On a Conjecture of Givental

These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line, whose Gromov-Witten invariants are well-known and easy to compute. We make some simple checks supporting his conjecture.Comment: 13 pages, no figures; v.2: new title, minor change

On Perturbation Spectra of N-flation

In this note we study the adiabatic perturbation spectrum of N-flation with power law potential. We show that the scalar spectrum of N-flation is generally redder than that of its corresponding single field. The result obtained for that with unequal massive fields is consistent with the recent numerical investigation of Kim and Liddle.Comment: 3 pages, refs. added, comments added, typos corrected, abstract changed, to publish in PRD brief repor

A Model of Consistent Node Types in Signed Directed Social Networks

Signed directed social networks, in which the relationships between users can be either positive (indicating relations such as trust) or negative (indicating relations such as distrust), are increasingly common. Thus the interplay between positive and negative relationships in such networks has become an important research topic. Most recent investigations focus upon edge sign inference using structural balance theory or social status theory. Neither of these two theories, however, can explain an observed edge sign well when the two nodes connected by this edge do not share a common neighbor (e.g., common friend). In this paper we develop a novel approach to handle this situation by applying a new model for node types. Initially, we analyze the local node structure in a fully observed signed directed network, inferring underlying node types. The sign of an edge between two nodes must be consistent with their types; this explains edge signs well even when there are no common neighbors. We show, moreover, that our approach can be extended to incorporate directed triads, when they exist, just as in models based upon structural balance or social status theory. We compute Bayesian node types within empirical studies based upon partially observed Wikipedia, Slashdot, and Epinions networks in which the largest network (Epinions) has 119K nodes and 841K edges. Our approach yields better performance than state-of-the-art approaches for these three signed directed networks.Comment: To appear in the IEEE/ACM International Conference on Advances in Social Network Analysis and Mining (ASONAM), 201

Large Scale Structure Formation of Normal Branch in DGP Brane World Model

In this paper, we study the large scale structure formation of the normal branch in DGP model (Dvail, Gabadadze and Porrati brane world model) by applying the scaling method developed by Sawicki, Song and Hu for solving the coupled perturbed equations of motion of on-brane and off-brane. There is detectable departure of perturbed gravitational potential from LCDM even at the minimal deviation of the effective equation of state w_eff below -1. The modified perturbed gravitational potential weakens the integrated Sachs-Wolfe effect which is strengthened in the self-accelerating branch DGP model. Additionally, we discuss the validity of the scaling solution in the de Sitter limit at late times.Comment: 6 pages, 2 figure

Quantum correction for electron transfer rates. Comparison of polarizable versus nonpolarizable descriptions of solvent

The electron transfer rate constant is treated using the spin-boson Hamiltonian model. The spectral density is related to the experimentally accessible data on the dielectric dispersion of the solvent, using a dielectric continuum approximation. On this basis the quantum correction for the ferrous–ferric electron transfer rate is found to be a factor 9.6. This value is smaller than the corresponding result (36) of Chandler and co-workers in their pioneering quantum simulation using a molecular model of the system [J. S. Bader, R. A. Kuharski, and D. Chandler, J. Chem. Phys. 93, 230 (1990)]. The likely reason for the difference lies in use of a rigid water molecular model in the simulation, since we find that other models for water in the literature which neglect the electronic and vibrational polarizability also give a large quantum effect. Such models are shown to overestimate the dielectric dispersion in one part of the quantum mechanically important region and to underestimate it in another part. It will be useful to explore a polarizable molecular model which reproduces the experimental dielectric response over the relevant part of the frequency spectrum

Stack- and Queue-like Dynamics in Recurrent Neural Networks

What dynamics do simple recurrent networks (SRNs) develop to represent stack-like and queue-like memories? SRNs have been widely used as models in cognitive science. However, they are interesting in their own right as non-symbolic computing devices from the viewpoints of analogue computing and dynamical systems theory. In this paper, SRNs are trained oil two prototypical formal languages with recursive structures that need stack-like or queue-like memories for processing, respectively. The evolved dynamics are analysed, then interpreted in terms of simple dynamical systems, and the different ease with which SRNs aquire them is related to the properties of these simple dynamical Within the dynamical systems framework, it is concluded that the stack-like language is simpler than the queue-like language, without making use of arguments from symbolic computation theory

Unit roots in moving averages beyond first order

The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root and near unit root cases of a first-order moving average model. Previous studies of the MA(1) unit root problem rely on the special autocovariance structure of the MA(1) process, in which case, the eigenvalues and eigenvectors of the covariance matrix of the data vector have known analytical forms. In this paper, we take a different approach to first consider the joint likelihood by including an augmented initial value as a parameter and then recover the exact likelihood by integrating out the initial value. This approach by-passes the difficulty of computing an explicit decomposition of the covariance matrix and can be used to study unit root behavior in moving averages beyond first order. The asymptotics of the generalized likelihood ratio (GLR) statistic for testing unit roots are also studied. The GLR test has operating characteristics that are competitive with the locally best invariant unbiased (LBIU) test of Tanaka for some local alternatives and dominates for all other alternatives.Comment: Published in at http://dx.doi.org/10.1214/11-AOS935 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An asymptotic sampling formula for the coalescent with Recombination

Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. In the population genetics community, extending the underlying random-mating model to include recombination has received much attention in the past, but no general closed-form sampling formula is currently known even for the simplest extension, that is, a model with two loci. In this paper, we show that it is possible to obtain useful closed-form results in the case the population-scaled recombination rate $\rho$ is large but not necessarily infinite. Specifically, we consider an asymptotic expansion of the two-locus sampling formula in inverse powers of $\rho$ and obtain closed-form expressions for the first few terms in the expansion. Our asymptotic sampling formula applies to arbitrary sample sizes and configurations.Comment: Published in at http://dx.doi.org/10.1214/09-AAP646 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org