A self-normalized approach to confidence interval construction in time series

We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent approaches, our method has the attractive convenience of being free of choosing any user-chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution-free self-normalized statistic, in which the normalizing matrix is computed using recursive estimates. Under mild conditions, we establish the theoretical validity of our method for a broad class of statistics that are functionals of the empirical distribution of fixed or growing dimension. From a practical point of view, our method is conceptually simple, easy to implement and can be readily used by the practitioner. Monte-Carlo simulations are conducted to compare the finite sample performance of the new method with those delivered by the normal approximation and the block bootstrap approach.Comment: 35 pages, 4 figures, 5 table

Fluid limit of threshold voter models on tori

In this paper, we are concerned with threshold voter models on tori. Assuming that the initial distribution of the process is product measure with density p, we obtain a fluid limit of the proportion of vertices in state 1 as the dimension of the torus grows to infinity. The fluid limit performs a phase transition phenomenon from p 1/2.Comment: 18 page

Survival probabilities of high-dimensional stochastic SIS and SIR models with random edge weights

In this paper, we are concerned with the stochastic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) models on high-dimensional lattices with random edge weights, where a susceptible vertex is infected by an infectious neighbor at rate proportional to the weight on the edge connecting them. All the edge weights are assumed to be i.i.d.. Our main result gives mean field limits for survival probabilities of the two models as the dimension grows to infinity, which extends the main conclusion given in \cite{Xue2017} for classic stochastic SIS model.Comment: 25 page

Efficient schemes with unconditionally energy stability for the anisotropic Cahn-Hilliard Equation using the stabilized-Scalar Augmented Variable (S-SAV) approach

In this paper, we consider numerical approximations for the anisotropic Cahn-Hilliard equation. The main challenge of constructing numerical schemes with unconditional energy stabilities for this model is how to design proper temporal discretizations for the nonlinear terms with the strong anisotropy. We propose two, second order time marching schemes by combining the recently developed SAV approach with the linear stabilization approach, where three linear stabilization terms are added. These terms are shown to be crucial to remove the oscillations caused by the anisotropic coefficients, numerically. The novelty of the proposed schemes is that all nonlinear terms can be treated semi-explicitly, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. We further prove the unconditional energy stabilities rigorously, and present various 2D and 3D numerical simulations to demonstrate the stability and accuracy

Numerical approximations for the binary Fluid-Surfactant Phase Field Model with fluid flow: Second-order, Linear, Energy stable schemes

In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two Cahn-Hilliard type equations. We develop two, linear and second order time marching schemes for solving this system, by combining the "Invariant Energy Quadratization" approach for the nonlinear potentials, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective terms. We prove the well-posedness of the linear system and its unconditional energy stability rigorously. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.Comment: arXiv admin note: substantial text overlap with arXiv:1701.0744

Spanning rigid subgraph packing and sparse subgraph covering

Rigidity, arising in discrete geometry, is the property of a structure that does not flex. Laman provides a combinatorial characterization of rigid graphs in the Euclidean plane, and thus rigid graphs in the Euclidean plane have applications in graph theory. We discover a sufficient partition condition of packing spanning rigid subgraphs and spanning trees. As a corollary, we show that a simple graph $G$ contains a packing of $k$ spanning rigid subgraphs and $l$ spanning trees if $G$ is $(4k+2l)$-edge-connected, and $G-Z$ is essentially $(6k+2l - 2k|Z|)$-edge-connected for every $Z\subset V(G)$. Thus every $(4k+2l)$-connected and essentially $(6k+2l)$-connected graph $G$ contains a packing of $k$ spanning rigid subgraphs and $l$ spanning trees. Utilizing this, we show that every $6$-connected and essentially $8$-connected graph $G$ contains a spanning tree $T$ such that $G-E(T)$ is $2$-connected. These improve some previous results. Sparse subgraph covering problems are also studied.Comment: 12 page

The critical infection rate of the high-dimensional two-stage contact process

In this paper we are concerned with the two-stage contact process on the lattice $\mathbb{Z}^d$ introduced in \cite{Krone1999}. We gives a limit theorem of the critical infection rate of the process as the dimension $d$ of the lattice grows to infinity. A linear system and a two-stage SIR model are two main tools for the proof of our main result.Comment: 13 page

Fluctuations of Conserved Quantities in High Energy Nuclear Collisions at RHIC

Fluctuations of conserved quantities in heavy-ion collisions are used to probe the phase transition and the QCD critical point for the strongly interacting hot and dense nuclear matter. The STAR experiment has carried out moment analysis of net-proton (proxy for net-baryon (B)), net-kaon (proxy for net-strangeness (S)), and net-charge (Q). These measurements are important for understanding the quantum chromodynamics phase diagram. We present the analysis techniques used in the moment analysis by the STAR experiment and discuss the moments of net-proton and net-charge distributions from the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider.Comment: 5 pages, 2 figures, Proceedings of Workshop for Young Scientists with Research Interests Focused on Physics at FAIR, Italy, Sept. 22-27, 2014 (FAIRNESS Workshop 2014

A generalized portmanteau test of independence between two stationary time series

We propose generalized portmanteau-type test statistics in the frequency domain to test independence between two stationary time series. The test statistics are formed analogous to the one in Chen and Deo (2004, Econometric Theory 20, 382-416), who extended the applicability of portmanteau goodness-of-fit test to the long memory case. Under the null hypothesis of independence, the asymptotic standard normal distributions of the proposed statistics are derived under fairly mild conditions. In particular, each time series is allowed to possess short memory, long memory or anti-persistence. A simulation study shows that the tests have reasonable size and power properties.Comment: 39 pages, 4 table

Nonstationarity-extended Whittle Estimation

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso and Giraitis (2007, Journal of Econometrics 141, 1353-1384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.Comment: 32 pages, 3 table