28,735 research outputs found
Stochastic Models for the 3x+1 and 5x+1 Problems
This paper discusses stochastic models for predicting the long-time behavior
of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1
problem. The stochastic models are rigorously analyzable, and yield heuristic
predictions (conjectures) for the behavior of 3x+1 orbits and 5x+1 orbits.Comment: 68 pages, 9 figures, 4 table
Intrinsic Motivation and Mental Replay enable Efficient Online Adaptation in Stochastic Recurrent Networks
Autonomous robots need to interact with unknown, unstructured and changing
environments, constantly facing novel challenges. Therefore, continuous online
adaptation for lifelong-learning and the need of sample-efficient mechanisms to
adapt to changes in the environment, the constraints, the tasks, or the robot
itself are crucial. In this work, we propose a novel framework for
probabilistic online motion planning with online adaptation based on a
bio-inspired stochastic recurrent neural network. By using learning signals
which mimic the intrinsic motivation signalcognitive dissonance in addition
with a mental replay strategy to intensify experiences, the stochastic
recurrent network can learn from few physical interactions and adapts to novel
environments in seconds. We evaluate our online planning and adaptation
framework on an anthropomorphic KUKA LWR arm. The rapid online adaptation is
shown by learning unknown workspace constraints sample-efficiently from few
physical interactions while following given way points.Comment: accepted in Neural Network
A primer on noise-induced transitions in applied dynamical systems
Noise plays a fundamental role in a wide variety of physical and biological
dynamical systems. It can arise from an external forcing or due to random
dynamics internal to the system. It is well established that even weak noise
can result in large behavioral changes such as transitions between or escapes
from quasi-stable states. These transitions can correspond to critical events
such as failures or extinctions that make them essential phenomena to
understand and quantify, despite the fact that their occurrence is rare. This
article will provide an overview of the theory underlying the dynamics of rare
events for stochastic models along with some example applications
Learning Ground Traversability from Simulations
Mobile ground robots operating on unstructured terrain must predict which
areas of the environment they are able to pass in order to plan feasible paths.
We address traversability estimation as a heightmap classification problem: we
build a convolutional neural network that, given an image representing the
heightmap of a terrain patch, predicts whether the robot will be able to
traverse such patch from left to right. The classifier is trained for a
specific robot model (wheeled, tracked, legged, snake-like) using simulation
data on procedurally generated training terrains; the trained classifier can be
applied to unseen large heightmaps to yield oriented traversability maps, and
then plan traversable paths. We extensively evaluate the approach in simulation
on six real-world elevation datasets, and run a real-robot validation in one
indoor and one outdoor environment.Comment: Webpage: http://romarcg.xyz/traversability_estimation
The 2d-directed spanning forest converges to the Brownian web
The two-dimensional directed spanning forest (DSF) introduced by Baccelli and
Bordenave is a planar directed forest whose vertex set is given by a
homogeneous Poisson point process on . If the DSF
has direction , the ancestor of a vertex is
the nearest Poisson point (in the distance) having strictly larger
-coordinate. This construction induces complex geometrical dependencies. In
this paper we show that the collection of DSF paths, properly scaled, converges
in distribution to the Brownian web (BW). This verifies a conjecture made by
Baccelli and Bordenave in 2007
Ageing in Mortal Superdiffusive L\'evy Walkers
A growing body of literature examines the effects of superdiffusive
subballistic movement pre-measurement (ageing or time lag) on observations
arising from single-particle tracking. A neglected aspect is the finite
lifetime of these L\'{e}vy walkers, be they proteins, cells or larger
structures. We examine the effects of ageing on the motility of mortal walkers,
and discuss the means by which permanent stopping of walkers may be categorised
as arising from `natural' death or experimental artefacts such as low
photostability or radiation damage. This is done by comparison of the walkers'
mean squared displacement (MSD) with the front velocity of propagation of a
group of walkers, which is found to be invariant under time lags. For any
running time distribution of a mortal random walker, the MSD is tempered by the
stopping rate . This provides a physical interpretation for truncated
heavy-tailed diffusion processes and serves as a tool by which to better
classify the underlying running time distributions of random walkers. Tempering
of aged MSDs raises the issue of misinterpreting superdiffusive motion which
appears Brownian or subdiffusive over certain time scales
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