A finite difference solution for the cylindrical expansion of a gas cloud into vacuum

Finite difference method for solution of cylindrical expansion of gas cloud into vacuu

Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems

Towards Interpretable Deep Learning Models for Knowledge Tracing

As an important technique for modeling the knowledge states of learners, the traditional knowledge tracing (KT) models have been widely used to support intelligent tutoring systems and MOOC platforms. Driven by the fast advancements of deep learning techniques, deep neural network has been recently adopted to design new KT models for achieving better prediction performance. However, the lack of interpretability of these models has painfully impeded their practical applications, as their outputs and working mechanisms suffer from the intransparent decision process and complex inner structures. We thus propose to adopt the post-hoc method to tackle the interpretability issue for deep learning based knowledge tracing (DLKT) models. Specifically, we focus on applying the layer-wise relevance propagation (LRP) method to interpret RNN-based DLKT model by backpropagating the relevance from the model's output layer to its input layer. The experiment results show the feasibility using the LRP method for interpreting the DLKT model's predictions, and partially validate the computed relevance scores from both question level and concept level. We believe it can be a solid step towards fully interpreting the DLKT models and promote their practical applications in the education domain

Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities

The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.Comment: 18 pages, 5 figures, pdfLatex, RevTe

Optical conductivity for a dimer in the Dynamic Hubbard model

The Dynamic Hubbard Model represents the physics of a multi-band Hubbard model by using a pseudo-spin degree of freedom to dynamically modify the on-site Coulomb interaction. Here we use a dimer system to obtain analytical results for this model. The spectral function and the optical conductivity are calculated analytically for any number of electrons, and the distribution of optical spectral weight is analyzed in great detail. The impact of polaron-like effects due to overlaps between pseudo-spin states on the optical spectral weight distribution is derived analytically. Our conclusions support results obtained previously with different models and techniques: holes are less mobile than electrons.Comment: 11 pages, 4 figure

Field evolution of the magnetic structures in Er2_2Ti2_2O7_7 through the critical point

We have measured neutron diffraction patterns in a single crystal sample of the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase (T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the [110] direction. We determine all the characteristics of the magnetic structure throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er moments align along the field at $H_c$ and their values reach a minimum. Using a four-sublattice self-consistent calculation, we show that the evolution of the magnetic structure and the value of the critical field are rather well reproduced using the same anisotropic exchange tensor as that accounting for the local paramagnetic susceptibility. In contrast, an isotropic exchange tensor does not match the moment variations through the critical point. The model also accounts semi-quantitatively for other experimental data previously measured, such as the field dependence of the heat capacity, energy of the dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure

A finite difference solution for the two- dimensional expansion of a finite cylindrical gas cloud into a vacuum

Interaction of radial and axial rarefaction waves investigated by considering expansion of finite length cylindrical gas cloud into vacuu

Ground State and Resonances in the Standard Model of Non-relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change

Establishing operant conflict tests for the translational study of anxiety in mice

Rationale In conflict-based anxiety tests, rodents decide between actions with simultaneous rewarding and aversive outcomes. In humans, computerised operant conflict tests have identified response choice, latency, and vigour as distinct behavioural components. Animal operant conflict tests for measurement of these components would facilitate translational study. Objectives In C57BL/6 mice, two operant conflict tests for measurement of response choice, latency, and vigour were established, and effects of chlordiazepoxide (CDZ) thereon investigated. Methods Mice were moderately diet-restricted to increase sucrose reward salience. A 1-lever test required responding under medium-effort reward/threat conditions of variable ratio 2–10 resulting in sucrose at p = 0.7 and footshock at p = 0.3. A 2-lever test mandated a choice between low-effort reward/threat with a fixed-ratio (FR) 2 lever yielding sucrose at p = 0.7 and footshock at p = 0.3 versus high-effort reward/no threat with a FR 20 lever yielding sucrose at p = 1. Results In the 1-lever test, CDZ (7.5 or 15 mg/kg i.p.) reduced post-trial pause (response latency) following either sucrose or footshock and reduced inter-response interval (increased response vigour) after footshock. In the 2-lever test, mice favoured the FR2 lever and particularly at post-reward trials. CDZ increased choice of FR2 and FR20 responding after footshock, reduced response latency overall, and increased response vigour at the FR2 lever and after footshock specifically. Conclusions Mouse operant conflict tests, especially 2-lever choice, allow for the translational study of distinct anxiety components. CDZ influences each component by ameliorating the impact of both previous punishment and potential future punishment