Qualitative properties of large buckled states of spherical shells

A system of 6th-order quasi-linear Ordinary Differential Equations is analyzed to show the global existence of axisymmetrically buckled states. A surprising nodal property is obtained which shows that everywhere along a branch of solutions that bifurcates from a simple eigenvalue of the linearized equation, the number of simultaneously vanishing points of both shear resultant and circumferential bending moment resultant remains invariant, provided that a certain auxiliary condition is satisfied

An approach for jointly modeling multivariate longitudinal measurements and discrete time-to-event data

In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS339 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Empires of the Sinophone

This paper will consider how Sinophone literature from different parts of the world can serve as interventions to major theoretical and disciplinary issues in the humanities today in our new age of empires.postprin

Alignment and orientation of an adsorbed dipole molecule

Half-cycle laser pulse is applied on an absorbed molecule to investigate its alignment and orientation behavior. Crossover from field-free to hindered rotation motion is observed by varying the angel of hindrance of potential well. At small hindered angle, both alignment and orientation show sinusoidal-like behavior because of the suppression of higher excited states. However, mean alignment decreases monotonically as the hindered angle is increased, while mean orientation displays a minimum point at certain hindered angle. The reason is attributed to the symmetry of wavefunction and can be explained well by analyzing the coefficients of eigenstates.Comment: 4 pages, 4 figures, to appear in Phys. Rev. B (2004

Dual Field Theories In (d-1)+1 Emergent Spacetimes From A Unifying Field Theory In d+2 Spacetime

According to Two-Time Physics, there is more to space-time than can be garnered with the ordinary formulation of physics. Two-Time Physics has shown that the Standard Model of Particles and Forces is successfully reproduced by a two-time field theory in 4 space and 2 time dimensions projected as a holographic image on an emergent spacetime in 3+1 dimensions. Among the successes of this approach is the resolution of the strong CP problem of QCD as an outcome of the restrictions imposed by the higher symmetry structures in 4+2 dimensions. In this paper we launch a program to construct the duals of the Standard Model as other holographic images of the same 4+2 dimensional theory on a variety of emergent spacetimes in 3+1 dimensions. These dual field theories are obtained as a family of gauge choices in the master 4+2 field theory. In the present paper we deal with some of the simpler gauge choices which lead to interacting Klein-Gordon field theories for the conformal scalar with a predicted SO(d,2) symmetry in a variety of interesting curved spacetimes in (d-1)+1 dimensions. More challenging and more interesting gauge choices (including some that relate to mass) which are left to future work are also outlined. Through this approach we discover a new realm of previously unexplored dualities and hidden symmetries that exist both in the macroscopic and microscopic worlds, at the classical and quantum levels. Such phenomena predicted by 2T-physics can in principle be confirmed both by theory and experiment. 1T-physics can be used to analyze the predictions but in most instances gives no clue that the predicted phenomena exist in the first place. This point of view suggests a new paradigm for the construction of a fundamental theory that is likely to impact on the quest for unification.Comment: LaTeX, 35 page

The Big Bang and Inflation United by an Analytic Solution

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the Big Bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Fridemann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time, rather it oscillates around the potential minimum while settling down, unlike the slow roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.Comment: V2 improve computation with better agreement with WMAP 7 years data, and also point out an exact solution for cyclic cosmolog

Steady-state entanglement in a double-well Bose-Einstein condensate through coupling to a superconducting resonator

We consider a two-component Bose-Einstein condensate in a double-well potential, where the atoms are magnetically coupled to a single-mode of the microwave field inside a superconducting resonator. We find that the system has the different dark-state subspaces in the strong- and weak-tunneling regimes, respectively. In the limit of weak tunnel coupling, steady-state entanglement between the two spatially separated condensates can be generated by evolving to a mixture of dark states via the dissipation of the photon field. We show that the entanglement can be faithfully indicated by an entanglement witness. Long-lived entangled states are useful for quantum information processing with atom-chip devices.Comment: 9 pages, 7 figures, minor revisio

Gradient categories in lexically-conditioned phonology: An example from sound symbolism

There are many approaches to modeling lexically-conditioned phonology in current formal theories, including lexically-indexed constraints and cophonologies. Nearly all of these existing approaches assume categorical membership in the lexical classes that condition differential phonotactics or phonological behaviours: for example, a lexical item is either a noun or a verb, or of one gender class or another. This paper proposes an implementation of Maximum Entropy Harmonic Grammar with lexically-indexed constraints and gradient symbolic activations over classes that allows us to model differences in phonological patterns over both discrete and gradient class membership. This theoretical implementation is a natural extension of the scales and gradient activations that have been shown to be necessary in recent phonological theory: sound symbolic evidence highlights the necessity for such increased explanatory power in our phonological models. Crucially, we find gradient lexically-conditioned patterns not only in sound symbolism—where they are often most obvious—but also in what is considered “core” language (e.g., morphosyntactic classes), and allowing gradient class structures in our phonological models may ultimately make for cleaner interfaces with other parts of grammar such as morphosyntax

Impact of Carbon Price Policies on U.S. Industry

This paper informs the discussion of carbon price policies by examining the potential for adverse impacts on domestic industries, with a focus on detailed sector-level analysis. The assumed policy scenario involves a unilateral economy-wide $10/ton CO2 charge without accompanying border tax adjustments or other complementary policies. Four modeling approaches are developed as a proxy for the different time horizons over which firms can pass through added costs, change input mix, adopt new technologies, and reallocate capital. Overall, we find that a readily identifiable set of industries experience particularly adverse impacts as measured by reduced output and that the relative burdens on different industries are remarkably consistent across the four time horizons. Output rebounds considerably over longer time horizons, and the adverse impacts on profits diminish even more rapidly in most cases. Over the short term employment losses mirror output declines, while gains in other industries fully offset the losses over the longer horizons. At the same time, leakage abroad is considerable in some sectors, particularly when reductions in exports are considered.carbon price, competitiveness, input-output analysis