5,263 research outputs found
An Online Unsupervised Structural Plasticity Algorithm for Spiking Neural Networks
In this article, we propose a novel Winner-Take-All (WTA) architecture
employing neurons with nonlinear dendrites and an online unsupervised
structural plasticity rule for training it. Further, to aid hardware
implementations, our network employs only binary synapses. The proposed
learning rule is inspired by spike time dependent plasticity (STDP) but differs
for each dendrite based on its activation level. It trains the WTA network
through formation and elimination of connections between inputs and synapses.
To demonstrate the performance of the proposed network and learning rule, we
employ it to solve two, four and six class classification of random Poisson
spike time inputs. The results indicate that by proper tuning of the inhibitory
time constant of the WTA, a trade-off between specificity and sensitivity of
the network can be achieved. We use the inhibitory time constant to set the
number of subpatterns per pattern we want to detect. We show that while the
percentage of successful trials are 92%, 88% and 82% for two, four and six
class classification when no pattern subdivisions are made, it increases to
100% when each pattern is subdivided into 5 or 10 subpatterns. However, the
former scenario of no pattern subdivision is more jitter resilient than the
later ones.Comment: 11 pages, 10 figures, journa
Magnetic fields in nearby normal galaxies: Energy equipartition
We present maps of total magnetic field using 'equipartition' assumptions for
five nearby normal galaxies at sub-kpc spatial resolution. The mean magnetic
field is found to be ~11 \mu G. The field is strongest near the central regions
where mean values are ~20--25 \mu G and falls to ~15 \mu G in disk and ~10 \mu
G in the outer parts. There is little variation in the field strength between
arm and interarm regions, such that, in the interarms, the field is < 20
percent weaker than in the arms. There is no indication of variation in
magnetic field as one moves along arm or interarm after correcting for the
radial variation of magnetic field. We also studied the energy densities in
gaseous and ionized phases of the interstellar medium and compared to the
energy density in the magnetic field. The energy density in the magnetic field
was found to be similar to that of the gas within a factor of <2 at sub-kpc
scales in the arms, and thus magnetic field plays an important role in pressure
balance of the interstellar medium. Magnetic field energy density is seen to
dominate over the kinetic energy density of gas in the interarm regions and
outer parts of the galaxies and thereby helps in maintaining the large scale
ordered fields seen in those regions.Comment: 12 Pages, 6 Figures, Accepted to be published in MNRA
Bounding the radii of balls meeting every connected component of semi-algebraic sets
We prove explicit bounds on the radius of a ball centered at the origin which
is guaranteed to contain all bounded connected components of a semi-algebraic
set S \subset \mathbbm{R}^k defined by a quantifier-free formula involving
polynomials in \mathbbm{Z}[X_1, ..., X_k] having degrees at most , and
whose coefficients have bitsizes at most . Our bound is an explicit
function of and , and does not contain any undetermined
constants. We also prove a similar bound on the radius of a ball guaranteed to
intersect every connected component of (including the unbounded
components). While asymptotic bounds of the form on these
quantities were known before, some applications require bounds which are
explicit and which hold for all values of and . The bounds
proved in this paper are of this nature.Comment: 11 page
Liquid State Machine with Dendritically Enhanced Readout for Low-power, Neuromorphic VLSI Implementations
In this paper, we describe a new neuro-inspired, hardware-friendly readout
stage for the liquid state machine (LSM), a popular model for reservoir
computing. Compared to the parallel perceptron architecture trained by the
p-delta algorithm, which is the state of the art in terms of performance of
readout stages, our readout architecture and learning algorithm can attain
better performance with significantly less synaptic resources making it
attractive for VLSI implementation. Inspired by the nonlinear properties of
dendrites in biological neurons, our readout stage incorporates neurons having
multiple dendrites with a lumped nonlinearity. The number of synaptic
connections on each branch is significantly lower than the total number of
connections from the liquid neurons and the learning algorithm tries to find
the best 'combination' of input connections on each branch to reduce the error.
Hence, the learning involves network rewiring (NRW) of the readout network
similar to structural plasticity observed in its biological counterparts. We
show that compared to a single perceptron using analog weights, this
architecture for the readout can attain, even by using the same number of
binary valued synapses, up to 3.3 times less error for a two-class spike train
classification problem and 2.4 times less error for an input rate approximation
task. Even with 60 times larger synapses, a group of 60 parallel perceptrons
cannot attain the performance of the proposed dendritically enhanced readout.
An additional advantage of this method for hardware implementations is that the
'choice' of connectivity can be easily implemented exploiting address event
representation (AER) protocols commonly used in current neuromorphic systems
where the connection matrix is stored in memory. Also, due to the use of binary
synapses, our proposed method is more robust against statistical variations.Comment: 14 pages, 19 figures, Journa
Magnus Force in High Temperature Superconductivity and Berry Phase
In the topological framework of high temperature superconductivity we have
discussed the Magnus force acting on its vortices
Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets
In this paper we describe a singly exponential algorithm for computing the
first Betti number of a given semi-algebraic set. Singly exponential algorithms
for computing the zero-th Betti number, and the Euler-Poincar\'e
characteristic, were known before. No singly exponential algorithm was known
for computing any of the individual Betti numbers other than the zero-th one.
We also give algorithms for obtaining semi-algebraic descriptions of the
semi-algebraically connected components of any given real algebraic or
semi-algebraic set in single-exponential time improving on previous results
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