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

The impact of crop management regime on oil content and fatty acid composition in hulless and covered spring barley

Received: November 11th, 2021 ; Accepted: January 30th, 2022 ; Published: March 17th, 2022 ; Correspondence: [email protected] are a minor nutritional component of barley (Hordeum vulgare L.) grain and have not been as widely explored as the major components. The aim of this study was to investigate the effect of genotype and environment, including conventional farming system with three crop management regimes, differing in agrochemical input, and organic farming system, on oil content and fatty acid composition in grain of two covered and four hulless spring barley genotypes during two growing seasons. Genotype significantly affected oil content and it was on average 4.26% and ranged in individual barley samples from 2.87 to 5.53%. We found linoleic, oleic, palmitic, α-linolenic, stearic and capric fatty acids in average proportions of 55.6; 21.3; 18.6; 3.7; 0.6 and 0.4%, respectively. Higher average oil content and proportion of α-linolenic acid was found in covered barley. Crop management regime did not significantly affect oil content but had some effect on the proportion of linoleic, α-linolenic, oleic and stearic acid. Decrease of chemical inputs was in favour of oil content and proportion of α-linolenic, oleic and stearic acids but did not promote linoleic acid. Waxy hulless barley line with high oil content and a very high proportion of linoleic acid was identified

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

Combined investigation of collective amplitude and phase modes in a quasi-one-dimensional charge-density-wave system over a wide spectral range

We investigate experimentally both the amplitude and phase channels of the collective modes in the quasi-1D charge-density-wave (CDW) system, K0.3MoO3, by combining (i) optical impulsive-Raman pump-probe and (ii) terahertz time-domain spectroscopy (THz-TDS), with high resolution and a detailed analysis of the full complex-valued spectra in both cases. This allows an unequivocal assignment of the observed bands to CDW modes across the THz range up to 9 THz. We revise and extend a time-dependent Ginzburg-Landau model to account for the observed temperature dependence of the modes, where the combination of both amplitude and phase modes allows one to robustly determine the bare-phonon and electron-phonon coupling parameters. While the coupling is indeed strongest for the lowest-energy phonon, dropping sharply for the immediately subsequent phonons, it grows back significantly for the higher-energy phonons, demonstrating their important role in driving the CDW formation. We also include a reassessment of our previous analysis of the lowest-lying phase modes, whereby assuming weaker electronic damping for the phase channel results in a qualitative picture more consistent with quantum-mechanical treatments of the collective modes, with a strongly coupled amplitudon and phason as the lowest modes

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