Self-Regularity of Non-Negative Output Weights for Overparameterized Two-Layer Neural Networks

We consider the problem of finding a two-layer neural network with sigmoid, rectified linear unit (ReLU), or binary step activation functions that "fits" a training data set as accurately as possible as quantified by the training error; and study the following question: \emph{does a low training error guarantee that the norm of the output layer (outer norm) itself is small?} We answer affirmatively this question for the case of non-negative output weights. Using a simple covering number argument, we establish that under quite mild distributional assumptions on the input/label pairs; any such network achieving a small training error on polynomially many data necessarily has a well-controlled outer norm. Notably, our results (a) have a polynomial (in $d$) sample complexity, (b) are independent of the number of hidden units (which can potentially be very high), (c) are oblivious to the training algorithm; and (d) require quite mild assumptions on the data (in particular the input vector $X\in\mathbb{R}^d$ need not have independent coordinates). We then leverage our bounds to establish generalization guarantees for such networks through \emph{fat-shattering dimension}, a scale-sensitive measure of the complexity class that the network architectures we investigate belong to. Notably, our generalization bounds also have good sample complexity (polynomials in $d$ with a low degree), and are in fact near-linear for some important cases of interest.Comment: 34 pages. Some of the results in the present paper are significantly strengthened versions of certain results appearing in arXiv:2003.1052

Longevity of organic pepper (Capsicum annuum L.) seeds

This study was carried out to determine seed longevity in organic and conventionally produced pepper seeds from four different pepper cultivars. Seeds were stored at 20± 2 oC with 7.5±0.5 seed moisture over 48 months. Longevity of seeds were evaluated with Ki (initial seed quality), P50 (half-viability period), σ (standard deviation of distribution of seed deaths in time), and regression coefficient values. The highest longevity was observed in ‘Corbaci’ and ‘Yaglik’ cultivars, while ‘Surmeli’ and ‘K. Dolma’ were found to have shorter longevity. P50 was 43.4 and 40.2 months for ‘Corbacı’ and 34.9 and 39.7 months for ‘Yaglık’ organic and conventional cultivars, respectively, whereas it was about 21.4 and 23.7 months in ‘K. Dolma’ and ‘Surmeli’ cultivars. Similarly, the highest σ and regression coefficient values were observed for ‘Corbaci’ and the lowest for ‘Surmeli’ cultivars. Organic and conventional pepper seed longevity was not different in the same species. Regression coefficient values were 0.043 in organic and 0.046 in conventional seeds for ‘Corbaci’. Very close values were found between the two production systems for the other cultivars too. Results indicate that organic seeds had similar longevity to conventional ones. The main differences originated from the cultivars, not from the production system

Componential coding in the condition monitoring of electrical machines Part 2: application to a conventional machine and a novel machine

This paper (Part 2) presents the practical application of componential coding, the principles of which were described in the accompanying Part 1 paper. Four major issues are addressed, including optimization of the neural network, assessment of the anomaly detection results, development of diagnostic approaches (based on the reconstruction error) and also benchmarking of componential coding with other techniques (including waveform measures, Fourier-based signal reconstruction and principal component analysis). This is achieved by applying componential coding to the data monitored from both a conventional induction motor and from a novel transverse flux motor. The results reveal that machine condition monitoring using componential coding is not only capable of detecting and then diagnosing anomalies but it also outperforms other conventional techniques in that it is able to separate very small and localized anomalies

Caspase-mediated cleavage of raptor participates in the inactivation of mTORC1 during cell death.

The mammalian target of rapamycin complex 1 (mTORC1) is a highly conserved protein complex regulating key pathways in cell growth. Hyperactivation of mTORC1 is implicated in numerous cancers, thus making it a potential broad-spectrum chemotherapeutic target. Here, we characterized how mTORC1 responds to cell death induced by various anticancer drugs such rapamycin, etoposide, cisplatin, curcumin, staurosporine and Fas ligand. All treatments induced cleavage in the mTORC1 component, raptor, resulting in decreased raptor-mTOR interaction and subsequent inhibition of the mTORC1-mediated phosphorylation of downstream substrates (S6K and 4E-BP1). The cleavage was primarily mediated by caspase-6 and occurred at two sites. Mutagenesis at one of these sites, conferred resistance to cell death, indicating that raptor cleavage is important in chemotherapeutic apoptosis

Invasive and non-invasive congeneric Centaurea (Asteraceae) show contrasting patterns of herbivory by snails

Background and aims – Once introduced into new regions, exotic species often experience shifts in resource allocation in response to the different environmental conditions found in the introduction range. Plants naturally respond to specialist herbivores with quantitative defences, by producing large amounts of toxic and non-toxic compounds that typically difficult digestion (e.g. tannins, cellulose), and to generalist herbivores with qualitative defences, like specialized noxious chemicals (e.g. alkaloids). The Shifting Defence Hypothesis (SDH) poses that invasive plants decrease the production of defences against specialist herbivores in their introduction range, where specialist herbivores are usually absent, while boosting the production of defences against generalist herbivores. Methods – We empirically assessed the response of a generalist herbivore, the common garden snail (Helix aspersa), to feeding with leaves of the annual herb Centaurea sulphurea, native to Europe and naturalized in North America; and the congeneric species C. solstitialis, which is also native to Europe and invasive in the Americas. Key results – Snails fed with leaves from Spanish native populations the non-invasive C. sulphurea grew significantly less compared to snails fed with leaves from non-native California. For snails fed with the invasive C. solstitialis significant differences were also found among regions, but the response was more complex, depending on population, with snails fed with Turkish and Australian plants presenting higher growth rates than the rest of the regions. Conclusions – Overall, our results stressed the importance of colonization history in shaping adaptive responses, and the stochasticity associated with colonization events of two closely related species, with contrasting invasive success and responses to herbivory.Fil: Filipe, João C.. Universidad de Coimbra; PortugalFil: Jorge, Andreia. Universidad de Coimbra; PortugalFil: Eren, Ozkan. Adnan Menderes Universitesi; TurquíaFil: Sotes, Gastón. Universidad de Concepción. Facultad de Ciencias Naturales y Oceanográficas. Departamento de Botánica; Chile. Universidad de Chile; ChileFil: Hierro, Jose Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Ciencias de la Tierra y Ambientales de La Pampa. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales. Instituto de Ciencias de la Tierra y Ambientales de La Pampa; Argentina. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Montesinos, Daniel. Universidad de Coimbra; Portuga

Financing Entrepreneurship and the Old-Boy Network

Abstract We study entrepreneurs' start-up …nancing from banks and local …nanciers. An informal network, whose membership cannot be observed by outsiders, conveys the good signals it gets about the hidden types of network entrepreneurs to local …nanciers, which are then re ‡ected in di¤erent loan terms. We show that there are winners and losers as a result of the network even among its members. Because all projects have positive net value, it is e¢ cient to …nance them even in the absence of a network. Thus, the formation of the network is ine¢ cient as entrepreneurs incur networking costs for purely redistributive gains in the form of better loan terms as network members