Spike Timing-Dependent Plasticity as the Origin of the Formation of Clustered Synaptic Efficacy Engrams

Synapse location, dendritic active properties and synaptic plasticity are all known to play some role in shaping the different input streams impinging onto a neuron. It remains unclear however, how the magnitude and spatial distribution of synaptic efficacies emerge from this interplay. Here, we investigate this interplay using a biophysically detailed neuron model of a reconstructed layer 2/3 pyramidal cell and spike timing-dependent plasticity (STDP). Specifically, we focus on the issue of how the efficacy of synapses contributed by different input streams are spatially represented in dendrites after STDP learning. We construct a simple feed forward network where a detailed model neuron receives synaptic inputs independently from multiple yet equally sized groups of afferent fibers with correlated activity, mimicking the spike activity from different neuronal populations encoding, for example, different sensory modalities. Interestingly, ensuing STDP learning, we observe that for all afferent groups, STDP leads to synaptic efficacies arranged into spatially segregated clusters effectively partitioning the dendritic tree. These segregated clusters possess a characteristic global organization in space, where they form a tessellation in which each group dominates mutually exclusive regions of the dendrite. Put simply, the dendritic imprint from different input streams left after STDP learning effectively forms what we term a “dendritic efficacy mosaic.” Furthermore, we show how variations of the inputs and STDP rule affect such an organization. Our model suggests that STDP may be an important mechanism for creating a clustered plasticity engram, which shapes how different input streams are spatially represented in dendrite

Efficient Design of Triplet Based Spike-Timing Dependent Plasticity

Spike-Timing Dependent Plasticity (STDP) is believed to play an important role in learning and the formation of computational function in the brain. The classical model of STDP which considers the timing between pairs of pre-synaptic and post-synaptic spikes (p-STDP) is incapable of reproducing synaptic weight changes similar to those seen in biological experiments which investigate the effect of either higher order spike trains (e.g. triplet and quadruplet of spikes), or, simultaneous effect of the rate and timing of spike pairs on synaptic plasticity. In this paper, we firstly investigate synaptic weight changes using a p-STDP circuit and show how it fails to reproduce the mentioned complex biological experiments. We then present a new STDP VLSI circuit which acts based on the timing among triplets of spikes (t-STDP) that is able to reproduce all the mentioned experimental results. We believe that our new STDP VLSI circuit improves upon previous circuits, whose learning capacity exceeds current designs due to its capability of mimicking the outcomes of biological experiments more closely; thus plays a significant role in future VLSI implementation of neuromorphic systems

Design and Implementation of BCM Rule Based on Spike-Timing Dependent Plasticity

The Bienenstock-Cooper-Munro (BCM) and Spike Timing-Dependent Plasticity (STDP) rules are two experimentally verified form of synaptic plasticity where the alteration of synaptic weight depends upon the rate and the timing of pre- and post-synaptic firing of action potentials, respectively. Previous studies have reported that under specific conditions, i.e. when a random train of Poissonian distributed spikes are used as inputs, and weight changes occur according to STDP, it has been shown that the BCM rule is an emergent property. Here, the applied STDP rule can be either classical pair-based STDP rule, or the more powerful triplet-based STDP rule. In this paper, we demonstrate the use of two distinct VLSI circuit implementations of STDP to examine whether BCM learning is an emergent property of STDP. These circuits are stimulated with random Poissonian spike trains. The first circuit implements the classical pair-based STDP, while the second circuit realizes a previously described triplet-based STDP rule. These two circuits are simulated using 0.35 um CMOS standard model in HSpice simulator. Simulation results demonstrate that the proposed triplet-based STDP circuit significantly produces the threshold-based behaviour of the BCM. Also, the results testify to similar behaviour for the VLSI circuit for pair-based STDP in generating the BCM

Generalised Minkowski spacetime

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the default framework within which to describe physical laws. In this paper, we show how a four-dimensional Minkowski spacetime structure naturally arises from three-dimensional physical space when modeled with Clifford geometric algebra $C\ell(\Re^3)$. This expanded eight-dimensional framework allows a generalisation of the invariant interval and the Lorentz transformations. Also, with this geometric oriented approach the fixed speed of light, the laws of special relativity and the form of Maxwell's equations, arise naturally from the intrinsic properties of the algebra without recourse to physical arguments. We also find new insights into the nature of time, a unified treatment of energy-momentum and spin, a Lagrangian unifying gravity and electromagnetism as well as predictions of a new class of physical effects and interactions.Comment: 20 pages, no figure

Physical implementation of pair-based spike-timing-dependent plasticity

Objective Spike-timing-dependent plasticity (STDP) is one of several plasticity rules which leads to learning and memory in the brain. STDP induces synapticweight changes based on the timing of the pre- and postsynaptic neurons. A neural network which can mimic the adaptive capability of biological brains in the temporal domain, requires the weight of single connections to be altered by spike timing. To physically realise this network into silicon, a large number of interconnected STDP circuits on the same substrate is required. This imposes two significant limitations in terms of power and area. To cover these limitations, very large scale integrated circuit (VLSI) technology provides attractive features in terms of low power and small area requirements. An example is demonstrated by (Indiveri et al. 2006). The objective of this paper is to present a newimplementation of the STDPcircuit which demonstrates better power and area in comparison to previous implementations. Methods The proposed circuit uses complementary metal oxide semiconductor (CMOS) technology as depicted in Fig. 1. The synaptic weight can be stored on a capacitor and charging/discharging current can lead to potentiation and depression. Results and Conclusion: HSpice simulation results demonstrate that the average power, peak power, and area of the proposed circuit have been reduced by 6, 8 and 15%, respectively, in comparison with Indiveri's implementation. These improvements naturally lead to packing more STDP circuits onto the same substrate, when compared to previous proposals. Hence, this new implementation is quite interesting for real-world large neural networks

Motif-role-fingerprints: the building-blocks of motifs, clustering-coefficients and transitivities in directed networks

Complex networks are frequently characterized by metrics for which particular subgraphs are counted. One statistic from this category, which we refer to as motif-role fingerprints, differs from global subgraph counts in that the number of subgraphs in which each node participates is counted. As with global subgraph counts, it can be important to distinguish between motif-role fingerprints that are 'structural' (induced subgraphs) and 'functional' (partial subgraphs). Here we show mathematically that a vector of all functional motif-role fingerprints can readily be obtained from an arbitrary directed adjacency matrix, and then converted to structural motif-role fingerprints by multiplying that vector by a specific invertible conversion matrix. This result demonstrates that a unique structural motif-role fingerprint exists for any given functional motif-role fingerprint. We demonstrate a similar result for the cases of functional and structural motif-fingerprints without node roles, and global subgraph counts that form the basis of standard motif analysis. We also explicitly highlight that motif-role fingerprints are elemental to several popular metrics for quantifying the subgraph structure of directed complex networks, including motif distributions, directed clustering coefficient, and transitivity. The relationships between each of these metrics and motif-role fingerprints also suggest new subtypes of directed clustering coefficients and transitivities. Our results have potential utility in analyzing directed synaptic networks constructed from neuronal connectome data, such as in terms of centrality. Other potential applications include anomaly detection in networks, identification of similar networks and identification of similar nodes within networks. Matlab code for calculating all stated metrics following calculation of functional motif-role fingerprints is provided as S1 Matlab File.Mark D. McDonnell, Ömer Nebil Yaveroğlu, Brett A. Schmerl, Nicolangelo Iannella, Lawrence M. War

Memristor-based Synaptic Networks and Logical Operations Using In-Situ Computing

We present new computational building blocks based on memristive devices. These blocks, can be used to implement either supervised or unsupervised learning modules. This is achieved using a crosspoint architecture which is an efficient array implementation for nanoscale two-terminal memristive devices. Based on these blocks and an experimentally verified SPICE macromodel for the memristor, we demonstrate that firstly, the Spike-Timing-Dependent Plasticity (STDP) can be implemented by a single memristor device and secondly, a memristor-based competitive Hebbian learning through STDP using a $1\times 1000$ synaptic network. This is achieved by adjusting the memristor's conductance values (weights) as a function of the timing difference between presynaptic and postsynaptic spikes. These implementations have a number of shortcomings due to the memristor's characteristics such as memory decay, highly nonlinear switching behaviour as a function of applied voltage/current, and functional uniformity. These shortcomings can be addressed by utilising a mixed gates that can be used in conjunction with the analogue behaviour for biomimetic computation. The digital implementations in this paper use in-situ computational capability of the memristor.Comment: 18 pages, 7 figures, 2 table

Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $i c t$, with the unit imaginary producing the correct spacetime distance $x^2 - c^2 t^2$, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary $i = \sqrt{-1}$, with the Clifford bivector $\iota = e_1 e_2$ for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis $e_1$ and $e_2$. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.Comment: 29 pages, 2 figure