On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Design of speaker identification schemes for large number of speakers (A)

Design of speaker identification schemes for a small number of speakers (around 10) with a high degree of accuracy in controlled environment is a practical proposition today. When the number of speakers is large (say 50–100), many of these schemes cannot be directly extended, as both recognition error and computation time increase monotonically with population size. The feature selection problem is also complex for such schemes. Though there were earlier attempts to rank order features based on statistical distance measures, it has been observed only recently that the best two independent measurements are not the same as the combination in two's for pattern classification. We propose here a systematic approach to the problem using the decision tree or hierarchical classifier with the following objectives: (1) Design of optimal policy at each node of the tree given the tree structure i.e., the tree skeleton and the features to be used at each node. (2) Determination of the optimal feature measurement and decision policy given only the tree skeleton. Applicability of optimization procedures such as dynamic programming in the design of such trees is studied. The experimental results deal with the design of a 50 speaker identification scheme based on this approach.

Synthesis, crystal structures and magnetic behavior of two 3D coordination polymers using N-(4/3-arboxyphenyl)iminodiacetic acids as bridging ligands

Research on structure and magnetic properties of polynuclear metal complexes to understand the structural and chemical factors governing the electronic exchange coupling mediated by multi-atom bridging ligands is of growing interest. Hydrothermal treatment of Ni(NO3)(2)center dot 6H(2)O with N-(4-carboxyphenyl)iminodiacetic acid N-4(H(3)CPIDA)] at 150 degrees C yielded a 3D coordination polymer of general formula Ni-3{N-4( CPIDA)}(2)(H2O)(3)]center dot 6H(2)O (1). An analogous network of general formula Co-3{N-3(CPIDA)}(2)(H2O)(3)]center dot 3H(2)O (2) was synthesized using N-(3-carboxyphenyl) iminodiacetic acid N-3(H(3)CPIDA)] in combination with Co(NO3)(2)center dot 6H(2)O under identical reaction condition. Both the complexes contain trinuclear secondary building unit, and crystallized in monoclinic system with space groups C2/c (1) and P2(1)/c (2), respectively. Variable temperature magnetic characterization of these complexes in the temperature range of 2-300 K indicated the presence of overall ferromagnetic and antiferromagnetic behavior for 1 and 2, respectively. Density functional theory calculations (B3LYP functional) were performed for further insight on the trinuclear units to provide a qualitative theoretical interpretation on the overall magnetic behavior of the complexes 1 and 2. (C) 2010 Elsevier B.V. All rights reserved.

Correlations between frequency of infra-red active vibrational modes and copper-oxygen distance in copper oxides. Application to superconductors

The infra-red spectra of a large number of ternary Cu(II) oxides with at least a quasi square-planar coordination of oxygen around the copper ions have been studied. The frequency of the bands with the highest frequency,v max, is found to correlate extremely well with the shortest Cu–O distance.v max increases at an impressive rate of sim20 cm–1 per 0.01 Å when the Cu–O distance becomes less than 1.97 Å, which is the Cu2+–O2– distance in square-planar CuO4 complexes as obtained from empirical ionic radii considerations. The marked sensitivity may be used as a ldquotitrationrdquo procedure not only to assign bands but also to obtain diagnostic information about local coordination in compounds derived, for example, from the YBa2Cu3O7–d structure such as LaCaBaCu3O7–d . The only example where this correlation fails is in the two-layer non-superconducting oxides derived from La2(Ca, Sr)Cu2O6. The significance of this result is discussed. The marked dependence of frequency on the bond-distance is qualitatively examined in terms of an increased electron-phonon coupling to account for the observed tendency of the superconducting transition temperature to go through a maximum as the average basal plane Cu–O distance is decreased.

Novel coordination behaviour of gem-bis (pyrazolyl) cyclotriphosphazenes as tridentate NNN-donor ligands: The crystal structure of [Mo(CO)3{N3P3Ph4(3,5-Me2C3HN2)2}]

Reactions of group 6 metal carbonyls with bis(pyrazolyl) phosphazenes yield metal tricarbonyl complexes, [M(CO)3.L] [L = N3P3Ph4 (3, 5-Me2C3HN2)2 (1) or N3P3(MeNCH2CH2O)2 (3,5-Me2C3HN2)2(4)]. The structure of the complex [Mo(CO)3.1], determined by single-crystal X-ray analysis, shows that the (pyrazolyl) phosphazene acts as a tridentate ligand; the two pyridinic pyrazolyl nitrogen atoms and a phosphazene ring nitrogen atom are coordinated to the metal. A similar structure is proposed for the complexes [M(CO)3.4] (M = Mo or W] on the basis of their spectroscopic data.

Nuclear-quadrupole resonance in coordination chemistry- identification of bridiging and therminal chlorines in the mercuric chloride-4-picoline n-oxide complex

The temperature dependence of the chlorine-35 n.q.r. in the mercuric chloride-4-picoline N-oxide complex has been studied from 77 K to room temperature, and the results are used to assign the observed frequencies to terminal and bridging chlorines.

Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Ruthenium-Oxygen Coordination-Driven Self-Assembly of a Ru-8(II) Incomplete Prism: Synthesis, Structure, and Shape-Selective Molecular Recognition Study

Coordination-driven self-assembly of 1,3,5-benzenetricarboxylate (tma; 1) and oxalato-bridged p-cymeneruthenium(II) building block Ru-2(mu-eta(4)-C2O4)(MeOH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (2) affords an unusual octanuclear incomplete prism Ru-8(eta(6)-p-cymene)(8)(tma)(2)(mu-eta(4)-C2O4)(2)(OMe)(4)](O3SCF3)( 2) (3), which exhibits a remarkable shape-selective binding affinity for neutral phenolic compounds via hydrogen-bonding interactions (p-cymene = p-(PrC6H4Me)-Pr-i). Such a binding was confirmed by single-crystal X-ray diffraction analysis using 1,3,5-trihydroxybenzene as an analyte.

Effect of coordinated ions on structure and flexiblity of parallel G-quandruplexes: a molecular dynamics study

Single tract guanine residues can associate to form stable parallel quadruplex structures in the presence of certain cations. Nanosecond scale molecular dynamics simulations have been performed on fully solvated fibre model of parallel d(G7) quadruplex structures with Na+ or K+ ions coordinated in the cavity formed by the 06 atoms of the guanine bases. The AMBER 4.1 force field and Particle Mesh Ewald technique for electrostatic interactions have been used in all simulations. These quadruplex structures are stable during the simulation, with the middle four base tetrads showing root mean square deviation values between 0.5 to 0.8 A from the initial structure as well the high resolution crystal structure. Even in the absence of any coordinated ion in the initial structure, the G-quadruplex structure remains intact throughout the simulation. During the 1.1 ns MD simulation, one Na+ counter ion from the solvent as well as several water molecules enter the central cavity to occupy the empty coordination sites within the parallel quadruplex and help stabilize the structure. Hydrogen bonding pattern depends on the nature of the coordinated ion, with the G-tetrad undergoing local structural variation to accommodate cations of different sizes. In the absence of any coordinated ion, due to strong mutual repulsion, 06 atoms within G-tetrad are forced farther apart from each other, which leads to a considerably different hydrogen bonding scheme within the G-tetrads and very favourable interaction energy between the guanine bases constituting a G-tetrad. However, a coordinated ion between G-tetrads provides extra stacking energy for the G-tetrads and makes the quadruplex structure more rigid. Na+ ions, within the quadruplex cavity, are more mobile than coordinated K+ ions. A number of hydrogen bonded water molecules are observed within the grooves of all quadruplex structures

Chemical Shift of the X-Ray K-Absorption Edge of Cu in Some of Its Compounds, Complexes and Superconductors

Chemical shifts, ΔE, of the X-ray K-absorption edge in several compounds, complexes of copper including its superconducting oxides possessing formal oxidation states +1 and +2 have been measured. It has been shown that the chemical shift is primarily governed by the effective ionic charge on the absorbing ion and the nature of the atoms in the first coordination shell around the absorbing ion. The relation between the chemical shift, ΔE , and the effective charge q on the absorbing ion is found to be ΔE=Aq+Bq2+Cq3+Dq4 (A, B, C and D are constants). The effects of electronegativity, atomic number, oxidation state, crystal structure, the valence d-orbital electrons, etc. on the X-ray absorption chemical shift have been discussed. ©1990 The Physical Society of Japan