5,048 research outputs found
Tensor decomposition with generalized lasso penalties
We present an approach for penalized tensor decomposition (PTD) that
estimates smoothly varying latent factors in multi-way data. This generalizes
existing work on sparse tensor decomposition and penalized matrix
decompositions, in a manner parallel to the generalized lasso for regression
and smoothing problems. Our approach presents many nontrivial challenges at the
intersection of modeling and computation, which are studied in detail. An
efficient coordinate-wise optimization algorithm for (PTD) is presented, and
its convergence properties are characterized. The method is applied both to
simulated data and real data on flu hospitalizations in Texas. These results
show that our penalized tensor decomposition can offer major improvements on
existing methods for analyzing multi-way data that exhibit smooth spatial or
temporal features
Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes
We define a family of probability distributions for random count matrices
with a potentially unbounded number of rows and columns. The three
distributions we consider are derived from the gamma-Poisson, gamma-negative
binomial, and beta-negative binomial processes. Because the models lead to
closed-form Gibbs sampling update equations, they are natural candidates for
nonparametric Bayesian priors over count matrices. A key aspect of our analysis
is the recognition that, although the random count matrices within the family
are defined by a row-wise construction, their columns can be shown to be i.i.d.
This fact is used to derive explicit formulas for drawing all the columns at
once. Moreover, by analyzing these matrices' combinatorial structure, we
describe how to sequentially construct a column-i.i.d. random count matrix one
row at a time, and derive the predictive distribution of a new row count vector
with previously unseen features. We describe the similarities and differences
between the three priors, and argue that the greater flexibility of the gamma-
and beta- negative binomial processes, especially their ability to model
over-dispersed, heavy-tailed count data, makes these well suited to a wide
variety of real-world applications. As an example of our framework, we
construct a naive-Bayes text classifier to categorize a count vector to one of
several existing random count matrices of different categories. The classifier
supports an unbounded number of features, and unlike most existing methods, it
does not require a predefined finite vocabulary to be shared by all the
categories, and needs neither feature selection nor parameter tuning. Both the
gamma- and beta- negative binomial processes are shown to significantly
outperform the gamma-Poisson process for document categorization, with
comparable performance to other state-of-the-art supervised text classification
algorithms.Comment: To appear in Journal of the American Statistical Association (Theory
and Methods). 31 pages + 11 page supplement, 5 figure
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
We exemplify the way the rigged Hilbert space deals with the
Lippmann-Schwinger equation by way of the spherical shell potential. We
explicitly construct the Lippmann-Schwinger bras and kets along with their
energy representation, their time evolution and the rigged Hilbert spaces to
which they belong. It will be concluded that the natural setting for the
solutions of the Lippmann-Schwinger equation--and therefore for scattering
theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur
Short turn-around intercontinental clock synchronization using very-long-baseline interferometry
During the past year work was accomplished to bring into regular operation a VLBI system for making intercontinental clock comparisons with a turn around of a few days from the time of data taking. Earlier VLBI systems required several weeks to produce results. The present system, which is not yet complete, incorporates a number of refinements not available in earlier systems, such as dual frequency inosopheric delay cancellation and wider synthesized bandwidths with instrumental phase calibration
Study on k-shortest paths with behavioral impedance domain from the intermodal public transportation system perspective
Behavioral impedance domain consists of a theory on route planning for pedestrians, within which constraint management is considered. The goal of this paper is to present the k-shortest path model using the behavioral impedance approach. After the mathematical model building, optimization problem and resolution problem by a behavioral impedance algorithm, it is discussed how behavioral impedance cost function is embedded in the k-shortest path model. From the pedestrian's route planning perspective, the behavioral impedance cost function could be used to calculate best subjective paths in the objective way.Postprint (published version
The Importance of Boundary Conditions in Quantum Mechanics
We discuss the role of boundary conditions in determining the physical
content of the solutions of the Schrodinger equation. We study the
standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary
conditions. As well, we rephrase Feynman's prescription as a
time-asymmetric, causal boundary condition, and discuss the connection of
Feynman's prescription with the arrow of time of Quantum
Electrodynamics. A parallel of this arrow of time with that of Classical
Electrodynamics is made. We conclude that in general, the time evolution of a
closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible
Quantum Dynamics," Trieste, Italy, July 200
Development of the Cassini Ground Data System in a multimission environment
As baselined, the Cassini Ground Data System (GDS) will be composed of Project specific and multimission elements. The former will be developed by the Cassini Project and the latter by two JPL institutional organizations, the Telecommunications and Data Acquisition Office (TDA) and the Multimission Operations Systems Office (MOSO). The GDS will be developed in three principal phases: Spacecraft Test, Launch-cruise, and Science Tour, with a significant part of the development deferred until the post-launch period. New capabilities are being introduced that are key to the achievement of more cost effective operations. Successful development of the system will require careful planning and will involve participation of diverse disciplines. This paper introduces the Cassini Project from the Ground Data System perspective and discusses development approaches expected to produce systems which meet functional and performance requirements and which will be delivered on schedule and within budget
On the inconsistency of the Bohm-Gadella theory with quantum mechanics
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum
Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom
asserts that the solutions of the Lippmann-Schwinger equation are functionals
over spaces of Hardy functions. The preparation-registration arrow of time
provides the physical justification for the Hardy axiom. In this paper, it is
shown that the Hardy axiom is incorrect, because the solutions of the
Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also
shown that the derivation of the preparation-registration arrow of time is
flawed. Thus, Hardy functions neither appear when we solve the
Lippmann-Schwinger equation nor they should appear. It is also shown that the
Bohm-Gadella theory does not rest on the same physical principles as quantum
mechanics, and that it does not solve any problem that quantum mechanics cannot
solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page
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