Optimal stopping for non-linear expectations—Part II

Relying on the stochastic analysis tools developed in Bayraktar and Yao (2011) [1], we solve the optimal stopping problems for non-linear expectations.     

Optimal stopping for non-linear expectations—Part I

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards. Our development is presented in two parts. In the first part, we will develop the stochastic analysis tools that will be essential in solving the optimal stopping problems, which will be presented in Bayraktar and Yao (2011) [1].     

The hysteresis loops of FM/AFM two-layer Bethe lattice

The distinct hysteresis loops (HLs) of ferromagnetic/antiferromagnetic (FM/AFM) two-layer Bethe lattice with the Ising spins of the top layer having only FM interactions and the bottom ones having only AFM interactions with the interlayer coupling is either FM or AFM type are studied by using a pairwise approach. The sublattice magnetizations are studied by increasing and decreasing the external magnetic field (H) to obtain the HLs. The shapes of the HLs are strongly dependent on the competitions among the system parameters and on the phase configurations. The HLs are formed only when the AFM-type interactions are involved. The small loops of hysteresis are also formed because of the reentrant behavior in the FM region.     

Fast fluorescence switching within hydrophilic supramolecular assemblies

We designed a supramolecular strategy to modulate fluorescence in water under optical control. It is based on the entrapment of fluorophore-photochrome dyads within the hydrophobic interior of an amphiphilic polymer. The polymeric envelope around the dyads protects them from the aqueous environment, while imposing hydrophilic character on the overall supramolecular construct. In the resulting assemblies, the photochromic component can be operated reversibly on a microsecond timescale under the influence of ultraviolet stimulations. In turn, the reversible transformations control the emission intensity of the adjacent fluorophore. As a result, the fluorescence of such nanostructured constructs can be photomodulated for hundreds of cycles in water with microsecond switching speeds. Thus, our protocol for fast fluorescence switching in aqueous solutions can eventually lead to the realization of functional probes for the investigation of biological samples.     

A Lagrangian relaxation approach to large-scale flow interception problems

The paper presents a tight Lagrangian bound and an efficient dual heuristic for the flow interception problem. The proposed Lagrangian relaxation decomposes the problem into two subproblems that are easy to solve. Information from one of the subproblems is used within a dual heuristic to construct feasible solutions and is used to generate valid cuts that strengthen the relaxation. Both the heuristic and the relaxation are integrated into a cutting plane method where the Lagrangian bound is calculated using a subgradient algorithm. In the course of the algorithm, a valid cut is added and integrated efficiently in the second subproblem and is updated whenever the heuristic solution improves. The algorithm is tested on randomly generated test problems with up to 500 vertices, 12,483 paths, and 43 facilities. The algorithm finds a proven optimal solution in more than 75% of the cases, while the feasible solution is on average within 0.06% from the upper bound.     

Site‐Resolved Observation of Vibrational Energy Transfer Using a Genetically Encoded Ultrafast Heater

Allosteric information transfer in proteins has been linked to distinct vibrational energy transfer (VET) pathways in a number of theoretical studies. Experimental evidence for such pathways, however, is sparse because site‐selective injection of vibrational energy into a protein, that is, localized heating, is required for their investigation. Here, we solved this problem by the site‐specific incorporation of the non‐canonical amino acid β‐(1‐azulenyl)‐l ‐alanine (AzAla) through genetic code expansion. As an exception to Kasha's rule, AzAla undergoes ultrafast internal conversion and heating after S₁ excitation while upon S₂ excitation, it serves as a fluorescent label. We equipped PDZ3, a protein interaction domain of postsynaptic density protein 95, with this ultrafast heater at two distinct positions. We indeed observed VET from the incorporation sites in the protein to a bound peptide ligand on the picosecond timescale by ultrafast IR spectroscopy. This approach based on genetically encoded AzAla paves the way for detailed studies of VET and its role in a wide range of proteins.     

Computation of thermal fracture parameters for orthotropic functionally graded materials using Jk-integral

This article introduces a computational method based on the J_k-integral for mixed-mode fracture analysis of orthotropic functionally graded materials (FGMs) that are subjected to thermal stresses. The generalized definition of the J_k-integral is recast into a domain independent form composed of line and area integrals by utilizing the constitutive relations of plane orthotropic thermoelasticity. Implementation of the domain independent J_k-integral is realized through a numerical procedure developed by means of the finite element method. The outlined computational approach enables the evaluation of the modes I and II stress intensity factors, the energy release rate, and the T-stress. The developed technique is validated numerically by considering two different problems, the first of which is the problem of an embedded crack in an orthotropic FGM layer subjected to steady-state thermal stresses; and the second one is that of periodic cracks under transient thermal loading. Comparisons of the mixed-mode stress intensity factors evaluated by the J_k-integral based method to those calculated through the displacement correlation technique (DCT) and to those available in the literature point out that, the proposed form of the J_k-integral possesses the required domain independence and leads to numerical results of high accuracy. Further results are presented to illustrate the influences of the geometric and material constants on the thermal fracture parameters.     

A route toward multifunctional polyurethanes using triple click reactions

The aliphatic polyurethane with pendant alkyne, perfluorophenyl, and anthracene moieties (PU‐anthracene) was prepared from polycondensation of anthracene, alkyne, and perfluorophenyl functional‐diols with hexamethylenediisocyanate in the presence of dibutyltindilaurate (DBTL) in CH₂Cl₂ at room temperature for 10 days. Thereafter, the PU‐(anthracene‐co‐alkyne‐co‐perfluorophenyl) (M_n,GPC = 15,400 g/mol, M_w/M_n= 1.37, relative to PS standards) was sequentially clicked with benzyl azide, octylamine, and 4‐(2‐hydroxyethyl)?10‐oxa‐4‐azatricyclo[5.2.1.02,6]dec‐8‐ene‐3,5‐dione (adduct alcohol) via copper‐catalyzed azide‐alkyne cycloaddition, active ester substitution and Diels–Alder reactions, respectively, to finally yield PU‐(hydroxyl‐co‐benzyltriazole‐co‐octylamine). The PUs were characterized using ¹H NMR, GPC, and DSC. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 480–486