Valued Graphs and the Representation Theory of Lie Algebras

Quivers (directed graphs) and species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this paper, we discuss the most important results in the representation theory of species, such as Dlab and Ringel's extension of Gabriel's theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field). Namely, we show that the category of K-species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles that do not appear in the literature. Specifically, we prove that two such species have isomorphic tensor rings if and only if they are isomorphic as "crushed" species, and we show that if K is a perfect field, then the tensor algebra of a K-species tensored with the algebraic closure of K is isomorphic to, or Morita equivalent to, the path algebra of a quiver.Comment: 36 page

On Extracting Heavy Quark Parameters from Moments with Cuts

We point out that applying the photon energy cut significantly modifies the moments of energy spectrum in B->X_s+gamma decays, with a certain class of effects not accounted for in the mostly used OPE expressions. This leads to a systematic bias in the extracted values of the b quark mass and other heavy quark parameters. The apparent b quark mass increases typically by 70MeV or more, together with an even more dramatic downward shift in the kinetic expectation value. Accounting for these cut-related shifts brings different measurements into a good agreement, when the OPE-based theory employs the robust approach. These nonperturbative effects are exponential in the effective hardness severely lowered by high cuts, and do not signify a breakdown of the 1/m_b expansion itself. Similar effects in semileptonic b->c decays are briefly addressed. We stress the utility of the second moment of E_gamma once these effects are incorporated.Comment: 8 pages, LaTeX, two figure. Contributed to the Lepton-Photon Conference, 2003, FNA

X-rays and hard UV radiation From the First Galaxies: Ionization Bubbles and 21 cm Observations

The first stars and quasars are known sources of hard ionizing radiation in the first billion years of the Universe. We examine the joint effects of X-rays and hard UV radiation from such first-light sources on the hydrogen and helium reionization of the intergalactic medium (IGM) at early times, and the associated heating. We study the growth and evolution of individual HII, HeII and HeIII regions around early galaxies with first stars and/or QSO populations. We find that in the presence of helium-ionizing radiation, X-rays may not dominate the ionization and thermal history of the IGM at redshifts, z, of 10-20, contributing relatively modest increases to IGM ionization, and heating up to about 10^3--10^5 K in IGM temperatures. We also calculate the 21 cm signal expected from a number of scenarios with metal-free starbursts and quasars at these redshifts. The peak values for the spin temperature reach about 10^4 to 10^5 K in such cases. The maximum values for the 21 cm brightness temperature are around 30-40 mK in emission, while the net values of the 21 cm absorption signal range from about a few to 60 mK on scales of 0.01-1 Mpc. We find that the 21 cm signature of X-ray versus UV ionization could be distinct, with the emission signal expected from X-rays alone occurring at smaller scales than that from UV radiation, resulting from the inherently different spatial scales at which X-ray and UV ionization/heating manifest. This difference is time-dependent, and becomes harder to distinguish with an increasing X-ray contribution to the total ionizing photon production. Such differing scale-dependent contributions from X-ray and UV photons may therefore "blur" the 21 cm signature of the percolation of ionized bubbles around early halos (depending on whether a cosmic X-ray or UV background built up first), and affect the interpretation of 21 cm data constraints on reionization.Comment: Accepted for publication in MNRAS; 15 pages, 14 figure

Compositional Deep Probabilistic Models of DNA Encoded Libraries

DNA-Encoded Library (DEL) has proven to be a powerful tool that utilizes combinatorially constructed small molecules to facilitate highly-efficient screening assays. These selection experiments, involving multiple stages of washing, elution, and identification of potent binders via unique DNA barcodes, often generate complex data. This complexity can potentially mask the underlying signals, necessitating the application of computational tools such as machine learning to uncover valuable insights. We introduce a compositional deep probabilistic model of DEL data, DEL-Compose, which decomposes molecular representations into their mono-synthon, di-synthon, and tri-synthon building blocks and capitalizes on the inherent hierarchical structure of these molecules by modeling latent reactions between embedded synthons. Additionally, we investigate methods to improve the observation models for DEL count data such as integrating covariate factors to more effectively account for data noise. Across two popular public benchmark datasets (CA-IX and HRP), our model demonstrates strong performance compared to count baselines, enriches the correct pharmacophores, and offers valuable insights via its intrinsic interpretable structure, thereby providing a robust tool for the analysis of DEL data

System and method for controlling a drilling path based on drift estimates

A method includes receiving toolface information corresponding to a location of the bottom hole assembly (BHA) with respect to a target drilling path and drift information. The surface steerable system calculates a first toolface vector from a first location of the BHA to the target drilling path to create a convergence path to the target drilling path and calculates an adjustment of the first toolface vector to a second toolface vector to account for system drift defined by the drift information such that the BHA will converge with the target drilling path by drilling in accordance with the second toolface vector. The surface steerable system modifies at least one drilling parameter to alter a drilling direction of the BHA based on the calculated second toolface vector and transmits the at least one drilling parameter to the drilling rig to target the BHA in accordance with the second toolface vector.Board of Regents, University of Texas Syste

Synthesis and characterization of novel copolymeric resveratrol conjugates

Resveratrol (RSV), naturally found in plants, is known to have health benefits and has been proposed as a potential anticancer and cardioprotective drug. However, due to its molecular structure, it undergoes rapid metabolism in the body resulting in low bioavailability. Novel polymeric methoxy-poly(ethylene glycol)-block-poly(e-caprolactone) (mPEG-PCL) RSV conjugates with varying PCL chain lengths have been synthesised and formulated into micelles and/or nanoparticles for preliminary in vitro stability studies. RSV conjugated with mPEG2000-PCL9500 was found to have improved solubility and stability of RSV as compared to RSV alone. The length of the PCL chain was found to affect the micelle formation, hence the stability in physiological buffers and rat plasma

A Stability Indicating HPLC Assay Method for Analysis of Rivastigmine Hydrogen Tartrate in Dual-Ligand Nanoparticle Formulation Matrices and Cell Transport Medium

The objective of this study was to develop and validate a method for quantitative analysis of rivastigmine hydrogen tartrate (RHT) in dual-ligand polymeric nanoparticle formulation matrices, drug release medium, and cellular transport medium. An isocratic HPLC analysis method using a reverse phase C 18 column and a simple mobile phase without buffer was developed, optimised, and fully validated. Analyses were carried out at a flow rate of 1.5 mL/min at 50°C and monitored at 214 nm. This HPLC method exhibited good linearity, accuracy, and selectivity. The recovery (accuracy) of RHT from all matrices was greater than 99.2%. The RHT peak detected in the samples of a forced degradation study, drug loading study, release study, and cellular transport study was pure and free of matrix interference. The limit of detection (LOD) and limit of quantification (LOQ) of the assay were 60 ng/mL and 201 ng/mL, respectively. The method was rugged with good intra- and interday precision. This stability indicating HPLC method was selective, accurate, and precise for analysing RHT loading and its stability in nanoparticle formulation, RHT release, and cell transport medium

In-domain relation discovery with meta-constraints via posterior regularization

We present a novel approach to discovering relations and their instantiations from a collection of documents in a single domain. Our approach learns relation types by exploiting meta-constraints that characterize the general qualities of a good relation in any domain. These constraints state that instances of a single relation should exhibit regularities at multiple levels of linguistic structure, including lexicography, syntax, and document-level context. We capture these regularities via the structure of our probabilistic model as well as a set of declaratively-specified constraints enforced during posterior inference. Across two domains our approach successfully recovers hidden relation structure, comparable to or outperforming previous state-of-the-art approaches. Furthermore, we find that a small set of constraints is applicable across the domains, and that using domain-specific constraints can further improve performance.United States. Defense Advanced Research Projects Agency (Machine Reading Program under Air Force Research Laboratory (AFRL) prime contract no. FA8750-09-C-0172