Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.      

An algebraic index theorem for orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

Four‐dimensional couplings among BF and matter theories from BRST cohomology

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a “free” model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.     

A Characterization of the Optimal p-sum Labellingsof Unit Interval Graphs

1.IntroductionGraphsconsideredinthispaperarefiniteandsimple.FOragraphG,V(G)andE(G)denoteitssetofvenicesandedges,respectively.AbijectionwillbecalledalabellingofG.Letpbeapositiverealnumber.ForagivenlabellingTofagraphG,definethegndiscrepencya.(G,ac)ofTasTheobjectiveoftheminimum-p--sumproblemistofindalabelling7ofagraphGsuchthatac(G,T)isassmallaspossible.ThelabellingTminimizinga.(G,7)iscalledanoptimalHsumlabellingofG.Theminimumvalueiscalledtheminimum-psumofG.ItisshowninI31thattheminimum-…     

Hopf Modules and Noncommutative Differential Geometry

We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one-to-one correspondence between anti-Yetter–Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, and modules which admit a flat connection with respect to our differential calculus. Thus, we show that these coefficient modules can be regarded as “flat bundles” in the sense of Connes’ noncommutative differential geometry.     

Cohomology operations and the deligne conjecture

The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

Mixed micellization of an anionic gemini surfactant (GA) with conventional polyethoxylated nonionic surfactants in brine solution at pH 5 and 298 K

The micellization behavior of an anionic gemini surfactant, GA with nonionic surfactants C₁₂E₈ and C₁₂E₅ in presence of 0.1 M NaCl at 298 K temperature, has been studied tensiometrically in pure and mixed states, and the related physicochemical parameters (cmc, γ _cmc, pC ₂₀, Γ _max, and A _min) have been evaluated. Tensiometric profile (γ vs log [surfactant]), for conventional surfactants, generally consists of a single point of intersection; a gradually decreasing line (normally linear, or with slight curvature) ultimately saturates in γ at a particular [surfactant], corresponding to complete monolayer saturation. The gemini, in this report, led to two unequivocal breaks in the tensiometric isotherm. An attempt to the interpretation of the two breaks from molecular point of view is provided, depending solely on the chemical structure of the surfactant. The gemini, even in mixed state with the conventional nonionic surfactants C₁₂E₅ and C₁₂E₈, manifested the dual breaks; of course, the dominance of the feature decreases with increasing mole fraction of the nonionics in the mixture. Theories of Clint, Rosen, Rubingh, Motomura, Georgiev, Maeda, and Nagarajan have been used to determine the interaction between surfactants at the interface and micellar state of aggregation, the composition of the aggregates, the theoretical cmc in pure and mixed states, and the structural parameters according to Tanford and Israelachvili. Several thermodynamic parameters have also been predicted from those theories.     

用二维色谱技术测定聚合反应气体组成

介绍一种无阀切换的二维气相色谱分析方法。采用两根不同性质的色谱柱并联连接，样品分别经两根色谱柱分离后汇合在一起进入同一检测器。一次进样可同时测定Ｈ２、Ｏ２、Ｎ２及Ｃ１～Ｃ３的组分。