Neural frames: A Tool for Studying the Tangent Bundles Underlying Image Datasets and How Deep Learning Models Process Them

The assumption that many forms of high-dimensional data, such as images, actually live on low-dimensional manifolds, sometimes known as the manifold hypothesis, underlies much of our intuition for how and why deep learning works. Despite the central role that they play in our intuition, data manifolds are surprisingly hard to measure in the case of high-dimensional, sparsely sampled image datasets. This is particularly frustrating since the capability to measure data manifolds would provide a revealing window into the inner workings and dynamics of deep learning models. Motivated by this, we introduce neural frames, a novel and easy to use tool inspired by the notion of a frame from differential geometry. Neural frames can be used to explore the local neighborhoods of data manifolds as they pass through the hidden layers of neural networks even when one only has a single datapoint available. We present a mathematical framework for neural frames and explore some of their properties. We then use them to make a range of observations about how modern model architectures and training routines, such as heavy augmentation and adversarial training, affect the local behavior of a model.Comment: 21 page

Convolutional networks inherit frequency sensitivity from image statistics

It is widely acknowledged that trained convolutional neural networks (CNNs) have different levels of sensitivity to signals of different frequency. In particular, a number of empirical studies have documented CNNs sensitivity to low-frequency signals. In this work we show with theory and experiments that this observed sensitivity is a consequence of the frequency distribution of natural images, which is known to have most of its power concentrated in low-to-mid frequencies. Our theoretical analysis relies on representations of the layers of a CNN in frequency space, an idea that has previously been used to accelerate computations and study implicit bias of network training algorithms, but to the best of our knowledge has not been applied in the domain of model robustness.Comment: Comments welcome

Determination of association constants between 5 '-guanosine monophosphate gel and aromatic compounds by capillary electrophoresis

Hydro gel formed by 5'-guanosine monophosphate (GMP) in the presence of a potassium ion is expected to exhibit interesting selectivity in capillary electrophoretic separations. Here, we estimated the conditional association constants between the hydro gel (G-gel) and aromatic compounds by capillary electrophoresis in order to investigate the separation selectivity that is induced by the G-gel. Several aromatic compounds were separated in a solution containing GMP and potassium ion at different concentrations. The association constants were calculated by correlating the electrophoretic mobilities of the analytes obtained experimentally using a concentration of G-gel. During semi-quantitative estimation, naphthalene derivatives had larger association constants (K-ass = 10.3-16.8) compared with those of benzene derivatives (K-ass = 3.91-5.31), which means that the binding sites of G-gel match better to a naphthalene ring than to a benzene ring. A hydrophobic interaction was also found when the association constants for alkyl resorcinol were compared with those of different hydrocarbon chains. The association constants of nucleobases and tryptophan ranged from 6.05 to 12.6, which approximated the intermediate values between benzene and naphthalene derivatives. Consequently, the selective interaction between G-gel and aromatic compounds was classified as one of three types: (1) an intercalation into stacked planar GMP tetramers; (2) a hydrophobic interaction with a long alkyl chain; or, (3) a small contribution of steric hindrance and/or hydrogen bonding with functional groups such as amino and hydroxyl groups

Does Input Quality Drive Measured Differences In Firm Productivity? *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/88037/1/j.1468-2354.2011.00656.x.pd

The effects of financialisation and financial development on investment: Evidence from firm-level data in Europe

In this paper we estimate the effects of financialization on physical investment in selected western European countries using panel data based on the balance-sheets of publicly listed non-financial companies (NFCs) supplied by Worldscope for the period 1995-2015. We find robust evidence of an adverse effect of both financial payments (interests and dividends) and financial incomes on investment in fixed assets by the NFCs. This finding is robust for both the pool of all Western European firms and single country estimations. The negative impacts of financial incomes are non-linear with respect to the companies’ size: financial incomes crowd-out investment in large companies, and have a positive effect on the investment of only small, relatively more credit-constrained companies. Moreover, we find that a higher degree of financial development is associated with a stronger negative effect of financial incomes on companies’ investment. This finding challenges the common wisdom on ‘finance-growth nexus’. Our findings support the ‘financialization thesis’ that the increasing orientation of the non-financial sector towards financial activities is ultimately leading to lower physical investment, hence to stagnant or fragile growth, as well as long term stagnation in productivity

Growth and structural transformation

Structural transformation refers to the reallocation of economic activity across the broad sectors agriculture, manufacturing, and services. This review article synthesizes and evaluates recent advances in the research on structural transformation. We begin by presenting the stylized facts of structural transformation across time and space. We then develop a multi-sector extension of the one-sector growth model that encompasses the main existing theories of structural transformation. We argue that this multi-sector model serves as a natural benchmark to study structural transformation and that it is able to account for many salient features of structural transformation. We also argue that this multi-sector model delivers new and sharper insights for understanding economic development, regional income convergence, aggregate productivity trends, hours worked, business cycles, wage inequality, and greenhouse gas emissions. We conclude by suggesting several directions for future research on structural transformation.For financial support, Herrendorf thanks the Spanish Ministry of Education (Grants ECO2009-11165 and ECO2012-31358); Rogerson thanks both the NSF and the Korea Science Foundation (WCU-R33-10005); and Valentinyi thanks the Hungarian Scientific Research Fund (OTKA) (Project K-105660-ny

Expression differences by continent of origin point to the immortalization process

Analysis of recently available microarray expression data sets obtained from immortalized cell lines of the individuals represented in the HapMap project have led to inconclusive comparisons across cohorts with different ancestral continent of origin (ACOO). To address this apparent inconsistency, we applied a novel approach to accentuate population-specific gene expression signatures for the CEU [homogeneous US residents with northern and western European ancestry (HapMap samples)] and YRI [homogenous Yoruba people of Ibadan, Nigeria (HapMap samples)] trios. In this report, we describe how four independent data sets point to the differential expression across ACOO of gene networks implicated in transforming the normal lymphoblast into immortalized lymphoblastoid cells. In particular, Werner syndrome helicase and related genes are differentially expressed between the YRI and CEU cohorts. We further demonstrate that these differences correlate with viral titer and that both the titer and expression differences are associated with ACOO. We use the 14 genes most differentially expressed to construct an ACOO-specific ‘immortalization network’ comprised of 40 genes, one of which show significant correlation with genomic variation (eQTL). The extent to which these measured group differences are due to differences in the immortalization procedures used for each group or reflect ACOO-specific biological differences remains to be determined. That the ACOO group differences in gene expression patterns may depend strongly on the process of transforming cells to establish immortalized lines should be considered in such comparisons

Why did socialist economies fail? The role of factor inputs reconsidered

We re-estimate investment and present revised growth accounts for three socialist economies between 1950 and 1989. Government statistics reported distorted measures for both the rate and trajectory of productivity growth in Czechoslovakia, Hungary, and Poland. Researchers have benefited from revised output data, but continued to use official statistics on capital input, or estimated capital stock from official investment data. Investment levels and rates of capital accumulations were much lower than officially claimed and over-reporting worsened over time. A setback in factor accumulation, both equipment investment and labor input, contributed very significantly to the socialist growth failure of the 1980s

An 84 microGauss Magnetic Field in a Galaxy at Redshift z=0.692

The magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars. The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ~ 3 microGauss. The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain. Here we report a measurement of a magnetic field of B ~ 84 microGauss in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 microGauss in the neutral interstellar gas of our Galaxy. This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past rather than stronger