Enhancing Decision Tree based Interpretation of Deep Neural Networks through L1-Orthogonal Regularization

One obstacle that so far prevents the introduction of machine learning models primarily in critical areas is the lack of explainability. In this work, a practicable approach of gaining explainability of deep artificial neural networks (NN) using an interpretable surrogate model based on decision trees is presented. Simply fitting a decision tree to a trained NN usually leads to unsatisfactory results in terms of accuracy and fidelity. Using L1-orthogonal regularization during training, however, preserves the accuracy of the NN, while it can be closely approximated by small decision trees. Tests with different data sets confirm that L1-orthogonal regularization yields models of lower complexity and at the same time higher fidelity compared to other regularizers.Comment: 8 pages, 18th IEEE International Conference on Machine Learning and Applications (ICMLA) 201

Rotating three-dimensional solitons in Bose Einstein condensates with gravity-like attractive nonlocal interaction

We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of repulsive contact interaction does not prevent the existence of those solutions, but allows to control their rotation. We conjecture that self-trapped azimuthons are generic for condensates with attractive nonlocal interaction

Excitation of knotted vortex lines in matter waves

We study the creation of knotted ultracold matter waves in Bose–Einstein condensates via coherent two-photon Raman transitions with a Λ level configuration. The Raman transition allows an indirect transfer of atoms from the internal state $| a\rangle$ to the target state $| b\rangle$ via an excited state $| e\rangle$, that would be otherwise dipole-forbidden. This setup enables us to imprint three-dimensional knotted vortex lines embedded in the probe field to the density in the target state. We elaborate on experimental feasibility as well as on subsequent dynamics of the matter wave

Domoic Acid Transfer to Milk: Evaluation of a Potential Route of Neonatal Exposure

Domoic acid (DA), produced by the diatom genus Pseudo-nitzschia, is a glutamate analog and a neurotoxin in humans. During diatom blooms, DA can contaminate filter-feeding organisms, such as shellfish, and can be transferred by ingestion to higher trophic levels. Several intoxication events involving both humans and various marine mammals have been attributed to DA. Affected organisms show neurological symptoms such as seizures, ataxia, headweaving, and stereotypic scratching, as well as prolonged deficits in memory and learning. Neonatal animals have been shown to be substantially more sensitive to DA than adults. However, it has not been demonstrated whether DA can be transferred to nursing young from DA-exposed mothers. This study demonstrates transfer of DA from spiked milk (0.3 and 1.0 mg/kg) to the plasma of nursing neonatal rats and an overall longer DA retention in milk than in plasma after 8 hr in exposed dams. DA was detectable in milk up to 24 hr after exposure (1.0 mg/kg) of the mothers, although the amount of DA transferred to milk after exposure was not sufficient to cause acute symptoms in neonates

Structuring the three electric field components of light

International audienceUnless the beam's transverse electric field components are divergence-free in the two-dimensional transverse plane [1], tightly focused light typically leads to a non-negligible longitudinal electric field component [2], where the terms longitudinal and transverse electric field components refer to the components of the electric field that are parallel or perpendicular, respectively, to the direction of the mean Poynting flux. Having a longitudinal electric field component does not add a new degree of freedom, in the sense that all components of the electric and magnetic fields are still fixed by prescribing two electric field components in a plane. However, it is the electric field component parallel to the direction of the Poynting flux that makes it somewhat special

Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities

We study beam propagation in the framework of the nonlinear Schrödinger equation with competing Gaussian nonlocal nonlinearities. We demonstrate that such system can give rise to self-organization of light into stable states of trains or hexagonal arrays of filaments, depending on the transverse dimensionality. This long-range ordering can be achieved by mere unidirectional beam propagation. We discuss the dynamics of long-range ordering and the crucial role which the phase of the wavefunction plays for this phenomenon. Furthermore we discuss how transverse dimensionality affects the order of the phasetransition

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

Collapse in the nonlocal nonlinear Schr\"odinger equation

We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schr\"{o}dinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary dimension collapse does not occur. Then we study in detail the effect of singular nonlocal kernels in arbitrary dimension using both, Lyapunoff's method and virial identities. We find that for for a one-dimensional case, i.e. for $n=1$, collapse cannot happen for nonlocal nonlinearity. On the other hand, for spatial dimension $n\geq2$ and singular kernel $\sim 1/r^\alpha$, no collapse takes place if $\alpha<2$, whereas collapse is possible if $\alpha\ge2$. Self-similar solutions allow us to find an expression for the critical distance (or time) at which collapse should occur in the particular case of $\sim 1/r^2$ kernels. Moreover, different evolution scenarios for the three dimensional physically relevant case of Bose Einstein condensate are studied numerically for both, the ground state and a higher order toroidal state with and without an additional local repulsive nonlinear interaction. In particular, we show that presence of an additional local repulsive term can prevent collapse in those cases

Technical Note: Intercomparison of ILAS-II version 2 and 1.4 trace species with MIPAS-B measurements

The Improved Limb Atmospheric Spectrometer (ILAS)-II sensor aboard the Japanese ADEOS-II satellite was launched into its sun-synchronous orbit on 14 December 2002 and performed solar occultation measurements of trace species, aerosols, temperature, and pressure in the polar stratosphere until 25 October 2003. Vertical trace gas profiles obtained with the balloon version of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS-B) provide one of the sparse data sets for validating ILAS-II version 2 and 1.4 data. The MIPAS-B limb emission spectra were collected on 20 March 2003 over Kiruna (Sweden, 68&amp;deg; N) at virtually the same location that has been sounded by ILAS-II about 5.5 h prior to the sampling of MIPAS-B. The intercomparison of the new ILAS-II version 2 (Northern Hemispheric sunrise) data to MIPAS-B vertical trace gas profiles shows a good to excellent agreement within the combined error limits for the species O&lt;sub&gt;3&lt;/sub&gt;, N&lt;sub&gt;2&lt;/sub&gt;O, CH&lt;sub&gt;4&lt;/sub&gt;, H&lt;sub&gt;2&lt;/sub&gt;O (above 21 km), HNO&lt;sub&gt;3&lt;/sub&gt;, ClONO&lt;sub&gt;2&lt;/sub&gt;, and CFC-11 (CCl&lt;sub&gt;3&lt;/sub&gt;F) in the compared altitude range between 16 and 31 km such that these data appear to be very useful for scientific analysis. With regard to the previous version 1.4 ILAS-II data, significant improvements in the consistency with MIPAS-B are obvious especially for the species CH&lt;sub&gt;4&lt;/sub&gt; and H&lt;sub&gt;2&lt;/sub&gt;O, but also for O&lt;sub&gt;3&lt;/sub&gt;, HNO&lt;sub&gt;3&lt;/sub&gt;, ClONO&lt;sub&gt;2&lt;/sub&gt;, NO&lt;sub&gt;2&lt;/sub&gt;, and N&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;5&lt;/sub&gt;. However, comparing gases like NO&lt;sub&gt;2&lt;/sub&gt;, N&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;5&lt;/sub&gt;, and CFC-12 (CCl&lt;sub&gt;2&lt;/sub&gt;F&lt;sub&gt;2&lt;/sub&gt;) exhibits only poor agreement with MIPAS-B such that these species cannot be assumed to be validated at the present time