Molassembler: Molecular graph construction, modification and conformer generation for inorganic and organic molecules

We present the graph-based molecule software Molassembler for building organic and inorganic molecules. Molassembler provides algorithms for the construction of molecules built from any set of elements from the periodic table. In particular, poly-nuclear transition metal complexes and clusters can be considered. Structural information is encoded as a graph. Stereocenter configurations are interpretable from Cartesian coordinates into an abstract index of permutation for an extensible set of polyhedral shapes. Substituents are distinguished through a ranking algorithm. Graph and stereocenter representations are freely modifiable and chiral state is propagated where possible through incurred ranking changes. Conformers are generated with full stereoisomer control by four spatial dimension Distance Geometry with a refinement error function including dihedral terms. Molecules are comparable by an extended graph isomorphism and their representation is canonicalizeable. Molassembler is written in C++ and provides Python bindings.Comment: 81 pages, 26 figures, 3 table

Cyclic Stochastic Optimization: Generalizations, Convergence, and Applications in Multi-Agent Systems

Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, L(θ), with respect to a parameter vector θ, when only noisy observations of L(θ) or its gradient are available (through the natural connection between root-finding and minimization); SA algorithms can be thought of as stochastic line search methods where the entire parameter vector is updated at each iteration. The cyclic approach to SA is a variant of SA procedures where θ is divided into multiple subvectors that are updated one at a time in a cyclic manner. This dissertation focuses on studying the asymptotic properties of cyclic SA and of the generalized cyclic SA (GCSA) algorithm, a variant of cyclic SA where the subvector to update may be selected according to a random variable or according to a predetermined pattern, and where the noisy update direction can be based on the updates of any SA algorithm (e.g., stochastic gradient, Kiefer–Wolfowitz, or simultaneous perturbation SA). The convergence of GCSA, asymptotic normality of GCSA (related to rate of convergence), and efficiency of GCSA relative to its non-cyclic counterpart are investigated both analytically and numerically. Specifically, conditions are obtained for the convergence with probability one of the GCSA iterates and for the asymptotic normality of the normalized iterates of a special case of GCSA. Further, an analytic expression is given for the asymptotic relative efficiency (when efficiency is defined in terms of mean squared error) between a special case of GCSA and its non-cyclic counterpart. Finally, an application of the cyclic SA scheme to a multi-agent stochastic optimization problem is investigated. This dissertation also contains two appendices. The first appendix generalizes Theorem 2.2 in Fabian (1968) (a seminal paper in the SA literature that derives general conditions for the asymptotic normality of SA procedures) to make the result more applicable to some modern applications of SA including (but not limited to) the GCSA algorithm, certain root-finding SA algorithms, and certain second-order SA algorithms. The second appendix considers the problem of determining the presence and location of a static object within an area of interest by combining information from multiple sensors using a maximum-likelihood-based approach

A Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande

Document submitted to 18th J-PARC PAC meeting in May 2014. 50 pages, 41 figuresDocument submitted to 18th J-PARC PAC meeting in May 2014. 50 pages, 41 figuresDocument submitted to 18th J-PARC PAC meeting in May 2014. 50 pages, 41 figuresHyper-Kamiokande will be a next generation underground water Cherenkov detector with a total (fiducial) mass of 0.99 (0.56) million metric tons, approximately 20 (25) times larger than that of Super-Kamiokande. One of the main goals of Hyper-Kamiokande is the study of $CP$ asymmetry in the lepton sector using accelerator neutrino and anti-neutrino beams. In this document, the physics potential of a long baseline neutrino experiment using the Hyper-Kamiokande detector and a neutrino beam from the J-PARC proton synchrotron is presented. The analysis has been updated from the previous Letter of Intent [K. Abe et al., arXiv:1109.3262 [hep-ex]], based on the experience gained from the ongoing T2K experiment. With a total exposure of 7.5 MW $\times$ 10$^7$ sec integrated proton beam power (corresponding to $1.56\times10^{22}$ protons on target with a 30 GeV proton beam) to a $2.5$-degree off-axis neutrino beam produced by the J-PARC proton synchrotron, it is expected that the $CP$ phase $\delta_{CP}$ can be determined to better than 19 degrees for all possible values of $\delta_{CP}$, and $CP$ violation can be established with a statistical significance of more than $3\,\sigma$ ($5\,\sigma$) for $76$ ($58$) of the $\delta_{CP}$ parameter space

Convergence Analysis of Weighted SPSA-based Consensus Algorithm in Distributed Parameter Estimation Problem

In this paper, we study a distributed parameter estimation problem in a large-scale network of communication sensors. The goal of the sensors is to find a global estimate of an unknown parameter minimizing, which minimizes some aggregate cost function. Each sensor can communicated to a few “neighbors”, furthermore, the communication channels have limited capacities. To solve the resulting optimization problem, we use a weighted modification of the distributed consensus-based SPSA algorithm whose main advantage over the alternative method is its ability to work in presence of arbitrary unknown-but-bounded noises whose statistical characteristics can be unknown. We provide a convergence analysis of the weighted SPSA-based consensus algorithm and show its efficiency via numerical simulations

Applications of Vanadium Phthalocyanine in Catalytic, Acid-Based Medium to Couple Sugar Molecules

The vanadium-substituted tetraazatetrabenzoporphyrin, vanadium phthalocyanine, was synthesized via reflux and characterized using FITR and XRD analysis. Subsequent to synthesis, the vanadium phthalocyanine was studied as a catalyst in redox reactions to convert fructose to different molecules, the products were predominately levulinic methyl ester and heptadionic acid. The ability to convert fructose to other compounds, such as alkyl levulinic derivative, is an important process to help eliminate reliance on traditional chemical feed stocks and promote alternative fuels. Levulinic acid has been commonly used as a starting material in the synthesis of biofuels and a precursor for pharmaceuticals, plasticizers, THF derivatives, γ-valerolatone. In the present study reactions were performed under acidic conditions using strong acids, which included nitric, sulfuric, hydrochloric, and hydrobromic acids, open atmospheric reflux in methanol and the reaction products were analyzed using GC-MS. Levulinic methyl ester and heptadionic acid were identified along with other coupled carbon-carbon products resulting from the de-cyclization of the sugar and subsequent coupling in a single pot reflux. The reactions show that metal-porphyrin systems are catalytic in the generation of organic molecules from biological material such as sugars, cellular material and cell walls