Computing strategies for achieving acceptability: A Monte Carlo approach

We consider a trader who wants to direct his or her portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a Monte Carlo algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy for achieving acceptability. We also prove optimality of the capital obtained. Explicit theoretical evaluations of hedging strategies are extremely difficult, and we avoid the problem by resorting to such computational methods. The main idea is to utilize the finite Vapnik–C?ervonenkis dimension of a class of possible strategies.     

ZrOCl2•8H2O-Catalyzed One-Pot Multicomponent Synthesis of β′-Acetamido-β-dicarbonyl Compounds with Special Reference to pref-Selective β′-Acetamido-β-ketoesters

ZrOCl₂ · 8H₂O catalyzes the one-pot synthesis of β′-acetamido-β-dicarbonyl compounds in high yields from aldehyde, enolizable β-dicarbonyl compound, acetyl chloride, and acetonitrile in solvent as well as in solvent-free conditions. β′-Acetamido-β-ketoesters are formed in moderate to exclusive pref-diastereoselectivity.     

An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for L ₁-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in L ₁. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to get.     

The geometry of relative arbitrage

Consider an equity market with n stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function that assigns a portfolio vector to each possible value of the market weight, and we perform self-financing trading using this portfolio function. We study the problem of characterizing functions such that the resulting portfolio will outperform the market portfolio in the long run under the conditions of diversity and sufficient volatility. No other assumption on the future behavior of stock prices is made. We prove that the only solutions are functionally generated portfolios in the sense of Fernholz. A second characterization is given as the optimal maps of a remarkable optimal transport problem. Both characterizations follow from a novel property of portfolios called multiplicative cyclical monotonicity.     

Superb hydroxyl radical-mediated biocidal effect induced antibacterial activity of tuned ZnO/chitosan type II heterostructure under dark

Journal of Nanoparticle Research - With the widespread use of titanium dioxide (TiO2) human exposure is inevitable, but the exposure data on TiO2 are still limited. This study adopted off-line...     

Rapid,Label-free Optical Spectroscopy Platform for Diagnosis of Heparin-Induced Thrombocytopenia

The use of surface-enhanced Raman spectroscopy (SERS) to determine spectral markers for the diagnosis of heparin-induced thrombocytopenia (HIT), a difficult-to-diagnose immune-related complication that often leads to limb ischemia and thromboembolism, is proposed. The ability to produce distinct molecular signatures without the addition of labels enables unbiased inquiry and makes SERS an attractive complementary diagnostic tool. A capillary-tube-derived SERS platform offers ultrasensitive, label-free measurement as well as efficient handling of blood serum samples. This shows excellent reproducibility, long-term stability and provides an alternative diagnostic rubric for the determination of HIT by leveraging machine-learning-based classification of the spectroscopic data. We envision that a portable Raman instrument could be combined with the capillary-tube-based SERS analytical tool for diagnosis of HIT in the clinical laboratory, without perturbing the existing diagnostic workflow.     

Cytotoxic Oligomers and Fibrils Trapped in a Gel‐like State of α‐Synuclein Assemblies

α‐Synuclein (α‐Syn) aggregation is associated with Parkinson's disease (PD) pathogenesis. In PD, the role of oligomers versus fibrils in neuronal cell death is debatable, but recent studies suggest oligomers are a proximate neurotoxin. Herein, we show that soluble α‐Syn monomers undergo a transformation from a solution to a gel state on incubation at high concentration. Detailed characterization of the gel showed the coexistence of monomers, oligomers, and short fibrils. In vitro, the gel was highly cytotoxic to human neuroblastoma cells. The individual constituents of the gel are short‐lived species but toxic to the cells. They comprise a structurally heterogeneous population of α‐helical and β‐sheet‐rich oligomers and short fibrils with the cross‐β motif. Given the recent evidence of the gel‐like state of the protein associated with neurodegenerative diseases, the gel state of α‐Syn in this study represents a mechanistic and structural model for the in vivo toxicity of α‐Syn in PD.     

Cross‐Electrophile Coupling of Vinyl Halides with Alkyl Halides

An improved method for the reductive coupling of aryl and vinyl bromides with alkyl halides that gave high yields for a variety of substrates at room temperature with a low (2.5 to 0.5 mol %) catalyst loading is presented. Under the optimized conditions, difficult substrates, such as unhindered alkenyl bromides, can be coupled to give the desired olefins with minimal diene formation and good stereoretention. These improved conditions also worked well for aryl bromides. For example, a gram‐scale reaction was demonstrated with 0.5 mol % catalyst loading, whereas reactions at 10 mol % catalyst loading completed in as little as 20 minutes. Finally, a low‐cost single‐component pre‐catalyst, (bpy)NiI₂ (bpy=2,2′‐bipyridine) that is both air‐ and moisture‐stable over a period of months was introduced.     

A phase transition behavior for Brownian motions interacting through their ranks

Consider a time-varying collection of n points on the positive real axis, modeled as Exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If at each time point we divide the points by their sum, under suitable assumptions the rescaled point process converges to a stationary distribution (depending on n and the vector of drifts) as time goes to infinity. This stationary distribution can be exactly computed using a recent result of Pal and Pitman. The model and the rescaled point process are both central objects of study in models of equity markets introduced by Banner, Fernholz, and Karatzas. In this paper, we look at the behavior of this point process under the stationary measure as n tends to infinity. Under a certain ‘continuity at the edge’ condition on the drifts, we show that one of the following must happen: either (i) all points converge to 0, or (ii) the maximum goes to 1 and the rest go to 0, or (iii) the processes converge in law to a non-trivial Poisson–Dirichlet distribution. The underlying idea of the proof is inspired by Talagrand’s analysis of the low temperature phase of Derrida’s Random Energy Model of spin glasses. The main result establishes a universality property for the BFK models and aids in explicit asymptotic computations using known results about the Poisson–Dirichlet law.