Generalization Bounds with Data-dependent Fractal Dimensions

Providing generalization guarantees for modern neural networks has been a crucial task in statistical learning. Recently, several studies have attempted to analyze the generalization error in such settings by using tools from fractal geometry. While these works have successfully introduced new mathematical tools to apprehend generalization, they heavily rely on a Lipschitz continuity assumption, which in general does not hold for neural networks and might make the bounds vacuous. In this work, we address this issue and prove fractal geometry-based generalization bounds without requiring any Lipschitz assumption. To achieve this goal, we build up on a classical covering argument in learning theory and introduce a data-dependent fractal dimension. Despite introducing a significant amount of technical complications, this new notion lets us control the generalization error (over either fixed or random hypothesis spaces) along with certain mutual information (MI) terms. To provide a clearer interpretation to the newly introduced MI terms, as a next step, we introduce a notion of "geometric stability" and link our bounds to the prior art. Finally, we make a rigorous connection between the proposed data-dependent dimension and topological data analysis tools, which then enables us to compute the dimension in a numerically efficient way. We support our theory with experiments conducted on various settings

Comparison of convolutional neural networks for cloudy optical images reconstruction from single or multitemporal joint SAR and optical images

With the increasing availability of optical and synthetic aperture radar (SAR) images thanks to the Sentinel constellation, and the explosion of deep learning, new methods have emerged in recent years to tackle the reconstruction of optical images that are impacted by clouds. In this paper, we focus on the evaluation of convolutional neural networks that use jointly SAR and optical images to retrieve the missing contents in one single polluted optical image. We propose a simple framework that ease the creation of datasets for the training of deep nets targeting optical image reconstruction, and for the validation of machine learning based or deterministic approaches. These methods are quite different in terms of input images constraints, and comparing them is a problematic task not addressed in the literature. We show how space partitioning data structures help to query samples in terms of cloud coverage, relative acquisition date, pixel validity and relative proximity between SAR and optical images. We generate several datasets to compare the reconstructed images from networks that use a single pair of SAR and optical image, versus networks that use multiple pairs, and a traditional deterministic approach performing interpolation in temporal domain.Comment: 17 page

Flexible silicon photonic transmitter with segmented modulator and 32 nm CMOS driver IC

ConferenciaWe present a novel silicon photonic transmitter including 90nm CMOS segmented modulator co-packaged with low power 32nm CMOS driver IC. Optical equalization is demonstrated for the first time with the multi-segment Mach-Zehnder modulator at 22Gb/s. OCIS codes: (130.4110) Modulator; (250.3140) Integrated optoelectronic circuits

Flexible transmitter employing Silicon-segmented Mach–zehnder modulator with 32-nm CMOS distributed driver

Artículo científicoWe propose a flexible optical transmitter for shortreach optical interconnects that includes a silicon photonic segmented Mach-Zehnder modulator (MZM) driven by a distributed six-channel 32nm SOI CMOS driver integrated circuit. Optical equalization is demonstrated to extend the bandwidth limitation of the transmitter with NRZ signaling at 25Gb/s. We also generate four-level pulse amplitude modulation (PAM-4) signaling using the same transmitter architecture. Transmission of 46Gb/s PAM-4 signal with bit error rate (BER) well below hard-decision forward error correction limit (BER=3.8×10-3) is experimentally demonstrated. Low driver power consumption of 130 mW at 46Gb/s PAM-4, corresponding to 2.8 pJ/bit power efficiency, is also achieved

Genome-Wide Association with Select Biomarker Traits in the Framingham Heart Study

BACKGROUND: Systemic biomarkers provide insights into disease pathogenesis, diagnosis, and risk stratification. Many systemic biomarker concentrations are heritable phenotypes. Genome-wide association studies (GWAS) provide mechanisms to investigate the genetic contributions to biomarker variability unconstrained by current knowledge of physiological relations. METHODS: We examined the association of Affymetrix 100K GeneChip single nucleotide polymorphisms (SNPs) to 22 systemic biomarker concentrations in 4 biological domains: inflammation/oxidative stress; natriuretic peptides; liver function; and vitamins. Related members of the Framingham Offspring cohort (n = 1012; mean age 59 ± 10 years, 51% women) had both phenotype and genotype data (minimum-maximum per phenotype n = 507–1008). We used Generalized Estimating Equations (GEE), Family Based Association Tests (FBAT) and variance components linkage to relate SNPs to multivariable-adjusted biomarker residuals. Autosomal SNPs (n = 70,987) meeting the following criteria were studied: minor allele frequency ≥ 10%, call rate ≥ 80% and Hardy-Weinberg equilibrium p ≥ 0.001. RESULTS: With GEE, 58 SNPs had p < 10-6: the top SNPs were rs2494250 (p = 1.00*10-14) and rs4128725 (p = 3.68*10-12) for monocyte chemoattractant protein-1 (MCP1), and rs2794520 (p = 2.83*10-8) and rs2808629 (p = 3.19*10-8) for C-reactive protein (CRP) averaged from 3 examinations (over about 20 years). With FBAT, 11 SNPs had p < 10-6: the top SNPs were the same for MCP1 (rs4128725, p = 3.28*10-8, and rs2494250, p = 3.55*10-8), and also included B-type natriuretic peptide (rs437021, p = 1.01*10-6) and Vitamin K percent undercarboxylated osteocalcin (rs2052028, p = 1.07*10-6). The peak LOD (logarithm of the odds) scores were for MCP1 (4.38, chromosome 1) and CRP (3.28, chromosome 1; previously described) concentrations; of note the 1.5 support interval included the MCP1 and CRP SNPs reported above (GEE model). Previous candidate SNP associations with circulating CRP concentrations were replicated at p < 0.05; the SNPs rs2794520 and rs2808629 are in linkage disequilibrium with previously reported SNPs. GEE, FBAT and linkage results are posted at . CONCLUSION: The Framingham GWAS represents a resource to describe potentially novel genetic influences on systemic biomarker variability. The newly described associations will need to be replicated in other studies.National Heart, Lung, and Blood Institute's Framingham Heart Study (N01-HC25195); National Institutes of Health National Center for Research Resources Shared Instrumentation grant (1S10RR163736-01A1); National Institutes of Health (HL064753, HL076784, AG028321, HL71039, 2 K24HL04334, 1K23 HL083102); Doris Duke Charitable Foundation; American Diabetes Association Career Developement Award; National Center for Research Resources (GCRC M01-RR01066); US Department of Agriculture Agricultural Research Service (58-1950-001, 58-1950-401); National Institute of Aging (AG14759

Whole Blood Gene Expression and Atrial Fibrillation: The Framingham Heart Study

Background: Atrial fibrillation (AF) involves substantial electrophysiological, structural and contractile remodeling. We hypothesize that characterizing gene expression might uncover important pathways related to AF. Methods and Results: We performed genome-wide whole blood transcriptomic profiling (Affymetrix Human Exon 1.0 ST Array) of 2446 participants (mean age 66±9 years, 55% women) from the Offspring cohort of Framingham Heart Study. The study included 177 participants with prevalent AF, 143 with incident AF during up to 7 years follow up, and 2126 participants with no AF. We identified seven genes statistically significantly up-regulated with prevalent AF. The most significant gene, PBX1 (P = 2.8×10−7), plays an important role in cardiovascular development. We integrated differential gene expression with gene-gene interaction information to identify several signaling pathways possibly involved in AF-related transcriptional regulation. We did not detect any statistically significant transcriptomic associations with incident AF. Conclusion: We examined associations of gene expression with AF in a large community-based cohort. Our study revealed several genes and signaling pathways that are potentially involved in AF-related transcriptional regulation

Light-level geolocators reveal spatial variations in interactions between northern fulmars and fisheries

Seabird−fishery interactions are a common phenomenon of conservation concern. Here, we highlight how light-level geolocators provide promising opportunities to study these interactions. By examining raw light data, it is possible to detect encounters with artificial lights atnight, while conductivity data give insight on seabird behaviour during encounters. We used geolocator data from 336 northern fulmars Fulmarus glacialis tracked from 12 colonies in the North-East Atlantic and Barents Sea during the non-breeding season to (1) confirm that detections of artificial lights correspond to encounters with fishing vessels by comparing overlap between fishing effort and both the position of detections and the activity of birds during encounters, (2) assess spatial differences in the number of encounters among wintering areas and (3) test whethersome individuals forage around fishing vessels more often than others. Most (88.1%) of the track encountered artificial light at least once, with 9.5 ± 0.4 (SE) detections on average per 6 mo nonbreeding season. Encounters occurred more frequently where fishing effort was high, and birds from some colonies had higher probabilities of encountering lights at night. During encounters, fulmars spent more time foraging and less time resting, strongly suggesting that artificial lights reflect the activity of birds around fishing vessels. Inter-individual variability in the probability of encountering light was high (range: 0−68 encounters per 6 mo non-breeding season), meaning that some individuals were more often associated with fishing vessels than others, independently of their colony of origin. Our study highlights the potential of geolocators to study seabird−fisheryinteractions at a large scale and a low cost.publishedVersio

Erratum: Sequence data and association statistics from 12,940 type 2 diabetes cases and controls.

This corrects the article DOI: 10.1038/sdata.2017.179