15,638 research outputs found
The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations
It is well known that reconstruction problems, as the interdisciplinary
subject, have been studied in numerous contexts including statistical physics,
information theory and computational biology, to name a few. We consider a
-state symmetric model, with two categories of states in each category,
and 3 transition probabilities: the probability to remain in the same state,
the probability to change states but remain in the same category, and the
probability to change categories. We construct a nonlinear second order
dynamical system based on this model and show that the Kesten-Stigum
reconstruction bound is not tight when .Comment: Accepted, to appear Journal of Statistical Physic
Multiple Change-point Detection: a Selective Overview
Very long and noisy sequence data arise from biological sciences to social
science including high throughput data in genomics and stock prices in
econometrics. Often such data are collected in order to identify and understand
shifts in trend, e.g., from a bull market to a bear market in finance or from a
normal number of chromosome copies to an excessive number of chromosome copies
in genetics. Thus, identifying multiple change points in a long, possibly very
long, sequence is an important problem. In this article, we review both
classical and new multiple change-point detection strategies. Considering the
long history and the extensive literature on the change-point detection, we
provide an in-depth discussion on a normal mean change-point model from aspects
of regression analysis, hypothesis testing, consistency and inference. In
particular, we present a strategy to gather and aggregate local information for
change-point detection that has become the cornerstone of several emerging
methods because of its attractiveness in both computational and theoretical
properties.Comment: 26 pages, 2 figure
Computability, Noncomputability, and Hyperbolic Systems
In this paper we study the computability of the stable and unstable manifolds
of a hyperbolic equilibrium point. These manifolds are the essential feature
which characterizes a hyperbolic system. We show that (i) locally these
manifolds can be computed, but (ii) globally they cannot (though we prove they
are semi-computable). We also show that Smale's horseshoe, the first example of
a hyperbolic invariant set which is neither an equilibrium point nor a periodic
orbit, is computable
The Efficiency of Pension Plan Investment Menus: Investment Choices in Defined Contribution Pension Plans
Few previous studies have explored whether defined contribution retirement saving plans offer sufficiently diversified investment menus, though it is likely that these menus significantly shape workers’ accumulations of retirement wealth. This paper assesses the efficiency and performance of 401(k) investment options offered by a large group of US employers. We show that most plans are efficient compared to market benchmark indexes. Three performance measures underscore the fact that these plans tend to offer a sensible investment menu, when measured in terms of the menus’ mean-variance efficiency, diversification, and participant utility. The key factor contributing to plan efficiency and performance has to do with the types of funds offered, rather than the total number of investment options provided.
r-Process Nucleosynthesis in Shocked Surface Layers of O-Ne-Mg Cores
We demonstrate that rapid expansion of the shocked surface layers of an
O-Ne-Mg core following its collapse can result in r-process nucleosynthesis. As
the supernova shock accelerates through these layers, it makes them expand so
rapidly that free nucleons remain in disequilibrium with alpha-particles
throughout most of the expansion. This allows heavy r-process isotopes
including the actinides to form in spite of the very low initial neutron excess
of the matter. We estimate that yields of heavy r-process nuclei from this site
may be sufficient to explain the Galactic inventory of these isotopes.Comment: 11 pages, 1 figure, to appear in the Astrophysical Journal Letter
When and Where: Predicting Human Movements Based on Social Spatial-Temporal Events
Predicting both the time and the location of human movements is valuable but
challenging for a variety of applications. To address this problem, we propose
an approach considering both the periodicity and the sociality of human
movements. We first define a new concept, Social Spatial-Temporal Event (SSTE),
to represent social interactions among people. For the time prediction, we
characterise the temporal dynamics of SSTEs with an ARMA (AutoRegressive Moving
Average) model. To dynamically capture the SSTE kinetics, we propose a Kalman
Filter based learning algorithm to learn and incrementally update the ARMA
model as a new observation becomes available. For the location prediction, we
propose a ranking model where the periodicity and the sociality of human
movements are simultaneously taken into consideration for improving the
prediction accuracy. Extensive experiments conducted on real data sets validate
our proposed approach
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