559 research outputs found
A characterization of shortest geodesics on surfaces
Any finite configuration of curves with minimal intersections on a surface is
a configuration of shortest geodesics for some Riemannian metric on the
surface. The metric can be chosen to make the lengths of these geodesics equal
to the number of intersections along them.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-17.abs.htm
Geschichte des Wuchers in Deutschland bis zur Begründung der heutigen Zinsengesetze (1654) : aus handschriftlichen und gedruckten Quellen
Defending Active Directory by Combining Neural Network based Dynamic Program and Evolutionary Diversity Optimisation
Active Directory (AD) is the default security management system for Windows
domain networks. We study a Stackelberg game model between one attacker and one
defender on an AD attack graph. The attacker initially has access to a set of
entry nodes. The attacker can expand this set by strategically exploring edges.
Every edge has a detection rate and a failure rate. The attacker aims to
maximize their chance of successfully reaching the destination before getting
detected. The defender's task is to block a constant number of edges to
decrease the attacker's chance of success. We show that the problem is #P-hard
and, therefore, intractable to solve exactly. We convert the attacker's problem
to an exponential sized Dynamic Program that is approximated by a Neural
Network (NN). Once trained, the NN provides an efficient fitness function for
the defender's Evolutionary Diversity Optimisation (EDO). The diversity
emphasis on the defender's solution provides a diverse set of training samples,
which improves the training accuracy of our NN for modelling the attacker. We
go back and forth between NN training and EDO. Experimental results show that
for R500 graph, our proposed EDO based defense is less than 1% away from the
optimal defense
Mixing properties of nonstationary multivariate count processes
We prove absolute regularity (-mixing) for nonstationary and
multivariate versions of two popular classes of integer-valued processes. We
show how this result can be used to prove asymptotic normality of a least
squares estimator of an involved model parameter
Sub-Riemannian Random Walks: From Connections to Retractions
We study random walks on sub-Riemannian manifolds using the framework of
retractions, i.e., approximations of normal geodesics. We show that such walks
converge to the correct horizontal Brownian motion if normal geodesics are
approximated to at least second order. In particular, we (i) provide conditions
for convergence of geodesic random walks defined with respect to normal,
compatible, and partial connections and (ii) provide examples of
computationally efficient retractions, e.g., for simulating anisotropic
Brownian motion on Riemannian manifolds.Comment: 21 page
Phonon-assisted transitions from quantum dot excitons to cavity photons
For a single semiconductor quantum dot embedded in a microcavity, we
theoretically and experimentally investigate phonon-assisted transitions
between excitons and the cavity mode. Within the framework of the independent
boson model we find that such transitions can be very efficient, even for
relatively large exciton-cavity detunings of several millielectron volts.
Furthermore, we predict a strong detuning asymmetry for the exciton lifetime
that vanishes for elevated lattice temperature. Our findings are corroborated
by experiment, which turns out to be in good quantitative and qualitative
agreement with theory
Exploiting Local Communication Protocols for Learning Complex Swarm Behaviors with Deep Reinforcement Learning
Swarm systems constitute a challenging problem for reinforcement learning (RL) as the algorithm needs to learn decentralized control policies that can cope with limited local sensing and communication abilities of the agents. While it is often difficult to directly define the behavior of the agents, simple communication protocols can be defined more easily using prior knowledge about the given task. In this paper, we propose a number of simple communication protocols that can be exploited by deep reinforcement learning to find decentralized control policies in a multi-robot swarm environment. The protocols are based on histograms that encode the local neighborhood relations of the gents
and can also transmit task-specific information, such as the shortest distance and direction to a desired target. In our framework, we use an adaptation of Trust Region Policy Optimization to learn complex collaborative tasks, such as formation building and building a communication link. We evaluate our findings in a simulated 2D-physics environment, and compare the implications of different communication protocols
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