14,965 research outputs found
Modelling multiple time series via common factors
We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable (nonstationary) factors are identified via expanding the white noise space step by step; therefore solving a high-dimensional optimization problem by several low-dimensional subproblems. Asymptotic properties of the estimation were investigated. The proposed methodology was illustrated with both simulated and real data sets
On singular value distribution of large dimensional auto-covariance matrices
Let be a sequence of independent dimensional
random vectors and a given integer. From a sample
of the
sequence, the so-called lag auto-covariance matrix is
. When the
dimension is large compared to the sample size , this paper establishes
the limit of the singular value distribution of assuming that and
grow to infinity proportionally and the sequence satisfies a Lindeberg
condition on fourth order moments. Compared to existing asymptotic results on
sample covariance matrices developed in random matrix theory, the case of an
auto-covariance matrix is much more involved due to the fact that the summands
are dependent and the matrix is not symmetric. Several new techniques
are introduced for the derivation of the main theorem
Exact solution of the two-axis countertwisting Hamiltonian for the half-integer case
Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any
(integer and half-integer) are derived based on the Jordan-Schwinger
(differential) boson realization of the algebra after desired Euler
rotations, where is the total angular momentum quantum number of the
system. It is shown that solutions to the Bethe ansatz equations can be
obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of
solutions, with solution number being and respectively when is an
integer and each when is a half-integer, are obtained. Properties
of the zeros of the related extended Heine-Stieltjes polynomials for
half-integer cases are discussed. It is clearly shown that double
degenerate level energies for half-integer are symmetric with respect to
the axis. It is also shown that the excitation energies of the `yrast'
and other `yrare' bands can all be asymptotically given by quadratic functions
of , especially when is large.Comment: LaTex 12 pages, 3 figures. Major cosmetic type revision. arXiv admin
note: text overlap with arXiv:1609.0558
Personal Volunteer Computing
We propose personal volunteer computing, a novel paradigm to encourage
technical solutions that leverage personal devices, such as smartphones and
laptops, for personal applications that require significant computations, such
as animation rendering and image processing. The paradigm requires no
investment in additional hardware, relying instead on devices that are already
owned by users and their community, and favours simple tools that can be
implemented part-time by a single developer. We show that samples of personal
devices of today are competitive with a top-of-the-line laptop from two years
ago. We also propose new directions to extend the paradigm
Exact solution of the two-axis countertwisting Hamiltonian
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable
when the quantum number of the total angular momentum of the system is an
integer after the Jordan-Schwinger (differential) boson realization of the
SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with
the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz
equations of the problem is derived. It is shown that solutions of the Bethe
ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials.
The total number of the four sets of the zeros equals exactly to for a
given integer angular momentum quantum number , which proves the
completeness of the solutions. It is also shown that double degeneracy in level
energies may also occur in the limit for integer case
except a unique non-degenerate level with zero excitation energy.Comment: LaTex 10 pages. Version to appear in Annals of Physic
Only rational homology spheres admit to be union of DE attractors
If there exists a diffeomorphism on a closed, orientable -manifold
such that the non-wandering set consists of finitely many
orientable attractors derived from expanding maps, then must be a
rational homology sphere; moreover all those attractors are of topological
dimension .
Expanding maps are expanding on (co)homologies.Comment: 23 pages, 2 figure
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