Optimal Multi-Modes Switching Problem in Infinite Horizon

This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as an extended impulse control problem and solved by means of probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. A viscosity solutions approach is employed to carry out a finne analysis on the associated system of m variational inequalities with inter-connected obstacles. We show that the vector of value functions of the optimal problem is the unique viscosity solution to the system. This problem is in relation with the valuation of firms in a financial market

Identification of the lactococcal exonuclease/recombinase and its modulation by the putative Chi sequence

Studies of RecBCD–Chi interactions in Escherichia coli have served as a model to understand recombination events in bacteria. However, the existence of similar interactions has not been demonstrated in bacteria unrelated to E. coli. We developed an in vivo model to examine components of dsDNA break repair in various microorganisms. Here, we identify the major exonuclease in Lactococcus lactis, a Gram-positive organism evolutionarily distant from E. coli, and provide evidence for exonuclease–Chi interactions. Insertional mutants of L. lactis, screened as exonuclease-deficient, affected a single locus and resulted in UV sensitivity and recombination deficiency. The cloned lactococcal genes (called rexAB) restored UV resistance, recombination proficiency, and the capacity to degrade linear DNA, to an E. coli recBCD mutant. In this context, DNA degradation is specifically blocked by the putative lactococcal Chi site (5′-GCGCGTG-3′), but not by the E. coli Chi (5′-GCTGGTGG-3′) site. RexAB-mediated recombination was shown to be stimulated ≈27-fold by lactococcal Chi. Our results reveal that RexAB fulfills the biological roles of RecBCD and indicate that its activity is modulated by a short DNA sequence. We speculate that exonuclease/recombinase enzymes whose activities are modulated by short DNA sequences are widespread among bacteria

Supervised learning applied to high-dimensional millimeter wave transient absorption data for age prediction of perovskite thin-film

We have analyzed a limited sample set of 120 GHz, and 150 GHz time-resolved millimeter wave (mmW) photoconductive decay (mmPCD) signals of 300 nm thick air-stable encapsulated perovskite film (methyl-ammonium lead halide) excited using a pulsed 532-nm laser with fluence 10.6 micro-Joules per cm-2. We correlated 12 parameters derived directly from acquired mmPCD kinetic-trace data and its step-response, each with the sample-age based on the date of the experiment. Five parameters with a high negative correlation with sample age were finally selected as predictors in the Gaussian Process Regression (GPR) machine learning model for prediction of the age of the sample. The effects of aging (between 0 and 40,000 hours after film production) are quantified mainly in terms of a shift in peak voltage, the response ratio (conductance parameter), loss-compensated transmission coefficient, and the radiofrequency (RF) area of the transient itself (flux). Changes in the other step-response parameters and the decay length of the aging transients are also shown. The GPR model is found to work well for a forward prediction of the age of the sample using this method. It is noted that the Matern-5 over 2 GPR kernel for supervised learning provides the best realistic solution for age prediction with R squared around 0.97

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control

Machine Learning and Portfolio Optimization

The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution towards one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-CVaR problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a QCQP, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both Sample Average Approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right hand sides of the PBR constraints, we develop new, performance-based k-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1 and L2 regularizations and the equally-weighted portfolio. We find that PBR dominates all other benchmarks for two out of three of Fama-French data sets

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.Comment: 36 page

Finite horizon optimal stopping of time-discontinuous functionals with applications to impulse control with delay

We study finite horizon optimal stopping problems for continuous-time Feller–Markov processes. The functional depends on time, state, and external parameters and may exhibit discontinuities with respect to the time variable. Both left- and right-hand discontinuities are considered. We investigate the dependence of the value function on the parameters, on the initial state of the process, and on the stopping horizon. We construct $\varepsilon$-optimal stopping times and provide conditions under which an optimal stopping time exists. We demonstrate how to approximate this optimal stopping time by solutions to discrete-time problems. Our results are applied to the study of impulse control problems with finite time horizon, decision lag, and execution delay

On Markovian solutions to Markov Chain BSDEs

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs

Participatory design to lower the threshold for intelligent support authoring

One of the fundamental aims of authoring tools is to provide teachers with opportunities to configure, modify and generally appropriate the content and pedagogical strategies of intelligent systems. Despite some progress in the field, there is still a need for tools that have low thresholds in terms of the users’ technical expertise. Here, we demonstrate that designing systems with lower entry barrier can potentially be achieved through co-design activities with non-programmers and carefully observing novices. Following an iterative participatory co-design cycle with teachers who have little or no programming expertise, we reflect on their proposed enhancements. Our investigations focus on Authelo, an authoring tool that has been designed primarily for Exploratory Learning Objects, but we conclude the paper by providing transferable lessons, particularly the strong preference for visual interfaces and high-level pedagogical predicates for authoring analysis and feedback rules