Mixed up? That's good for motivation

An essential ingrediant in models of career concerns is ex ante uncertainty about an agent's type. This paper shows how career concerns can arise even in the absence of any such ex ante uncertainty, if the unobservable actions that an agent takes influence his future productivity. By implementing effort in mixed strategies the principal can endogenously induce uncertainty about the agent's ex post productivity and generate reputational incentives. Our main result is that creating such ambiguity can be optimal for the principal, even though this exposes the agent to additional risk and reduces output. This finding demonstrates the importance of mixed strategies in contracting environments with imperfect commitment, which contrasts with standard agency models where implementing mixed strategy actions typically is not optimal if pure strategies are also implementable

Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests

We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific clusters of variables, based on their contributions to the cross-entropy of the Ising model. Small contributions are discarded to avoid overfitting and to make the computation tractable. The properties of the cluster expansion and its performances on synthetic data are studied. To make the implementation easier we give the pseudo-code of the algorithm.Comment: Paper submitted to Journal of Statistical Physic

Principal component analysis of ensemble recordings reveals cell assemblies at high temporal resolution

Simultaneous recordings of many single neurons reveals unique insights into network processing spanning the timescale from single spikes to global oscillations. Neurons dynamically self-organize in subgroups of coactivated elements referred to as cell assemblies. Furthermore, these cell assemblies are reactivated, or replayed, preferentially during subsequent rest or sleep episodes, a proposed mechanism for memory trace consolidation. Here we employ Principal Component Analysis to isolate such patterns of neural activity. In addition, a measure is developed to quantify the similarity of instantaneous activity with a template pattern, and we derive theoretical distributions for the null hypothesis of no correlation between spike trains, allowing one to evaluate the statistical significance of instantaneous coactivations. Hence, when applied in an epoch different from the one where the patterns were identified, (e.g. subsequent sleep) this measure allows to identify times and intensities of reactivation. The distribution of this measure provides information on the dynamics of reactivation events: in sleep these occur as transients rather than as a continuous process

Neuronal Assembly Detection and Cell Membership Specification by Principal Component Analysis

In 1949, Donald Hebb postulated that assemblies of synchronously activated neurons are the elementary units of information processing in the brain. Despite being one of the most influential theories in neuroscience, Hebb's cell assembly hypothesis only started to become testable in the past two decades due to technological advances. However, while the technology for the simultaneous recording of large neuronal populations undergoes fast development, there is still a paucity of analytical methods that can properly detect and track the activity of cell assemblies. Here we describe a principal component-based method that is able to (1) identify all cell assemblies present in the neuronal population investigated, (2) determine the number of neurons involved in ensemble activity, (3) specify the precise identity of the neurons pertaining to each cell assembly, and (4) unravel the time course of the individual activity of multiple assemblies. Application of the method to multielectrode recordings of awake and behaving rats revealed that assemblies detected in the cerebral cortex and hippocampus typically contain overlapping neurons. The results indicate that the PCA method presented here is able to properly detect, track and specify neuronal assemblies, irrespective of overlapping membership

Evidence for the Re-Enactment of a Recently Learned Behavior during Sleepwalking

Animal studies have shown that sequenced patterns of neuronal activity may be replayed during sleep. However, the existence of such replay in humans has not yet been directly demonstrated. Here we studied patients who exhibit overt behaviors during sleep to test whether sequences of movements trained during the day may be spontaneously reenacted by the patients during sleep

Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep

Spatial Learning and Action Planning in a Prefrontal Cortical Network Model

The interplay between hippocampus and prefrontal cortex (PFC) is fundamental to spatial cognition. Complementing hippocampal place coding, prefrontal representations provide more abstract and hierarchically organized memories suitable for decision making. We model a prefrontal network mediating distributed information processing for spatial learning and action planning. Specific connectivity and synaptic adaptation principles shape the recurrent dynamics of the network arranged in cortical minicolumns. We show how the PFC columnar organization is suitable for learning sparse topological-metrical representations from redundant hippocampal inputs. The recurrent nature of the network supports multilevel spatial processing, allowing structural features of the environment to be encoded. An activation diffusion mechanism spreads the neural activity through the column population leading to trajectory planning. The model provides a functional framework for interpreting the activity of PFC neurons recorded during navigation tasks. We illustrate the link from single unit activity to behavioral responses. The results suggest plausible neural mechanisms subserving the cognitive “insight” capability originally attributed to rodents by Tolman & Honzik. Our time course analysis of neural responses shows how the interaction between hippocampus and PFC can yield the encoding of manifold information pertinent to spatial planning, including prospective coding and distance-to-goal correlates