Dynamical Optimization Theory of a Diversified Portfolio

We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random walk with identical drift and dispersion. The rules of our model naturally give rise to power law tails in the distribution of capital fractions invested in different stocks. The exponent of this scale free distribution is calculated in both discrete and continuous time formalism. It is demonstrated that the dynamical redistribution strategy results in a larger typical growth rate of the capital than a static ``buy-and-hold'' strategy. In the large N limit the typical growth rate is shown to asymptotically approach that of the expectation value of the stock price. The finite dimensional variant of the model is shown to describe the partition function of directed polymers in random media.Comment: 9 pages, 2 figures, accepted for publication in Physica A; Figure captions and PS-files of two figues are adde

A three-level BDDC algorithm for mortar discretizations

This is the published version, also available here: http://dx.doi.org/10.1137/07069081X.In this paper, a three-level balancing domain decomposition by constraints (BDDC) algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary value problems. The mortar discretization is considered on geometrically nonconforming subdomain partitions. In two-level BDDC algorithms, the coarse problem needs to be solved exactly. However, its size will increase with the increase of the number of the subdomains. To overcome this limitation, the three-level algorithm solves the coarse problem inexactly while a good rate of convergence is maintained. This is an extension of previous work: the three-level BDDC algorithms for standard finite element discretization. Estimates of the condition numbers are provided for the three-level BDDC method, and numerical experiments are also discussed

Energetic, relativistic and ultra-relativistic electrons: Comparison of long-term VERB code simulations with Van Allen Probes measurements

In this study, we compare long-term simulations performed by the Versatile Electron Radiation Belt (VERB) code with observations from the Magnetic Electron Ion Spectrometer and Relativistic Electron-Proton Telescope instruments on the Van Allen Probes satellites. The model takes into account radial, energy, pitch angle and mixed diffusion, losses into the atmosphere, and magnetopause shadowing. We consider the energetic (\u3e100 keV), relativistic (~0.5–1 MeV), and ultrarelativistic (\u3e2 MeV) electrons. One year of relativistic electron measurements (μ = 700 MeV/G) from 1 October 2012 to 1 October 2013 are well reproduced by the simulation during varying levels of geomagnetic activity. However, for ultrarelativistic energies (μ = 3500 MeV/G), the VERB code simulation overestimates electron fluxes and phase space density. These results indicate that an additional loss mechanism is operational and efficient for these high energies. The most likely mechanism for explaining the observed loss at ultrarelativistic energies is scattering by the electromagnetic ion cyclotron waves

Inactivation of mammalian Ero 1α is catalysed by specific protein disulfide isomerases

Disulfide formation within the endoplasmic reticulum is a complex process requiring a disulfide exchange protein such as protein disulfide isomerase and a mechanism to form disulfides de novo. In mammalian cells, the major pathway for de novo disulfide formation involves the enzyme Ero1α which couples oxidation of thiols to the reduction of molecular oxygen to form hydrogen peroxide. Ero1α activity is tightly regulated by a mechanism that requires the formation of regulatory disulfides. These regulatory disulfides are reduced to activate and reform to inactive the enzyme. To investigate the mechanism of inactivation we analysed regulatory disulfide formation in the presence of various oxidants under controlled oxygen concentration. Neither molecular oxygen, nor hydrogen peroxide was able to oxidise Ero1α efficiently to form the correct regulatory disulfides. However, specific members of the PDI family such as PDI or ERp46 were able to catalyse this process. Further studies showed that both active sites of PDI contribute to the formation of regulatory disulfides in Ero1α and that the PDI substrate binding domain is crucial to allow electron transfer between the two enzymes. These results demonstrate a simple feedback mechanism of regulation of mammalian Ero1α involving its primary substrate

Simple Hardware-Efficient PCFGs with Independent Left and Right Productions

Scaling dense PCFGs to thousands of nonterminals via a low-rank parameterization of the rule probability tensor has been shown to be beneficial for unsupervised parsing. However, PCFGs scaled this way still perform poorly as a language model, and even underperform similarly-sized HMMs. This work introduces \emph{SimplePCFG}, a simple PCFG formalism with independent left and right productions. Despite imposing a stronger independence assumption than the low-rank approach, we find that this formalism scales more effectively both as a language model and as an unsupervised parser. As an unsupervised parser, our simple PCFG obtains an average F1 of 65.1 on the English PTB, and as a language model, it obtains a perplexity of 119.0, outperforming similarly-sized low-rank PCFGs. We further introduce \emph{FlashInside}, a hardware IO-aware implementation of the inside algorithm for efficiently scaling simple PCFGs.Comment: Accepted to Findings of EMNLP, 202

On the Renormalization of the Kardar-Parisi-Zhang equation

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z* = 2 and the roughness exponent chi* = 0, which are exact to all orders in epsilon = (2 - d)/2. The expansion becomes singular in d = 4, which is hence identified with the upper critical dimension of the KPZ equation. The implications of this perturbation theory for the strong-coupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strong-coupling fixed point.Comment: 21 pp. (latex, now texable everywhere, no other changes), with 2 fig