Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Colloidal ionic complexes on periodic substrates: ground state configurations and pattern switching

We theoretically and numerically studied ordering of "colloidal ionic clusters" on periodic substrate potentials as those generated by optical trapping. Each cluster consists of three charged spherical colloids: two negatively and one positively charged. The substrate is a square or rectangular array of traps, each confining one such cluster. By varying the lattice constant from large to small, the observed clusters are first rod-like and form ferro- and antiferro-like phases, then they bend into a banana-like shape and finally condense into a percolated structure. Remarkably, in a broad parameter range between single-cluster and percolated structures, we have found stable supercomplexes composed of six colloids forming grape-like or rocket-like structures. We investigated the possibility of macroscopic pattern switching by applying external electrical fields.Comment: 14 pages, 13 figure

Ultrafast dynamics of coherent optical phonons and nonequilibrium electrons in transition metals

The femtosecond optical pump-probe technique was used to study dynamics of photoexcited electrons and coherent optical phonons in transition metals Zn and Cd as a function of temperature and excitation level. The optical response in time domain is well fitted by linear combination of a damped harmonic oscillation because of excitation of coherent $E_{2g}$ phonon and a subpicosecond transient response due to electron-phonon thermalization. The electron-phonon thermalization time monotonically increases with temperature, consistent with the thermomodulation scenario, where at high temperatures the system can be well explained by the two-temperature model, while below $\approx$ 50 K the nonthermal electron model needs to be applied. As the lattice temperature increases, the damping of the coherent $E_{2g}$ phonon increases, while the amplitudes of both fast electronic response and the coherent $E_{2g}$ phonon decrease. The temperature dependence of the damping of the $E_{2g}$ phonon indicates that population decay of the coherent optical phonon due to anharmonic phonon-phonon coupling dominates the decay process. We present a model that accounts for the observed temperature dependence of the amplitude assuming the photoinduced absorption mechanism, where the signal amplitude is proportional to the photoinduced change in the quasiparticle density. The result that the amplitude of the $E_{2g}$ phonon follows the temperature dependence of the amplitude of the fast electronic transient indicates that under the resonant condition both electronic and phononic responses are proportional to the change in the dielectric function.Comment: 10 pages, 9 figures, to appear in Physical Review

Global expression analysis of the yeast Lachancea (saccharomyces) kluyveri reveals new URC genes involved in pyrimidine catabolism

Pyrimidines are important nucleic acid precursors which are constantly synthesized, degraded, and rebuilt in the cell. Four degradation pathways, two of which are found in eukaryotes, have been described. One of them, the URC pathway, has been initially discovered in our laboratory in the yeast Lachancea kluyveri. Here, we present the global changes in gene expression in L. kluyveri in response to different nitrogen sources, including uracil, uridine, dihydrouracil, and ammonia. The expression pattern of the known URC genes, URC1-6, helped to identify nine putative novel URC genes with a similar expression pattern. The microarray analysis provided evidence that both the URC and PYD genes are under nitrogen catabolite repression in L. kluyveri and are induced by uracil or dihydrouracil, respectively. We determined the function of URC8, which was found to catalyze the reduction of malonate semialdehyde to 3-hydroxypropionate, the final degradation product of the pathway. The other eight genes studied were all putative permeases. Our analysis of double deletion strains showed that the L. kluyveri Fui1p protein transported uridine, just like its homolog in Saccharomyces cerevisiae, but we demonstrated that is was not the only uridine transporter in L. kluyveri. We also showed that the L. kluyveri homologs of DUR3 and FUR4 do not have the same function that they have in S. cerevisiae, where they transport urea and uracil, respectively. In L. kluyveri, both of these deletion strains grew normally on uracil and urea

The Dynamics of Viral Marketing

We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We analyze how user behavior varies within user communities defined by a recommendation network. Product purchases follow a 'long tail' where a significant share of purchases belongs to rarely sold items. We establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies communities, product and pricing categories for which viral marketing seems to be very effective

Determining γ\gamma using B±→DK±B^\pm \to D K^\pm with multibody D decays

We propose a method for determining $\gamma$ using $B^\pm\to D K^\pm$ decays followed by a multibody $D$ decay, such as $D \to K_S \pi^-\pi^+$, $D \to K_S K^-K^+$ and $D \to K_S \pi^-\pi^+\pi^0$. The main advantages of the method is that it uses only Cabibbo allowed $D$ decays, and that large strong phases are expected due to the presence of resonances. Since no knowledge about the resonance structure is needed, $\gamma$ can be extracted without any hadronic uncertainty.Comment: 17 pages, 1 figur

Flavor Violating Higgs Decays

We study a class of nonstandard interactions of the newly discovered 125 GeV Higgs-like resonance that are especially interesting probes of new physics: flavor violating Higgs couplings to leptons and quarks. These interaction can arise in many frameworks of new physics at the electroweak scale such as two Higgs doublet models, extra dimensions, or models of compositeness. We rederive constraints on flavor violating Higgs couplings using data on rare decays, electric and magnetic dipole moments, and meson oscillations. We confirm that flavor violating Higgs boson decays to leptons can be sizeable with, e.g., h -> tau mu and h -> tau e branching ratios of order 10% perfectly allowed by low energy constraints. We estimate the current LHC limits on h -> tau mu and h -> tau e decays by recasting existing searches for the SM Higgs in the tau-tau channel and find that these bounds are already stronger than those from rare tau decays. We also show that these limits can be improved significantly with dedicated searches and we outline a possible search strategy. Flavor violating Higgs decays therefore present an opportunity for discovery of new physics which in some cases may be easier to access experimentally than flavor conserving deviations from the Standard Model Higgs framework.Comment: 39 pages, 12 figures, 3 tables; v2: Improved referencing, updated mu -> 3e bounds to include large loop contributions, corrected single top constraints; conclusions unchanged; matches version to be published in JHEP; v3: included 2-loop contributions in mu -> e conversion, improved discussion of tau -> 3 mu and of EDM constraints on FV top-Higgs couplings; conclusions unchange

B --> pi and B --> K transitions in partially quenched chiral perturbation theory

We study the properties of the B-->pi and B-->K transition form factors in partially quenched QCD by using the approach of partially quenched chiral perturbation theory combined with the static heavy quark limit. We show that the form factors change almost linearly when varying the value of the sea quark mass, whereas the dependence on the valence quark mass contains both the standard and chirally divergent (quenched) logarithms. A simple strategy for the chiral extrapolations in the lattice studies with Nsea=2 is suggested. It consists of the linear extrapolations from the realistically accessible quark masses, first in the sea and then in the valence quark mass. From the present approach, we estimate the uncertainty induced by such extrapolations to be within 5%.Comment: Published versio