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Introduction Spike-Timing-Dependent Plasticity (STDP) describes the change in the strength (or weight) of neuronal connections depending on the pre- and post-synaptic firing activity, which in turn changes the spiking properties of the post-synaptic neurons on a slower time scale. The interplay between the parameters of the neurons, the plasticity rule and the input stimulation results in changes to the network structure by strengthening or weakening pathways. This leads to functional changes of the neuronal information processing that takes place in the network. In addition to learning spiking-rate-based information, STDP captures the effect of spike-time correlations on short time scales, down to milliseconds, which are neglected by rate-based learning. STDP has been demonstrated to capture, for example, interaural time differences and the presence of narrowly distributed correlations among input spike trains. Methods Extending a previously developed framework, we consider the effect of STDP in recurrent neuronal networks stimulated by pools of external inputs, where either the input or recurrent connections (or both) are plastic. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of "steady" inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. Results and discussion We show that, in all cases, STDP can generate two simultaneous effects on the weight dynamics: a homeostatic equilibrium that stabilizes neuronal activity (firing rates) and a diverging behavior according to the pairwise spiketime correlation structure. Our analysis suggests that weight-dependent STDP may be necessary in order to obtain stability when both the input and recurrent weights are plastic. At the scale of a neuronal network, inhomogeneities in the connectivity and in the input structure results in an interesting behavior where feed-forward synaptic pathways and areas with reinforced feedback emerge in the initially homogeneous recurrent network. This robust weight competition gives rise to neuronal specialization, which can be linked to self-organization that takes place in the primary visual cortex during the first weeks of new-born mammals. Our results support the idea that spike-time correlations play a major role in the functional organization resulting from synaptic learning in networks. [ABSTRACT FROM AUTHOR]

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error from $$120^{\circ }$$ . This notion arises in numerical approximations of minimum Steiner trees. We investigate the worst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. It has been conjectured that this relative error is at most linear in the maximum error at the angles, independent of the number of terminals. We verify this conjecture for the two-dimensional case as long as the maximum angle error is sufficiently small in terms of the number of terminals. In the two-dimensional case we derive a lower bound for the relative error in length. This bound is linear in terms of the maximum angle error when the angle error is sufficiently small in terms of the number of terminals. We find improved estimates of the relative error in length for larger values of the maximum angle error and calculate exact values in the plane for three and four terminals. [ABSTRACT FROM AUTHOR]

In the classical electricity grid power demand is nearly instantaneously matched by power supply. In this paradigm, the changes in power demand in a low voltage distribution grid are essentially nothing but a disturbance that is compensated for by control at the generators. The disadvantage of this methodology is that it necessarily leads to a transmission and distribution network that must cater for peak demand. So-called smart meters and smart grid technologies provide an opportunity to change this paradigm by using demand side energy storage to moderate instantaneous power demand so as to facilitate the supply-demand match within network limitations. A receding horizon model predictive control method can be used to implement this idea. In this paradigm demand is matched with supply, such that the required customer energy needs are met but power demand is moderated, while ensuring that power flow in the grid is maintained within the safe operating region, and in particular peak demand is limited. This enables a much higher utilisation of the available grid infrastructure, as it reduces the peak-to-base demand ratio as compared to the classical control methodology of power supply following power demand. This paper investigates this approach for matching energy demand to generation in the last mile of the power grid while maintaining all network constraints through a number of case studies involving the charging of electric vehicles in a typical suburban low voltage distribution network in Melbourne, Australia. [ABSTRACT FROM AUTHOR]

The history of the Euclidean Steiner tree problem, which is the problem of constructing a shortest possible network interconnecting a set of given points in the Euclidean plane, goes back to Gergonne in the early nineteenth century. We present a detailed account of the mathematical contributions of some of the earliest papers on the Euclidean Steiner tree problem. Furthermore, we link these initial contributions with results from the recent literature on the problem. [ABSTRACT FROM AUTHOR]

A fundamental goal of neuroscience is to understand how cognitive processes, such as operant conditioning, are performed by the brain. Typical and well studied examples of operant conditioning, in which the firing rates of individual cortical neurons in monkeys are increased using rewards, provide an opportunity for insight into this. Studies of reward-modulated spike-timing-dependent plasticity (RSTDP), and of other models such as R-max, have reproduced this learning behavior, but they have assumed that no unsupervised learning is present (i.e., no learning occurs without, or independent of, rewards). We show that these models cannot elicit firing rate reinforcement while exhibiting both reward learning and ongoing, stable unsupervised learning. To fix this issue, we propose a new RSTDP model of synaptic plasticity based upon the observed effects that dopamine has on long-term potentiation and depression (LTP and LTD). We show, both analytically and through simulations, that our new model can exhibit unsupervised learning and lead to firing rate reinforcement. This requires that the strengthening of LTP by the reward signal is greater than the strengthening of LTD and that the reinforced neuron exhibits irregular firing. We show the robustness of our findings to spike-timing correlations, to the synaptic weight dependence that is assumed, and to changes in the mean reward. We also consider our model in the differential reinforcement of two nearby neurons. Our model aligns more strongly with experimental studies than previous models and makes testable predictions for future experiments. [ABSTRACT FROM AUTHOR]

The Euclidean k -Steiner tree problem asks for a minimum-cost network connecting n given points in the plane, allowing at most k additional nodes referred to as Steiner points. In the classical Steiner tree problem in which there is no restriction on the number of nodes, every Steiner point must be of degree 3. The k -Steiner problem differs in that Steiner points of degree 4 may be included in an optimal solution. This simple change leads to a number of complexities when attempting to create a generation algorithm for optimal k -Steiner trees, which has proven to be a powerful component of the flagship algorithm, namely GeoSteiner, for solving the classical Steiner tree problem. In the present paper we firstly extend the basic framework of GeoSteiner's generation algorithm to include degree-4 Steiner points. We then introduce a number of novel results restricting the structural and geometric properties of optimal k -Steiner trees, and then show how these properties may be used as topological pruning methods underpinning our generation algorithm. Finally, we present experimental data to show the effectiveness of our pruning methods in reducing the number of sub-optimal solution topologies. [ABSTRACT FROM AUTHOR]

Learning rules, such as spike-timing-dependent plasticity (STDP), change the structure of networks of neurons based on the firing activity. A network level understanding of these mechanisms can help infer how the brain learns patterns and processes information. Previous studies have shown that STDP selectively potentiates feed-forward connections that have specific axonal delays, and that this underlies behavioral functions such as sound localization in the auditory brainstem of the barn owl. In this study, we investigate how STDP leads to the selective potentiation of recurrent connections with different axonal and dendritic delays during oscillatory activity. We develop analytical models of learning with additive STDP in recurrent networks driven by oscillatory inputs, and support the results using simulations with leaky integrate-and-fire neurons. Our results show selective potentiation of connections with specific axonal delays, which depended on the input frequency. In addition, we demonstrate how this can lead to a network becoming selective in the amplitude of its oscillatory response to this frequency. We extend this model of axonal delay selection within a single recurrent network in two ways. First, we show the selective potentiation of connections with a range of both axonal and dendritic delays. Second, we show axonal delay selection between multiple groups receiving out-of-phase, oscillatory inputs. We discuss the application of these models to the formation and activation of neuronal ensembles or cell assemblies in the cortex, and also to missing fundamental pitch perception in the auditory brainstem. [ABSTRACT FROM AUTHOR]

In the design of open pit mines, the region to be mined is partitioned into pushbacks, subregions that allow the mining to be divided into distinct phases. Practical pushbacks are connected, satisfy a minimum width for mining equipment and include a haulage ramp. Current pushback models typically relax some or all of these mineability conditions; consequently, the outputs from those models require significant intervention by mining engineers. We present a formulation to generate maximum value practical pushbacks. A closeness factor is introduced to quantify the design's mineability. Finally, a case study of a real mine shows that our model can produce pushbacks with more practical designs and better value than traditional approaches. [ABSTRACT FROM AUTHOR]

We introduce the concept of an obstacle skeleton, which is a set of line segments inside a polygonal obstacle ω that can be used in place of ω when performing intersection tests for obstacle-avoiding network problems in the plane. A skeleton can have significantly fewer line segments compared to the number of line segments in the boundary of the original obstacle, and therefore performing intersection tests on a skeleton (rather than the original obstacle) can significantly reduce the CPU time required by algorithms for computing solutions to obstacle-avoidance problems. A minimum skeleton is a skeleton with the smallest possible number of line segments. We provide an exact O (n 2) algorithm for computing minimum skeletons for rectilinear obstacles in the rectilinear plane that are rectilinearly convex. [ABSTRACT FROM AUTHOR]

Abstract We introduce the concepts of k -lunes and k -lune inequalities, which form the basis for new geometric pruning rules for limiting the number of candidate full components that need to be considered when solving the Euclidean Steiner tree problem or the Euclidean 2-connected Steiner network problem. For the latter problem, these new pruning rules constitute the first empty region properties to have been developed for the problem. We show how to implement these rules efficiently and run computational experiments, indicating the extent to which they can improve the performance of state-of-the-art algorithms for these problems. [ABSTRACT FROM AUTHOR]

Stability and power sharing properties of droop controlled inverter-based microgrid systems depend on various design factors. Little explored is the effect of component mismatches and parameters drifts on the stability, steady state behaviour and power sharing properties of these systems. In this paper, the behaviour of frequency droop controlled inverter based microgrid systems in the presence of non-identical clocks is analysed. It is shown that power sharing between converters in a microgrid can be sensitive to clock mismatches. Our proposal shows that a coordination control that uses sparse inter-node communications is useful in ensuring desired active power sharing. Conditions are derived to ensure stability in the presence of the proposed controller and simulation results are presented. [ABSTRACT FROM AUTHOR]

Component mismatches and parameters drifts drastically affect stability and long-term operation of droop-controlled inverter-based microgrids. This paper analyzes and illustrates the impact of design variations and parameter drifts between angle droop controlled inverter-interfaced sources in a microgrid. It is shown that microgrid stability is very sensitive to parameter drifts, especially in frequency. A coordination control scheme that uses internode communications is proposed for improving the stability margin and ensuring the desired power sharing. Conditions for stability are derived and simulation results are presented to validate the performance of the proposal. [ABSTRACT FROM PUBLISHER]

An abstract of the article "Requirements for the robust operant conditioning of neural firing rates" by Robert R. Kerr, David B. Grayden, Doreen A. Thomas, Matthieu Gilson and Anthony N. Burkitt is presented.

An abstract of the article "STDP encodes oscillation frequencies in the connections of recurrent networks of spiking neurons," by Robert R. Kerr, Anthony N. Burkitt, Doreen A. Thomas, and David B. Grayden is presented.

The article focuses on a study of the dynamics of recurrently connected linear Poisson neurons excited by steady external pulse trains with a correlation structure. According to the authors, the input synaptic weights are modified based on additive Spike-Timing-Dependent Plasticity (STDP) that relies upon both rate-based and pairwise-correlation-based changes. It concludes that the presence of recurrent connections impacts upon the learning of the input connections, which relates to the emergence of self-organised maps in neural networks.

The increasing uptake of electric vehicles suggests that vehicle charging will have a significant impact on the electricity grid. Finding ways to shift this charging to off-peak periods has been recognized as a key challenge for integration of electric vehicles into the electricity grid on a large scale. In this paper, electric vehicle charging is formulated as a receding horizon optimization problem that takes into account the present and anticipated constraints of the distribution network over a finite charging horizon. The constraint set includes transformer and line limitations, phase unbalance, and voltage stability within the network. By using a linear approximation of voltage drop within the network, the problem solution may be computed repeatedly in near real time, and thereby take into account the dynamic nature of changing demand and vehicle arrival and departure. It is shown that this linear approximation of the network constraints is quick to compute, while still ensuring that network constraints are respected. The approach is demonstrated on a validated model of a real network via simulations that use real vehicle travel profiles and real demand data. Using the optimal charging method, high percentages of vehicle uptake can be sustained in existing networks without requiring any further network upgrades, leading to more efficient use of existing assets and savings for the consumer. [ABSTRACT FROM PUBLISHER]

The 1-Steiner tree problem, the problem of constructing a Steiner minimum tree containing at most one Steiner point, has been solved in the Euclidean plane by Georgakopoulos and Papadimitriou using plane subdivisions called oriented Dirichlet cell partitions. Their algorithm produces an optimal solution within O( n) time. In this paper we generalise their approach in order to solve the k-Steiner tree problem, in which the Steiner minimum tree may contain up to k Steiner points for a given constant k. We also extend their approach further to encompass other normed planes, and to solve a much wider class of problems, including the k-bottleneck Steiner tree problem and other generalised k-Steiner tree problems. We show that, for any fixed k, such problems can be solved in O( n) time. [ABSTRACT FROM AUTHOR]

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity on a (much) slower time scale. This paper examines the effect of STDP in a recurrently connected network stimulated by external pools of input spike trains, where both input and recurrent synapses are plastic. Our previously developed theoretical framework is extended to incorporate weight-dependent STDP and dendritic delays. The weight dynamics is determined by an interplay between the neuronal activation mechanisms, the input spike-time correlations, and the learning parameters. For the case of two external input pools, the resulting learning scheme can exhibit a symmetry breaking of the input connections such that two neuronal groups emerge, each specialized to one input pool only. In addition, we show how the recurrent connections within each neuronal group can be strengthened by STDP at the expense of those between the two groups. This neuronal self-organization can be seen as a basic dynamical ingredient for the emergence of neuronal maps induced by activity-dependent plasticity. [ABSTRACT FROM AUTHOR]

In contrast to a feed-forward architecture, the weight dynamics induced by spike-timing-dependent plasticity (STDP) in a recurrent neuronal network is not yet well understood. In this article, we extend a previous study of the impact of additive STDP in a recurrent network that is driven by spontaneous activity (no external stimulating inputs) from a fully connected network to one that is only partially connected. The asymptotic state of the network is analyzed, and it is found that the equilibrium and stability conditions for the firing rates are similar for both full and partial connectivity: STDP causes the firing rates to converge toward the same value and remain quasi-homogeneous. However, when STDP induces strong weight competition, the connectivity affects the weight dynamics in that the distribution of the weights disperses more quickly for lower density than for higher density. The asymptotic weight distribution strongly depends upon that at the beginning of the learning epoch; consequently, homogeneous connectivity alone is not sufficient to obtain homogeneous neuronal activity. In the absence of external inputs, STDP can nevertheless generate structure in the network through autocorrelation effects, for example, by introducing asymmetry in network topology. [ABSTRACT FROM AUTHOR]

In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network. [ABSTRACT FROM AUTHOR]

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network. [ABSTRACT FROM AUTHOR]

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections. [ABSTRACT FROM AUTHOR]

The article presents a study which aims to investigate the role of the spike-timing-dependent plasticity (STDP) in determining the synaptic weights' input correlation structure. Accordingly, the STDP is capable of rendering competition among synapses' various weights as well as in assessing the neuronal specialization. Moreover, STDP's ability to assess the synapses' potentiation and depression is also noted.

Introduction Spike-timing-dependent plasticity (STDP) is believed to generate structure in neuronal networks by modifying synaptic weights depending on the spike-time information contained in the spike trains at the scale of milliseconds. In addition to spiking-rate-based information, STDP captures the effect of spike-time correlations at a short time scale (down to milliseconds), which is neglected by rate-based learning. This includes, for example, interaural time difference in auditory pathways and repeated coincident spikes within input trains. The impact of STDP in the presence of periodic neuronal activity has only just begun to be addressed, in particular the investigation of its role in modifying synchronisation in recurrently connected networks. Methods Extending a previously developed framework based on the Poisson neuron model, we investigate the effect of STPD on the recurrent connections of a neuronal network with no external input that is only driven by spontaneous oscillatory activity. We examine frequencies above 10 Hz, which correspond to the time scale of a typical choice for the learning window function of STDP. In this case, the weight dynamics is affected by the neuronal correlation structure induced by the periodic spiking activity. The asymptotic distribution of the weights is investigated using a fixed-point analysis upon a dynamical system of equations. Numerical simulations are used to support the analytical results. Results and discussion The strong competition resulting from STDP leads to the splitting of an initially homogeneous distribution of recurrent weights. In addition, STDP causes the firing rates to stabilise in a similar manner to the case of non-oscillatory spontaneous activity, which also ensures an equilibrium on the mean incoming recurrent weight for each neuron. We consider a network of two identical neuronal groups where only one group (A) has oscillatory spontaneous activity, while the other group (B) has a fixed spontaneous firing rate. The connections within group A and those from A to B tend to become either potentiated or depressed at the expense of the other recurrent connections, depending on the frequency of the oscillatory spontaneous activity for group A. When both groups A and B have oscillatory spontaneous activity, the frequencies and respective phases (if applicable) determine the evolution of the recurrent weights, which can result in the strengthening of within-group connections or the emergence of feed-forward pathways. Our results elucidate the rich interplay between STDP and the spike-time correlation structure in biological-like neuronal networks that have oscillatory activity. [ABSTRACT FROM AUTHOR]