Zoran Tiganj

The medial temporal lobe (MTL) is believed to support episodic memory, vivid recollection of a specific event situated in a particular place at a particular time. There is ample neurophysiological evidence that the MTL computes location in allocentric space and more recent evidence that the MTL also codes for time. Space and time represent a similar computational challenge; both are variables that cannot be simply calculated from the immediately available sensory information. We introduce a simple mathematical framework that computes functions of both spatial location and time as special cases of a more general computation. In this framework, experience unfolding in time is encoded via a set of leaky integrators. These leaky integrators encode the Laplace transform of their input. The information contained in the transform can be recovered using an approximation to the inverse Laplace transform. In the …

Studies on time cells in the hippocampus have so far focused on area CA1 in animals performing memory tasks. Some studies have suggested that temporal processing within the hippocampus may be exclusive to CA1 and CA2, but not CA3, and may occur only under strong demands for memory. Here we examined the temporal and spatial coding properties of CA3 and CA1 neurons in rats performing a maze task that demanded working memory and a control task with no explicit working memory demand. In the memory demanding task, CA3 cells exhibited robust temporal modulation similar to the pattern of time cell activity in CA1, and the same populations of cells also exhibited typical place coding patterns in the same task. Furthermore, the temporal and spatial coding patterns of CA1 and CA3 were equivalently robust when animals performed a simplified version of the task that made no demands on working …

A subset of hippocampal neurons, known as “time cells” fire sequentially for circumscribed periods of time within a delay interval. We investigated whether medial prefrontal cortex (mPFC) also contains time cells and whether their qualitative properties differ from those in the hippocampus and striatum. We studied the firing correlates of neurons in the rodent mPFC during a temporal discrimination task. On each trial, the animals waited for a few seconds in the stem of a T-maze. A subpopulation of units fired in a sequence consistently across trials for a circumscribed period during the delay interval. These sequentially activated time cells showed temporal accuracy that decreased as time passed as measured by both the width of their firing fields and the number of cells that fired at a particular part of the interval. The firing dynamics of the time cells was …

Single channel EEG systems are very useful in EEG based applications where real time processing, low computational complexity and low cumbersomeness are critical constrains. These include brain-computer interface and biofeedback devices and also some clinical applications such as EEG recording on babies or Alzheimer’s disease recognition. In this paper we address the problem of eye blink artifacts detection in such systems. We study an algebraic approach based on numerical differentiation, which is recently introduced from operational calculus. The occurrence of an artifact is modeled as an irregularity which appears explicitly in the time (generalized) derivative of the EEG signal as a delay. Manipulating such delay is easy with the operational calculus and it leads to a simple joint detection and localization algorithm. While the algorithm is devised based on continuous-time arguments, the final …

Recent work in computational neuroscience and cognitive psychology suggests that a set of cells that decay exponentially could be used to support memory for the time at which events took place. Analytically and through simulations on a biophysical model of an individual neuron, we demonstrate that exponentially decaying firing with a range of time constants up to minutes could be implemented using a simple combination of well‐known neural mechanisms. In particular, we consider firing supported by calcium‐controlled cation current. When the amount of calcium leaving the cell during an interspike interval is larger than the calcium influx during a spike, the overall decay in calcium concentration can be exponential, resulting in exponential decay of the firing rate. The time constant of the decay can be several orders of magnitude larger than the time constant of calcium clearance, and it could be controlled …

Cognitive theories suggest that working memory maintains not only the identity of recently presented stimuli but also a sense of the elapsed time since the stimuli were presented. Previous studies of the neural underpinnings of working memory have focused on sustained firing, which can account for maintenance of the stimulus identity, but not for representation of the elapsed time. We analyzed single-unit recordings from the lateral prefrontal cortex of macaque monkeys during performance of a delayed match-to-category task. Each sample stimulus triggered a consistent sequence of neurons, with each neuron in the sequence firing during a circumscribed period. These sequences of neurons encoded both stimulus identity and elapsed time. The encoding of elapsed time became less precise as the sample stimulus receded into the past. These findings suggest that working memory includes a compressed timeline …

In this paper, we propose a simple and straightforward algorithm for neural spike sorting. The algorithm is based on the observation that the distribution of a neural signal largely deviates from the uniform distribution and is rather unimodal. The detected spikes to be sorted are first processed with some feature extraction technique, such as PCA, and then represented in a space with reduced dimension by keeping only a few most important features. The resulting space is next filtered in order to emphasis the differences between the centers and the borders of the clusters. Using some prior knowledge on the lowest level activity of a neuron, such as eg the minimal firing rate, we find the number of clusters and the center of each cluster. The spikes are then sorted using a simple greedy algorithm which grabs the nearest neighbors. We have tested the proposed algorithm on real extracellular recordings and used the …

A new method for action potentials detection is proposed. The method is based on a numerical differentiation, as recently introduced from operational calculus. We show that it has good performance as compared to existing methods. We also combine the proposed method with ICA in order to obtain spike sorting.

Scale‐invariant timing has been observed in a wide range of behavioral experiments. The firing properties of recently described time cells provide a possible neural substrate for scale‐invariant behavior. Earlier neural circuit models do not produce scale‐invariant neural sequences. In this article, we present a biologically detailed network model based on an earlier mathematical algorithm. The simulations incorporate exponentially decaying persistent firing maintained by the calcium‐activated nonspecific (CAN) cationic current and a network structure given by the inverse Laplace transform to generate time cells with scale‐invariant firing rates. This model provides the first biologically detailed neural circuit for generating scale‐invariant time cells. The circuit that implements the inverse Laplace transform merely consists of off‐center/on‐surround receptive fields. Critically, rescaling temporal sequences can be …

A growing body of evidence suggests that short-term memory does not only store the identity of recently experienced stimuli, but also information about when they were presented. This representation of ‘what’ happened ‘when’ constitutes a neural timeline of recent past. Behavioral results suggest that people can sequentially access memories for the recent past, as if they were stored along a timeline to which attention is sequentially directed. In the short-term judgment of recency (JOR) task, the time to choose between two probe items depends on the recency of the more recent probe but not on the recency of the more remote probe. This pattern of results suggests a backward self-terminating search model. We review recent neural evidence from the macaque lateral prefrontal cortex (lPFC) (Tiganj, Cromer, Roy, Miller, & Howard, in press) and behavioral evidence from human JOR task (Singh & Howard, 2017 …

We propose a spike sorting method for multi-channel recordings. When applied in neural recordings, the performance of the independent component analysis (ICA) algorithm is known to be limited, since the number of recording sites is much lower than the number of neurons. The proposed method uses an iterative application of ICA and a deflation technique in two nested loops. In each iteration of the external loop, the spiking activity of one neuron is singled out and then deflated from the recordings. The internal loop implements a sequence of ICA and sorting for removing the noise and all the spikes that are not fired by the targeted neuron. Then a final step is appended to the two nested loops in order to separate simultaneously fired spikes. We solve this problem by taking all possible pairs of the sorted neurons and apply ICA only on the segments of the signal during which at least one of the neurons in a given …

Cognitive computation ought to be fast, efficient and flexible, reusing the same neural mechanisms to operate on many different forms of information. In order to develop neural models for cognitive computation we need to develop neurallyplausible implementations of fundamental operations. If the operations can be applied across sensory modalities, this requires a common form of neural coding. Weber-Fechner scaling is a general representational motif that is exploited by the brain not only in vision and audition, but also for efficient representations of time, space and numerosity. That is, for these variables, the brain appears to support functions f (x) by placing receptors at locations xi such that xi− xi− 1∝ xi. The existence of a common form of neural representation suggests the possibility of a common form of cognitive computation across information domains. Efficient Weber-Fechner representations of time, space and number can be constructed using the Laplace transform, which can be inverted using a neurally-plausible matrix operation. Access to the Laplace domain allows for a range of efficient computations that can be performed on Weber-Fechner scaled representations. For instance, translation of a function f (x) by an amount δ to give f (x+ δ) can be readily accomplished in the Laplace domain. We have worked out a neurally-plausible mapping hypothesis between translation and theta oscillations. Other operations, such as convolution and cross-correlation are extremely efficient in the Laplace domain, enabling the computation of addition and subtraction of neural representations. Implementation of neural circuits for these elemental …

Neural communication generates oscillations of electric potential in the extracellular medium. In feedback, these oscillations affect the electrochemical processes within the neurons, influencing the timing and the number of action potentials. It is unclear whether this influence should be considered only as noise or it has some functional role in neural communication. Through computer simulations we investigated the effect of various sinusoidal extracellular oscillations on the timing and number of action potentials. Each simulation is based on a multicompartment model of a single neuron, which is stimulated through spatially distributed synaptic activations. A thorough analysis is conducted on a large number of simulations with different models of CA3 and CA1 pyramidal neurons which are modeled using realistic morphologies and active ion conductances. We demonstrated that the influence of the weak extracellular oscillations, which are commonly present in the brain, is rather stochastic and modest. We found that the stronger fields, which are spontaneously present in the brain only in some particular cases (e.g. during seizures) or that can be induced externally, could significantly modulate spike timings.

Persistent firing has been observed in slice preparations from a variety of brain regions believed to be important in memory [1-3]. Information about a transient stimulus can be reflected in persistently elevated firing rate over many minutes. What computation could persistent firing cells support? In particular the lack of forgetting observed in slice preparations seems difficult to reconcile with the finding that memory degrades over time. A scale-invariant model for representing past stimuli has been proposed in [4]. This model utilizes two layers of nodes. The first layer is composed of leaky integrators and computes the Laplace transform of the input function. The first layer projects to the second through a linear operator which approximates the inverse Laplace transform so the activity of the second layer at any point of time gives a fuzzy representation of the input history leading up to the present moment. Comparison with behavioral results suggests that the history should be retained over at least a few thousand seconds. If we assume that each node of the above model corresponds to an individual neuron, the neurons encoding the Laplace transform should respond to a particular stimulus with a firing rate that decays exponentially over time. Critically, in order to encode the Laplace transform we require different rates of decay for different neurons in this layer. Moreover, the longest time constant across neurons determines the longest time scale that can be maintained in representation of the history. Persistent firing cells [5] are basically perfect integrators. We have been exploring the conditions under which persistently firing cells observed in the slice …

Natural learners must compute an estimate of future outcomes that follow from a stimulus in continuous time. Widely used reinforcement learning algorithms discretize continuous time and estimate either transition functions from one step to the next (model-based algorithms) or a scalar value of exponentially discounted future reward using the Bellman equation (model-free algorithms). An important drawback of model-based algorithms is that computational cost grows linearly with the amount of time to be simulated. An important drawback of model-free algorithms is the need to select a timescale required for exponential discounting. We present a computational mechanism, developed based on work in psychology and neuroscience, for computing a scale-invariant timeline of future outcomes. This mechanism efficiently computes an estimate of inputs as a function of future time on a logarithmically compressed scale …