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Jie Ding

Publications and source records attributed to Jie Ding.

At least 145 records · Page 8Linked to original sources
arXiv2017

Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations

The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits voltage-dependent switching between open and closed states. Different conductance states of a channel imply that the ssPNP equations probably have multiple solutions with different level of currents. We propose numerical approaches to study multiple solutions to the ssPNP equations with multiple ionic species. To find complete current-voltage (I-V ) and current-concentration (I-C) curves, we reformulate the ssPNP equations into four different boundary value problems (BVPs). Numerical continuation approaches are developed to provide good initial guesses for iteratively solving algebraic equations resulting from discretization. Numerical continuations on V , I, and boundary concentrations result in S-shaped and double S-shaped (I-V and I-C) curves for the ssPNP equations with multiple species of ions. There are five solutions to the ssPNP equations with five ionic species, when an applied voltage is given in certain intervals. Remarkably, the current through ion channels responds hysteretically to varying applied voltages and boundary concentrations, showing a memory effect. In addition, we propose a useful computational approach to locate turning points of an I-V curve. With obtained locations, we are able to determine critical threshold values for hysteresis to occur and the interval for V in which the ssPNP equations have multiple solutions. Our numerical results indicate that the developed numerical approaches have a promising potential in studying hysteretic conductance states of ion channels.

math.NA↗
arXiv2017

The Number of Independent Sets in Hexagonal Graphs

A new method is proposed to derive rigorous bounds on η, the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. Specifically, we prove that 1.546440708536001 <= η <= 1.5513, which improves upon the best known 1.5463 <= η <= 1.5527 due to Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point.

cs.IT↗
arXiv2017

Capacity of Hexagonal Checkerboard Codes

In this paper, we propose a new method to bound the capacity of checkerboard codes on the hexagonal lattice. This produces rigorous bounds that are tighter than those commonly known.

cs.IT↗
arXiv2016

SLANTS: Sequential Adaptive Nonlinear Modeling of Vector Time Series

We propose a method for adaptive nonlinear sequential modeling of vector-time series data. Data is modeled as a nonlinear function of past values corrupted by noise, and the underlying non-linear function is assumed to be approximately expandable in a spline basis. We cast the modeling of data as finding a good fit representation in the linear span of multi-dimensional spline basis, and use a variant of l1-penalty regularization in order to reduce the dimensionality of representation. Using adaptive filtering techniques, we design our online algorithm to automatically tune the underlying parameters based on the minimization of the regularized sequential prediction error. We demonstrate the generality and flexibility of the proposed approach on both synthetic and real-world datasets. Moreover, we analytically investigate the performance of our algorithm by obtaining both bounds of the prediction errors, and consistency results for variable selection.

stat.ME↗
arXiv2016

Bridging AIC and BIC: a new criterion for autoregression

We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is generated from a finite order autoregression, the Bayesian information criterion is known to be consistent, and so is the new criterion. When the true order is infinity or suitably high with respect to the sample size, the Akaike information criterion is known to be efficient in the sense that its prediction performance is asymptotically equivalent to the best offered by the candidate models; in this case, the new criterion behaves in a similar manner. Different from the two classical criteria, the proposed criterion adaptively achieves either consistency or efficiency depending on the underlying true model. In practice where the observed time series is given without any prior information about the model specification, the proposed order selection criterion is more flexible and robust compared with classical approaches. Numerical results are presented demonstrating the adaptivity of the proposed technique when applied to various datasets.

math.ST↗
arXiv2016

Multiple Change Point Analysis: Fast Implementation And Strong Consistency

One of the main challenges in identifying structural changes in stochastic processes is to carry out analysis for time series with dependency structure in a computationally tractable way. Another challenge is that the number of true change points is usually unknown, requiring a suitable model selection criterion to arrive at informative conclusions. To address the first challenge, we model the data generating process as a segment-wise autoregression, which is composed of several segments (time epochs), each of which modeled by an autoregressive model. We propose a multi-window method that is both effective and efficient for discovering the structural changes. The proposed approach was motivated by transforming a segment-wise autoregression into a multivariate time series that is asymptotically segment-wise independent and identically distributed. To address the second challenge, we derive theoretical guarantees for (almost surely) selecting the true number of change points of segment-wise independent multivariate time series. Specifically, under mild assumptions, we show that a Bayesian Information Criterion (BIC)-like criterion gives a strongly consistent selection of the optimal number of change points, while an Akaike Information Criterion (AIC)-like criterion cannot. Finally, we demonstrate the theory and strength of the proposed algorithms by experiments on both synthetic and real-world data, including the Eastern US temperature data and the El Nino data from 1854 to 2015. The experiment leads to some interesting discoveries about temporal variability of the summer-time temperature over the Eastern US, and about the most dominant factor of ocean influence on climate.

stat.ME↗
arXiv2015

Data-Driven Learning of the Number of States in Multi-State Autoregressive Models

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to check whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between AR filters based on mean squared prediction error (MSPE), and propose an efficient method to generate random stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.

stat.ML↗
arXiv2015

Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics

Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.

stat.ML↗
arXiv2015

Complementary Lattice Arrays for Coded Aperture Imaging

In this work, we consider complementary lattice arrays in order to enable a broader range of designs for coded aperture imaging systems. We provide a general framework and methods that generate richer and more flexible designs than existing ones. Besides this, we review and interpret the state-of-the-art uniformly redundant arrays (URA) designs, broaden the related concepts, and further propose some new design methods.

cs.IT↗
arXiv2015

Key Pre-Distributions From Graph-Based Block Designs

With the development of wireless communication technologies which considerably contributed to the development of wireless sensor networks (WSN), we have witnessed an ever-increasing WSN based applications which induced a host of research activities in both academia and industry. Since most of the target WSN applications are very sensitive, security issue is one of the major challenges in the deployment of WSN. One of the important building blocks in securing WSN is key management. Traditional key management solutions developed for other networks are not suitable for WSN since WSN networks are resource (e.g. memory, computation, energy) limited. Key pre-distribution algorithms have recently evolved as efficient alternatives of key management in these networks. In the key pre-distribution systems, secure communication is achieved between a pair of nodes either by the existence of a key allowing for direct communication or by a chain of keys forming a key-path between the pair. In this paper, we propose methods which bring prior knowledge of network characteristics and application constraints into the design of key pre-distribution schemes, in order to provide better security and connectivity while requiring less resources. Our methods are based on casting the prior information as a graph. Motivated by this idea, we also propose a class of quasi-symmetric designs referred here to as g-designs. These produce key pre-distribution schemes that significantly improve upon the existing constructions based on unital designs. We give some examples, and point out open problems for future research.

cs.NI↗
arXiv2014

A novel wireless sensor network topology with fewer links

This paper, based on $k$-NN graph, presents symmetric $(k,j)$-NN graph $(1 \leq j < k)$, a brand new topology which could be adopted by a series of network-based structures. We show that the $k$ nearest neighbors of a node exert disparate influence on guaranteeing network connectivity, and connections with the farthest $j$ ones among these $k$ neighbors are competent to build up a connected network, contrast to the current popular strategy of connecting all these $k$ neighbors. In particular, for a network with node amount $n$ up to $10^3$, as experiments demonstrate, connecting with the farthest three, rather than all, of the five nearest neighbor nodes, i.e. $(k,j)=(5,3)$, can guarantee the network connectivity in high probabilities. We further reveal that more than $0.75n$ links or edges in $5$-NN graph are not necessary for the connectivity. Moreover, a composite topology combining symmetric $(k,j)$-NN and random geometric graph (RGG) is constructed for constrained transmission radii in wireless sensor networks (WSNs) application.

cs.NI↗
arXiv2013

Hierarchical Bayesian analysis of somatic mutation data in cancer

Identifying genes underlying cancer development is critical to cancer biology and has important implications across prevention, diagnosis and treatment. Cancer sequencing studies aim at discovering genes with high frequencies of somatic mutations in specific types of cancer, as these genes are potential driving factors (drivers) for cancer development. We introduce a hierarchical Bayesian methodology to estimate gene-specific mutation rates and driver probabilities from somatic mutation data and to shed light on the overall proportion of drivers among sequenced genes. Our methodology applies to different experimental designs used in practice, including one-stage, two-stage and candidate gene designs. Also, sample sizes are typically small relative to the rarity of individual mutations. Via a shrinkage method borrowing strength from the whole genome in assessing individual genes, we reinforce inference and address the selection effects induced by multistage designs. Our simulation studies show that the posterior driver probabilities provide a nearly unbiased false discovery rate estimate. We apply our methods to pancreatic and breast cancer data, contrast our results to previous estimates and provide estimated proportions of drivers for these two types of cancer.

stat.AP↗
arXiv2013

Perturbation Analysis of Orthogonal Matching Pursuit

Orthogonal Matching Pursuit (OMP) is a canonical greedy pursuit algorithm for sparse approximation. Previous studies of OMP have mainly considered the exact recovery of a sparse signal $\bm x$ through $\bm Φ$ and $\bm y=\bm Φ\bm x$, where $\bm Φ$ is a matrix with more columns than rows. In this paper, based on Restricted Isometry Property (RIP), the performance of OMP is analyzed under general perturbations, which means both $\bm y$ and $\bm Φ$ are perturbed. Though exact recovery of an almost sparse signal $\bm x$ is no longer feasible, the main contribution reveals that the exact recovery of the locations of $k$ largest magnitude entries of $\bm x$ can be guaranteed under reasonable conditions. The error between $\bm x$ and solution of OMP is also estimated. It is also demonstrated that the sufficient condition is rather tight by constructing an example. When $\bm x$ is strong-decaying, it is proved that the sufficient conditions can be relaxed, and the locations can even be recovered in the order of the entries' magnitude.

cs.IT↗
arXiv2011

Performance of Orthogonal Matching Pursuit for Multiple Measurement Vectors

In this paper, we consider orthogonal matching pursuit (OMP) algorithm for multiple measurement vectors (MMV) problem. The robustness of OMPMMV is studied under general perturbations---when the measurement vectors as well as the sensing matrix are incorporated with additive noise. The main result shows that although exact recovery of the sparse solutions is unrealistic in noisy scenario, recovery of the support set of the solutions is guaranteed under suitable conditions. Specifically, a sufficient condition is derived that guarantees exact recovery of the sparse solutions in noiseless scenario.

cs.IT↗
arXiv2010

Numerically Representing A Stochastic Process Algebra

The syntactic nature and compositionality characteristic of stochastic process algebras make models to be easily understood by human beings, but not convenient for machines as well as people to directly carry out mathematical analysis and stochastic simulation. This paper presents a numerical representation schema for the stochastic process algebra PEPA, which can provide a platform to directly and conveniently employ a variety of computational approaches to both qualitatively and quantitatively analyse the models. Moreover, these approaches developed on the basis of the schema are demonstrated and discussed. In particular, algorithms for automatically deriving the schema from a general PEPA model and simulating the model based on the derived schema to derive performance measures are presented.

cs.LO↗
arXiv2010

Fundamental Results on Fluid Approximations of Stochastic Process Algebra Models

In order to avoid the state space explosion problem encountered in the quantitative analysis of large scale PEPA models, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying continuous time Markov chain (CTMC). This paper presents a mapping semantics from PEPA to ODEs based on a numerical representation scheme, which extends the class of PEPA models that can be subjected to fluid approximation. Furthermore, we have established the fundamental characteristics of the derived ODEs, such as the existence, uniqueness, boundedness and nonnegativeness of the solution. The convergence of the solution as time tends to infinity for several classes of PEPA models, has been proved under some mild conditions. For general PEPA models, the convergence is proved under a particular condition, which has been revealed to relate to some famous constants of Markov chains such as the spectral gap and the Log-Sobolev constant. This thesis has established the consistency between the fluid approximation and the underlying CTMCs for PEPA, i.e. the limit of the solution is consistent with the equilibrium probability distribution corresponding to a family of underlying density dependent CTMCs.

cs.LO↗
arXiv2004

The Absorption Signature of Six MgII-Selected Systems Over 0.5<z<0.9

We present the following results of photoionization modeling of six MgII-selected absorption systems, at redshift 0.5 < z 0.9, along lines of sight toward three quasars: PG 1241+176, PG 1248+401, and PG 1317+274. These are part of a larger sample of ~20 MgII absorbers at intermediate redshift, that facilitates a survey of the properties of, and processes active in, the multiple phases of gas, both in and outside of galaxies. We present new high resolution ultraviolet spectra from HST/STIS as well as high resolution optical spectra obtained with HIRES/Keck. Together, these spectra allow simultaneous study of a variety of ionization states of different chemical elements, with resolution of the kinematics providing strong constraints on multiphase properties. The six systems presented here include several that are likely to arise from lines of sight through disk and halo structures of spiral galaxies. For these we find that the high ionization gas, traced by CIV is consistent with coronal structures that resemble that of the Milky Way, along with high velocity clouds at 100-200 km/s. Another system has relatively weak CIV, relative to the low ionization absorption, which leads to a discussion of the circumstances in which a corona might be weak or absent in a galaxy, i.e. an early-type morphology or low star formation rate. Finally, we present systems that are examples of single-cloud and multiple-cloud weak MgII absorbers, which are as a class not likely to be within ~50 kpc of luminous galaxies. Based the physical conditions inferred from models, we discuss the nature of these types of systems, which may trace outer regions of galaxies, dwarf galaxy satellites, or metal-rich regions of the intergalactic medium.

astro-ph↗