5,797 research outputs found
The tail of the contact force distribution in static granular materials
We numerically study the distribution P(f) of contact forces in frictionless
bead packs, by averaging over the ensemble of all possible force network
configurations. We resort to umbrella sampling to resolve the asymptotic decay
of P(f) for large f, and determine P(f) down to values of order 10^{-45} for
ordered and disordered systems in two and three dimensions. Our findings
unambiguously show that, in the ensemble approach, the force distributions
decay much faster than exponentially: P(f) ~ exp(-f^{\alpha}), with alpha
\approx 2.0 for 2D systems, and alpha \approx 1.7 for 3D systems.Comment: 4 pages, 4 figures, submitted to Phys. Rev.
The Power of Linear Recurrent Neural Networks
Recurrent neural networks are a powerful means to cope with time series. We
show how a type of linearly activated recurrent neural networks, which we call
predictive neural networks, can approximate any time-dependent function f(t)
given by a number of function values. The approximation can effectively be
learned by simply solving a linear equation system; no backpropagation or
similar methods are needed. Furthermore, the network size can be reduced by
taking only most relevant components. Thus, in contrast to others, our approach
not only learns network weights but also the network architecture. The networks
have interesting properties: They end up in ellipse trajectories in the long
run and allow the prediction of further values and compact representations of
functions. We demonstrate this by several experiments, among them multiple
superimposed oscillators (MSO), robotic soccer, and predicting stock prices.
Predictive neural networks outperform the previous state-of-the-art for the MSO
task with a minimal number of units.Comment: 22 pages, 14 figures and tables, revised implementatio
Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three
The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges
of every bridgeless graph with edges can be covered by cycles of total
length at most . We show that every cubic bridgeless graph has a
cycle cover of total length at most and every bridgeless
graph with minimum degree three has a cycle cover of total length at most
Quantification of complementarity in multi-qubit systems
Complementarity was originally introduced as a qualitative concept for the
discussion of properties of quantum mechanical objects that are classically
incompatible. More recently, complementarity has become a \emph{quantitative}
relation between classically incompatible properties, such as visibility of
interference fringes and "which-way" information, but also between purely
quantum mechanical properties, such as measures of entanglement. We discuss
different complementarity relations for systems of 2-, 3-, or \textit{n}
qubits. Using nuclear magnetic resonance techniques, we have experimentally
verified some of these complementarity relations in a two-qubit system.Comment: 12 pages, 10 figures (A display error about the figures in the
previous version
On the algebraic structure of rational discrete dynamical systems
We show how singularities shape the evolution of rational discrete dynamical
systems. The stabilisation of the form of the iterates suggests a description
providing among other things generalised Hirota form, exact evaluation of the
algebraic entropy as well as remarkable polynomial factorisation properties. We
illustrate the phenomenon explicitly with examples covering a wide range of
models
A 2-D asymmetric exclusion model for granular flows
A 2-D version of the asymmetric exclusion model for granular sheared flows is
presented. The velocity profile exhibits two qualitatively different behaviors,
dependent on control parameters. For low friction, the velocity profile follows
an exponential decay while for large friction the profile is more accurately
represented by a Gaussian law. The phase transition occurring between these two
behavior is identified by the appearance of correlations in the cluster size
distribution. Finally, a mean--field theory gives qualitative and quantitative
good agreement with the numerical results.Comment: 13 pages, 5 figures; typos added, one definition change
Quantum Non-Demolition Test of Bipartite Complementarity
We present a quantum circuit that implements a non-demolition measurement of
complementary single- and bi-partite properties of a two-qubit system:
entanglement and single-partite visibility and predictability. The system must
be in a pure state with real coefficients in the computational basis, which
allows a direct operational interpretation of those properties. The circuit can
be realized in many systems of interest to quantum information.Comment: 4 pages, 2 figure
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