3) in the tumor can induce p-STAT-3 in tumor-associated immune cells that can return to the circulatory system. We hypothesized that the number of peripheral blood mononuclear cells (PBMCs) displaying p-STAT-3 would be increased in glioma patients, which would correlate with the extent of tumor-expressed p-STAT-3, and that higher p-STAT-3 levels in peripheral blood would correlate with a higher fraction of immune-suppressive regulatory T cells (Tregs).</p> <p>Methods</p> <p>We measured the percentage of PBMCs displaying p-STAT-3 in 19 healthy donors and 45 patients with primary brain tumors. The level of p-STAT-3 in tumor tissue was determined by immunohistochemistry. The degree of immune suppression was determined based on the fraction of Tregs in the CD4 compartment.</p> <p>Results</p> <p>Healthy donors had 4.8 ± 3.6% of PBMCs that expressed p-STAT-3, while the mean proportion of PBMCs displaying p-STAT-3 in patients with GBM was 11.8 ± 13.5% (<it>P </it>= 0.03). We did not observe a correlation by Spearman correlation between the degree of p-STAT-3 levels in the tumor and the percent of PBMCs displaying p-STAT-3. Furthermore, the percent of PBMCs displaying p-STAT-3 in glioma patients was not directly correlated with the fraction of Tregs in the CD4 compartment.</p> <p>Conclusion</p> <p>We conclude that the percent of PBMCs displaying p-STAT-3 may be increased in malignant glioma patients.</p

TNF-α promoter polymorphism: a factor contributing to the different immunological and clinical phenotypes in Japanese encephalitis

<p>Abstract</p> <p>Background</p> <p>More than three billion populations are living under the threat of Japanese encephalitis in South East Asian (SEA) countries including India. The pathogenesis of this disease is not clearly understood and is probably attributed to genomic variations in viral strains as well as the host genetic makeup. The present study is to determine the role of polymorphism of TNF-alpha promoter regions at positions -238G/A, -308G/A, -857C/T and -863C/A in the severity of Japanese encephalitis patients.</p> <p>Methods</p> <p>Total of 142 patients including 66 encephalitis case (IgM/RT-PCR positive), 16 fever cases (IgM positive) without encephalitis and 60 apparently healthy individuals (IgG positive) were included in the study. Polymerase chain reaction restriction fragment length polymorphism (PCR-RFLP) using site specific restriction enzymes were implemented for polymorphism study of TNF alpha promoter.</p> <p>Results</p> <p>Following the analysis of the digestion patterns of four polymorphic sites of the TNF- alpha promoter region, a significant association was observed between the allele -308A and -863C with the patients of Japanese encephalitis.</p> <p>Conclusions</p> <p>TNF- alpha 308 G/A has been shown to be associated with elevated TNF- alpha transcriptional activity. On the other hand, polymorphism at position -863C/A in the promoter region has been reported to be associated with reduced TNF- alpha promoter activity and lower plasma TNF levels. As per the literature search, this is the first study to identify the role of TNF- alpha promoter in JE infection. Our results show that subjects with - 308A and -863C alleles are more vulnerable to the severe form of JE infection.</p