Spherical Hamiltonian Monte Carlo for Constrained Target Distributions

We propose a new Markov Chain Monte Carlo (MCMC) method for constrained target distributions. Our method first maps the $D$-dimensional constrained domain of parameters to the unit ball ${\bf B}_0^D(1)$. Then, it augments the resulting parameter space to the $D$-dimensional sphere, ${\bf S}^D$. The boundary of ${\bf B}_0^D(1)$ corresponds to the equator of ${\bf S}^D$. This change of domains enables us to implicitly handle the original constraints because while the sampler moves freely on the sphere, it proposes states that are within the constraints imposed on the original parameter space. To improve the computational efficiency of our algorithm, we split the Lagrangian dynamics into several parts such that a part of the dynamics can be handled analytically by finding the geodesic flow on the sphere. We apply our method to several examples including truncated Gaussian, Bayesian Lasso, Bayesian bridge regression, and a copula model for identifying synchrony among multiple neurons. Our results show that the proposed method can provide a natural and efficient framework for handling several types of constraints on target distributions

A Semiparametric Bayesian Model for Detecting Synchrony Among Multiple Neurons

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1's (spike) and 0's (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a Gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows: the nonparametric component (i.e., the Gaussian process model) provides a flexible framework for modeling the underlying firing rates; the parametric component (i.e., the copula model) allows us to make inference regarding both contemporaneous and lagged relationships among neurons; using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of dependence structure among variables; our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas in rat's brain

Validity of the scattering length approximation in strongly interacting Fermi systems

We investigate the energy spectrum of systems of two, three and four spin-1/2 fermions with short range attractive interactions both exactly, and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the 2-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point kF a much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the 4-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the 4-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wavefunctions.Comment: 7 pages, 7 figure

Fan-Shaped Model for Generating the Anisotropic Catchment Area of Subway Stations based on Feeder Taxi Trips

The catchment areas of subway stations have always been considered as a circular shape in previous research. Although some studies show the catchment area may be affected by road conditions, public transportation, land use, and other factors, few studies have discussed the shape of the catchment area. This study focuses on analyzing the anisotropy of catchment areas and developing a sound methodology to generate them. Based on taxi global positioning system (GPS) data, this paper first proposes a data mining method to identify feeder taxi trips around subway stations. Then, a fan-shaped model is proposed and applied to Xi\u27an Metro Line 1 to generate catchment areas. The number and angle of fan areas are determined according to the spatial distribution characteristics of GPS points. Results show that the acceptable distance of the catchment area has significant differences in different directions. The average maximum acceptable distance of one station is 2.31 times the minimum. Furthermore, for feeder taxis, the overlap ratio of the catchment area is very high. Travelers in several places could choose several different stations during the travel. A multiple linear regression model was introduced to find the influencing factors, and the result shows the anisotropy of the catchment area is affected not only by neighboring subway stations, but also by the road network, distance from the city center, and so on

Understanding the Spatial Structure of Urban Commuting Using Mobile Phone Location Data: A Case Study of Shenzhen, China

Understanding commuting patterns has been a classic research topic in the fields of geography, transportation and urban planning, and it is significant for handling the increasingly serious urban traffic congestion and air pollution and their impacts on the quality of life. Traditional studies have used travel survey data to investigate commuting from the aspects of commuting mode, efficiency and influence factors. Due to the limited sample size of these data, it is difficult to examine the large-scale commuting patterns of urban citizens, especially when exploring the spatial structure of commuting. This study attempts to understand the spatial structure characteristics generated by human commutes to work by using massive mobile phone datasets. A three-step workflow was proposed to accomplish this goal, which includes extracting the home and work locations of phone users, detecting the communities from the commuting network, and identifying the commuting convergence and divergence areas for each community. A case study of Shenzhen, China was implemented to determine the commuting structure. We found that there are thirteen communities detected from the commuting network and that some of the communities are in accordance with urban planning; moreover, spatial polycentric polygons exist in each community. These findings can be referenced by urban planners or policy-makers to optimize the spatial layout of the urban functional zones. Document type: Articl