Generalization Error in Deep Learning

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still generally unclear what is the source of their generalization ability. Thus, an important question is what makes deep neural networks able to generalize well from the training set to new data. In this article, we provide an overview of the existing theory and bounds for the characterization of the generalization error of deep neural networks, combining both classical and more recent theoretical and empirical results

Entanglement in coined quantum walks on regular graphs

Published versio

Dual-gated bilayer graphene hot electron bolometer

Detection of infrared light is central to diverse applications in security, medicine, astronomy, materials science, and biology. Often different materials and detection mechanisms are employed to optimize performance in different spectral ranges. Graphene is a unique material with strong, nearly frequency-independent light-matter interaction from far infrared to ultraviolet, with potential for broadband photonics applications. Moreover, graphene's small electron-phonon coupling suggests that hot-electron effects may be exploited at relatively high temperatures for fast and highly sensitive detectors in which light energy heats only the small-specific-heat electronic system. Here we demonstrate such a hot-electron bolometer using bilayer graphene that is dual-gated to create a tunable bandgap and electron-temperature-dependent conductivity. The measured large electron-phonon heat resistance is in good agreement with theoretical estimates in magnitude and temperature dependence, and enables our graphene bolometer operating at a temperature of 5 K to have a low noise equivalent power (33 fW/Hz1/2). We employ a pump-probe technique to directly measure the intrinsic speed of our device, >1 GHz at 10 K.Comment: 5 figure

Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice

The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. Using cold atomic gases, various condensed matter models can be studied in a highly controllable environment. Weakly repulsive fermions in an optical lattice could undergo d-wave pairing at low temperatures, a possible mechanism for high temperature superconductivity in the cuprates. The lattice potential could also strongly increase the critical temperature for s-wave superfluidity. Recent experimental advances in the bulk include the observation of fermion pair condensates and high-temperature superfluidity. Experiments with fermions and bosonic bound pairs in optical lattices have been reported, but have not yet addressed superfluid behavior. Here we show that when a condensate of fermionic atom pairs was released from an optical lattice, distinct interference peaks appear, implying long range order, a property of a superfluid. Conceptually, this implies that strong s-wave pairing and superfluidity have now been established in a lattice potential, where the transport of atoms occurs by quantum mechanical tunneling and not by simple propagation. These observations were made for unitarity limited interactions on both sides of a Feshbach resonance. For larger lattice depths, the coherence was lost in a reversible manner, possibly due to a superfluid to insulator transition. Such strongly interacting fermions in an optical lattice can be used to study a new class of Hamiltonians with interband and atom-molecule couplings.Comment: accepted for publication in Natur

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

BLM and RMI1 alleviate RPA inhibition of topoIIIα decatenase activity

RPA is a single-stranded DNA binding protein that physically associates with the BLM complex. RPA stimulates BLM helicase activity as well as the double Holliday junction dissolution activity of the BLM-topoisomerase IIIα complex. We investigated the effect of RPA on the ssDNA decatenase activity of topoisomerase IIIα. We found that RPA and other ssDNA binding proteins inhibit decatenation by topoisomerase IIIα. Complex formation between BLM, TopoIIIα, and RMI1 ablates inhibition of decatenation by ssDNA binding proteins. Together, these data indicate that inhibition by RPA does not involve species-specific interactions between RPA and BLM-TopoIIIα-RMI1, which contrasts with RPA modulation of double Holliday junction dissolution. We propose that topoisomerase IIIα and RPA compete to bind to single-stranded regions of catenanes. Interactions with BLM and RMI1 enhance toposiomerase IIIα activity, promoting decatenation in the presence of RPA

Reversals in nature and the nature of reversals

The asymmetric shape of reversals of the Earth's magnetic field indicates a possible connection with relaxation oscillations as they were early discussed by van der Pol. A simple mean-field dynamo model with a spherically symmetric $\alpha$ coefficient is analysed with view on this similarity, and a comparison of the time series and the phase space trajectories with those of paleomagnetic measurements is carried out. For highly supercritical dynamos a very good agreement with the data is achieved. Deviations of numerical reversal sequences from Poisson statistics are analysed and compared with paleomagnetic data. The role of the inner core is discussed in a spectral theoretical context and arguments and numerical evidence is compiled that the growth of the inner core might be important for the long term changes of the reversal rate and the occurrence of superchrons.Comment: 24 pages, 12 figure

Proximity of Iron Pnictide Superconductors to a Quantum Tricritical Point

We determine the nature of the magnetic quantum critical point in the doped LaFeAsO using a set of constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The system turns out to be remarkably close to a quantum tricritical point, where the nature of the phase transition changes from first to second order. We compare with the effective field theory and discuss the experimental consequences.Comment: 4 pages, 4 figure

Optical detection of single non-absorbing molecules using the surface plasmon of a gold nanorod

Current optical detection schemes for single molecules require light absorption, either to produce fluorescence or direct absorption signals. This severely limits the range of molecules that can be detected, because most molecules are purely refractive. Metal nanoparticles or dielectric resonators detect non-absorbing molecules by a resonance shift in response to a local perturbation of the refractive index, but neither has reached single-protein sensitivity. The most sensitive plasmon sensors to date detect single molecules only when the plasmon shift is amplified by a highly polarizable label or by a localized precipitation reaction on the particle's surface. Without amplification, the sensitivity only allows for the statistical detection of single molecules. Here we demonstrate plasmonic detection of single molecules in realtime, without the need for labeling or amplification. We monitor the plasmon resonance of a single gold nanorod with a sensitive photothermal assay and achieve a ~ 700-fold increase in sensitivity compared to state-of-the-art plasmon sensors. We find that the sensitivity of the sensor is intrinsically limited due to spectral diffusion of the SPR. We believe this is the first optical technique that detects single molecules purely by their refractive index, without any need for photon absorption by the molecule. The small size, bio-compatibility and straightforward surface chemistry of gold nanorods may open the way to the selective and local detection of purely refractive proteins in live cells

Electrophysiological Heterogeneity of Fast-Spiking Interneurons: Chandelier versus Basket Cells

In the prefrontal cortex, parvalbumin-positive inhibitory neurons play a prominent role in the neural circuitry that subserves working memory, and alterations in these neurons contribute to the pathophysiology of schizophrenia. Two morphologically distinct classes of parvalbumin neurons that target the perisomatic region of pyramidal neurons, chandelier cells (ChCs) and basket cells (BCs), are generally thought to have the same "fast-spiking" phenotype, which is characterized by a short action potential and high frequency firing without adaptation. However, findings from studies in different species suggest that certain electrophysiological membrane properties might differ between these two cell classes. In this study, we assessed the physiological heterogeneity of fast-spiking interneurons as a function of two factors: species (macaque monkey vs. rat) and morphology (chandelier vs. basket). We showed previously that electrophysiological membrane properties of BCs differ between these two species. Here, for the first time, we report differences in ChCs membrane properties between monkey and rat. We also found that a number of membrane properties differentiate ChCs from BCs. Some of these differences were species-independent (e.g., fast and medium afterhyperpolarization, firing frequency, and depolarizing sag), whereas the differences in the first spike latency between ChCs and BCs were species-specific. Our findings indicate that different combinations of electrophysiological membrane properties distinguish ChCs from BCs in rodents and primates. Such electrophysiological differences between ChCs and BCs likely contribute to their distinctive roles in cortical circuitry in each species. © 2013 Povysheva et al