Ranking relations using analogies in biological and information networks

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects $\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}$, measures how well other pairs A:B fit in with the set $\mathbf{S}$. Our work addresses the following question: is the relation between objects A and B analogous to those relations found in $\mathbf{S}$? Such questions are particularly relevant in information retrieval, where an investigator might want to search for analogous pairs of objects that match the query set of interest. There are many ways in which objects can be related, making the task of measuring analogies very challenging. Our approach combines a similarity measure on function spaces with Bayesian analysis to produce a ranking. It requires data containing features of the objects of interest and a link matrix specifying which relationships exist; no further attributes of such relationships are necessary. We illustrate the potential of our method on text analysis and information networks. An application on discovering functional interactions between pairs of proteins is discussed in detail, where we show that our approach can work in practice even if a small set of protein pairs is provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS321 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Single spin asymmetries in inclusive hadron production from SIDIS to hadronic collisions: universality and phenomenology

In a perturbative QCD approach, with inclusion of spin and transverse momentum effects, experimental data on azimuthal asymmetries observed in polarized semi-inclusive deeply inelastic scattering and e+ e- annihilations can be used to determine the Sivers, transversity and Collins soft functions. By using these functions, within the same scheme, we predict p(transv. polarized) p -> h + X single spin asymmetries in remarkable agreement with RHIC experimental data.Comment: 5 pages, 6 ps figure

Lambda polarization in pp -> p\Lambda K^+ \pi^+\pi^-\pi^+\pi^-

We show that there is a correlation between the invariant mass of the produced \Lambda K^+, \Lambda K^+\pi^+\pi^- or \Lambda K^+ \pi^+\pi^-\pi^+\pi^- system in the exclusive reaction pp\to p\Lambda K^+\pi^+\pi^-\pi^+\pi^- and the longitudinal or transverse momentum of $\Lambda$. Together with the longitudinal and transverse momentum dependence of Lambda polarization observed in inclusive reactions, such a correlation implies a dependence of Lambda polarization on these invariant masses. The qualitative features of this dependence are consistent with the recent observation by E766 collaboration at BNL. A quantitative estimation has been made using an event generator for $pp$ collisions. A detailed comparison with the data is made.Comment: 10 pages with 3 figures, submitted to J. Phys.

Quantum Flux and Reverse Engineering of Quantum Wavefunctions

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wavefunction, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wavefunction.Comment: Accepted to EP

Imaging and manipulating electrons in a 1D quantum dot with Coulomb blockade microscopy

Motivated by the recent experiments by the Westervelt group using a mobile tip to probe the electronic state of quantum dots formed on a segmented nanowire, we study the shifts in Coulomb blockade peak positions as a function of the spatial variation of the tip potential, which can be termed "Coulomb blockade microscopy". We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high density electronic liquid state from a Wigner crystal state by microscopy with a weak tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other, and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one particle potential and kinetic energies. Finally, we propose that a weak tip Coulomb blockade micrograph focusing on the transition between electron number N=0 and N=1 states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.Comment: 4 pages 7 figure