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 $s$ polynomials in \mathbbm{Z}[X_1, ..., X_k] having degrees at most $d$, and whose coefficients have bitsizes at most $\tau$. Our bound is an explicit function of $s, d, k$ and $\tau$, 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 $S$ (including the unbounded components). While asymptotic bounds of the form $2^{\tau d^{O (k)}}$ on these quantities were known before, some applications require bounds which are explicit and which hold for all values of $s, d, k$ and $\tau$. 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