Mechanisms with learning for stochastic multi-armed bandit problems

The multi-armed bandit (MAB) problem is a widely studied problem in machine learning literature in the context of online learning. In this article, our focus is on a specific class of problems namely stochastic MAB problems where the rewards are stochastic. In particular, we emphasize stochastic MAB problems with strategic agents. Dealing with strategic agents warrants the use of mechanism design principles in conjunction with online learning, and leads to non-trivial technical challenges. In this paper, we first provide three motivating problems arising from Internet advertising, crowdsourcing, and smart grids. Next, we provide an overview of stochastic MAB problems and key associated learning algorithms including upper confidence bound (UCB) based algorithms. We provide proofs of important results related to regret analysis of the above learning algorithms. Following this, we present mechanism design for stochastic MAB problems. With the classic example of sponsored search auctions as a backdrop, we bring out key insights in important issues such as regret lower bounds, exploration separated mechanisms, designing truthful mechanisms, UCB based mechanisms, and extension to multiple pull MAB problems. Finally we provide a bird’s eye view of recent results in the area and present a few issues that require immediate future attention.     

Sobolev estimates for constructive uniform-grid FFT interpolatory approximations of spherical functions

The fast Fourier transform (FFT) based matrix-free ansatz interpolatory approximations of periodic functions are fundamental for efficient realization in several applications. In this work we design, analyze, and implement similar constructive interpolatory approximations of spherical functions, using samples of the unknown functions at the poles and at the uniform spherical-polar grid locations \(\left (\frac {j\pi }{N}, \frac {k \pi }{N}\right )\), for j=1,…,N?1, k=0,…,2N?1. The spherical matrix-free interpolation operator range space consists of a selective subspace of two dimensional trigonometric polynomials which are rich enough to contain all spherical polynomials of degree less than N. Using the \({\mathcal {O}}(N^{2})\) data, the spherical interpolatory approximation is efficiently constructed by applying the FFT techniques (in both azimuthal and latitudinal variables) with only \({\mathcal {O}}(N^{2} \log N)\) complexity. We describe the construction details using the FFT operators and provide complete convergence analysis of the interpolatory approximation in the Sobolev space framework that are well suited for quantification of various computer models. We prove that the rate of spectrally accurate convergence of the interpolatory approximations in Sobolev norms (of order zero and one) are similar (up to a log term) to that of the best approximation in the finite dimensional ansatz space. Efficient interpolatory quadratures on the sphere are important for several applications including radiation transport and wave propagation computer models. We use our matrix-free interpolatory approximations to construct robust FFT-based quadrature rules for a wide class of non-, mildly-, and strongly-oscillatory integrands on the sphere. We provide numerical experiments to demonstrate fast evaluation of the algorithm and various theoretical results presented in the article.     

Stability analysis of memristor‐based complex‐valued recurrent neural networks with time delays

This article addresses stability analysis of a general class of memristor‐based complex‐valued recurrent neural networks (MCVNNs) with time delays. Some sufficient conditions to guarantee the boundedness on a compact set that globally attracts all trajectories of the MCVNNs are obtained by utilizing local inhibition. Moreover, some sufficient conditions for exponential stability and the global stability of the MCVNNs are established with the help of local invariant sets and linear matrix inequalities using Lyapunov–Krasovskii functional. The analysis results in the article, based on the results from the theory of differential equations with discontinuous right‐hand sides as introduced by Filippov. Finally, two numerical examples are also presented to show the effectiveness and usefulness of our theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–39, 2016     

WebProp: Web interface for ab initio calculation of molecular one-electron properties

This note describes the features and implementation issues of WebProp, a web-based interface for evaluating ab initio quality one-electron properties. The interface code is written in HTML and Python, while the backend is handled using Python and our indigenously developed code INDPROP for property evaluation. A novel feature of this setup is that it provides a simple interface for computing first principle one-electron properties of small to medium sized molecules. To facilitate computation of otherwise expensive calculations on large molecular systems, we employ the Molecular Tailoring Approach (MTA) developed in our laboratory to obtain the density matrix (DM). This DM is then employed for computing the one-electron properties of these systems. The backend transparently handles jobs submitted by the user and runs them either on a single machine or over a grid of compute nodes. The results of the calculations, which include the summary and the files necessary for visualization of one-electron properties, are e-mailed to the user. The user can either directly use the data or visualize it using visualization tools such as UNIVIS-2000 or Drishti.     

Use of enantiomerically pure 7-azabicyclo[2.2.1]heptan-2-ol as a chiral template for the synthesis of aminocyclitols

Using enantiopure 7-azabicyclo[2.2.1]heptane-2-ol, the synthesis of cis- as well as trans-2-aminocyclohexanols, dihydroconduramine E-1, and ent-conduramine F-1 has been described.     

Comparative study of machine-learning and chemometric tools for analysis of in-vivo high-throughput screening data

High-throughput screening (HTS) has become a central tool of many pharmaceutical and crop-protection discovery operations. If HTS screening is carried out at the level of the intact organism, as is commonly done in crop protection, this strategy has the potential of uncovering a completely new mechanism of actions. The challenge in running a cost-effective HTS operation is to identify ways in which to improve the overall success rate in discovering new biologically active compounds. To this end, we describe our efforts directed at making full use of the data stream arising from HTS. This paper describes a comparative study in which several machine learning and chemometric methodologies were used to develop classifiers on the same data sets derived from in vivo HTS campaigns and their predictive performances compared in terms of false negative and false positive error profiles.     

Structure-property relationship for two-photon absorbing multiporphyrins: supramolecular assembly of highly-conjugated multiporphyrinic ladders and prisms

Two-photon absorption (TPA) phenomena of a series of single-strand as well as supramolecular self-assembled ladders and prisms of highly conjugated ethyne bridged multiporphyrin dimer, trimer, and star shaped pentamer have been investigated. The ligand mediated self-assembled supramolecular structures were characterized by UV-visible spectroscopy and small- and wide-angle X-ray scattering (SAXS/WAXS) analysis. The TPA cross section values of multiporphyrins increase nonlinearly from approximately 100 to approximately 18000 GM with an increased number of porphyrin units and elongated pi-conjugation length by virtue of charge transfer and excited-state cumulenic configurations. The observed opposite TPA behavior between their supramolecular ladder and prism configurations necessitates the importance of interstrand interactions between the multiporphyrinic units and the overall shape of the assembly. Furthermore, the diminished TPA cross section of the pentamer, despite the increased pi-conjugation resulting from duplex formation suggests that destabilizing the essential functional configurations at the cost of elongation of pi-delocalization pathway must cause unfavorable effects. We have also shown that one- and two-photon allowed energy-levels of linear multiporphyrins are nearly isoenergetic and the latter transition originates exclusively from the extent of pi-delocalization within the molecule. The identical TPA maximum position of the trimer and pentamer indicates that the TPA of the pentamer arises only from its basic trimer unit in spite of its extended two-dimensional pi-conjugation pathway involving five porphyrinic units.     

Catalyst-free one-pot synthesis of 2,4,5-tri- and 1,2,4,5-tetrasubstituted imidazoles

The present work emphasizes catalyst-free 2,4,5-tri- and 1,2,4,5-tetra substituted imidazole synthesis using diversified aldehydes with benzil, ammonium acetate, or amines. Ammonium acetate plays a vital role as a reactant catalyst by dissociating into acetic acid to afford imine and diamine formation to ascertain the 2,4,5-tri- and 1,2,4,5-tetra substituted imidazoles. The key advantages of the current approach are efficient, greener, eco-friendly, and facile, with moderate to excellent yield in shorter reaction time at the temperature of 80°C. Ethanol:water as a solvent makes the reaction process eco-friendly. Overall, the described approach offers a promising route for the efficient and sustainable synthesis of substituted imidazoles, which have a wide range of applications in various fields, including pharmaceuticals, agrochemicals, and materials science.     

Direct calculation of 1-octanol-water partition coefficients from adaptive biasing force molecular dynamics simulations

The 1-octanol-water partition coefficient log K(ow) of a solute is a key parameter used in the prediction of a wide variety of complex phenomena such as drug availability and bioaccumulation potential of trace contaminants. In this work, adaptive biasing force molecular dynamics simulations are used to determine absolute free energies of hydration, solvation, and 1-octanol-water partition coefficients for n-alkanes from methane to octane. Two approaches are evaluated; the direct transfer of the solute from 1-octanol to water phase, and separate transfers of the solute from the water or 1-octanol phase to vacuum, with both methods yielding statistically indistinguishable results. Calculations performed with the TIP4P and SPC∕E water models and the TraPPE united-atom force field for n-alkanes show that the choice of water model has a negligible effect on predicted free energies of transfer and partition coefficients for n-alkanes. A comparison of calculations using wet and dry octanol phases shows that the predictions for log K(ow) using wet octanol are 0.2-0.4 log units lower than for dry octanol, although this is within the statistical uncertainty of the calculation.     

Computational prediction of ionic liquid 1-octanol/water partition coefficients

Wet 1-octanol/water partition coefficients (log?K(ow)) predicted for imidazolium-based ionic liquids using adaptive bias force-molecular dynamics (ABF-MD) simulations lie in excellent agreement with experimental values. These encouraging results suggest prospects for this computational tool in the a priori prediction of log?K(ow) values of ionic liquids broadly with possible screening implications as well (e.g., prediction of CO(2)-philic ionic liquids).