Horocycle Decision Boundaries for Large Margin Classification in Hyperbolic Space

Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries in a large margin classifiers setting leading to a non-convex optimization problem. In this paper, we propose a novel large margin classifier based on horocycle (horosphere) decision boundaries that leads to a geodesically convex optimization problem that can be optimized using any Riemannian gradient descent technique guaranteeing a globally optimal solution. We present several experiments depicting the performance of our classifier

Giant Cross Kerr Effect for Propagating Microwaves Induced by an Artificial Atom

We have investigated the cross Kerr phase shift of propagating microwave fields strongly coupled to an artificial atom. The artificial atom is a superconducting transmon qubit in an open transmission line. We demonstrate average phase shifts of 11 degrees per photon between two coherent microwave fields both at the single-photon level. At high control power, we observe phase shifts up to 30 degrees. Our results provide an important step towards quantum gates with propagating photons in the microwave regime.Comment: 5 pages, 4 figure

Unified theory for Goos-H\"{a}nchen and Imbert-Fedorov effects

A unified theory is advanced to describe both the lateral Goos-H\"{a}nchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a 3-dimensional light beam in terms of a 2-form angular spectrum consisting of its 2 orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the 2 orthogonal linear polarizations in this 2-form representation, and the eigenstates of the IF displacement are the 2 orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.Comment: 15 pages, 3 figure

Integral equation method for the electromagnetic wave propagation in stratified anisotropic dielectric-magnetic materials

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.Comment: 14pages, 3figure

Cloning, expression, and functional analysis of human dopamine D1 receptors

Aim : To construct an HEK293 cell line stably expressing human dopamine D 1 receptor (D 1 R). Methods : cDNA was amplified by RT-PCR using total RNA from human embryo brain tissue as the template. The PCR products were subcloned into the plasmid pcDNA3 and cloned into the plasmid pcDNA3.1. The cloned D 1 R cDNA was sequenced and stably expressed in HEK293 cells. Expression of D 1 R in HEK293 cells was monitored by the [ 3 H]SCH23390 binding assay. The function of D 1 R was studied by the cAMP accumulation assay, CRE-SEAP reporter gene activity assay, and intracellular calcium assay. Results : An HEK293 cell line stably expressing human D 1 R was obtained. A saturation radioligand binding experiment with [ 3 H]SCH23390 demonstrated that the K d and B max values were 1.5±0.2 nmol/L and 2.94±0.15 nmol/g of protein, respectively. In the [ 3 H]SCH23390 competition assay, D 1 R agonist SKF38393 displaced [ 3 H]SCH23390 with an IC 50 value of 2.0 (1.5–2.8) Μmol/L. SKF38393 increased the intracellular cAMP level and CRE-SEAP activity through D 1 R expressed in HEK293 cells in a concentration-dependent manner with an EC 50 value of 0.25 (0.12–0.53) Μmol/L and 0.39 (0.27–0.57) Μmol/L at 6 h/0.59 (0.22–1.58) Μmol/L at 12 h, respectively. SKF38393 also increased the intracellular calcium level in a concentration-dependent manner with EC 50 value of 27 (8.6–70) nmol/L. Conclusion : An HEK293 cell line stably expressing human D 1 R was obtained successfuly. The study also demonstrated that the CRE-SEAP activity assay could be substituted for the cAMP accumulation assay for measuring increase in cAMP levels. Thus, both intracellular calcium measurements and the CRE-SEAP activity assay are suitable for high-throughput screening in drug research.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75187/1/j.1745-7254.2005.00017.x.pd

A powerful and efficient multivariate approach for voxel-level connectome-wide association studies

We describe an approach to multivariate analysis, termed structured kernel principal component regression (sKPCR), to identify associations in voxel-level connectomes using resting-state functional magnetic resonance imaging (rsfMRI) data. This powerful and computationally efficient multivariate method can identify voxel-phenotype associations based on the whole-brain connectivity pattern of voxels, and it can detect linear and non-linear signals in both volume-based and surface-based rsfMRI data. For each voxel, sKPCR first extracts low-dimensional signals from the spatially smoothed connectivities by structured kernel principal component analysis, and then tests the voxel-phenotype associations by an adaptive regression model. The method's power is derived from appropriately modelling the spatial structure of the data when performing dimension reduction, and then adaptively choosing an optimal dimension for association testing using the adaptive regression strategy. Simulations based on real connectome data have shown that sKPCR can accurately control the false-positive rate and that it is more powerful than many state-of-the-art approaches, such as the connectivity-wise generalized linear model (GLM) approach, multivariate distance matrix regression (MDMR), adaptive sum of powered score (aSPU) test, and least-square kernel machine (LSKM). Moreover, since sKPCR can reduce the computational cost of non-parametric permutation tests, its computation speed is much faster. To demonstrate the utility of sKPCR for real data analysis, we have also compared sKPCR with the above methods based on the identification of voxel-wise differences between schizophrenic patients and healthy controls in four independent rsfMRI datasets. The results showed that sKPCR had better between-sites reproducibility and a larger proportion of overlap with existing schizophrenia meta-analysis findings. Code for our approach can be downloaded from https://github.com/weikanggong/sKPCR. [Abstract copyright: Copyright © 2018 Elsevier Inc. All rights reserved.

Breakdown of the cross-kerr scheme for photon counting

We show, in the context of single-photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarizability model known as the cross-Kerr effect.We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single-photon applications. Our results are presented in the context of a transmon in a one-dimensional microwave waveguide, but the conclusions also apply to optical systems

Topological Pattern Recognition of Severe Alzheimer's Disease via Regularized Supervised Learning of EEG Complexity

Alzheimer's disease (AD) is a progressive brain disorder with gradual memory loss that correlates to cognitive deficits in the elderly population. Recent studies have shown the potentials of machine learning algorithms to identify biomarkers and functional brain activity patterns across various AD stages using electroencephalography (EEG). In this study, we aim to discover the altered spatio-temporal patterns of EEG complexity associated with AD pathology in different severity levels. We employed the multiscale entropy (MSE), a complexity measure of time series signals, as the biomarkers to characterize the nonlinear complexity at multiple temporal scales. Two regularized logistic regression methods were applied to extracted MSE features to capture the topographic pattern of MSEs of AD cohorts compared to healthy baseline. Furthermore, canonical correlation analysis was performed to evaluate the multivariate correlation between EEG complexity and cognitive dysfunction measured by the Neuropsychiatric Inventory scores. 123 participants were recruited and each participant was examined in three sessions (length = 10 seconds) to collect resting-state EEG signals. MSE features were extracted across 20 time scale factors with pre-determined parameters (m = 2, r = 0.15). The results showed that comparing to logistic regression model, the regularized learning methods performed better for discriminating severe AD cohort from normal control, very mild and mild cohorts (test accuracy ~ 80%), as well as for selecting significant biomarkers arcoss the brain regions. It was found that temporal and occipitoparietal brain regions were more discriminative in regard to classifying severe AD cohort vs. normal controls, but more diverse and distributed patterns of EEG complexity in the brain were exhibited across individuals in early stages of AD