A multiobjective continuation method to compute the regularization path of deep neural networks

Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. In machine learning approaches based on linear models, it is well known that there exists a connecting path between the sparsest solution in terms of the $\ell^1$ norm (i.e., zero weights) and the non-regularized solution, which is called the regularization path. Very recently, there was a first attempt to extend the concept of regularization paths to DNNs by means of treating the empirical loss and sparsity ($\ell^1$ norm) as two conflicting criteria and solving the resulting multiobjective optimization problem. However, due to the non-smoothness of the $\ell^1$ norm and the high number of parameters, this approach is not very efficient from a computational perspective. To overcome this limitation, we present an algorithm that allows for the approximation of the entire Pareto front for the above-mentioned objectives in a very efficient manner. We present numerical examples using both deterministic and stochastic gradients. We furthermore demonstrate that knowledge of the regularization path allows for a well-generalizing network parametrization.Comment: 7 pages, 6 figure

A Note on the Slim Accretion Disk Model

We show that when the gravitational force is correctly calculated in dealing with the vertical hydrostatic equilibrium of black hole accretion disks, the relationship that is valid for geometrically thin disks, i.e., $c_s/\Omega_K H =$ constant, where $c_s$ is the sound speed, $\Omega_K$ is the Keplerian angular velocity, and $H$ is the half-thickness of the disk, does not hold for slim disks. More importantly, by adopting the correct vertical gravitational force in studies of thermal equilibrium solutions, we find that there exists a maximally possible accretion rate for each radius in the outer region of optically thick accretion flows, so that only the inner region of these flows can possibly take the form of slim disks, and strong outflows from the outer region are required to reduce the accretion rate in order for slim disks to be realized.Comment: 14 pages, 5 figures, accepted by Ap

Line Emission from an Accretion Disk around a Black hole: Effects of Disk Structure

The observed iron K-alpha fluorescence lines in Seyfert-1 galaxies provide strong evidence for an accretion disk near a supermassive black hole as a source of the line emission. These lines serve as powerful probes for examining the structure of inner regions of accretion disks. Previous studies of line emission have considered geometrically thin disks only, where the gas moves along geodesics in the equatorial plane of a black hole. Here we extend this work to consider effects on line profiles from finite disk thickness, radial accretion flow and turbulence. We adopt the Novikov and Thorne (1973) solution, and find that within this framework, turbulent broadening is the dominant new effect. The most prominent change in the skewed, double-horned line profiles is a substantial reduction in the maximum flux at both red and blue peaks. The effect is most pronounced when the inclination angle is large, and when the accretion rate is high. Thus, the effects discussed here may be important for future detailed modeling of high quality observational data.Comment: 21 pages including 8 figures; LaTeX; ApJ format; accepted by ApJ; short results of this paper appeared before as a conference proceedings (astro-ph/9711214

Estudo preliminar antimicrobiano e fitoquímico do óleo essencial foliar da Nectandra grandiflora Ness (canela-amarela).

SBQ SUL

Infrastructure Upgrades and Foreclosure with Coexistence of Service-Based and Facility-Based Firms

We investigate the incentives for facility-based firms to invest in infrastructure upgrades and to foreclose service-based firms. We focus on asymmetric regulation regarding servicebased firms' access to the infrastructure held by a facility-based firm. Spillovers from the infrastructure upgrades made by a regulated facility-based firm on service-based firms play a key role in the incentives for making these upgrades. The spillover effect can enhance the incentives for the regulated facility-based firm to make upgrades if access prices are not regulated. The existence of rival facility-based firms strengthens the incentives for a regulated facility-based firm to make infrastructure upgrades, especially when the spillover effect is significant. Furthermore, if access prices are not regulated, the existence of rival facility-based firms weakens the incentives for a regulated facility-based firm to foreclose service-based firms

Boson Stars as Gravitational Lenses

We discuss boson stars as possible gravitational lenses and study the lensing effect by these objects made of scalar particles. The mass and the size of a boson star may vary from an individual Newtonian object similar to the Sun to the general relativistic size and mass of a galaxy close to its Schwarzschild radius. We assume boson stars to be transparent which allows the light to pass through them though the light is gravitationally deflected. We assume boson stars of the mass $M = 10^{10}M_\odot$ to be on non-cosmological distance from the observer. We discuss the lens equation for these stars as well as the details of magnification. We find that there are typically three images of a star but the deflection angles may vary from arcseconds to even degrees. There is one tangential critical curve (Einstein ring) and one radial critical curve for tangential and radial magnification, respectively. Moreover, the deflection angles for the light passing in the gravitational field of boson stars can be very large (even of the order of degrees) which reflects the fact they are very strong relativistic objects. We also propose a suitable formula for the lens equation for such large deflection angles, and with the reservation that large deflection angle images are highly demagnified but in the area of the tangential critical curve, their existence may help in observational detection of suitable lenses possessing characteristic features of boson stars which could also serve as a direct evidence for scalar fields in the universe.Comment: accepted by Astrophys. J., 31 pages, AASTeX, 6 figure

Bringing to light the physiological and pathological firing patterns of human induced pluripotent stem cell-derived neurons using optical recordings

Human induced pluripotent stem cells (hiPSCs) are a promising approach to study neurological and neuropsychiatric diseases. Most methods to record the activity of these cells have major drawbacks as they are invasive or they do not allow single cell resolution. Genetically encoded voltage indicators (GEVIs) open the path to high throughput visualization of undisturbed neuronal activity. However, conventional GEVIs perturb membrane integrity through inserting multiple copies of transmembrane domains into the plasma membrane. To circumvent large add-ons to the plasma membrane, we used a minimally invasive novel hybrid dark quencher GEVI to record the physiological and pathological firing patterns of hiPSCs-derived sensory neurons from patients with inherited erythromelalgia, a chronic pain condition associated with recurrent attacks of redness and swelling in the distal extremities. We observed considerable differences in action potential firing patterns between patient and control neurons that were previously overlooked with other recording methods. Our system also performed well in hiPSC-derived forebrain neurons where it detected spontaneous synchronous bursting behavior, thus opening the path to future applications in other cell types and disease models including Parkinson’s disease, Alzheimer’s disease, epilepsy, and schizophrenia, conditions associated with disturbances of neuronal activity and synchrony