21,277 research outputs found
Monotone Volume Formulas for Geometric Flows
We consider a closed manifold M with a Riemannian metric g(t) evolving in
direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove
that if S satisfies a certain tensor inequality, then one can construct a
forwards and a backwards reduced volume quantity, the former being
non-increasing, the latter being non-decreasing along the flow. In the case
where S=Ric is the Ricci curvature of M, the result corresponds to Perelman's
well-known reduced volume monotonicity for the Ricci flow. Some other examples
are given in the second section of this article, the main examples and
motivation for this work being List's extended Ricci flow system, the Ricci
flow coupled with harmonic map heat flow and the mean curvature flow in
Lorentzian manifolds with nonnegative sectional curvatures. With our approach,
we find new monotonicity formulas for these flows.Comment: v2: final version (as published
Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems
It is known that perturbation theory converges in fermionic field theory at
weak coupling if the interaction and the covariance are summable and if certain
determinants arising in the expansion can be bounded efficiently, e.g. if the
covariance admits a Gram representation with a finite Gram constant. The
covariances of the standard many--fermion systems do not fall into this class
due to the slow decay of the covariance at large Matsubara frequency, giving
rise to a UV problem in the integration over degrees of freedom with Matsubara
frequencies larger than some Omega (usually the first step in a multiscale
analysis). We show that these covariances do not have Gram representations on
any separable Hilbert space. We then prove a general bound for determinants
associated to chronological products which is stronger than the usual Gram
bound and which applies to the many--fermion case. This allows us to prove
convergence of the first integration step in a rather easy way, for a
short--range interaction which can be arbitrarily strong, provided Omega is
chosen large enough. Moreover, we give - for the first time - nonperturbative
bounds on all scales for the case of scale decompositions of the propagator
which do not impose cutoffs on the Matsubara frequency.Comment: 29 pages LaTe
PAMELA Positron Excess as a Signal from the Hidden Sector
The recent positron excess observed in the PAMELA satellite experiment
strengthens previous experimental findings. We give here an analysis of this
excess in the framework of the Stueckelberg extension of the standard model
which includes an extra gauge field and matter in the hidden sector.
Such matter can produce the right amount of dark matter consistent with the
WMAP constraints. Assuming the hidden sector matter to be Dirac fermions it is
shown that their annihilation can produce the positron excess with the right
positron energy dependence seen in the HEAT, AMS and the PAMELA experiments.
Further test of the proposed model can come at the Large Hadron Collider. The
predictions of the flux ratio also fit the data.Comment: 9 pages,3 figures; Breit-Wigner enhancement emphasized; published in
PR
Tight-binding study of structure and vibrations of amorphous silicon
We present a tight-binding calculation that, for the first time, accurately
describes the structural, vibrational and elastic properties of amorphous
silicon. We compute the interatomic force constants and find an unphysical
feature of the Stillinger-Weber empirical potential that correlates with a much
noted error in the radial distribution function associated with that potential.
We also find that the intrinsic first peak of the radial distribution function
is asymmetric, contrary to usual assumptions made in the analysis of
diffraction data. We use our results for the normal mode frequencies and
polarization vectors to obtain the zero-point broadening effect on the radial
distribution function, enabling us to directly compare theory and a high
resolution x-ray diffraction experiment
Nearly optimal solutions for the Chow Parameters Problem and low-weight approximation of halfspaces
The \emph{Chow parameters} of a Boolean function
are its degree-0 and degree-1 Fourier coefficients. It has been known
since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of
any linear threshold function uniquely specify within the space of all
Boolean functions, but until recently (O'Donnell and Servedio) nothing was
known about efficient algorithms for \emph{reconstructing} (exactly or
approximately) from exact or approximate values of its Chow parameters. We
refer to this reconstruction problem as the \emph{Chow Parameters Problem.}
Our main result is a new algorithm for the Chow Parameters Problem which,
given (sufficiently accurate approximations to) the Chow parameters of any
linear threshold function , runs in time \tilde{O}(n^2)\cdot
(1/\eps)^{O(\log^2(1/\eps))} and with high probability outputs a
representation of an LTF that is \eps-close to . The only previous
algorithm (O'Donnell and Servedio) had running time \poly(n) \cdot
2^{2^{\tilde{O}(1/\eps^2)}}.
As a byproduct of our approach, we show that for any linear threshold
function over , there is a linear threshold function which
is \eps-close to and has all weights that are integers at most \sqrt{n}
\cdot (1/\eps)^{O(\log^2(1/\eps))}. This significantly improves the best
previous result of Diakonikolas and Servedio which gave a \poly(n) \cdot
2^{\tilde{O}(1/\eps^{2/3})} weight bound, and is close to the known lower
bound of (1/\eps)^{\Omega(\log \log (1/\eps))}\} (Goldberg,
Servedio). Our techniques also yield improved algorithms for related problems
in learning theory
Quantum matchgate computations and linear threshold gates
The theory of matchgates is of interest in various areas in physics and
computer science. Matchgates occur in e.g. the study of fermions and spin
chains, in the theory of holographic algorithms and in several recent works in
quantum computation. In this paper we completely characterize the class of
boolean functions computable by unitary two-qubit matchgate circuits with some
probability of success. We show that this class precisely coincides with that
of the linear threshold gates. The latter is a fundamental family which appears
in several fields, such as the study of neural networks. Using the above
characterization, we further show that the power of matchgate circuits is
surprisingly trivial in those cases where the computation is to succeed with
high probability. In particular, the only functions that are
matchgate-computable with success probability greater than 3/4 are functions
depending on only a single bit of the input
Interior Point Decoding for Linear Vector Channels
In this paper, a novel decoding algorithm for low-density parity-check (LDPC)
codes based on convex optimization is presented. The decoding algorithm, called
interior point decoding, is designed for linear vector channels. The linear
vector channels include many practically important channels such as inter
symbol interference channels and partial response channels. It is shown that
the maximum likelihood decoding (MLD) rule for a linear vector channel can be
relaxed to a convex optimization problem, which is called a relaxed MLD
problem. The proposed decoding algorithm is based on a numerical optimization
technique so called interior point method with barrier function. Approximate
variations of the gradient descent and the Newton methods are used to solve the
convex optimization problem. In a decoding process of the proposed algorithm, a
search point always lies in the fundamental polytope defined based on a
low-density parity-check matrix. Compared with a convectional joint message
passing decoder, the proposed decoding algorithm achieves better BER
performance with less complexity in the case of partial response channels in
many cases.Comment: 18 pages, 17 figures, The paper has been submitted to IEEE
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