An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csiszar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner bases method to compute an implicit representation of minimum KL-divergence models.

Two forms of Pf1 Inovirus: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the asymmetric unit

Inovirus is a helical array of alpha-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Bile-Acids in Asymmetric-Synthesis.2. Cholic-Acid Derived Novel Chiral Auxiliaries For Asymmetric Diels-Alder Reactions

Cholic acid-based chiral acrylate 5 yields a Diels-Alder adduct with cyclopent

Interaction of ecoP15I DNA methyltransferase with oligonucleotides containing the asymmetric sequence 5?-CAGCAG-3

EcoP15I DNA methyltransferase (Mtase) recognizes the asymmeteric sequence CAGCAG and catalyzes the transfer of a methyl group from S-adenosyl-L-methionine to the second adenine residue. We have investigated the DNA binding properties of EcoP15I DNA Mtase using gel mobility shift assays. EcoP15I DNA Mtase binds approximately threefold more tightly to DNA containing its recognition sequence, CAGCAG, than to non-specific sequences in the absence or presence of cofactors. Interestingly, in the presence of ATP the discrimination between specific and non-specific sequences increases significantly. These results suggest for the first time a role for ATP in DNA recognition by type III restriction-modification enzymes. In addition, we have shown that bromodeoxyuridine-containing oligonucleotides form complexes with EcoP15I DNA Mtase that are crosslinked upon irradiation. More importantly, we have shown that the crosslink site is at the site of DNA binding, since it can be suppressed by an excess of unmodified oligonucleotide. EcoP15I DNA Mtase exhibited Michaelis-Menten kinetics with both unmodified and bromodeoxyuridine-substituted DNA, with a higher specificity constant for the latter. Furthermore, gel mobility shift assays showed that proteolyzed EcoP15I DNA Mtase formed a specific complex with DNA, which had similar mobility as the native protein-DNA complex. Taken together these results form the basis fora detailed structure-function analysis of EcoP15I DNA Mtase.

Target space of an asymmetric chiral gauged wzw model

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the chiral gauged SL(2,R) WZW model, with the gauging of subgroups SO(1, 1) in the left and U(1) in the right moving sector, is obtained. We then analyze the symmetries of the background and show the presence of a non-trivial isometry in the canonical parametrization of the WZW model. Using these results, the equivalence of the asymmetric models with the symmetric ones is demonstrated.

Asymmetric Diels-Alder Reactions of Chiral Acrylates of Cholic Acid Derivatives

New steroid-based chiral auxiliaries 6, 9, and 12 have been synthesized from readily available cholic acid. These new chiral auxiliaries place the reactive and the shielding sites in a 1,5 relationship to each other. Diels-Alder reaction of cyclopentadiene with corresponding acrylate esters (7, 10, and 13) have been examined. Acrylates 7 and 10 yielded cycloadducts with 29-88% diastereomeric excess with excellent endo selectivity in the presence of an excess of Lewis acids such as AlCl3, BF3.OEt(2), FeCl3, SnCl4, TiCl4, and ZnCl2. Treatment of acrylate 7 with cyclopentadiene in the presence of BF3.OEt(2) at -80 degrees C gave the endo adduct (>99%) with 88% de. Lewis acid catalyzed and uncatalyzed reactions of acrylates 7 and 10 with cyclopentadiene yielded cycloadducts with opposite stereochemistry. The chiral auxiliary was recovered in a nondestructive manner only via iodolactonization. Acrylate ester of alcohol 12 did not show any selectivity in either catalyzed and uncatalyzed reactions with cyclopentadiene. The presence of a flat aromatic surface at C-7 of the steroid was found to be essential to effect high diastereoselection.

Asymmetric synthesis of steroidal Tröger's base analogues. X-Ray molecular structure of methyl 3?,12?-{6H,12H-5,11-methanodibenzo[b,f][1,5]diazocine-2,8-bisacetoxy}-5?-cholan-24-oate

Cyclization of compound 5c in trifluoroacetic acid/hexamethylenetetramine produces Tröger's base analogue 6c in 75% yield with 70% diastereoselectivity.

Bile acids in asymmetric synthesis and molecular recognition

This account summarizes the progress made in our laboratory towards the development of new uses of naturally occurring bile acids. Applications in Asymmetric Synthesis (intramolecular coupling, and intermolecular reactions) and Molecular Recognition are described with suitable examples.

Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

Template directed asymmetric synthesis of the 1,1?-binaphthol unit

An oxidative binaphthol coupling with 65% yield and 65% selectivity has been accomplished using 7-deoxycholic acid as a chiral template.

Analytical Study of Low-Field Diffusive Transport in Highly Asymmetric Bilayer Graphene Nanoribbon

We present a simplified theory of carrier backscattering coefficient in a twofold degenerate asymmetric bilayer graphene nanoribbon (BGN) under the application of a low static electric field. We show that for a highly asymmetric BGN(Delta = gamma), the density of states in the lower subband increases more that of the upper, in which Delta and gamma are the gap and the interlayer coupling constant, respectively. We also demonstrate that under the acoustic phonon scattering regime, the formation of two distinct sets of energy subbands signatures a quantized transmission coefficient as a function of ribbon width and provides an extremely low carrier reflection coefficient for a better Landauer conductance even at room temperature. The well-known result for the ballistic condition has been obtained as a special case of the present analysis under certain limiting conditions which forms an indirect validation of our theoretical formalism.

Asymmetric Warps in Disk Galaxies: Dependence on Dark Matter Halo

Recent observations have shown that most of the warps in the disk galaxies are asymmetric. However there exists no generic mechanism to generate these asymmetries in warps. We have shown that a rich variety of possible asymmetries in the z-distribution of the spiral galaxies can naturally arise due to a dynamical wave interference between the first two bending modes i.e. bowl-shaped mode(m=0) and S-shaped warping mode(m = 1) in the galactic disk embedded in a dark matter halo. We show that the asymmetric warps are more pronounced when the dark matter content within the optical disk is lower as in early-type galaxies.

An asymmetric cascaded H-Bridge inverters for generating 12-sided polygonal space vector diagrams for Motor drives

A new topology of asymmetric cascaded H-Bridge inverter is presented in this paper It consists of two cascaded H-bridge cells per phase. They are fed from isolated dc sources having a dc bus ratio of 1:0.366. Out of many space vectors possible from this circuit, only those are chosen that lie on 12-sided polygons. Thus, the overall space vector diagram produced by this circuit consists of multiple numbers of 12-sided polygons. With a proper PWM timing calculations based on these selected space vectors, it is possible to eliminate all the 6n +/- 1, (n = odd) harmonics from the phase voltage under all operating conditions. The switching frequency of individual H-Bridge cells is also substantially low. Extensive experimental results have been presented in this paper to validate the proposed concept.