Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi

Multi-camera Realtime 3D Tracking of Multiple Flying Animals

Automated tracking of animal movement allows analyses that would not otherwise be possible by providing great quantities of data. The additional capability of tracking in realtime - with minimal latency - opens up the experimental possibility of manipulating sensory feedback, thus allowing detailed explorations of the neural basis for control of behavior. Here we describe a new system capable of tracking the position and body orientation of animals such as flies and birds. The system operates with less than 40 msec latency and can track multiple animals simultaneously. To achieve these results, a multi target tracking algorithm was developed based on the Extended Kalman Filter and the Nearest Neighbor Standard Filter data association algorithm. In one implementation, an eleven camera system is capable of tracking three flies simultaneously at 60 frames per second using a gigabit network of nine standard Intel Pentium 4 and Core 2 Duo computers. This manuscript presents the rationale and details of the algorithms employed and shows three implementations of the system. An experiment was performed using the tracking system to measure the effect of visual contrast on the flight speed of Drosophila melanogaster. At low contrasts, speed is more variable and faster on average than at high contrasts. Thus, the system is already a useful tool to study the neurobiology and behavior of freely flying animals. If combined with other techniques, such as `virtual reality'-type computer graphics or genetic manipulation, the tracking system would offer a powerful new way to investigate the biology of flying animals.Comment: pdfTeX using libpoppler 3.141592-1.40.3-2.2 (Web2C 7.5.6), 18 pages with 9 figure

Docosahexaenoic Acid Promotes Recovery of Motor Function by Neuroprotection and Neuroplasticity Mechanisms

The omega-3 polyunsaturated fatty acid, docosahexaenoic acid (DHA), has been shown to promote recovery of motor function after spinal cord injury. This is likely to be at least partly due to neuroprotective effects of DHA. However, recent studies have shown that DHA also supports neuroplasticity after injury, such as promoting sprouting of spared corticospinal tract (CST) axons. In this chapter, we review the published studies showing that DHA promotes recovery of motor function in rodent models of spinal cord injury (SCI), and consider the available data on the underlying mechanisms. This includes effects on inflammation and on neuronal and oligodendrocyte survival at the injury site, and effects on spared CST axons and serotonergic axons. Current data support the hypothesis that DHA promotes recovery of motor function by both neuroprotection and neuroplasticity mechanisms. The significance of this, and the implications of combining DHA with rehabilitation strategies, will be discussed

Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect

The classification of point gap topology in all local non-Hermitian symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical interpretation in terms of their bulk-boundary correspondence. Here, we derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. While in one dimension point gap topology invariably leads to the non-Hermitian skin effect, non-Hermitian boundary physics is significantly richer in two dimensions. We find two broad classes of non-Hermitian edge states: (1) Infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Under semi-infinite boundary conditions, the point gap thereby closes completely, but only at a single edge momentum. (2) Non-Hermitian exceptional point dispersions, where edge states persist at all edge momenta and furnish an anomalous number of symmetry-protected exceptional points. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations. Instead, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of non-Hermitian spectral flow.Comment: 6 pages, 3 figures, 13 pages supplementary materia

Infernal and exceptional edge modes: non-Hermitian topology beyond the skin effect

The classification of point gap topology in all local non-Hermitian (NH) symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical interpretation in terms of their bulk-boundary correspondence. Here, we derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. While in one dimension point gap topology invariably leads to the NH skin effect, NH boundary physics is significantly richer in two dimensions. We find two broad classes of non-Hermitian edge states: (1) infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Under semi-infinite boundary conditions, the point gap thereby closes completely, but only at a single edge momentum. (2) NH exceptional point dispersions, where edge states persist at all edge momenta and furnish an anomalous number of symmetry-protected exceptional points. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations. Concomitantly, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of NH spectral flow

The case studies: authentic learning

Moving from theory to practice in higher education is deeply challenging. While exploring pedagogical models in the literature may lead to tacit understanding of general principles, actually implementing these principles in practice can be an entirely different matter

Impact of Monetary Policy on Inflationary Process in Nigeria

The paper examines the Impact of Monetary Policy on Inflationary Process in Nigeria from 1986 – 2013, using ordinary least squared regression. We started with investigating the stochastic properties of the data using the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests for unit roots. Both tests suggest that all the variables of interest which comprise of inflation rate, Money supply, interest rate and Unemployment are integrated at the second difference. The regression results showed that monetary policy have significant influence on inflation.  It is recommended that the government should embark on joint coordination of fiscal and monetary authorities with respect to liquidity flows in the economy to aid curb inflation. Furthermore, where deficit financing is inevitable, it should be put into productive activities in order to create more employment opportunities, raise national output, and increase the living standard of the people. Keywords: Monetary policy, inflation, money supply, interest rate, unemploymen