8,166 research outputs found
Parametric Fokker-Planck equation
We derive the Fokker-Planck equation on the parametric space. It is the
Wasserstein gradient flow of relative entropy on the statistical manifold. We
pull back the PDE to a finite dimensional ODE on parameter space. Some
analytical example and numerical examples are presented
A Bivariate Measure of Redundant Information
We define a measure of redundant information based on projections in the
space of probability distributions. Redundant information between random
variables is information that is shared between those variables. But in
contrast to mutual information, redundant information denotes information that
is shared about the outcome of a third variable. Formalizing this concept, and
being able to measure it, is required for the non-negative decomposition of
mutual information into redundant and synergistic information. Previous
attempts to formalize redundant or synergistic information struggle to capture
some desired properties. We introduce a new formalism for redundant information
and prove that it satisfies all the properties necessary outlined in earlier
work, as well as an additional criterion that we propose to be necessary to
capture redundancy. We also demonstrate the behaviour of this new measure for
several examples, compare it to previous measures and apply it to the
decomposition of transfer entropy.Comment: 16 pages, 15 figures, 1 table, added citation to Griffith et al 2012,
Maurer et al 199
A Combined Signal Approach To Technical Analysis On The S&P 500
This paper examines the effectiveness of nine technical trading rules on the S&P 500 from January 1950 to March 2008 (14,646 daily observations). The annualized returns from each trading rule are compared to a naïve buy-and-hold strategy to determine profitability. Over the 59 year period, only the moving-average cross-over (1,200) and (5,150) trading rules were able to outperform the buy-and-hold trading strategy after adjusting for transaction costs. However, excess returns were generated by employing a Combined Signal Approach (CSA) on the individual trading rules. Statistical significance was confirmed through bootstrap simulations and robustness through sub-period analysis. 
Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
We define a theory of Galilean gravity in 2+1 dimensions with cosmological
constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke
group, extending our previous study of classical and quantum gravity in 2+1
dimensions in the Galilean limit. We exhibit an r-matrix which is compatible
with our Chern-Simons action (in a sense to be defined) and show that the
associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the
classical double of the extended Heisenberg algebra. We deduce that, in the
quantisation of the theory according to the combinatorial quantisation
programme, much of the quantum theory is determined by the quantum double of
the extended q-deformed Heisenberg algebra.Comment: 22 page
Froggatt-Nielsen models from E8 in F-theory GUTs
This paper studies F-theory SU(5) GUT models where the three generations of
the standard model come from three different curves. All the matter is taken to
come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving
a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen
approach to flavour structure. A scan is performed over all possible models and
the results are filtered using phenomenological constraints. We find a unique
model that fits observations of quark and lepton masses and mixing well. This
model suffers from two drawbacks: R-parity must be imposed by hand and there is
a doublet-triplet splitting problem.Comment: 42 pages; v2:journal version; v3:corrected typo in neutrino masse
Reductions of Hidden Information Sources
In all but special circumstances, measurements of time-dependent processes
reflect internal structures and correlations only indirectly. Building
predictive models of such hidden information sources requires discovering, in
some way, the internal states and mechanisms. Unfortunately, there are often
many possible models that are observationally equivalent. Here we show that the
situation is not as arbitrary as one would think. We show that generators of
hidden stochastic processes can be reduced to a minimal form and compare this
reduced representation to that provided by computational mechanics--the
epsilon-machine. On the way to developing deeper, measure-theoretic foundations
for the latter, we introduce a new two-step reduction process. The first step
(internal-event reduction) produces the smallest observationally equivalent
sigma-algebra and the second (internal-state reduction) removes sigma-algebra
components that are redundant for optimal prediction. For several classes of
stochastic dynamical systems these reductions produce representations that are
equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at
http://www.santafe.edu/~cm
A Rydberg Quantum Simulator
Following Feynman and as elaborated on by Lloyd, a universal quantum
simulator (QS) is a controlled quantum device which reproduces the dynamics of
any other many particle quantum system with short range interactions. This
dynamics can refer to both coherent Hamiltonian and dissipative open system
evolution. We investigate how laser excited Rydberg atoms in large spacing
optical or magnetic lattices can provide an efficient implementation of a
universal QS for spin models involving (high order) n-body interactions. This
includes the simulation of Hamiltonians of exotic spin models involving
n-particle constraints such as the Kitaev toric code, color code, and lattice
gauge theories with spin liquid phases. In addition, it provides the
ingredients for dissipative preparation of entangled states based on
engineering n-particle reservoir couplings. The key basic building blocks of
our architecture are efficient and high-fidelity n-qubit entangling gates via
auxiliary Rydberg atoms, including a possible dissipative time step via optical
pumping. This allows to mimic the time evolution of the system by a sequence of
fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg
gates.Comment: 8 pages, 4 figure
Non-Abelian vortex dynamics: Effective world-sheet action
The low-energy vortex effective action is constructed in a wide class of
systems in a color-flavor locked vacuum, which generalizes the results found
earlier in the context of U(N) models. It describes the weak fluctuations of
the non-Abelian orientational moduli on the vortex worldsheet. For instance,
for the minimum vortex in SO(2N) x U(1) or USp(2N) x U(1) gauge theories, the
effective action found is a two-dimensional sigma model living on the Hermitian
symmetric spaces SO(2N)/U(N) or USp(2N)/U(N), respectively. The fluctuating
moduli have the structure of that of a quantum particle state in spinor
representations of the GNO dual of the color-flavor SO(2N) or USp(2N) symmetry,
i.e. of SO(2N) or of SO(2N+1). Applied to the benchmark U(N) model our
procedure reproduces the known CP(N-1) worldsheet action; our recipe allows us
to obtain also the effective vortex action for some higher-winding vortices in
U(N) and SO(2N) theories.Comment: LaTeX, 25 pages, 0 figure
On hypercharge flux and exotics in F-theory GUTs
We study SU(5) Grand Unified Theories within a local framework in F-theory
with multiple extra U(1) symmetries arising from a small monodromy group. The
use of hypercharge flux for doublet-triplet splitting implies massless exotics
in the spectrum that are protected from obtaining a mass by the U(1)
symmetries. We find that lifting the exotics by giving vacuum expectation
values to some GUT singlets spontaneously breaks all the U(1) symmetries which
implies that proton decay operators are induced. If we impose an additional
R-parity symmetry by hand we find all the exotics can be lifted while proton
decay operators are still forbidden. These models can retain the gauge coupling
unification accuracy of the MSSM at 1-loop. For models where the generations
are distributed across multiple curves we also present a motivation for the
quark-lepton mass splittings at the GUT scale based on a Froggatt-Nielsen
approach to flavour.Comment: 38 pages; v2: emphasised possibility of avoiding exotics in models
without a global E8 structure, added ref, journal versio
Network Physiology reveals relations between network topology and physiological function
The human organism is an integrated network where complex physiologic
systems, each with its own regulatory mechanisms, continuously interact, and
where failure of one system can trigger a breakdown of the entire network.
Identifying and quantifying dynamical networks of diverse systems with
different types of interactions is a challenge. Here, we develop a framework to
probe interactions among diverse systems, and we identify a physiologic
network. We find that each physiologic state is characterized by a specific
network structure, demonstrating a robust interplay between network topology
and function. Across physiologic states the network undergoes topological
transitions associated with fast reorganization of physiologic interactions on
time scales of a few minutes, indicating high network flexibility in response
to perturbations. The proposed system-wide integrative approach may facilitate
the development of a new field, Network Physiology.Comment: 12 pages, 9 figure
- …