1,320 research outputs found
On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
No full textLet R be a real closed field. We prove that for any fixed d, the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of Rk defined by polynomials of degrees bounded by d vanishes in dimensions d and larger. This vanishing result is tight. Using a new geometric approach we also prove an upper bound of [mathematical formula] on the equivariant Betti numbers of closed symmetric semi-algebraic subsets of Rk defined by quantifier-free formulas involving s symmetric polynomials of degrees bounded by d, where 1d≪s,k. This bound is tight up to a factor depending only on d. These results significantly improve upon those obtained previously in Basu and Riener (Adv Math 305:803–855, 2017) which were proved using different techniques. Our new methods are quite general, and also yield bounds on the equivariant Betti numbers of certain special classes of symmetric definable sets (definable sets symmetrized by pulling back under symmetric polynomial maps of fixed degree) in arbitrary o-minimal structures over R. Finally, we utilize our new approach to obtain an algorithm with polynomially bounded complexity for computing these equivariant Betti numbers. In contrast, the problem of computing the ordinary Betti numbers of (not necessarily symmetric) semi-algebraic sets is considered to be an intractable problem, and all known algorithms for this problem have doubly exponential complexity
Some quantitative results in real algebraic geometry
No full textReal algebraic geometry is the study of semi-algebraic sets, subsets of Rk defined by boolean combinations of polynomial equalities and inequalities. The focus of this thesis is to study quantitative results in real algebraic geometry, primarily upper bounds on the topological complexity of semi-algebraic sets as measured, for example, by their Betti numbers
Generalized TASE-RK methods for stiff problems
No full textA family of Time-Accurate and Stable Explicit (TASE) methods for the numerical integration of Initial Value Problems in stiff Ordinary Differential Equations (ODEs) y'(t) = f (t, y) was recently introduced in [1]. The main idea was to make local extrapolation of a stabilized Euler method. More recently, in [3] a similar approach by considering the stabilization of arbitrary explicit Runge-Kutta methods (TASE-RK) was analyzed. In this case the explicit Runge-Kutta method integrates a transformed ODE obtained by multiplying the vector field f (t, y) by a certain operator which approximates the identity mapping up to a given order p. The main inconvenience of both approaches is that to reach order p the solution of p2 linear systems plus the evaluation of p derivatives are required per integration step.In order to substantially reduce the computational costs of the former approaches in the linear system solution, but maintaining the good accuracy and stability properties, a new family of TASE-RK methods which allow to introduce a few more free parameters are considered. The formulation of the methods was conceived to be implemented not only in sequential mode but it admits parallelism in a straightforward way. Furthermore, since these methods are linearly implicit, connections to the class of W-methods [19] are properly established. The order conditions for the new class of methods are widely studied by using the rooted tree theory. For p = 3, 4, new methods with p sequential stages and order p are derived and compared on semidiscrete 1D and 2D Partial Differential Equations (PDEs) to those in [1,3] and other standard Rosenbrock and W-methods in the literature.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by-nc -nd /4 .0/)
Human papillomavirus prevalence in postradiotherapy uterine cervical carcinoma patients: correlation with recurrence of the disease
No full textSingh RK, Maulik S, Mitra S, Mondal RK, Basu PS, Roychowdhury S, Panda CK. Human papillomavirus
prevalence in postradiotherapy uterine cervical carcinoma patients: correlation with recurrence of
the disease. Int J Gynecol Cancer 2006;16:1048–1054.
To understand the role of human papillomavirus (HPV) in recurrence of uterine cervical cancer (CA-CX)
after radiotherapy, we have analyzed the HPV prevalence in the exfoliated cells of 56 patients and their
corresponding plasma. HPV DNA was detected in exfoliated cells of 78% (44/56) patients (HPV-16, 68%;
HPV-18, 14%; HPV-X [other than 16, 18], 11%; and mixed infection of HPV-16 and HPV-18 in three cases).
HPV DNA in plasma was present in only 25% (11/44) of the HPV-positive exfoliated cells (positive predictive
value, 100%; negative predictive value, 27%) with concordance in HPV types. The recurrence of the
disease was significantly associated with the presence of HPV in the exfoliated cell (P ¼ 0.01) and plasma
(P ¼ 0.007) as well as high viral load in the exfoliated cell (P ¼ 0.0002). Kaplan–Meier disease-free estimates
have also shown the significant association between HPV prevalence in plasma and recurrence of the
disease (P ¼ 0.045). Thus, it indicates that in postradiotherapy CA-CX patients, the high viral load in the
exfoliated cell as well as HPV presence in the plasma samples could be used in early detection of the patients
at increased risk for disease recurrence and progressio
An assessment of factors affecting free radical formation in infants receiving parenteral nutrition
No full textThe development of parenteral nutrition has been a major advance in the care of neonates undergoing surgery. However, long-term parenteral nutrition can result in complications, some of which may result from an increased free radical activity associated with the lipid component of the regimen. This thesis describes studies undertaken to determine the effects of total parenteral nutrition (TPN) on free radical formation in neonatal surgical patients. The parenteral nutrition regimen was then modified in an attempt to reduce free radical formation. Lipid peroxides and malondialdehyde (MDA), some of the products of free radical formation, were assayed in parenteral nutrition solutions. The mean lipid peroxide concentration was 19.25umol/l and the mean MDA concentration was 8.69umol/l. Neonates receiving TPN had significantly greater MDA concentrations than those not receiving TPN (p<0.0001). Stopping the lipid infusion resulted in a significant decrease in the mean plasma MDA concentration (p<0.01). Promoting oxidation of the administered lipid by reducing the carbohydrate to lipid ratio of the TPN also resulted in significantly decreased plasma MDA concentrations (p<0.01). The administration of a medium chain triglyceride emulsion was, however, associated with significantly greater plasma MDA concentrations than when a long chain triglyceride emulsion was used (p<0.05). Partial enteral feeding during parenteral nutrition did not have any significant effect on free radical activity. A relationship between free radical activity and illness severity in sick neonates was sought. There was no significant correlation between plasma MDA concentrations and the Paediatric Risk of Mortality (PRISM) score. However MDA concentrations showed a positive correlation with plasma TNF-a (p<0.05) and IL-6 (p<0.001) concentrations
The morphological effects of sediment diversions the Lower Mississippi River
No full textThe wetlands in the Mississippi delta (USA) are drastically subsiding and eroding. Many projects and researches are ongoing to determine how this “drowning effect” of the delta can be stopped. One of the solutions that could be feasible is implementing sediment diversions in the levees of the Lower Mississippi River in order to divert sediment into the delta. This thesis addresses the morphological effects of river diversions on the Lower Mississippi River. The main objective is to analyze and optimize trade-offs between delta building and river navigability. For this purpose a 2DH numerical model with Delf3D has been created; the model simulates the hydro- and morphodynamic behavior. The river reach which has been studied is the final 110 km of the river from Point a la Hache at River Kilometer 78 (RK 78) down to the mouth of the river (RK -30), below Head of Passes. The hydrodynamic model has been calibrated and verified with flow and stage data from daily observations on the river. With the available sediment data a calibration has been carried out of the morphological behavior in the river. The model has been used to simulate several scenarios to get insight in the problems in the delta. From analysis of the model results the river bed in the study area can be divided into three categories. Upstream of RK 4 the bed is subject to erosion, around RK 4 the bed is practically in equilibrium and downstream of RK 4 the bed is subject to sedimentation. The reach downstream of RK 4 is the dredging reach; after analyzing the long-term simulation of 20 years it is not expected that the dredging quantities will decrease in the future. Closing off West Bay diversion has a positive effect on the dredging quantities. The best diversion site for this study area is found in the inner bend of the river upstream of Empire (RK 47) at RK 53. This site is most efficient and diverts the largest quantities of sand through the diversion.Hydraulic EngineeringCivil Engineering and Geoscience
The Dunston Manuscript
No full textVariously titled 80 Slides and a Memory, Fit for a King and others this is the definitive performed version as an invited reading in 2001 to the Urban Design Group. It describes in blank verse the early stages of the Gateshead Garden Festival illustrated with slide
Characterization of the traditional fermented fish product <i>Lona ilish </i>of Northeast India
No full text453-458Lona ilish is a traditional
salt fermented fish product widely consumed in Bangladesh and Northeast parts
of India. It is prepared exclusively from
Hilsa, Tenualosa ilisha (Ham-Buch, 1822), a high fat fish. Biochemical composition of
market sample of lona ilish has been studied. The moisture, salt
and pH of the product have been estimated as 54%, 15% and 5.66%,
respectively. The product is stable when remains immersed in brine at ambient
temperature. Lowering of water activity due to osmotic action of salt as well
as effect of salt on spoilage bacteria are presumed to be the reasons behind
this salt fermentation technique. High
peroxide value is the indicative of lipid peroxidation but, however, did not
impart any undesirable rancid taint to the product. The bacterial flora
comprised of Micrococcus and Bacillus species. Lack of scientific
study to standardize the methods, use of poor quality raw material fish,
improper salting, inadequate fermentation period as well as adulteration in the
process, etc. are some of the reasons for gradual deterioration of the quality
of lona ilish
Divide and conquer roadmap for algebraic sets
No full textAbstract. Let R be a real closed field, and D ⊂ R an ordered domain. We describe an algorithm that given as input a polynomial P ∈ D[X1,..., Xk], and a finite set, A = {p1,..., pm}, of points contained in V = Zer(P, Rk) described by real univariate representations, computes a roadmap of V containing A. The complexity of the algorithm, measured by the number of arithmeti
- …
