Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science

Through the success of deep learning in various domains, artificial neural networks are currently among the most used artificial intelligence methods. Taking inspiration from the network properties of biological neural networks (e.g. sparsity, scale-freeness), we argue that (contrary to general practice) artificial neural networks, too, should not have fully-connected layers. Here we propose sparse evolutionary training of artificial neural networks, an algorithm which evolves an initial sparse topology (Erdős–Rényi random graph) of two consecutive layers of neurons into a scale-free topology, during learning. Our method replaces artificial neural networks fully-connected layers with sparse ones before training, reducing quadratically the number of parameters, with no decrease in accuracy. We demonstrate our claims on restricted Boltzmann machines, multi-layer perceptrons, and convolutional neural networks for unsupervised and supervised learning on 15 datasets. Our approach has the potential to enable artificial neural networks to scale up beyond what is currently possible

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

The number of eigenstates: counting function and heat kernel

The main aim of this paper is twofold: (1) revealing a relation between the counting function N(lambda) (the number of the eigenstates with eigenvalue smaller than a given number) and the heat kernel K(t), which is still an open problem in mathematics, and (2) introducing an approach for the calculation of N(lambda), for there is no effective method for calculating N(lambda) beyond leading order. We suggest a new expression of N(lambda) which is more suitable for practical calculations. A renormalization procedure is constructed for removing the divergences which appear when obtaining N(lambda) from a nonuniformly convergent expansion of K(t). We calculate N(lambda) for D-dimensional boxes, three-dimensional balls, and two-dimensional multiply-connected irregular regions. By the Gauss-Bonnet theorem, we generalize the simply-connected heat kernel to the multiply-connected case; this result proves Kac's conjecture on the two-dimensional multiply-connected heat kernel. The approaches for calculating eigenvalue spectra and state densities from N(lambda) are introduced.Comment: 17 pages, 1 figure. v2: Equivalent forms of Eqs. (4.8) and (9.2) are adde

Vulnerable plaques and patients: state-of-the-art

Despite advanced understanding of the biology of atherosclerosis, coronary heart disease remains the leading cause of death worldwide. Progress has been challenging as half of the individuals who suffer sudden cardiac death do not experience premonitory symptoms. Furthermore, it is well-recognized that also a plaque that does not cause a haemodynamically significant stenosis can trigger a sudden cardiac event, yet the majority of ruptured or eroded plaques remain clinically silent. In the past 30 years since the term 'vulnerable plaque' was introduced, there have been major advances in the understanding of plaque pathogenesis and pathophysiology, shifting from pursuing features of 'vulnerability' of a specific lesion to the more comprehensive goal of identifying patient 'cardiovascular vulnerability'. It has been also recognized that aside a thin-capped, lipid-rich plaque associated with plaque rupture, acute coronary syndromes (ACS) are also caused by plaque erosion underlying between 25% and 60% of ACS nowadays, by calcified nodule or by functional coronary alterations. While there have been advances in preventive strategies and in pharmacotherapy, with improved agents to reduce cholesterol, thrombosis, and inflammation, events continue to occur in patients receiving optimal medical treatment. Although at present the positive predictive value of imaging precursors of the culprit plaques remains too low for clinical relevance, improving coronary plaque imaging may be instrumental in guiding pharmacotherapy intensity and could facilitate optimal allocation of novel, more aggressive, and costly treatment strategies. Recent technical and diagnostic advances justify continuation of interdisciplinary research efforts to improve cardiovascular prognosis by both systemic and 'local' diagnostics and therapies. The present state-of-the-art document aims to present and critically appraise the latest evidence, developments, and future perspectives in detection, prevention, and treatment of 'high-risk' plaques occurring in 'vulnerable' patients

A stabilized pairing functional

We propose a modified pairing functional for nuclear structure calculations which avoids the abrupt phase transition between pairing and non-pairing states. The intended application is the description of nuclear collective motion where the smoothing of the transition is compulsory to remove singularities. The stabilized pairing functional allows a thoroughly variational formulation, unlike the Lipkin-Nogami (LN) scheme which is often used for the purpose of smoothing. First applications to nuclear ground states and collective excitations prove the reliability and efficiency of the proposed stabilized pairing.Comment: 6 pages, 5 figure

Search for Neutral Higgs Bosons of the Minimal Supersymmetric Standard Model in e+e- Interactions at \sqrt{s} = 189 GeV

A search for the lightest neutral scalar and neutral pseudoscalar Higgs bosons in the Minimal Supersymmetric Standard Model is performed using 176.4 pb^-1 of integrated luminosity collected by L3 at a center-of-mass energy of 189 GeV. No signal is observed, and the data are consistent with the expected Standard Model background. Lower limits on the masses of the lightest neutral scalar and pseudoscalar Higgs bosons are given as a function of tan(beta). Lower mass limits for tan(beta)>1 are set at the 95% confidence level to be m_h > 77.1 GeV and m_A > 77.1 GeV

Search for Extra Dimensions in Boson and Fermion Pair Production in e+e- Interactions at LEP

Extra spatial dimensions are proposed by recent theories that postulate the scale of gravity to be of the same order as the electroweak scale. A sizeable interaction between gravitons and Standard Model particles is then predicted. Effects of these new interactions in boson and fermion pair production are searched for in the data sample collected at centre-of-mass energies above the Z pole by the L3 detector at LEP. In addition, the direct production of a graviton associated with a Z boson is investigated. No statistically significant hints for the existence of these effects are found and lower limits in excess of 1 TeV are derived on the scale of this new theory of gravity

Measurement of the Probability of Gluon Splitting into Charmed Quarks in Hadronic Z Decays

We have measured the probability, n(g->cc~), of a gluon splitting into a charm-quark pair using 1.7 million hadronic Z decays collected by the L3 detector. Two independent methods have been applied to events with a three-jet topology. One method relies on tagging charmed hadrons by identifying a lepton in the lowest energy jet. The other method uses a neural network based on global event shape parameters. Combining both methods, we measure n(g->cc~)= [2.45 +/- 0.29 +/- 0.53]%

Measurement of Triple-Gauge-Boson Couplings of the W Boson at LEP

We report on measurements of the triple-gauge-boson couplings of the W boson in e+e- collisions with the L3 detector at LEP. W-pair, single-W and single-photon events are analysed in a data sample corresponding to a total luminosity of 76.7 pb^{-1} collected at centre-of-mass energies between 161 GeV and 183 GeV. CP-conserving as well as both C- and P-conserving triple-gauge-boson couplings are determined. The results, in good agreement with the Standard-Model expectations, confirm the existence of the self coupling among the electroweak gauge bosons and constrain its structure

Measurement of Hadron and Lepton-Pair Production at 130GeV < \sqrt{s} < 189 GeV at LEP

We report on measurements of e+e- annihilation into hadrons and lepton pairs. The data have been collected with the L3 detector at LEP at centre-of-mass energies between 130 and 189 GeV. Using a total integrated luminosity of 243.7 pb^-1, 25864 hadronic and 8573 lepton-pair events are selected for the measurement of cross sections and leptonic forward-backward asymmetries. The results are in good agreement with Standard Model predictions