Online Local Learning via Semidefinite Programming

In many online learning problems we are interested in predicting local information about some universe of items. For example, we may want to know whether two items are in the same cluster rather than computing an assignment of items to clusters; we may want to know which of two teams will win a game rather than computing a ranking of teams. Although finding the optimal clustering or ranking is typically intractable, it may be possible to predict the relationships between items as well as if you could solve the global optimization problem exactly. Formally, we consider an online learning problem in which a learner repeatedly guesses a pair of labels (l(x), l(y)) and receives an adversarial payoff depending on those labels. The learner's goal is to receive a payoff nearly as good as the best fixed labeling of the items. We show that a simple algorithm based on semidefinite programming can obtain asymptotically optimal regret in the case where the number of possible labels is O(1), resolving an open problem posed by Hazan, Kale, and Shalev-Schwartz. Our main technical contribution is a novel use and analysis of the log determinant regularizer, exploiting the observation that log det(A + I) upper bounds the entropy of any distribution with covariance matrix A.Comment: 10 page

A Kinetic Model for the Enzymatic Action of Cellulase

We develop a mechanochemical model for the dynamics of cellulase, a two-domain enzyme connected by a peptide linker, as it extracts and hydrolyzes a cellulose polymer from a crystalline substrate. We consider two random walkers, representing the catalytic domain (CD) and the carbohydrate binding module (CBM), whose rates for stepping are biased by the coupling through the linker and the energy required to lift the cellulose polymer from the crystalline surface. Our results show that the linker length and stiffness play a critical role in the cooperative action of the CD and CBM domains and that, for a given linker length, the steady-state hydrolysis shows a maximum at some intermediate linker stiffness. The maximum hydrolysis rate corresponds to a transition of the linker from a compressed to an extended conformation, where the system exhibits maximum fluctuation, as measured by the variance of the separation distance between the two domains and the dispersion around the mean hydrolysis speed. In the range of experimentally known values of the parameters of our model, improving the intrinsic hydrolytic activity of the CD leads to a proportional increase in the overall hydrolysis rate

Magnitude of Magnetic Field Dependence of a Possible Selective Spin Filter in ZnSe/Zn_{1-x}Mn_{x}Se Multilayer Heterostructure

Spin-polarized transport through a band-gap-matched ZnSe/Zn_{1-x}Mn_{x} Se/ZnSe/Zn_{1-x}Mn_{x}Se/ZnSe multilayer structure is investigated. The resonant transport is shown to occur at different energies for different spins owing to the split of spin subbands in the paramagnetic layers. It is found that the polarization of current density can be reversed in a certain range of magnetic field, with the peak of polarization moving towards a stronger magnetic field for increasing the width of central ZnSe layer while shifting towards an opposite direction for increasing the width of paramagnetic layer. The reversal is limited in a small-size system. A strong suppression of the spin up component of the current density is present at high magnetic field. It is expected that such a reversal of the polarization could act as a possible mechanism for a selective spin filter device

Forecasting Livestock Feed Cost Risks Using Futures and Options

The costs of corn- and soybean-based feeds compose a substantial proportion of the variable costs faced by both mainstream and emergent confined livestock producers. This research develops a method to provide a joint distribution of prices of corn and soybean meal at a future time. Black's 1976 option model and stochastic volatility jump diffusion (SVJD) model are compared in volatility forecasting performance. In general, SVJD is superior to Black's model, though their performance is both commodity-specific and forecasting horizon specific.Livestock Production/Industries, Marketing,

Radial-breathing-like phonon modes of double-walled carbon nanotubes

The radial-breathing-like phonon modes (RBLMs) of the double-walled carbon nanotubes are studied in a simple analytical model, in which the interaction force constants (FCs) can be obtained analytically from the continuous model. The RBLMs frequencies are obtained by solving the dynamical matrix, and their relationship with the tube radii can be obtained analytically, offering a powerful experimental tool for determining precisely the radii of the multi-walled carbon nanotubes

Empirical Performance of Alternative Option Pricing Models for Commodity Futures Options

The central part of pricing agricultural commodity futures options is to find appropriate stochastic process of the underlying assets. The Black's (1976) futures option pricing model laid the foundation for a new era of futures option valuation theory. The geometric Brownian motion assumption girding the Black's model, however, has been regarded as unrealistic in numerous empirical studies. Option pricing models incorporating discrete jumps and stochastic volatility have been studied extensively in the literature. This study tests the performance of major alternative option pricing models and attempts to find the appropriate model for pricing commodity futures options.Marketing,

Managing Livestock Feed Cost Risks Using Futures and Options

The costs of corn- and soybean-based feeds compose a substantial proportion of the variable costs faced by both mainstream and emergent confined livestock producers. This research develops a method to provide a joint distribution of prices of corn and soybean meal at a future time. Black's 1976 option model and stochastic volatility jump diffusion (SVJD) model are compared in volatility forecasting performance. In general, SVJD is superior to Black's model, though their performance is both commodity-specific and forecasting horizon specific. The price forecast can assist livestock producers to assess different feed procurement strategies in terms of the distribution of costs projected for each strategy.Risk and Uncertainty,