A Kernel-Based Calculation of Information on a Metric Space

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual information between stimuli and spiking responses; the space of these responses is a metric space. It is shown that kernel density estimation on a metric space resembles the k-nearest-neighbor approach. This approach is applied to a toy dataset designed to mimic electrophysiological data

Two monopoles of one type and one of another

The metric on the moduli space of charge (2,1) SU(3) Bogomolny-Prasad-Sommerfield monopoles is calculated and investigated. The hyperKahler quotient construction is used to provide an alternative derivation of the metric. Various properties of the metric are derived using the hyperKahler quotient construction and the correspondence between BPS monopoles and rational maps. Several interesting limits of the metric are also considered.Comment: 48 pages, LaTeX, 2 figures. Typos corrected. Version in JHE

Parameter estimation of neuron models using <i>in-vitro </i>and<i> in-vivo </i>electrophysiological data

Spiking neuron models can accurately predict the response of neurons to somatically injected currents if the model parameters are carefully tuned. Predicting the response of in-vivo neurons responding to natural stimuli presents a far more challenging modeling problem. In this study, an algorithm is presented for parameter estimation of spiking neuron models. The algorithm is a hybrid evolutionary algorithm which uses a spike train metric as a fitness function. We apply this to parameter discovery in modeling two experimental data sets with spiking neurons; in-vitro current injection responses from a regular spiking pyramidal neuron are modeled using spiking neurons and in-vivo extracellular auditory data is modeled using a two stage model consisting of a stimulus filter and spiking neuron model

Dentate gyrus and hilar region revisited

AbstractIt is suggested that the dentate gyrus and hilar region in the hippocampus perform memory selection and that the selectivity of the gating of memory by this circuit is modulated by the norepinephrine–glutamate loop described by Mather et al.</jats:p

Diffusion Modelling Reveals the Decision Making Processes Underlying Negative Judgement Bias in Rats:Modelling Decision Making during Negative Affect

Human decision making is modified by emotional state. Rodents exhibit similar biases during interpretation of ambiguous cues that can be altered by affective state manipulations. In this study, the impact of negative affective state on judgement bias in rats was measured using an ambiguous-cue interpretation task. Acute treatment with an anxiogenic drug (FG7142), and chronic restraint stress and social isolation both induced a bias towards more negative interpretation of the ambiguous cue. The diffusion model was fit to behavioural data to allow further analysis of the underlying decision making processes. To uncover the way in which parameters vary together in relation to affective state manipulations, independent component analysis was conducted on rate of information accumulation and distances to decision threshold parameters for control data. Results from this analysis were applied to parameters from negative affective state manipulations. These projected components were compared to control components to reveal the changes in decision making processes that are due to affective state manipulations. Negative affective bias in rodents induced by either FG7142 or chronic stress is due to a combination of more negative interpretation of the ambiguous cue, reduced anticipation of the high reward and increased anticipation of the low reward

Accounting for uncertainty: inhibition for neural inference in the cerebellum

Sensorimotor coordination is thought to rely on cerebellar-based internal models for state estimation, but the underlying neural mechanisms and specific contribution of the cerebellar components is unknown. A central aspect of any inferential process is the representation of uncertainty or conversely precision characterizing the ensuing estimates. Here, we discuss the possible contribution of inhibition to the encoding of precision of neural representations in the granular layer of the cerebellar cortex. Within this layer, Golgi cells influence excitatory granule cells, and their action is critical in shaping information transmission downstream to Purkinje cells. In this review, we equate the ensuing excitation–inhibition balance in the granular layer with the outcome of a precision-weighted inferential process, and highlight the physiological characteristics of Golgi cell inhibition that are consistent with such computations

Topological and simplicial features in reservoir computing networks

Reservoir computing is a framework which uses the nonlinearinternal dynamics of a recurrent neural network to perform complexnon-linear transformations of the input. This enables reservoirs tocarry out a variety of tasks involving the processing of time-dependent orsequential-based signals. Reservoirs are particularly suited for tasks thatrequire memory or the handling of temporal sequences, common in areassuch as speech recognition, time series prediction, and signal processing.Learning is restricted to the output layer and can be thought of as“reading out” or “selecting from” the states of the reservoir. With all butthe output weights fixed they do not have the costly and difficult trainingassociated with deep neural networks. However, while the reservoircomputing framework shows a lot of promise in terms of efficiency andcapability, it can be unreliable. Existing studies show that small changesin hyperparameters can markedly affect the network’s performance. Herewe studied the role of network topologies in reservoir computing in thecarrying out of three conceptually different tasks: working memory, perceptualdecision making, and chaotic time-series prediction. We implementedthree different network topologies (ring, lattice, and random)and tested reservoir network performances on the tasks. We then usedalgebraic topological tools of directed simplicial cliques to study deeperconnections between network topology and function, making comparisonsacross performance and linking with existing reservoir research