Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs---in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification.Comment: 42 pages, 10 figure

Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework

We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the complementarity measure and a nonlinear programming with general constraints. A strategy generalizing ideas of Byrd-Omojokun's trust region method is used to compute steps. By penalizing the tangential constraints into the objective function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like strategy is used to balance the improvements on feasibility and optimality. We show that, under MPEC-MFCQ, if the algorithm does not terminate in finite steps, then at least one accumulation point of the iterates sequence is an S-stationary point

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

A 3D cell death assay to quantitatively determine ferroptosis in spheroids

The failure of drug efficacy in clinical trials remains a big issue in cancer research. This is largely due to the limitations of two-dimensional (2D) cell cultures, the most used tool in drug screening. Nowadays, three-dimensional (3D) cultures, including spheroids, are acknowledged to be a better model of the in vivo environment, but detailed cell death assays for 3D cultures (including those for ferroptosis) are scarce. In this work, we show that a new cell death analysis method, named 3D Cell Death Assay (3DELTA), can efficiently determine different cell death types including ferroptosis and quantitatively assess cell death in tumour spheroids. Our method uses Sytox dyes as a cell death marker and Triton X-100, which efficiently permeabilizes all cells in spheroids, was used to establish 100% cell death. After optimization of Sytox concentration, Triton X-100 concentration and timing, we showed that the 3DELTA method was able to detect signals from all cells without the need to disaggregate spheroids. Moreover, in this work we demonstrated that 2D experiments cannot be extrapolated to 3D cultures as 3D cultures are less sensitive to cell death induction. In conclusion, 3DELTA is a more cost-effective way to identify and measure cell death type in 3D cultures, including spheroids.</jats:p

Design of Electrophoresis Device for Optimation of Dna Visualization and Dna Concentration Using Software

Molecules of deoxyribo nucleic acid (DNA) show a strong polarization allowing for both motions of the dielectrophoresis induced by polarization and electrophoresis based on its negative charge. Considering high subjective and less quantifiable result of the visualization based qualitative test of DNA on gel electrophoresis, designing the tool using a combination of the principles of electrophoresis and dielectrophoresis completed with a software for optimization of DNA visualization and to measure the concentration of small and large–sized DNA fragment is very needed. Accuracy of measurement of DNA concentration using a spectrophotometer UV /VIS is depend on its availability in the laboratory. The aim of this study was to design device for optimization of DNA visualization and measuring the concentration in the gel electrophoresis using MatLab- based software. Experiment using this software measured the concentration of DNA based on its visualization and compared it with calculation obtained from spectrophotometer UV/VIS. The research results showed that the amount of DNA analysed using a spectrophotometer tend to similar with the measurement results using the MatLab-based software although there was differences in quantitative values

Optimal design of piezoelectric vibration devices with constrained variable algorithm and FEA

Optimal design of piezoelectric vibration devices used in medical fields is a typical inequality constrained optimization problem. Constrained variable method, as the best algorithm to solve nonlinear constraint optimization problem is used in the optimal design of the piezoelectric devices. The object functions and constrain functions are automatically calculated with Finite Element Analysis software ANSYS, and the results will return to the main optimization program. Results show that compared with the given initial parameters, the vibration amplitude of the optimum piezoelectric vibration device is dramatically increased under the constraint that the stress concentration of the cutting tool is within limit. Experiments are also performed to measure the vibration amplitude. Results are in great agreement with the theoretical one

Estimating Pure Diffusion Contributions in Alkaline Pulping Processes

A model that predicts isothermal alkali diffusion and reaction with acetyl groups in moist wood chips was derived and approximated. System parameters were estimated from unsteady-state experimental data. Simulation results reinforce the idea that the diffusion effect is not fully exploited in pulping processes. Traditionally, digestion is conducted at high temperature, where delignification reaction kinetics is enhanced and the reaction effect is predominant. This approach is being reviewed by modern industry since energy and environmental savings associated with low temperature operation might compensate for high-yield productivity. The concentration of alkali at the center of the chip is a measure of the completeness of wood deacetylation, which translates into the aptitude of the final product for pulping purposes. This concentration is predicted here from the solution to a pair of coupled ODE’s. Since alternatives combining both low and high-temperature processes are being studied, the results in this paper provide basic data for optimization analysis.Fil: Costanza, Vicente. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Costanza, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin