Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Stochastic discount factor bounds and rare events: a review

We aim to provide a review of the stochastic discount factor bounds usually applied to diagnose asset pricing models. In particular, we mainly discuss the bounds used to analyze the disaster model of Barro (2006). Our attention is focused in this disaster model since the stochastic discount factor bounds that are applied to study the performance of disaster models usually consider the approach of Barro (2006). We first present the entropy bounds that provide a diagnosis of the analyzed disaster model which are the methods of Almeida and Garcia (2012, 2016); Ghosh et al. (2016). Then, we discuss how their results according to the disaster model are related to each other and also present the findings of other methodologies that are similar to these bounds but provide different evidence about the performance of the framework developed by Barro (2006).

Effect of cooling rate on properties of plasma nitrided AISI 1010 steel

In this work, AISI 1010 steel samples were plasma nitrided into 20% N 2 100 Pa and 400 Pa for N 2 and H 2 , respectively), temperatures of 500 and 580 °C, during 2 h. Three different procedures for cooling were accomplished after nitriding. In the first procedure the cooling occurred naturally, that is, the sample was kept on substrate holder. In the second one the sample was pulled off and cooling in a cold surface. Finally, in the third cooling process the sample was pulled off the substrate holder down into special reservoir filled with oil held at ambient temperature. The properties of the AISI 1010 steel samples were characterized by optical and electron microscopy, X-ray diffraction, Mössbauer spectroscopy and microhardness tests. Thermal gradient inside the sample kept on substrate holder during cooling process was measured by three inserted thermocouples at different depths. When samples were cooled rapidly the transformation of ϵ-Fe 2 − 3 N to γ′-Fe 4 N was inhibited. Such effect is indicated by the high concentration of ϵ-Fe compound zone. To get solid state solution of nitrogen in the diffusion zone, instead of precipitates of nitride phases, the cooling rate should be higher than a critical value of about 0.95 °C/s. When this value is reached at any depth of the diffusion zone, two distinct diffusion zones will appear. Temperature gradients were measured inside the samples as a consequence of the plasma treatment. It's suggested the need for standardization of the term “treatment temperature” for plasma treatment because different nitrided layer properties could be reported for the same “treatment temperature”.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stochastic modelling considering ionospheric scintillation effects on GNSS relative and point positioning

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Improving the GNSS positioning stochastic model in the presence of ionospheric scintillation

Ionospheric scintillations are caused by time-varying electron density irregularities in the ionosphere, occurring more often at equatorial and high latitudes. This paper focuses exclusively on experiments undertaken in Europe, at geographic latitudes between similar to 50 degrees N and similar to 80 degrees N, where a network of GPS receivers capable of monitoring Total Electron Content and ionospheric scintillation parameters was deployed. The widely used ionospheric scintillation indices S4 and sigma(phi) represent a practical measure of the intensity of amplitude and phase scintillation affecting GNSS receivers. However, they do not provide sufficient information regarding the actual tracking errors that degrade GNSS receiver performance. Suitable receiver tracking models, sensitive to ionospheric scintillation, allow the computation of the variance of the output error of the receiver PLL (Phase Locked Loop) and DLL (Delay Locked Loop), which expresses the quality of the range measurements used by the receiver to calculate user position. The ability of such models of incorporating phase and amplitude scintillation effects into the variance of these tracking errors underpins our proposed method of applying relative weights to measurements from different satellites. That gives the least squares stochastic model used for position computation a more realistic representation, vis-a-vis the otherwise 'equal weights' model. For pseudorange processing, relative weights were computed, so that a 'scintillation-mitigated' solution could be performed and compared to the (non-mitigated) 'equal weights' solution. An improvement between 17 and 38% in height accuracy was achieved when an epoch by epoch differential solution was computed over baselines ranging from 1 to 750 km. The method was then compared with alternative approaches that can be used to improve the least squares stochastic model such as weighting according to satellite elevation angle and by the inverse of the square of the standard deviation of the code/carrier divergence (sigma CCDiv). The influence of multipath effects on the proposed mitigation approach is also discussed. With the use of high rate scintillation data in addition to the scintillation indices a carrier phase based mitigated solution was also implemented and compared with the conventional solution. During a period of occurrence of high phase scintillation it was observed that problems related to ambiguity resolution can be reduced by the use of the proposed mitigated solution.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Studies on the cooling minimum quantity and conventional cooling at hardened steels in grinding process

The purpose of this work is to explain the concept of cutting fluids reasonable usage through the fluid minimum quantity in grinding processes. on that purpose, the development of a new nozzle and an own and adequate methodology should be required in order to obtain good results and compare them to the conventional methods. The analysis of the grinding wheel/cutting fluid performance was accomplished from the following input parameters: flow rate variation by nozzle diameter changes (three diameters values: 3mm, 4mm and 5mm), besides the conventional round nozzle already within the machine. Integral oil and a synthetic emulsion were used as cutting fluids and a conventional grinding wheel was employed. The workpieces were made of steel VC 131, tempered and quenched with 60HRc. Thus, as the flow rate and the nozzle diameter changes, keeping steady fluid jet velocity (equal to cutting velocity), attempted to find the best machining conditions, with the purpose to obtain a decrease on the cutting fluid volume, taking into consideration the analysis of the process output variables such as cutting strength, cutting specific energy, grinding wheel wear and surface roughness. It was verified that the 3mm diameter optimized nozzle and the integral oil, in general, was the best combination among all proposed.

Analysis of the Influence of Sparkout Time on Grinding Using Several Lubrication/Cooling Methods

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A sustainable alternative for cooling the machining processes using a refrigerant fluid in recirculation inside the toolholder

This article presents a cooling system for cutting tool in turning based in a toolholder with cooling fluid flowing inside its body being that this fluid must necessarily be able to phase change due to heat generated from machining processes. In this way, the fluid evaporates just under the cutting tool allowing a heat transfer more efficient than if were used a fluid without phase change once the latent heat of evaporation is beneficial for removal heat. Following, the cooling fluid evaporated passes through a condenser located out of the toolholder where it is condensated and returns to the toolholder again and a new cycle is started. In this study, the R-123, a hydrochlorofluorocarbon (HCFC) fluid, was selected for the turning of a Cr-Ni-Nb-Mn-N austenitic steel of hard machinability. The machining tests were carried out under three different machining conditions: dry machining, external cutting fluid (conventional method), and with the toolholder proposed. As result, the developed system allows a surface roughness up to 10% better than dry machining and a tool life close to the conventional method, but 32% superior to dry machining; moreover, there are environmental and economics advantages once the cooling fluid is maintained in a loop circuit.

Superconductors of the BPSCCO system obtained from rapid cooling process

Bi-based (BPSCCO) superconductors have been extensively studied due to their interesting superconducting properties, especially those that present high transition temperature (T-c). In this work, superconductors of the BPSCCO system were prepared from rapid cooling process and studied under its structural and magnetic properties. Sample as-prepared shows an amorphous behavior, which is converted progressively into 2223 phase. This process permits the control of Pb or Bi loss and the crystallization of the desired phase using several heat annealing processes. The 2201 and 2212 phases were also observed as intermediate phases, before the crystallization of the 2223 phase. The superconductor obtained in this work presented a T-c around 77-K. (C) 2005 Springer Science + Business Media, Inc.

Cold Renal Ischemia: Comparison of Efficacy Between Two Techniques of Cooling, in a Swine Model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)