Simultaneous perturbation methods for adaptive labor staffing in service systems

We consider the problem of optimizing the workforce of a service system. Adapting the staffing levels in such systems is non-trivial due to large variations in workload and the large number of system parameters do not allow for a brute force search. Further, because these parameters change on a weekly basis, the optimization should not take longer than a few hours. Our aim is to find the optimum staffing levels from a discrete high-dimensional parameter set, that minimizes the long run average of the single-stage cost function, while adhering to the constraints relating to queue stability and service-level agreement (SLA) compliance. The single-stage cost function balances the conflicting objectives of utilizing workers better and attaining the target SLAs. We formulate this problem as a constrained parameterized Markov cost process parameterized by the (discrete) staffing levels. We propose novel simultaneous perturbation stochastic approximation (SPSA)-based algorithms for solving the above problem. The algorithms include both first-order as well as second-order methods and incorporate SPSA-based gradient/Hessian estimates for primal descent, while performing dual ascent for the Lagrange multipliers. Both algorithms are online and update the staffing levels in an incremental fashion. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter tuned by our algorithms onto the discrete set. The smoothness is necessary to ensure that the underlying transition dynamics of the constrained Markov cost process is itself smooth (as a function of the continuous-valued parameter): a critical requirement to prove the convergence of both algorithms. We validate our algorithms via performance simulations based on data from five real-life service systems. For the sake of comparison, we also implement a scatter search based algorithm using state-of-the-art optimization tool-kit OptQuest. From the experiments, we observe that both our algorithms converge empirically and consistently outperform OptQuest in most of the settings considered. This finding coupled with the computational advantage of our algorithms make them amenable for adaptive labor staffing in real-life service systems.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell

In this paper, a suitable nondimensional `orthotropy parameter' is defined and asymptotic expansions are found for the wavenumbers in in vacuo and fluid-filled orthotropic circular cylindrical shells modeled by the Donnell-Mushtari theory. Here, the elastic moduli in the two directions are greatly different; the particular case of E-x >> E-theta is studied in detail, i.e., the elastic modulus in the longitudinal direction is much larger than the elastic modulus in the circumferential direction. These results are compared with the corresponding results for a `slightly orthotropic' shell (E-x approximate to E-theta) and an isotropic shell. The novelty of this presentation lies in obtaining closed-form expansions for the in vacuo and coupled wavenumbers in an orthotropic shell using perturbation methods aiding in a better physical understanding of the problem.

Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Angelica archengelica extract induced perturbation of rat skin and tight junctional protein (ZO-1) of HaCaT cells

Background and purpose of the study: Herbal enhancers compared to the synthetic ones have shown less toxis effects. Coumarins have been shown at concentrations inhibiting phospoliphase C-Y (Phc-Y) are able to enhance tight junction (TJ) permeability due to hyperpoalation of Zonolous Occludense-1 (ZO-1) proteins. The purpose of this study was to evaluate the influence of ethanolic extract of Angelica archengelica (AA-E) which contain coumarin on permeation of repaglinide across rat epidermis and on the tight junction plaque protein ZO-1 in HaCaT cells. Methods: Transepidermal water loss (TEWL) from the rat skin treated with different concentrations of AA-E was assessed by Tewameter. Scanning and Transmission Electron Microscopy (TEM) on were performed on AA-E treated rat skin portions. The possibility of AA-E influence on the architecture of tight junctions by adverse effect on the cytoplasmic ZO-1 in HaCaT cells was investigated. Finally, the systemic delivery of repaglinide from the optimized transdermal formulation was investigated in rats. Results: The permeation of repaglinide across excised rat epidermis was 7-fold higher in the presence of AA-E (5% w/v) as compared to propylene glycol:ethanol (7:3) mixture. The extract was found to perturb the lipid microconstituents in both excised and viable rat skin, although, the effect was less intense in the later. The enhanced permeation of repaglinide across rat epidermis excised after treatment with AA-E (5% w/v) for different periods was in concordance with the high TEWL values of similarly treated viable rat skin. Further, the observed increase in intercellular space, disordering of lipid structure and corneocyte detachment indicated considerable effect on the ultrastructure of rat epidermis. Treatment of HaCaT cell line with AA-E (0.16% w/v) for 6 hrs influenced ZO-1 as evidenced by reduced immunofluorescence of anti-TJP1 (ZO-1) antibody in Confocal Laser Scanning Microscopy studies (CLSM) studies. The plasma concentration of repaglinide from transdermal formulation was maintained higher and for longer time as compared to oral administration of repaglinide. Major conclusion: Results suggest the overwhelming influence of Angelica archengelica in enhancing the percutaneous permeation of repaglinide to be mediated through perturbation of skin lipids and tight junction protein (ZO-1).

SPSA Based Feature Relevance Estimation For Video Retrieval

With the availability of a huge amount of video data on various sources, efficient video retrieval tools are increasingly in demand. Video being a multi-modal data, the perceptions of ``relevance'' between the user provided query video (in case of Query-By-Example type of video search) and retrieved video clips are subjective in nature. We present an efficient video retrieval method that takes user's feedback on the relevance of retrieved videos and iteratively reformulates the input query feature vectors (QFV) for improved video retrieval. The QFV reformulation is done by a simple, but powerful feature weight optimization method based on Simultaneous Perturbation Stochastic Approximation (SPSA) technique. A video retrieval system with video indexing, searching and relevance feedback (RF) phases is built for demonstrating the performance of the proposed method. The query and database videos are indexed using the conventional video features like color, texture, etc. However, we use the comprehensive and novel methods of feature representations, and a spatio-temporal distance measure to retrieve the top M videos that are similar to the query. In feedback phase, the user activated iterative on the previously retrieved videos is used to reformulate the QFV weights (measure of importance) that reflect the user's preference, automatically. It is our observation that a few iterations of such feedback are generally sufficient for retrieving the desired video clips. The novel application of SPSA based RF for user-oriented feature weights optimization makes the proposed method to be distinct from the existing ones. The experimental results show that the proposed RF based video retrieval exhibit good performance.

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples.

A comparative Raman study of the interaction of electron donor and acceptor molecules with graphene prepared by different methods

Interaction of tetrathiafulvalene (TTF) and tetracyanoethylene (TCNE) with few-layer graphene samples prepared by the exfoliation of graphite oxide (EG), conversion of nanodiamond (DG) and arc-evaporation of graphite in hydrogen (HG) has been investigated by Raman spectroscopy to understand the role of the graphene surface. The position and full-width at half maximum of the Raman G-band are affected on interaction with TTF and TCNE and the effect is highest with EG and least with HG. The effect of TTF and TCNE on the 2D-band is also maximum with EG. The magnitude of interaction between the donor/acceptor molecules varies in the same order as the surface areas of the graphenes. (C) 2009 Published by Elsevier B. V.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

A comparison of the molecular orbital (ab initio, CNDO and EHT) methods applied to the conformational study of thiocarbonohydrazide in its basic and diprotonated forms

Conformational preferences of thiocarbonohydrazide (H2NNHCSNHNH2) in its basic and N,N′-diprotonated forms are examined by calculating the barrier to internal rotation around the C---N bonds, using the theoretical LCAO—MO (ab initio and semiempirical CNDO and EHT) methods. The calculated and experimental results are compared with each other and also with values for N,N′-dimethylthiourea which is isoelectronic with thiocarbonohydrazide. The suitability of these methods for studying rotational isomerism seems suspect when lone pair interactions are present.

Some Methods for Summarizing Survivorship Data in Nonstandard Situations

One difficulty in summarising biological survivorship data is that the hazard rates are often neither constant nor increasing with time or decreasing with time in the entire life span. The promising Weibull model does not work here. The paper demonstrates how bath tub shaped quadratic models may be used in such a case. Further, sometimes due to a paucity of data actual lifetimes are not as certainable. It is shown how a concept from queuing theory namely first in first out (FIFO) can be profitably used here. Another nonstandard situation considered is one in which lifespan of the individual entity is too long compared to duration of the experiment. This situation is dealt with, by using ancilliary information. In each case the methodology is illustrated with numerical examples.