57 research outputs found
Mathai-Quillen forms and Lefschetz theory
No full textMathai-Quillen forms are used to give an integral formula for the Lefschetz number of a smooth map of a closed manifold. Applied to the identity map, this formula reduces to the Chern-Gauss-Bonnet theorem. The formula is computed explicitly for constant curvature metrics. There is in fact a one-parameter family of integral expressions. As the parameter goes to infinity, a topological version of the heat equation proof of the Lefschetz fixed submanifold formula is obtained. As the parameter goes to zero and under a transversality assumption, a lower bound for the number of points mapped into their cut locus is obtained. For diffeomorphisms with Lefschetz number unequal to the Euler characteristic, this number is infinite for most metrics, in particular for metrics of non-positive curvature.First author draf
On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data
No full textAn entropy for the scalar variable case, parallel to Havrda-Charvat entropy, was introduced by the first author, and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper, we extend the entropy to cover the scalar case, multivariable case, and matrix variate case. Then, this measure is optimized under different types of restrictions, and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical and physical sciences are pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data by applying standard deviation analysis and diffusion entropy analysis is provided
Evolution and future trends in battle injuries to the CNS
No full textDespite advances in personal protection, brain and spinal injuries amongst combatants pose significant management challenges. Battle field medical care has evolved over the year. In this article we discuss evolutions of military medicine, study current protocols and outcomes and discuss future perspectives. Mention is also made of some original work by the author
Dynamics of finite-sized light spheres in turbulence
No full textWe report experimental results on the Lagrangian dynamics of finite-size light particles in turbulence. Using an orthogonal camera setup and 3D particle tracking, we study the velocity and acceleration statistics of rigid light spheres in a water tunnel with nearly homogeneous and isotropic turbulence. The Reynolds number (ReY) is varied from 180 to 300, and the study covers a range of size ratios (4 < D/η < 16) for marginally light spheres. We find that the normalised acceleration PDF decreases in intermittency with increasing size ratio - in qualitative agreement with the predictions of the Faxén corrected model. We also present preliminary results on the rotational dynamics of large light spheres in turbulence
Algebra cochains, the bivariant JLO cocycle and the Mathai-Quillen form
No full textThis is a first investigation by the author of the similarity between
Quillen's superconnection formalism, his constructions of (periodic) cyclic
cocycles via algebra cochains on a bar construction, and Kasparov bimodules for
KK-theory. In this article, we do so by deriving a slight extension of the
Mathai-Quillen Thom form via a bivariant JLO cocycle. The main idea (which is
in fact not really new) is that KK-cycles should be thought of as
superconnection forms; these methods will be applied to other contexts
elsewhere
Non-invasive ventilation in the postoperative period: Is there a role?
No full textNon-invasive positive pressure ventilation or non-invasive ventilation (NIV) has emerged as a simpler and safer alternative to invasive mechanical ventilation in patients developing acute postoperative respiratory failure. The benefits of NIV as compared to intubation and mechanical ventilation include lower complications, shorter duration of hospital stay, reduced morbidity, lesser cost of treatment and even reduced mortality rates. However, its use may not be uniformly applicable in all patient groups. This article reviews the indications, contraindications and evidence supporting the use of NIV in individual patient groups in the postoperative period. The anaesthesiologist needs to recognise the subset of patients most likely to benefit from NIV therapy so as to apply it most effectively. It is equally important to promptly identify signs of failure of NIV therapy and be prepared to initiate alternate ways of respiratory support. The author searched PubMed and Ovid MEDLINE, without date restrictions. Search terms included Non-invasive ventilation, postoperative and respiratory failure. Foreign literature was included, though only articles with English translation were used
T-duality of singular spacetime compactifications in an H-flux
No full textWe begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalizing the results there. We then initiate the study of twisted equivariant Courant algebroids and equivariant generalized geometry and apply it to our context. As before, T-duality exchanges type II role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative; \u3eIIA and type II role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative; \u3eIIB string theories. In our theory, both spacetime and the T-dual spacetime can be singular spaces when the fixed point set is non-empty; the singularities correspond to Kaluza–Klein monopoles. We propose that the Ramond–Ramond charges of type II role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative; \u3eII string theories on the singular spaces are classified by twisted equivariant cohomology groups, consistent with the previous work of Mathai and Wu, and prove that they are naturally isomorphic. We also establish the corresponding isomorphism of twisted equivariant Courant algebroids
Digestible indispensable amino acid scores for food proteins
No full textThree experiments were conducted to determine protein quality and to evaluate digestible indispensable amino acid scoring (DIAAS) methodology. Experiment 1 was conducted to compare protein digestibility corrected amino acid scores (PDCAAS) and DIAAS for various plant and animal proteins. Values for standardized total tract digestibility (STTD) of crude protein (CP) and standardized ileal digestibility (SID) of amino acids were calculated for whey protein isolate (WPI), whey protein concentrate (WPC), milk protein concentrate (MPC), skim milk powder (SMP), pea protein concentrate (PPC), soy protein isolate (SPI), soy flour, and whole grain wheat. The PDCAAS-like values were calculated using the STTD of CP to estimate amino acid digestibility and values for DIAAS were calculated from values for SID of amino acids. Results indicated that values for SID of most indispensable amino acids in WPI, WPC, and MPC were greater (P < 0.05) than for SMP, PPC, SPI, soy flour, and wheat. If the same scoring pattern for children between 6 and 36 months was used to calculate PDCAAS-like values and DIAAS, PDCAAS-like values were greater (P < 0.05) than DIAAS values for SMP, PPC, SPI, soy flour, and wheat indicating that PDCAAS-like values estimated in pigs may overestimate the quality of these proteins. Experiment 2 was conducted to determine the DIAAS values for pork loin and to evaluate the effect of roasting, frying, or grilling of pork loin on protein quality. The DIAAS were calculated based on ileal digestibility of amino acids in pigs for raw pork loin, roasted pork loin, grilled pork loin, fried pork loin, and casein. Six ileal-cannulated barrows were allotted to a 6 × 6 Latin square design with 6 diets and 6 periods during which ileal effluent samples were collected to determine amino acid digestibility. A N-free diet was formulated to determine basal endogenous losses of amino acids and crude protein (CP) and to enable the calculation of standardized ileal digestibility (SID) of amino acids. The remaining diets were formulated with each test ingredient as the sole source of amino acids. Using determined values for SID of amino acids for each ingredient and established reference protein patterns, DIAAS were calculated. For children from birth to 6 m, fried pork loin had the greatest (P < 0.05) DIAAS followed by grilled pork loin, roasted pork loin, raw pork loin, and casein. For children from 6 m to 3 y, DIAAS were greatest (P < 0.05) for grilled and fried pork loin and least (P < 0.05) for raw pork loin and the DIAAS of roasted pork loin was greater (P < 0.05) than that of casein. For DIAAS calculated for children older than 3 y, there were no differences in the DIAAS among grilled pork loin, fried pork loin, and casein, but these 3 ingredients had greater (P < 0.05) DIAAS than roasted pork loin, which in turn had a greater (P < 0.05) DIAAS than raw pork loin. Results indicate that prepared pork loins can be considered excellent protein sources based on their DIAAS and these data make it possible to calculate DIAAS for meals containing commonly consumed pork loin products. Additionally, results of this research indicate that even for high-quality proteins, such as pork loin, correct preparation can improve DIAAS. Experiment 3 was conducted to determine DIAAS values for 10 different foods known to have different protein values: wheat bread, whey protein isolate, zein, sorghum flour, bovine collagen, black beans, pigeon peas, chick peas, roasted peanuts, and Kellogg’s® All-Bran®. The second objective was to determine the variability among replications in the determination of the DIAAS values. Thirteen ileal-cannulated gilts were assigned to an incomplete 13 × 6 Latin square design with 13 diets and 6 periods. The 10 ingredients were used to formulate 10 different diets where each ingredient was the sole source of amino acids in the diet. Pigs on treatments 1 to 10 were fed the 10 diets containing the 10 food sources. Pigs on treatments 11, 12, and 13 were fed the whey protein isolate diet, the sorghum diet, and the pigeon pea diet, respectively. These extra replications enabled determination of intra-experiment variability. The SID for total amino acids was greater (P < 0.05) in toasted wheat bread and sorghum flour than in all other proteins except for chickpeas. The SID for mean indispensable amino acids, mean dispensable amino acids and total amino acids was lower (P < 0.05) in All-Bran® than in all other proteins except roasted peanuts. The DIAAS was 0 for zein, bovine collagen, roasted peanuts, and All-Bran® for all reference ratios. Whey protein isolate had the greatest (P < 0.05) DIAAS for infants, followed by chickpeas, pigeon peas, sorghum flour, black beans, and toasted wheat bread, in descending order. Whey protein isolate had the greatest (P < 0.05) DIAAS for children (6 m to 3 y) followed by chick peas and pigeon peas. Black beans and sorghum flour had DIAAS values that were not different, but these values were greater (P < 0.05) than the DIAAS for toasted wheat bread. Whey protein isolate had the greatest (P < 0.05) DIAAS for older children (3 y and older), followed by chickpeas. Pigeon peas had a greater (P < 0.05) DIAAS than sorghum flour, which in turn had a greater (P < 0.05) DIAAS than black beans, and black beans had a greater (P < 0.05) DIAAS than toasted wheat bread. For DIAAS calculated for all 3 reference ratios, there were no differences between replications for whey protein isolate, sorghum, or pigeon peas. The DIAAS values determined in this experiment indicate that most legumes and cereal grain products tested in this experiment are not adequate as the sole sources of protein for humans. Results of this experiment demonstrate that the pig model is a consistent model for determination of amino acid digestibility and DIAAS determination even when disparate protein sources are used.Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2020-12-01The student, John Mathai, accepted the attached license on 2018-09-18 at 09:51.The student, John Mathai, submitted this Dissertation for approval on 2018-09-18 at 09:52.This Dissertation was approved for publication on 2018-09-21 at 13:16.DSpace SAF Submission Ingestion Package generated from Vireo submission #13017 on 2019-02-07 at 14:16:38Made available in DSpace on 2019-02-07T20:35:53Z (GMT). No. of bitstreams: 3
MATHAI-DISSERTATION-2018.pdf: 1175823 bytes, checksum: 80f857041e36b02044407a33be4013a3 (MD5)
Dissertation - JK Mathai Sep 21 2018.docx: 192860 bytes, checksum: 741f799c7d5abc867b8178f6a6c59538 (MD5)
LICENSE.txt: 4208 bytes, checksum: 9e2397938593232f55493fef07b9e05e (MD5)
Previous issue date: 2018-09-21Embargo set by: Seth Robbins for item 109804
Lift date: 2021-02-07T20:36:09Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemEmbargo set by: Seth Robbins for item 109804
Lift date: 2021-02-07T20:39:46Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemEmbargo set by: Seth Robbins for item 109804
Lift date: 2021-02-07T20:44:35Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemU of I Only Restriction Lifted for Item 109804 on 2021-02-08T10:15:32Z
Some Matrix-Variate Models Applicable in Different Areas
No full textMatrix-variate Gaussian-type or Wishart-type distributions in the real domain are widely used in the literature. When the exponential trace has an arbitrary power and when the factors involving a determinant and a trace enter into the model or a matrix-variate gamma-type or Wishart-type model with an exponential trace having an arbitrary power, they are extremely difficult to handle. One such model with factors involving a trace and a determinant and the exponential trace having an arbitrary power, in the real domain, is known in the literature as the Kotz model. No explicit evaluation of the normalizing constant in the Kotz model seems to be available. The normalizing constant that is widely used in the literature, is interpreted as the normalizing constant in the general model, and that is referred to as a Kotz model does not seem to be correct. One of the main contributions in this paper is the introduction of matrix-variate distributions in the real and complex domains belonging to the Gaussian-type, gamma-type, and type 1 and type 2 beta-types, or Mathai’s pathway family, when the exponential trace has an arbitrary power and explicit evaluations of the normalizing constants therein. All of these models are believed to be new. Another new contribution is the logistic-based extensions of the models in the real and complex domains, with the exponential trace having an arbitrary exponent and connecting to extended zeta functions introduced by this author recently. The techniques and steps used at various stages in this paper will be highly useful for people working in multivariate statistical analysis, as well as for people applying such models in engineering problems, communication theory, quantum physics, and related areas, apart from statistical applications
Thom form in equivariant Cech-de Rham theory
No full textIn the present paper, we provide the foundation of a G-equivariant Cechde Rham theory for a compact Lie group G by using the Cartan model of equivariant differential forms. Our approach is quite elementary without referring to the Mathai Quillen framework. In particular, by a direct computation, we give an explicit formula of the U(l)-equivariant Thom form of C-l, which deforms the classical BochnorMartinelli kernel. Also, we discuss a version of equivariant RiemannRoch formula
- …
