Sorting under partial information (without the ellipsoid algorithm)

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown linear extension of P, using pairwise comparisons. The information-theoretic lower bound on the number of comparisons needed in the worst case is log e(P), the binary logarithm of the number of linear extensions of P. In a breakthrough paper, Jeff Kahn and Jeong Han Kim (STOC 1992) showed that there exists a polynomial-time algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our approach relies on graph entropy. However, our algorithms differ in essential ways from theirs. Rather than resorting to convex programming for computing the entropy, we approximate the entropy, or make sure it is computed only once in a restricted class of graphs, permitting the use of a simpler algorithm. Specifically, we present: an O(n2) algorithm performing O(log n·log e(P)) comparisons; an O(n2.5) algorithm performing at most (1+ε) log e(P) + Oε(n) comparisons; an O(n2.5) algorithm performing O(log e(P)) comparisons. All our algorithms are simple to implement. © 2010 ACM.

Solo and Chamber Music of Pulitzer Prize-Winning Composers

The Pulitzer Prize in Music, established in 1943, is one of America's most prestigious awards. It has been awarded to fifty-three composers for a "distinguished musical composition of significant dimension by an American that has had its first performance in the United States during the year." Composers who have won the Pulitzer Prize are considered to be at the pinnacle of their creativity and have provided the musical world with classical music compositions worthy of future notice. By tracing the history of Pulitzer Prize-winning composers and their compositions, researchers and musicians enhance their understanding of the historical evolution of American music, and its impact on American culture. Although the clarinet music of some of these composers is rarely performed today, their names will be forever linked to the Pulitzer, and because of that, their compositions will enjoy a certain sense of immortality. Of the fifty-four composers who have won the award, forty-seven have written for the clarinet in a solo or chamber music setting (five or less instruments). Just as each Pulitzer Prize-winning composition is a snapshot of the state of American music at that time, these works trace the history of American clarinet musical development, and therefore, they are valuable additions to the clarinet repertoire and worthy of performance. This dissertation project consists of two recitals featuring the solo and chamber clarinet music of sixteen Pulitzer Prize-winning composers, extended program notes containing information on each composer's life, their music, the Pulitzer Prize-winning composition and the recital selection, and a complete list of all Pulitzer Prize-winning composers and their solo and chamber clarinet music. Featured Composers Dominick Argento, To Be Sung Upon the Water Leslie Bassett, Soliloquies William Bolcom, Little Suite of Four Dances Aaron Copland, As it Fell Upon a Day John Corigliano, Soliloquy Norman Dello Joio, Concertante Morton Gould, Benny's Gig Charles Ives, Largo Douglas Moore, Quintet for Clarinet and Strings George Perle, Three Sonatas Quincy Porter, Quintet for Clarinet and Strings Mel Powell, Clarinade Shulamit Ran, Private Game Joseph Schwantner, Entropy Leo Sowerby, Sonata Ernst Toch, Adagio elegiaco

Constructal dendritic configuration for the radiation heating of a solid stream

Here we show that the configuration of a slender enclosure can be optimized such that the radiation heating of a stream of solid is performed with minimal fuel consumption at the global level. The solid moves longitudinally at constant rate through the enclosure. The enclosure is heated by gas burners distributed arbitrarily, in a manner that is to be determined. The total contact area for heat transfer between the hot enclosure and the cold solid is fixed. We find that minimal global fuel consumption is achieved when the longitudinal distribution of heaters is nonuniform, with more heaters near the exit than the entrance. The reduction in fuel consumption relative to when the heaters are distributed uniformly is of order 10%. Tapering the plan view (the floor) of the heating area yields an additional reduction in overall fuel consumption. The best shape is when the floor area is a slender triangle on which the cold solid enters by crossing the base. These architectural features recommend the proposal to organize the flow of the solid as a dendritic design, which enters as several branches, and exits as a single hot stream of prescribed temperature. The thermodynamics of heating is presented in modern terms in the Sec. (exergy destruction, entropy generation). The contribution is that to optimize "thermodynamically" is the same as reducing the consumption of fuel. © 2010 American Institute of Physics.

Identification and inhibitory properties of a novel Ca(2+)/calmodulin antagonist.

We developed a high-throughput yeast-based assay to screen for chemical inhibitors of Ca(2+)/calmodulin-dependent kinase pathways. After screening two small libraries, we identified the novel antagonist 125-C9, a substituted ethyleneamine. In vitro kinase assays confirmed that 125-C9 inhibited several calmodulin-dependent kinases (CaMKs) competitively with Ca(2+)/calmodulin (Ca(2+)/CaM). This suggested that 125-C9 acted as an antagonist for Ca(2+)/CaM rather than for CaMKs. We confirmed this hypothesis by showing that 125-C9 binds directly to Ca(2+)/CaM using isothermal titration calorimetry. We further characterized binding of 125-C9 to Ca(2+)/CaM and compared its properties with those of two well-studied CaM antagonists: trifluoperazine (TFP) and W-13. Isothermal titration calorimetry revealed that binding of 125-C9 to CaM is absolutely Ca(2+)-dependent, likely occurs with a stoichiometry of five 125-C9 molecules to one CaM molecule, and involves an exchange of two protons at pH 7.0. Binding of 125-C9 is driven overall by entropy and appears to be competitive with TFP and W-13, which is consistent with occupation of similar binding sites. To test the effects of 125-C9 in living cells, we evaluated mitogen-stimulated re-entry of quiescent cells into proliferation and found similar, although slightly better, levels of inhibition by 125-C9 than by TFP and W-13. Our results not only define a novel Ca(2+)/CaM inhibitor but also reveal that chemically unique CaM antagonists can bind CaM by distinct mechanisms but similarly inhibit cellular actions of CaM.

Universal quantum viscosity in a unitary Fermi gas.

A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, in which the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale ħ n, where n is the density and ħ is Planck's constant h divided by 2π, whereas at high temperatures the natural scale is p(T)(3)/ħ(2), where p(T) is the thermal momentum. We used breathing mode damping to measure the shear viscosity at low temperature. At high temperature T, we used anisotropic expansion of the cloud to find the viscosity, which exhibits precise T(3/2) scaling. In both experiments, universal hydrodynamic equations including friction and heating were used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare it with that of a perfect fluid.

Communications inspired linear discriminant analysis

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods, and comparisons are also made with a method in which Rényi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets. Copyright 2012 by the author(s)/owner(s).

Statistical analysis of crystallization database links protein physico-chemical features with crystallization mechanisms.

X-ray crystallography is the predominant method for obtaining atomic-scale information about biological macromolecules. Despite the success of the technique, obtaining well diffracting crystals still critically limits going from protein to structure. In practice, the crystallization process proceeds through knowledge-informed empiricism. Better physico-chemical understanding remains elusive because of the large number of variables involved, hence little guidance is available to systematically identify solution conditions that promote crystallization. To help determine relationships between macromolecular properties and their crystallization propensity, we have trained statistical models on samples for 182 proteins supplied by the Northeast Structural Genomics consortium. Gaussian processes, which capture trends beyond the reach of linear statistical models, distinguish between two main physico-chemical mechanisms driving crystallization. One is characterized by low levels of side chain entropy and has been extensively reported in the literature. The other identifies specific electrostatic interactions not previously described in the crystallization context. Because evidence for two distinct mechanisms can be gleaned both from crystal contacts and from solution conditions leading to successful crystallization, the model offers future avenues for optimizing crystallization screens based on partial structural information. The availability of crystallization data coupled with structural outcomes analyzed through state-of-the-art statistical models may thus guide macromolecular crystallization toward a more rational basis.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.

Comparison of the thermodynamics and base-pair dynamics of a full LNA:DNA duplex and of the isosequential DNA:DNA duplex

Locked nucleic acids (LNA), conformationally restricted nucleotide analogues, are known to enhance pairing stability and selectivity toward complementary strands. With the aim to contribute to a better understanding of the origin of these effects, the structure, thermal stability, hybridization thermodynamics, and base-pair dynamics of a full-LNA:DNA heteroduplex and of its isosequential DNA:DNA homoduplex were monitored and compared. CD measurements highlight differences in the duplex structures: the homoduplex and heteroduplex present B-type and A-type helical conformations, respectively. The pairing of the hybrid duplex is characterized, at all temperatures monitored (between 15 and 37 degrees C), by a larger stability constant but a less favorable enthalpic term. A major contribution to this thermodynamic profile emanates from the presence of a hairpin structure in the LNA single strand which contributes favorably to the entropy of interaction but leads to an enthalpy penalty upon duplex formation. The base-pair opening dynamics of both systems was monitored by NMR spectroscopy via imino protons exchange measurements. The measurements highlight that hybrid G-C base-pairs present a longer base-pair lifetime and higher stability than natural G-C base-pairs, but that an LNA substitution in an A-T base-pair does not have a favorable effect on the stability. The thermodynamic and dynamic data confirm a more favorable stacking of the bases in the hybrid duplex. This study emphasizes the complementarities between dynamic and thermodynamical studies for the elucidation of the relevant factors in binding events.

Analysis of species hyper-diversity in the tropical rain forests of Indonesia: the problem of non-observance

The main interest in the assessment of forest species diversity for conservation purposes is in the rare species. The main problem in the tropical rain forests is that most of the species are rare. Assessment of species diversity in the tropical rain forests is therefore often concerned with estimating that which is not observed in recorded samples. Statistical methodology is therefore required to try to estimate the truncated tail of the species frequency distribution, or to estimate the asymptote of species/diversity-area curves. A Horvitz-Thompson estimator of the number of unobserved (“virtual”) species in each species intensity class is proposed. The approach allows a definition of an extended definition of diversity, ( or generalised Renyi entropy). The paper presents a case study from data collected in Jambi, Sumatra, and the “extended diversity measure” is used on the species data.

Novel inclusion complex of ibuprofen tromethamine with cyclodextrins: Physico-chemical characterization

Guest-host interactions of ibuprofen tromethamine salt (Ibu.T) with native and modified cyclodextrins (CyDs) have been investigated using several techniques, namely phase solubility diagrams (PSDs), proton nuclear magnetic resonance (H-1 NMR), differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), X-ray powder diffractometry (XRPD). scanning-electron microscopy (SEM) and molecular mechanics (MM). From the analysis of PSD data (A(L)-type) it is concluded that the anionic tromethamine salt of ibuprofen (pK(a) = 4.55) forms 1: 1 soluble complexes with all CyDs investigated in buffered water at pH 7.0, while the neutral form of Ibu forms an insoluble complex with beta-CyD (B-S-type) in buffered water at pH 2.0. Ibu.T has a lower tendency to complex with beta-CyD (K-11 = 58 M-1 at pH 7.0) compared with the neutral Ibu (K-11 = 4200 M (1)) in water. Complex formation of Ibu.T with beta-CyD (Delta G degrees = -20.4 kJ/mol) is enthalpy driven (Delta H degrees = -22.9 kJ/mol) and is accompanied by a small unfavorable entropy (Delta S degrees = -8.4 J/mol K) change. H-1 NMR studies and MM computations revealed that, on complexation, the hydrophobic central benzene ring of lbu.T and part of the isobutyl group reside within the beta-CyD cavity leaving the peripheral groups (carboxylate, tromethamine and methyl groups) located near the hydroxyl group networks at either rim of beta-CyD. PSD, H-1 NMR, DSC, FT-IR, XRPD, SEM and MM studies confirmed the formation of Ibu.T/beta-CyD inclusion complex in solution and the solid state. (C) 2009 Elsevier B.V. All rights reserved.

Determination of micelle/water partition coefficients and associated thermodynamic data for dialkyl phthalate esters

Micelle/water partition coefficients for three dialkyl phthalate esters - dimethyl phthalate ester (DMP), diethyl phthalate ester (DEP) and dipropyl phthalate ester (DPP) were obtained by micellar liquid chromatography (MLC). Experiments were conducted over a temperature range which led to calculation of a Gibbs free energy, enthalpy and entropy of transfer for the phthalate esters. In addition, small angle neutron scattering (SANS) experiments were conducted with no substantial change observed in micelle size before and after phthalate ester incorporation. Overall, a novel method for obtaining thermodynamic information, based on partitioning data, has been developed for dialkyl phthalate esters using micellar liquid chromatography.

A machine vision approach to the grading of crushed aggregate

The grading of crushed aggregate is carried out usually by sieving. We describe a new image-based approach to the automatic grading of such materials. The operational problem addressed is where the camera is located directly over a conveyor belt. Our approach characterizes the information content of each image, taking into account relative variation in the pixel data, and resolution scale. In feature space, we find very good class separation using a multidimensional linear classifier. The innovation in this work includes (i) introducing an effective image-based approach into this application area, and (ii) our supervised classification using wavelet entropy-based features.

A reactive force field simulation of liquid-liquid phase transitions in phosphorus

A force field model of phosphorus has been developed based on density functional (DF) computations and experimental results, covering low energy forms of local tetrahedral symmetry and more compact (simple cubic) structures that arise with increasing pressure. Rules tailored to DF data for the addition, deletion, and exchange of covalent bonds allow the system to adapt the bonding configuration to the thermodynamic state. Monte Carlo simulations in the N-P-T ensemble show that the molecular (P-4) liquid phase, stable at low pressure P and relatively low temperature T, transforms to a polymeric (gel) state on increasing either P or T. These phase changes are observed in recent experiments at similar thermodynamic conditions, as shown by the close agreement of computed and measured structure factors in the molecular and polymer phases. The polymeric phase obtained by increasing pressure has a dominant simple cubic character, while the polymer obtained by raising T at moderate pressure is tetrahedral. Comparison with DF results suggests that the latter is a semiconductor, while the cubic form is metallic. The simulations show that the T-induced polymerization is due to the entropy of the configuration of covalent bonds, as in the polymerization transition in sulfur. The transition observed with increasing P is the continuation at high T of the black P to arsenic (A17) structure observed in the solid state, and also corresponds to a semiconductor to metal transition. (C) 2004 American Institute of Physics.

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains [Part I, J. Chem. Phys. 118, 9257 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450less than or equal toTless than or equal to850 K and P=0 starting from monodisperse S-8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T-max that depends on DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(max), because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S-8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S-8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.