Centre de Recerca Matemàtica

While depth tends to improve network performances, it also makes gradient-based training more difficult since deeper networks tend to be more non-linear. The recently proposed knowledge distillation approach is aimed at obtaining small and fast-to-execute models, and it has shown that a student network could imitate the soft output of a larger teacher network or ensemble of networks. In this paper, we extend this idea to allow the training of a student that is deeper and thinner than the teacher, using not only the outputs but also the intermediate representations learned by the teacher as hints to improve the training process and final performance of the student. Because the student intermediate hidden layer will generally be smaller than the teacher's intermediate hidden layer, additional parameters are introduced to map the student hidden layer to the prediction of the teacher hidden layer. This allows one to train deeper students that can generalize better or run faster, a trade-off that is controlled by the chosen student capacity. For example, on CIFAR-10, a deep student network with almost 10.4 times less parameters outperforms a larger, state-of-the-art teacher network.

We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg 2 of griz imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric-redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while "blind" to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat CDM and wCDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for CDM) or 7 (for wCDM) cosmological parameters including the neutrino mass density and including the 457 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions and from their combination obtain S 8 8 m =0.3 0.5 0.773 0.026 -0.020 and m 0.267 0.030 -0.017 for CDM; for wCDM, we find S 8 0.782 0.036 -0.024 , m 0.284 0.033 -0.030 , and w -0.82 0.21 -0.20 at 68% C.L. The precision of these DES Y1 constraints rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very

Deep networks trained on demonstrations of human driving have learned to follow roads and avoid obstacles. However, driving policies trained via imitation learning cannot be controlled at test time. A vehicle trained end-to-end to imitate an expert cannot be guided to take a specific turn at an upcoming intersection. This limits the utility of such systems. We propose to condition imitation learning on high-level command input. At test time, the learned driving policy functions as a chauffeur that handles sensorimotor coordination but continues to respond to navigational commands. We evaluate different architectures for conditional imitation learning in vision-based driving. We conduct experiments in realistic three-dimensional simulations of urban driving and on a 1/5 scale robotic truck that is trained to drive in a residential area. Both systems drive based on visual input yet remain responsive to high-level navigational commands.

The application of theoretical methods based on the density functional theory with hybrid functionals provides good estimates of the exchange coupling constants for polynuclear transition metal complexes. The accuracy is similar to that previously obtained for dinuclear compounds. We present test calculations on simple model systems based on H. He and CH(2). He units to compare with Hartree-Fock and multiconfigurational results. Calculations for complete, nonmodeled polynuclear transition metal complexes yield coupling constants in very good agreement with available experimental data.

Altres ajuts: Antonio M. Lopez acknowledges the financial support by ICREA under the ICREA Academia Program. As CVC/UAB researchers, they also acknowledge the Generalitat de Catalunya CERCA Program and its ACCIO agency.

Has there been an increase in positive assortative mating? Does assortative mating contribute to household income inequality? Data from the United States Census Bureau suggests there has been a rise in assortative mating. Additionally, assortative mating affects household income inequality. In particular, if matching in 2005 between husbands and wives had been random, instead of the pattern observed in the data, then the Gini coefficient would have fallen from the observed 0.43 to 0.34, so that income inequality would be smaller. Thus, assortative mating is important for income inequality. The high level of married female labor-force participation in 2005 is important for this result.

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen, in particular, in its Palatini formulation. We analyze here a specific nonlinear gravity-scalar system in the first-order Palatini formalism which leads to a Friedmann-Robertson-Walker cosmology different from the purely metric one. It is shown that the emerging Friedmann-Robertson-Walker cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first-order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.

C1q is a versatile recognition protein that binds to an amazing variety of immune and non-immune ligands and triggers activation of the classical pathway of complement. The crystal structure of the C1q globular domain responsible for its recognition properties has now been solved and refined to 1.9 A of resolution. The structure reveals a compact, almost spherical heterotrimeric assembly held together mainly by non-polar interactions, with a Ca2+ ion bound at the top. The heterotrimeric assembly of the C1q globular domain appears to be a key factor of the versatile recognition properties of this protein. Plausible three-dimensional models of the C1q globular domain in complex with two of its physiological ligands, C-reactive protein and IgG, are proposed, highlighting two of the possible recognition modes of C1q. The C1q/human IgG1 model suggests a critical role for the hinge region of IgG and for the relative orientation of its Fab domain in C1q binding.

Understanding memory and decision making in the human brain requires generating models of how neurons fire. Using ordinary differential equations, researchers formulate an exact firing rate description for an ensemble of spiking neurons.

A major goal of neuroscience, statistical physics, and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here, we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network, including states of synchronous spiking activity. Finally, we show that the firing-rate description is related, via a conformal map, to a low-dimensional description in terms of the Kuramoto order parameter, called Ott-Antonsen theory. We anticipate that our results will be an important tool in investigating how large networks of spiking neurons self-organize in time to process and encode information in the brain.

Boron clusters and organic molecules display manifestly different electronic, physical, chemical and geometrical characteristics. These differences highlight the complementarity of organic synthons and boron clusters, and therefore the feasibility of producing hybrid polymers incorporating both types of fragments. This review focuses on the development of hybrid organic-inorganic π conjugated, silane, siloxane and coordination polymers containing icosahedral boron clusters in the last few decades, which have received considerable academic and technological interest due to the combination of the electronic, optical and thermal properties of traditional inorganic materials with many of the desirable properties of organic plastics, including mechanical flexibility and low production costs.

The classical Łojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, and tame geometry. This paper provides alternative characterizations of this type of inequality for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In the framework of metric spaces, we show that a generalized form of the Łojasiewicz inequality (hereby called the Kurdyka-Łojasiewicz inequality) is related to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="minus partial-differential f"> <mml:semantics> <mml:mrow> <mml:mo> − </mml:mo> <mml:mi mathvariant="normal"> ∂ </mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">-\partial f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka-Łojasiewicz inequality is satisfied. Further characterizations in terms of <italic>talweg</italic> lines —a concept linked to the location of the less steepest points at the level sets of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding="application/x-tex">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> — and integrability conditions are given. In the convex case these results are significantly reinforced, allowing us in particular to establish a kind of asymptotic equivalence for discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C squared"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">C^{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> function in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R squared"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {R}^{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka-Łojasiewicz inequality.

It has long been stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallels between these so separate phenomena. We study the acoustic emission events produced during the compression of Vycor (SiO(2)). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate.

Abstract We analyze the two‐dimensional parabolic‐elliptic Patlak‐Keller‐Segel model in the whole Euclidean space ℝ 2 . Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local‐in‐time existence for any mass of “free‐energy solutions,” namely weak solutions with some free‐energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free‐energy solutions with initial data as before for the critical mass 8π/χ. Actually, we prove that solutions blow up as a delta Dirac at the center of mass when t → ∞ when their second moment is kept constant at any time. Furthermore, all moments larger than 2 blowup as t → ∞ if initially bounded. © 2007 Wiley Periodicals, Inc.

Thirty-three pigs affected by porcine dermatitis and nephropathy syndrome, 30 from Spain and three from the USA, were investigated in order to detect porcine circovirus (PCV) in their tissues. A standard in situ hybridisation technique using a specific DNA 317-bp probe based on a well-conserved sequence of PCV (which recognises both PCV-1 and PCV-2) was applied to formalin-fixed, paraffin-embedded tissues. Twenty-eight of the 30 Spanish pigs and all three American pigs had PCV in at least one tissue. Viral nucleic acid was detected mainly in lymphoid organs, and especially the lymph nodes. The viral genome was also found, in order of decreasing quantity, in Peyer's patches, tonsil, lung, spleen, kidney, liver, and skin. Viral nucleic acid was located mainly within the cytoplasm of monocyte/macrophage lineage cells, including follicular dendritic cells, macrophages, histiocytes and Kupffer cells. No viral nucleic acid was found in damaged glomeruli or arteriolar walls. In frozen samples available from three Spanish pigs, the virus was identified as type 2 by using the polymerase chain reaction and restriction fragment length polymorphism. Most of the pigs from which serum was available were seropositive against porcine respiratory and reproductive syndrome virus (PRRSV), and PRRSV antigen was detected in the lung of two of the Spanish pigs. These results suggested that PCV is present in tissues of almost all pigs affected by PDNS, and PCV has to be considered as a possible agent involved in the pathogenesis of the syndrome.

The gamut mapping algorithm is one of the most promising methods to achieve computational color constancy. However, so far, gamut mapping algorithms are restricted to the use of pixel values to estimate the illuminant. Therefore, in this paper, gamut mapping is extended to incorporate the statistical nature of images. It is analytically shown that the proposed gamut mapping framework is able to include any linear filter output. The main focus is on the local n-jet describing the derivative structure of an image. It is shown that derivatives have the advantage over pixel values to be invariant to disturbing effects (i.e. deviations of the diagonal model) such as saturated colors and diffuse light. Further, as the n-jet based gamut mapping has the ability to use more information than pixel values alone, the combination of these algorithms are more stable than the regular gamut mapping algorithm. Different methods of combining are proposed. Based on theoretical and experimental results conducted on large scale data sets of hyperspectral, laboratory and real-world scenes, it can be derived that (1) in case of deviations of the diagonal model, the derivative-based approach outperforms the pixel-based gamut mapping, (2) state-of-the-art algorithms are outperformed by the n-jet based gamut mapping, (3) the combination of the different n-jet based gamut mappings provide more stable solutions, and (4) the fusion strategy based on the intersection of feasible sets provides better color constancy results than the union of the feasible sets.

Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains formally unknown. Here we unveil a number of patterns and metrics characterizing the generic usage of primary musical facets such as pitch, timbre, and loudness in contemporary western popular music. Many of these patterns and metrics have been consistently stable for a period of more than fifty years. However, we prove important changes or trends related to the restriction of pitch transitions, the homogenization of the timbral palette, and the growing loudness levels. This suggests that our perception of the new would be rooted on these changing characteristics. Hence, an old tune could perfectly sound novel and fashionable, provided that it consisted of common harmonic progressions, changed the instrumentation, and increased the average loudness.

We present a novel route for the synthesis of CuO thin films. The nano-flower like nanostructures provide high surface area, and the CuO shows excellent supercapacitive properties.

Neuronal variability in sensory cortex predicts perceptual decisions. This relationship, termed choice probability (CP), can arise from sensory variability biasing behaviour and from top-down signals reflecting behaviour. To investigate the interaction of these mechanisms during the decision-making process, we use a hierarchical network model composed of reciprocally connected sensory and integration circuits. Consistent with monkey behaviour in a fixed-duration motion discrimination task, the model integrates sensory evidence transiently, giving rise to a decaying bottom-up CP component. However, the dynamics of the hierarchical loop recruits a concurrently rising top-down component, resulting in sustained CP. We compute the CP time-course of neurons in the medial temporal area (MT) and find an early transient component and a separate late contribution reflecting decision build-up. The stability of individual CPs and the dynamics of noise correlations further support this decomposition. Our model provides a unified understanding of the circuit dynamics linking neural and behavioural variability.

In the last few years, several researchers have proposed different procedures for the fusion of multispectral and panchromatic images based on the wavelet transform, which provide satisfactory high spatial resolution images keeping the spectral properties of the original multispectral data. The discrete approach of the wavelet transform can be performed with different algorithms, Mallat's and the ‘à trous’ being the most popular ones for image fusion purposes. Each algorithm has its particular mathematical properties and leads to different image decompositions. In this article, both algorithms are compared by the analysis of the spectral and spatial quality of the merged images which were obtained by applying several wavelet based, image fusion methods. All these have been used to merge Ikonos multispectral and panchromatic spatially degraded images. Comparison of the fused images is based on spectral and spatial characteristics and it is performed visually and quantitatively using statistical parameters and quantitative indexes. In spite of its a priori lower theoretical mathematical suitability to extract detail in a multiresolution scheme, the ‘à trous’ algorithm has worked out better than Mallat's algorithm for image merging purposes.