A Computationally Motivated Definition Of Parametric Estimation And Its Applications To The Gaussian Distribution

We introduce a treatment of parametric estimation in which optimality of an estimator is measured in probability rather than in variance (the measure for which the strongest general results are known in statistics). Our motivation is that the quality of an approximation algorithm is measured by the probability that it fails to approximate the desired quantity within a set tolerance. We concentrate on the Gaussian distribution and show that the sample mean is the unique “best” estimator, in probability, for the mean of a Gaussian distribution. We also extend this method to general penalty functions and to multidimensional spherically symmetric Gaussians. The algorithmic significance of studying the Gaussian distribution is established by showing that determining the average matching size in a graph is #P-hard, and moreover approximating it reduces to estimating the mean of a random variable that (under some mild conditions) has a distribution closely approximating a Gaussian. This random variable is (essentially) polynomial time samplable, thereby yielding an FPRAS for the problem.     

Kinetic models of natural gas combustion in an internal combustion engine

In this study, combustion of methane was simulated using four kinetic models of methane in CHEMKIN 4.1.1 for 0-D closed internal combustion (IC) engine reactor. Two detailed (GRIMECH3.0 & UBC MECH2.0) and two reduced (One step & Four steps) models were examined for various IC engine designs. The detailed models (GRIMECH3.0, & UBC MECH2.0) and 4-step models successfully predicted the combustion while global model was unable to predict any combustion reaction. This study illustrated that the detailed model sh...     

Deformations of permutation representations of Coxeter groups

The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat order and a flat deformation over ?[q] to a representation of the corresponding Hecke algebra. In this paper we define a larger class of “quasiparabolic” subgroups (more generally, quasiparabolic W-sets), and show that they also inherit these properties. Our motivating example is the action of the symmetric group on fixed-point-free involutions by conjugation.     

A polyhedron with alls—t cuts as vertices,and adjacency of cuts

Consider the polyhedron represented by the dual of the LP formulation of the maximums–t flow problem. It is well known that the vertices of this polyhedron are integral, and can be viewed ass–t cuts in the given graph. In this paper we show that not alls–t cuts appear as vertices, and we give a characterization. We also characterize pairs of cuts that form edges of this polyhedron. Finally, we show a set of inequalities such that the corresponding polyhedron has as its vertices alls–t cuts.Work done at the Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, India.     

Photoinduced electron transfer between triplet erythrosin dianion and highly charged ionic quenchers

Abstract  

The lifetime of the lowest triplet state of the dianion erythrosin B depends on its concentration because of self-quenching. The self-quenching rate constants vary with the solution viscosity at room temperature. Dextrose was used to change the viscosity of aqueous solutions in the range 1 ≤ η ≤ 5.31 cP. Photoinduced electron transfer reactions between the triplet state of the erythrosin dianion and the highly charged ionic quenchers K₄[Fe(CN)₆] and K₄[Mo(CN)₈] were investigated in aqueous borate buffer solutions at pH 9.2 using flash photolysis. Electron transfer rates vary from 3.0 × 10⁸ to 1.4 × 10⁸ M⁻¹ s⁻¹ depending on viscosity.     

New geometry-inspired relaxations and algorithms for the metric Steiner tree problem

Determining the integrality gap of the bidirected cut relaxation for the metric Steiner tree problem, and exploiting it algorithmically, is a long-standing open problem. We use geometry to define an LP whose dual is equivalent to this relaxation. This opens up the possibility of using the primal-dual schema in a geometric setting for designing an algorithm for this problem. Using this approach, we obtain a 4/3 factor algorithm and integrality gap bound for the case of quasi-bipartite graphs; the previous best integrality gap upper bound being 3/2 (Rajagopalan and Vazirani in On the bidirected cut relaxation for the metric Steiner tree problem, 1999). We also obtain a factor \({\sqrt{2}}\) strongly polynomial algorithm for this class of graphs. A key difficulty experienced by researchers in working with the bidirected cut relaxation was that any reasonable dual growth procedure produces extremely unwieldy dual solutions. A new algorithmic idea helps finesse this difficulty—that of reducing the cost of certain edges and constructing the dual in this altered instance—and this idea can be extracted into a new technique for running the primal-dual schema in the setting of approximation algorithms.     

Absorption and Fluorescence Emission Attributes of a Fluorescent dye: 2,3,5,6-Tetracyano-p-Hydroquinone

Four cyano groups have been substituted on the aromatic ring of p-hydroquinone (2,3,5,6-tetracyanohydroquinone) in order to study the enhanced photoacidity of this molecule. The acid-base equilibria have been studied using absorption (for ground state pK_a) and fluorescence (excited state pK_a) spectra. Three distinct species (neutral, anionic and dianionic forms) were observed in the ground state and only two species (anionic and dianionic forms) were found in the excited state when studied at different pH/H_o in water. Absorption and emission characteristics were studied in various organic solvents, including protic and aprotic solvents. Deprotonation was also investigated using binary mixtures. It has been revealed that absorption and emission spectra are considerably changed with change in media. Proton transfer to the solvent has been observed in various solvents.     

Counting Shi Regions with a Fixed Separating Wall

Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin.     

Posted price profit maximization for multicast by approximating fixed points

We describe an iterative fixed point approach for the following stochastic optimization problem: given a multicast tree and probability distributions of user utilities, find an optimal posted price mechanism—i.e., compute prices to offer the users in order to maximize the expected profit of the service provider. We show that any optimum pricing is a fixed point of an efficiently computable function. We can then apply the non-linear Jacobi and Gauss–Seidel methods of coordinate descent. We provide proof of convergence to the optimum prices for special cases of utility distributions and tree edge costs.     

Radiosynthesis and Biodistribution of <Superscript>99m</Superscript>Tc-Metronidazole as an <Emphasis Type="Italic">Escherichia coli</Emphasis> Infection Imaging Radiopharmaceutical

Bacterial infection poses life-threatening challenge to humanity and stimulates to the researchers for developing better diagnostic and therapeutic agents complying with existing theranostic techniques. Nuclear medicine technique helps to visualize hard-to-diagnose deep-seated bacterial infections using radionuclide-labeled tracer agents. Metronidazole is an antiprotozoal antibiotic that serves as a preeminent anaerobic chemotherapeutic agent. The aim of this study was to develop technetium-99m-labeled metronidazole radiotracer for the detection of deep-seated bacterial infections. Radiosynthesis of ^99mTc-metronidazole was carried by reacting reduced technetium-99m and metronidazole at neutral pH for 30 min. The stannous chloride dihydrate was used as the reducing agent. At optimum radiolabeling conditions, ~ 94% radiochemical was obtained. Quality control analysis was carried out with a chromatographic paper and instant thin-layer chromatographic analysis. The biodistribution study of radiochemical was performed using Escherichia coli bacterial infection-induced rat model. The scintigraphic study was performed using E. coli bacterial infection-induced rabbit model. The results showed promising accumulation at the site of infection and its rapid clearance from the body. The tracer showed target-to-non-target ratio 5.57 ± 0.04 at 1 h post-injection. The results showed that ^99mTc-MNZ has promising potential to accumulate at E. coli bacterial infection that can be used for E. coli infection imaging.