3,285 research outputs found
Critical brain networks
Highly correlated brain dynamics produces synchronized states with no
behavioral value, while weakly correlated dynamics prevents information flow.
We discuss the idea put forward by Per Bak that the working brain stays at an
intermediate (critical) regime characterized by power-law correlations.Comment: Contribution to the Niels Bohr Summer Institute on Complexity and
Criticality (2003); to appear in a Per Bak Memorial Issue of PHYSICA
Biologically inspired learning in a layered neural net
A feed-forward neural net with adaptable synaptic weights and fixed, zero or
non-zero threshold potentials is studied, in the presence of a global feedback
signal that can only have two values, depending on whether the output of the
network in reaction to its input is right or wrong.
It is found, on the basis of four biologically motivated assumptions, that
only two forms of learning are possible, Hebbian and Anti-Hebbian learning.
Hebbian learning should take place when the output is right, while there should
be Anti-Hebbian learning when the output is wrong.
For the Anti-Hebbian part of the learning rule a particular choice is made,
which guarantees an adequate average neuronal activity without the need of
introducing, by hand, control mechanisms like extremal dynamics. A network with
realistic, i.e., non-zero threshold potentials is shown to perform its task of
realizing the desired input-output relations best if it is sufficiently
diluted, i.e. if only a relatively low fraction of all possible synaptic
connections is realized
A Quadtree for Hyperbolic Space
We propose a data structure in d-dimensional hyperbolic space that can be
considered a natural counterpart to quadtrees in Euclidean spaces. Based on
this data structure we propose a so-called L-order for hyperbolic point sets,
which is an extension of the Z-order defined in Euclidean spaces. We
demonstrate the usefulness of our hyperbolic quadtree data structure by giving
an algorithm for constant-approximate closest pair and dynamic
constant-approximate nearest neighbours in hyperbolic space of constant
dimension d
Self-organized Critical Model Of Biological Evolution
A punctuated equilibrium model of biological evolution with relative fitness
between different species being the fundamental driving force of evolution is
introduced. Mutation is modeled as a fitness updating cellular automaton
process where the change in fitness after mutation follows a Gaussian
distribution with mean and standard deviation . Scaling behaviors
are observed in our numerical simulation, indicating that the model is
self-organized critical. Besides, the numerical experiment suggests that models
with different and belong to the same universality class. PACS
numbers: 87.10.+e, 05.40.+jComment: 8 pages in REVTEX 3.0 with 4 figures (Figures available on request by
sending e-mail to [email protected]
Dissipative Abelian Sandpiles and Random Walks
We show that the dissipative Abelian sandpile on a graph L can be related to
a random walk on a graph which consists of L extended with a trapping site.
From this relation it can be shown, using exact results and a scaling
assumption, that the dissipative sandpiles' correlation length exponent \nu
always equals 1/d_w, where d_w is the fractal dimension of the random walker.
This leads to a new understanding of the known results that \nu=1/2 on any
Euclidean lattice. Our result is however more general and as an example we also
present exact data for finite Sierpinski gaskets which fully confirm our
predictions.Comment: 10 pages, 1 figur
Nearly ETH-Tight Algorithms for Planar Steiner Tree with Terminals on Few Faces
The Planar Steiner Tree problem is one of the most fundamental NP-complete
problems as it models many network design problems. Recall that an instance of
this problem consists of a graph with edge weights, and a subset of vertices
(often called terminals); the goal is to find a subtree of the graph of minimum
total weight that connects all terminals. A seminal paper by Erickson et al.
[Math. Oper. Res., 1987] considers instances where the underlying graph is
planar and all terminals can be covered by the boundary of faces. Erickson
et al. show that the problem can be solved by an algorithm using
time and space, where denotes the number of vertices of the
input graph. In the past 30 years there has been no significant improvement of
this algorithm, despite several efforts.
In this work, we give an algorithm for Planar Steiner Tree with running time
using only polynomial space. Furthermore, we show
that the running time of our algorithm is almost tight: we prove that there is
no algorithm for Planar Steiner Tree for any computable
function , unless the Exponential Time Hypothesis fails.Comment: 32 pages, 8 figures, accepted at SODA 201
How does object fatness impact the complexity of packing in d dimensions?
Packing is a classical problem where one is given a set of subsets of
Euclidean space called objects, and the goal is to find a maximum size subset
of objects that are pairwise non-intersecting. The problem is also known as the
Independent Set problem on the intersection graph defined by the objects.
Although the problem is NP-complete, there are several subexponential
algorithms in the literature. One of the key assumptions of such algorithms has
been that the objects are fat, with a few exceptions in two dimensions; for
example, the packing problem of a set of polygons in the plane surprisingly
admits a subexponential algorithm. In this paper we give tight running time
bounds for packing similarly-sized non-fat objects in higher dimensions.
We propose an alternative and very weak measure of fatness called the
stabbing number, and show that the packing problem in Euclidean space of
constant dimension for a family of similarly sized objects with
stabbing number can be solved in time. We
prove that even in the case of axis-parallel boxes of fixed shape, there is no
algorithm under ETH. This result smoothly bridges the
whole range of having constant-fat objects on one extreme () and a
subexponential algorithm of the usual running time, and having very "skinny"
objects on the other extreme (), where we cannot hope to
improve upon the brute force running time of , and thereby
characterizes the impact of fatness on the complexity of packing in case of
similarly sized objects. We also study the same problem when parameterized by
the solution size , and give a algorithm, with an
almost matching lower bound.Comment: Short version appears in ISAAC 201
Optimized differential energy loss estimation for tracker detectors
The estimation of differential energy loss for charged particles in tracker
detectors is studied. The robust truncated mean method can be generalized to
the linear combination of the energy deposit measurements. The optimized
weights in case of arithmetic and geometric means are obtained using a detailed
simulation. The results show better particle separation power for both
semiconductor and gaseous detectors.Comment: 16 pages, 8 figures, submitted to Nucl. Istrum. Meth.
Self-organized critical neural networks
A mechanism for self-organization of the degree of connectivity in model
neural networks is studied. Network connectivity is regulated locally on the
basis of an order parameter of the global dynamics which is estimated from an
observable at the single synapse level. This principle is studied in a
two-dimensional neural network with randomly wired asymmetric weights. In this
class of networks, network connectivity is closely related to a phase
transition between ordered and disordered dynamics. A slow topology change is
imposed on the network through a local rewiring rule motivated by
activity-dependent synaptic development: Neighbor neurons whose activity is
correlated, on average develop a new connection while uncorrelated neighbors
tend to disconnect. As a result, robust self-organization of the network
towards the order disorder transition occurs. Convergence is independent of
initial conditions, robust against thermal noise, and does not require fine
tuning of parameters.Comment: 5 pages RevTeX, 7 figures PostScrip
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