Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones

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

Comprehensive Synthesis of Monohydroxy-Cucurbit[n]urils (n=5, 6, 7, 8): High Purity and High Conversions

We describe a photochemical method to introduce a single alcohol function directly on cucurbit[n]urils (n = 5, 6, 7, 8) with conversions of the order 95-100% using hydrogen peroxide and UV light. The reaction was easily scaled up to 1 g for CB[6] and CB[7]. Spin trapping of cucurbituril radicals combined with MS experiments allowed us to get insights about the reaction mechanism and characterize CB [5], CB[6], CB[7], and C13[8] monofunctional compounds. Experiments involving O-18 isotopically labeled water indicated that the mechanism was complex and showed signs of both radical and ionic intermediates. DFT calculations allowed estimating the Bond Dissociation Energies (BDEs) of each hydrogen atom type in the CB series, providing an explanation of the higher reactivity of the "equatorial" C-H position of CB[n] compounds. These results also showed that, for CB [8], direct functionalization on the cucurbituril skeleton is more difficult because one of the methylene hydrogen atoms (H-b) has its BDE lowering within the series and coming close to that of H-c, thus opening the way to other types of free radicals generated on the CB[8] skeleton leading to several side products. Yet CB[5]-(OH)(1) and CB[8]-(OH)(1), the first CB[8] derivative, were obtained in excellent yields thanks to the soft method presented here

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

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

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