Rebalancing Multiple Assets with Mutual Price Impact

We find asymptotically optimal trading policies for long-term investors with constant relative risk aversion, in a multiple-assets market, where expected returns and covariances are constant, and the execution price of each asset is linear in the trading intensities of all assets. Trading toward the frictionless target is optimal, when the current portfolio differs from the target by a principal portfolio—an eigenvector of the inverse impact matrix times the covariance matrix. Optimal policies approach the frictionless target along nonlinear, power-shaped paths, trading faster in more liquid directions, while tolerating wider oscillations along less liquid directions.     

A method of proving non-unitarity of representations of p-adic groups I

In this paper we exhibit a new method of proving non-unitarity of representations, based on semi simplicity of unitarizable representations. Non-unitarity is proved for a half of all irreducible representations of classical p-adic groups whose infinitesimal character is the same as the infinitesimal character of a generalized Steinberg representation (as defined in Tadić, Am J Math 120:159–210, 1998). Only the Steinberg representation and its Aubert dual are expected to be unitary here. In this way we partially generalize a result of Casselman to the case of classical groups. Our argument is completely different from Casselman’s argument (which is hard to extend to this case). It requires a very limited knowledge of the inducing cuspidal representation.     

Microbial Baeyer-Villiger oxidation: stereopreference and substrate acceptance of cyclohexanone monooxygenase mutants prepared by directed evolution

[reaction: see text] An array of random mutants of cyclohexanone monooxygenase (CHMO) from Acinetobacter sp. NCIMB 9871 was screened against a library of structurally diverse ketones for modifications in the substrate acceptance profile and stereopreference of the enzymatic Baeyer-Villiger biooxidation. While the set of mutant biocatalysts was initially evolved for the enantiocomplementary oxidation of 4-hydroxycyclohexanone, improved and/or divergent stereoselectivities were observed for several substrates. In addition, expanded substrate acceptance to facilitate biotransformation of sterically demanding ketones was found.     

A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates

This paper presents a novel method of multi-objective optimization by learning automata (MOLA) to solve complex multi-objective optimization problems. MOLA consists of multiple automata which perform sequential search in the solution domain. Each automaton undertakes dimensional search in the selected dimension of the solution domain, and each dimension is divided into a certain number of cells. Each automaton performs a continuous search action, instead of discrete actions, within cells. The merits of MOLA have been demonstrated, in comparison with a multi-objective evolutionary algorithm based on decomposition (MOEA/D) and non-dominated sorting genetic algorithm II (NSGA-II), on eleven multi-objective benchmark functions and an optimal problem in the midwestern American electric power system which is integrated with wind power, respectively. The simulation results have shown that MOLA can obtain more accurate and evenly distributed Pareto fronts, in comparison with MOEA/D and NSGA-II.     

Transport in a disordered tight-binding chain with dephasing

We studied transport properties of a disordered tight-binding model (XX spin chain) in the presence of dephasing. Focusing on diffusive behaviour in the thermodynamic limit at high energies, we analytically derived the dependence of conductivity on dephasing and disorder strengths. As a function of dephasing, conductivity exhibits a single maximum at the optimal dephasing strength. The scaling of the position of this maximum with disorder strength is different for small and large disorders. In addition, we studied periodic disorder for which we found a resonance phenomenon, with conductivity having two maxima as a function of dephasing strength. If the disorder is non-zero only at a random fraction of all sites, conductivity is approximately the same as in the case of a disorder on all sites but with a rescaled disorder strength.     

Structure Switching and Modulation of the Magnetic Properties in Diarylethene‐Bridged Metallosupramolecular Compounds by Controlled Coordination‐Driven Self‐Assembly

We report three self‐assembled iron complexes that comprised an anti‐parallel open form (o‐ L _anti), a parallel open form (o‐ L _syn), and a closed form (c‐ L ) of diarylethene conformers. Under kinetic control, Fe^II₂(o‐ L _anti)₃ was isolated, which exhibited a dinuclear structure with diamagnetic properties. Under light‐irradiation control, Fe^II₂(c‐ L )₃ was prepared and exhibited paramagnetism and spin‐crossover behaviour. Under thermodynamic control and in the presence of indispensable [Fe^III(Tp*)(CN)₃]^?, Fe^II₂(o‐ L _anti)₃ and Fe^II₂(c‐ L )₃ transformed into tetranuclear Fe^III₂Fe^II₂(o‐ L _syn)₂, which exhibited complete spin‐crossover behaviour at T_1/2=353 K.     

Protein‐Specific,Multicolor and 3D STED Imaging in Cells with DNA‐Labeled Antibodies

Photobleaching is a major challenge in fluorescence microscopy, in particular if high excitation light intensities are used. Signal‐to‐noise and spatial resolution may be compromised, which limits the amount of information that can be extracted from an image. Photobleaching can be bypassed by using exchangeable labels, which transiently bind to and dissociate from a target, thereby replenishing the destroyed labels with intact ones from a reservoir. Here, we demonstrate confocal and STED microscopy with short, fluorophore‐labeled oligonucleotides that transiently bind to complementary oligonucleotides attached to protein‐specific antibodies. The constant exchange of fluorophore labels in DNA‐based STED imaging bypasses photobleaching that occurs with covalent labels. We show that this concept is suitable for targeted, two‐color STED imaging of whole cells.