Behavior Of Function Research Articles

Robust maximum likelihood estimation of stochastic frontier models

When analysing the efficiency of decision-making units, the robustness of efficiency scores to changes in the data is desirable, especially in the context of managerial or regulatory benchmarking. However, the robustness of maximum likelihood estimation of stochastic frontier models remains underexplored. We examine the behaviour of the influence function of the estimator in a stochastic frontier context, and derive some sufficient conditions for robust maximum likelihood estimation in terms of the properties of the marginal distributions of the error components and, in cases where they are dependent, the copula density. We find that the canonical distributional assumptions do not satisfy these conditions. The Student’s t noise distribution is found to have some particularly attractive properties which means it can be paired with a broad class of inefficiency distributions while still satisfying our conditions under independence. We show that parameter estimates and efficiency predictions from robust specifications are significantly less sensitive to contaminating observations than those from non-robust specifications.

CFT description of BH’s and ECO’s: QNMs, superradiance, echoes and tidal responses

Using conformal field theory and localization tecniques we study the propagation of scalar waves in gravity backgrounds described by Schrödinger like equations with Fuchsian singularities. Exact formulae for the connection matrices relating the asymptotic behaviour of the wave functions near the singularities are obtained in terms of braiding and fusion rules of the CFT. The results are applied to the study of quasi normal modes, absorption cross sections, amplification factors, echoes and tidal responses of black holes (BH) and exotic compact objects (ECO) in four and five dimensions. In particular, we propose a definition of dynamical Love numbers in gravity.

Cosmological aspects of anisotropic chameleonic Brans–Dicke gravity

We study the cosmological implications of non-minimal coupling of a scalar field with matter sector in the Brans–Dicke gravity. In particular, in the context of locally rotationally symmetric Bianchi-I (LRS BI) metric, we derived the field equations and used these equations to find a relation between scale factor and scalar field. We use this relation to find two different solutions, namely an eternally accelerating universe and a transit universe. By the power-law solutions for scalar field and coupling function, we find the allowed range of exponents for an accelerating universe. We further explore the direction and magnitude of energy transfer between scalar field and matter sector. We show by using the second law of thermodynamics that the direction and magnitude of energy transfer are closely related to the behavior of coupling function. In the transit universe, we investigate the dependence of the effective equation of state parameter and the effective energy density on the anisotropy parameter. The model explains the late-time accelerating universe evolution.

Traversable wormholes in Rastall teleparallel gravity with non-commutative geometry

The current study explores new wormhole models with the framework of Rastall teleparallel theory. For this study, we are working with non-commutative geometry with Gaussian and Lorentzian distributions. The static and spherically symmetric spacetime is taken with the anisotropic source of fluid. Further, we compare the matter density with the Gaussian and Lorentzian distributions and get two different differential equations involving shape functions. The exact solution for the wormhole shape function is calculated for both distributions. The expression for energy conditions is provided. The graphical behavior of shape functions and energy conditions is presented for Rastall teleparallel theory under the current scenario. All the inquired results with necessary findings are concluded.

Region-based approximation in approximate dynamic programming

This paper introduces a region-based approximation method to solve optimal control problems with Approximate Dynamic Programming (ADP). The backbone of the proposed solution is partitioning the domain of training to smaller regions in which the value function varies slowly. Afterward, for each region, a Linear in Parameter Neural Network (LIPNN) is trained to capture the behaviour of the value function in that region. It is shown that the method improves the precision in value function approximation, which leads to improvement in the performance of the closed-loop system. Meanwhile, the possibility of expanding the domain of training in ADP solutions by region-based approximation is discussed. At last, it is shown how the method can potentially eliminate the need for trial & error to select a proper neural network in classical ADP solutions.

Optimal order execution under price impact: a hybrid model

In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamics of their aggregated inventory considering a proper scaling limit. The resulting price impact profile is shown to depend on the characteristics and relative importance of their inventories. The model is flexible enough to reproduce the empirically documented power law behavior of the price impact function. For any choice of the market makers characteristics, optimal execution within this modeling approach can be recast as a linear-quadratic stochastic control problem. The value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the performance of the resulting optimal liquidation strategy in relation to standard benchmarks. Remarkably, they show that the increase in performance is determined by a substantial reduction of higher order moment risk.

An induction principle for the Bombieri-Vinogradov theorem over [formula omitted] and a variant of the Titchmarsh divisor problem

Let Fq[t] be the polynomial ring over the finite field Fq. For arithmetic functions ψ1,ψ2:Fq[t]→C, we establish that if a Bombieri-Vinogradov type equidistribution result holds for ψ1 and ψ2, then it also holds for their Dirichlet convolution ψ1⁎ψ2. As an application of this, we resolve a version of the Titchmarsh divisor problem in Fq[t]. More precisely, we obtain an asymptotic for the average behaviour of the divisor function over shifted products of two primes in Fq[t].

Boundedness of composition operator on several variable Paley-Wiener space

In this paper we have considered composition operators on the several variable Paley-Wiener space Lπ2(Cn). We have proved that for any continuous function ϕ:Cn→Cn the composition operator Cϕ on Lπ2(Cn) is bounded iff ϕ has the following form:ϕ(z)=Az+b,z∈Cn, where A∈GL(n,R) with ||A||op≤1 and b∈Cn. Our proof is different from the single variable case and mainly depends on a theorem of Malgrange, some techniques from harmonic analysis and certain asymptotic behaviour of Bessel's function.

Dingle’s final main rule, Berry’s transition, and Howls’ conjecture *

The Stokes phenomenon is the apparent discontinuous change in the form of the asymptotic expansion of a function across certain rays in the complex plane, known as Stokes lines, as additional expansions, pre-factored by exponentially small terms, appear in its representation. It was first observed by G G Stokes while studying the asymptotic behaviour of the Airy function. R B Dingle proposed a set of rules for locating Stokes lines and continuing asymptotic expansions across them. Included among these rules is the ‘final main rule’ stating that half the discontinuity in form occurs on reaching the Stokes line, and half on leaving it the other side. M V Berry demonstrated that, if an asymptotic expansion is terminated just before its numerically least term, the transition between two different asymptotic forms across a Stokes line is effected smoothly and not discontinuously as in the conventional interpretation of the Stokes phenomenon. On a Stokes line, in accordance with Dingle’s final main rule, Berry’s law predicts a multiplier of for the emerging small exponentials. In this paper, we consider two closely related asymptotic expansions in which the multipliers of exponentially small contributions may no longer obey Dingle’s rule: their values can differ from on a Stokes line and can be non-zero only on the line itself. This unusual behaviour of the multipliers is a result of a sequence of higher-order Stokes phenomena. We show that these phenomena are rapid but smooth transitions in the remainder terms of a series of optimally truncated hyperasymptotic re-expansions. To this end, we verify a conjecture due to C J Howls.

Analysis of the Evolution of the Surface Density Function During Premixed V-Shaped Flame–Wall Interaction in a Turbulent Channel Flow at Reτ = 395

ABSTRACT The flame–turbulence interaction and statistical behavior of the surface density function (SDF; i.e. magnitude of the reaction progress variable gradient) in the vicinity of the wall for a stoichiometric methane-air flame are investigated using a three-dimensional direct numerical simulation of a turbulent premixed V-flame interacting with an isothermal inert wall in a fully developed turbulent channel flow at a friction Reynolds number . The results show that the mean SDF significantly decreases in the viscous sublayer in comparison to the corresponding values for the same reaction progress variable in the unstretched laminar flame. Moreover, the mean values of SDF for a given value of reaction progress variable decrease in the downstream direction with the progress of flame quenching in all zones of turbulent boundary layer. The effective normal strain rate (), which acts to reduce the SDF as it increases, is much higher in the viscous sublayer than in the other layers. In the viscous sublayer, the contribution of the gradient of displacement speed in the flame-normal direction () to has been shown to dominate the fluid-dynamic normal strain rate (). This tendency is qualitatively similar to the previous findings for a V-flame interacting with an isothermal inert wall at . However, the maximum mean value of at is approximately twice of that at , which causes a sharper drop in the SDF in the viscous sublayer at higher .

The association of health behaviors prior to cancer diagnosis and functional aging trajectories after diagnosis: Longitudinal cohort study of middle-aged and older US cancer survivors

We aimed to determine the influence of modifiable health behaviors prior to a cancer diagnosis on functional aging trajectories after diagnosis among middle-aged and older cancer survivors in the United States. Data were from biennial interviews with 2,717 survivors of a first incident cancer diagnosis after age 50 in the population-based US Health and Retirement Study from 1998 to 2016. Smoking status, alcohol use, and vigorous physical activity frequency were assessed at the interview prior to cancer diagnosis. Confounder-adjusted multinomial logistic regression was used to determine the associations between each pre-diagnosis health behavior and post-diagnosis trajectories of memory function and limitations to activities of daily living (ADLs), which were identified using group-based trajectory modeling. Overall, 20.7 % of cancer survivors were current smokers, 30.6 % drank alcohol, and 27.1 % engaged in vigorous physical activity >=once a week prior to their diagnosis. In the years following diagnosis, those who had engaged in vigorous physical activity > once a week were less likely to have a medium–high (OR: 0.5; 95 % CI: 0.2–0.9) or medium–low memory loss trajectories (OR: 0.6; 95 % CI: 0.3–1.0) versus very low memory loss trajectory, and were less likely to have a high, increasing ADL limitation trajectory (OR: 0.3; 95 % CI: 0.2, 0.6) versus no ADL limitation trajectory. Vigorous physical activity, but not smoking or alcohol use, was associated with better post-diagnosis functional aging trajectories after a first incident cancer diagnosis in mid-to-later life in this population-based study. Identification of modifiable risk factors can inform targeted interventions to promote healthy aging among cancer survivors.

Метод численного решения уравнений квантовой теории рассеяния для системы нескольких частиц

A methods of numerical solution of the Faddeev equations for the bound and scattering state problems are presented. To solve the Faddeev’s equations with corresponding boudary conditions the mrthod is used wich is a generalization of the cooon scheme of solution of Schrodinger equations. In this method a finit-difference approximation of equations in polar coordinates is used. By means of the net with knots on the arc and knots on the beam the finit-difference approximation of Faddeev’s equations is performed. The increase the calculation accurace and to provide an effetive operation of the corresponding software support the net knots must be located nonuiformly are disscased. The net must be dens in the regions adjacent to an axes x = 0, while at → ∞ becomes less dense. Such an arrangment of the net rnots is necessary for sufficienty accurate description of the complex behaviour of wave function in the region, where x ≪ y. In the region → ∞ the wave function takes asymptotical depends smoothly on angular variable, hence in this region the net must be chosen to be less dense. At calculations on the inhomogeneous net, in very important to comply with the condition of self-consistence, which implies that the error due to introducing the cut off radius must be far less than the quantizing error in the vicinty of boundary. The stability and self-consistence of the calculations may be check by various methods determinations of the net, the cut off radius and the scattering amplitude. This approach to the numerical solution of the Faddeev’ equations combines the advantages of integral equations (the solution existens and uniqieness) with the computational scheme simplicity. Also it has the advantage that unknow two-particle quantities are specified not T-matrices but potentials and eigenfunctions corresponding to the bound states. The simplicity of the computational algorithm allows to consider few-body problems in real systems. The results of calculations binding energies and scattering state of are presented.

Increasing Biomanufacturing Yield with Bleed–Feed: Optimal Policies and Insights

Problem definition: Bleed–feed is a novel technology that allows biomanufacturers to skip intermediary bioreactor setups. However, the specific time at which bleed–feed is performed is critical for success. The process is stringently regulated, and its implementation involves unique tradeoffs in operational decision making. Our analysis formalizes the operational challenges related to bleed–feed decisions, and our results inform biomanufacturers and policymakers on the potential impact of this technology on current practice. Academic/practical relevance: Operations management (OM) methodologies have not yet been widely adopted in the biomanufacturing industry. This research presents one of the first attempts to demonstrate how OM can complement biomanufacturing to improve operational decisions. We present a practically relevant problem and a rigorous solution approach that is relevant to both OM and biomanufacturing. Methodology: We develop a finite-horizon, discrete-time Markov decision processes model and analyze the structural characteristics of optimal bleed–feed policies. Moreover, we characterize the behavior of the value function as a function of regulatory restrictions. As a salient feature, the MDP model captures both the biological dynamics of fermentation and the operational tradeoffs in biomanufacturing. Results: We show that optimal bleed–feed policies have a three-way control-limit structure under mild conditions that were validated with industry data. Moreover, our analysis reveals that the marginal benefits of bleed–feed diminish as additional bleed–feeds are performed. As a practically relevant benchmark, we consider a risk-averse heuristic and identify sufficient conditions for its optimality. Managerial implications: Our analysis (supported with an industry case study) shows that bleed–feed implementation can provide benefits. Real-world implementation at MSD resulted in an 82.5% improvement in the batch yield per setup (using one bleed–feed). We find that low-risk fermentation systems benefit the most from bleed–feed implementation. We also find that the performance gap between optimal policies and the risk-averse heuristic is higher when the failure risks or the critical biomass levels are lower. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek, NWO-VENI scheme. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2022.1163 .

Finite-temperature dynamics in gapped one-dimensional models in the sine-Gordon family

The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, nonintegrable systems belonging to the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on timescales where the effect of nontrivial quasiparticle scatterings becomes relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling nonuniformly in time.

Casimir traversable wormholes for GUP corrected energy densities in f (T) gravity

Traversable wormholes are always supported by negative energy and therefore an exotic matter source is required for their principle existence. In this work, we consider Casimir energy density as an exotic matter source in the framework of f (T) gravity. In this way, we examine the behavior of shape function, equation of state parameters, energy conditions and stability conditions for wormhole geometry in teleparallel and f (T) gravity. We also assume three different generalized uncertainty principle corrected Casimir wormhole models. We analyze the effect of the generalized uncertainty principle minimal parameter on the constructed wormhole properties in f (T) gravity.

A deductible comparison of cost per-loss, cost per-payment event, loss elimination ratio under exponentially and lognormally distributed severities

The maximum amount of losses retained by the insured under deductible policy modifications is usually set as part of the terms of the policy conditions. The objective of this study are to (i) estimate mean losses of an insured risk by means of the operational behavior of density function with deductible modifications and (ii) compare the mean severities under exponentially and log-normally distributed arbitrary policy in a cost per loss and cost per payment contingencies. The results show that despite the established fact in literature that log-normal severity distribution has a thicker tail than the exponential distribution, its cost per loss payment is correspondingly lower than the corresponding values of the exponential mean loss. Computational evidence over the trend of the change in the loss eliminated in the domain for which deductible has been defined revealed that the cost per loss amount is less than the cost per payment amount in the two models. The method can be used to estimate aggregate claims as the deductible level increases for every scheme holder and such that the estimated claims could be compared with the hypothetical observed claims which can be arrived at by applying the hypothetical deductible value to the background losses.

The emerging world of digital exploration services

This research draws on two global surveys of customers of IT services to identify an emerging IT space we call “Digital Exploration” services. In contrast with Traditional IT services and cloud-based Digital Exploitation services, Digital Exploration services involve conceiving and implementing new business strategies and processes using new digital technologies (e.g., blockchain, augmented reality, deep learning, IoT). In a follow-on study involving depth interviews with IT customers, the research identifies several factors critical to successful Digital Exploration. These include customer selectivity, close collaboration between IT providers and customers, strategic and systemic thinking, an open innovation approach, and use of performance directionality (versus precise KPIs). In addition, the depth interviews help identify specific changes needed in the mindsets and behaviors of business unit leaders and various functions in IT providers and customers for the promise of Digital Exploration services to be realized.

Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics

In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a result, the BIE is found for a thermodiffusion problem of binary melt crystallization with convection. Analyzing this equation coupled with the selection criterion for a stationary dendritic growth in the form of a parabolic cylinder, we show that nonlinear effects stemming from the liquidus equation and atomic kinetics play a decisive role. Namely, the dendrite tip velocity and diameter, respectively, become greater and lower with the increasing deviation of the liquidus equation from a linear form. In addition, the dendrite tip velocity can substantially change with variations in the power exponent of the atomic kinetics. In general, the theory under consideration describes the evolution of a curvilinear crystallization front, as well as the growth of solid phase perturbations and patterns in undercooled binary melts at local equilibrium conditions (for low and moderate Péclet numbers). In addition, our theory, combined with the unsteady selection criterion, determines the non-stationary growth rate of dendritic crystals and the diameter of their vertices.

A New Interval Type-2 Fuzzy Aggregation Approach for Combining Multiple Neural Networks in Clustering and Prediction of Time Series

Inspired by how some cognitive abilities affect the human decision-making process, the proposed approach combines neural networks with type-2 fuzzy systems. The proposal consists of combining computational models of artificial neural networks and fuzzy systems to perform clustering and prediction of time series corresponding to the population, urban population, particulate matter (PM2.5), carbon dioxide (CO2), registered cases and deaths from COVID-19 for certain countries. The objective is to associate these variables by country based on the identification of similarities in the historical information for each variable. The hybrid approach consists of computationally simulating the behavior of cognitive functions in the human brain in the decision-making process by using different types of neural models and interval type-2 fuzzy logic for combining their outputs. Simulation results show the advantages of the proposed approach, because starting from an input data set, the artificial neural networks are responsible for clustering and predicting values of multiple time series, and later a set of fuzzy inference systems perform the integration of these results, which the user can then utilize as a support tool for decision-making with uncertainty.

Asymptotic Behavior of a Function of a Complex Variable With a Parameter and Zeros

The study of the asymptotic behavior of solutions of singularly perturbed equations in complex domains reduces to the study of integrals of exponential functions of a complex variable with a parameter. The problem is to study the asymptotic behavior of such functions. The functions in the exponent have zeros. The study of such functions is hampered by the fact that it is necessary to select a certain part from a given region and choose integration paths that ensure the boundedness of the considered functions with respect to a small parameter. The saddle point method is not applicable to such integrals. To solve the problem, the level lines of harmonic functions generated by analytic functions are applied. The level lines divide the area in the complex plane into parts. Integration paths are chosen that ensure boundedness of integrals with respect to a small parameter. Boundary-layer lines, areas where the integrals have no limit with respect to a small parameter, but are limited with respect to the modulus, are revealed; regular domains (integrals have a limit); singular regions (integrals are not limited). All constructions are accompanied by corresponding drawings. In the future, the results of this paper can be used for the theory of singularly perturbed equations in a complex domain.