Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm

As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality, samples are rarely noiseless. In this paper, we introduce a novel stochastic algorithm to reconstruct a signal with finite rate of innovation from its noisy samples. Even though variants of this problem has been approached previously, satisfactory solutions are only available for certain classes of sampling kernels, for example kernels which satisfy the Strang-Fix condition. In this paper, we consider the infinite-support Gaussian kernel, which does not satisfy the Strang-Fix condition. Other classes of kernels can be employed. Our algorithm is based on Gibbs sampling, a Markov chain Monte Carlo (MCMC) method. Extensive numerical simulations demonstrate the accuracy and robustness of our algorithm.Comment: Submitted to IEEE Transactions on Signal Processin

Pentaquark Masses in Chiral Perturbation Theory

Heavy baryon chiral perturbation theory for pentaquarks is applied beyond leading order. The mass splitting in the pentaquark anti-decuplet is calculated up to NNLO. An expansion in the coupling of pentaquarks to non-exotic baryons simplifies calculations and makes the pentaquark masses insensitive to the pentaquark-nucleon mass difference. The possibility of determining coupling constants in the chiral Lagrangian on the lattice is discussed. Both positive and negative parities are considered.Comment: 11 pages; reference added, minor changes in wordin

Asymmetric additions to dienes catalysed by a dithiophosphoric acid.

Chiral Brønsted acids (proton donors) have been shown to facilitate a broad range of asymmetric chemical transformations under catalytic conditions without requiring additional toxic or expensive metals. Although the catalysts developed thus far are remarkably effective at activating polarized functional groups, it is not clear whether organic Brønsted acids can be used to catalyse highly enantioselective transformations of unactivated carbon-carbon multiple bonds. This deficiency persists despite the fact that racemic acid-catalysed Markovnikov additions to alkenes are well known chemical transformations. Here we show that chiral dithiophosphoric acids can catalyse the intramolecular hydroamination and hydroarylation of dienes and allenes to generate heterocyclic products in exceptional yield and enantiomeric excess. We present a mechanistic hypothesis that involves the addition of the acid catalyst to the diene, followed by nucleophilic displacement of the resulting dithiophosphate intermediate; we also report mass spectroscopic and deuterium labelling studies in support of the proposed mechanism. The catalysts and concepts revealed in this study should prove applicable to other asymmetric functionalizations of unsaturated systems

Robust Dynamic Pricing with Strategic Customers

We consider the canonical revenue management (RM) problem wherein a seller must sell an inventory of some product over a finite horizon via an anonymous, posted price mechanism. Unlike typical models in RM, we assume that customers are forward looking. In particular, customers arrive randomly over time and strategize about their times of purchases. The private valuations of these customers decay over time and the customers incur monitoring costs; both the rates of decay and these monitoring costs are private information. This setting has resisted the design of optimal dynamic mechanisms heretofore. Optimal pricing schemes-an almost necessary mechanism format for practical RM considerations-have been similarly elusive. The present paper proposes a mechanism we dub robust pricing. Robust pricing is guaranteed to achieve expected revenues that are at least within 29% of those under an optimal (not necessarily posted price) dynamic mechanism. We thus provide the first approximation algorithm for this problem. The robust pricing mechanism is practical, since it is an anonymous posted price mechanism and since the seller can compute the robust pricing policy for a problem without any knowledge of the distribution of customer discount factors and monitoring costs. The robust pricing mechanism also enjoys the simple interpretation of solving a dynamic pricing problem for myopic customers with the additional requirement of a novel “restricted sub-martingale constraint” on prices that discourages rapid discounting. We believe this interpretation is attractive to practitioners. Finally, numerical experiments suggest that the robust pricing mechanism is, for all intents, near optimal

High-Resolution Thin-Film Device to Sense Texture by Touch

Touch (or tactile) sensors are gaining renewed interest as the level of sophistication in the application of minimum invasive surgery and humanoid robots increases. The spatial resolution of current large-area (greater than 1 cm2) tactile sensor lags by more than an order of magnitude compared with the human finger. By using metal and semi conducting nanoparticles, a 100-nm-thick, large-area thin-film device is self-assembled such that the change in current density through the film and the electroluminescent light intensity are linearly proportional to the local stress. A stress image is obtained by pressing a copper grid and a United States 1-cent coin on the device and focusing the resulting electroluminescent light directly on the charge-coupled device. Both the lateral and height resolution of texture are comparable to the human finger at similar stress levels of 10 kilopascals

Strange nonchaotic stars

The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Kepler's "golden" stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars.Comment: 5 pages, 4 figures, published in Physical Review Letter

A Data-Driven Approach to Modeling Choice

We visit the following fundamental problem: For a 'generic' model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal preference information), how may one predict revenues from offering a particular assortment of choices? This problem is central to areas within operations research, marketing and econometrics. We present a framework to answer such questions and design a number of tractable algorithms (from a data and computational standpoint) for the same.National Science Foundation (U.S.) (CAREER CNS 0546590