A State Space Approach for Piecewise-Linear Recurrent Neural Networks for Reconstructing Nonlinear Dynamics from Neural Measurements

The computational properties of neural systems are often thought to be implemented in terms of their network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit (MSU) recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a state space representation of the dynamics, but would wish to have access to its governing equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, the approach is applied to MSU recordings from the rodent anterior cingulate cortex obtained during performance of a classical working memory task, delayed alternation. A model with 5 states turned out to be sufficient to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover the relevant dynamics underlying observed neuronal time series, and directly link them to computational properties

The complete mitochondrial genome of Yarrowia lipolytica

We here report the complete nucleotide sequence of the 47.9 kb mitochondrial (mt) genome from the obligate aerobic yeast Yarrowia lipolytica. It encodes, all on the same strand, seven subunits of NADH: ubiquinone oxidoreductase (ND1-6, ND4L), apocytochrome b (COB), three subunits of cytochrome oxidase (COX1, 2, 3), three subunits of ATP synthetase (ATP6, 8 and 9), small and large ribosomal RNAs and an incomplete set of tRNAs. The Y. lipolytica mt genome is very similar to the Hansenula wingei mt genome, as judged from blocks of conserved gene order and from sequence homology. The extra DNA in the Y. lipolytica mt genome consists of 17 group 1 introns and stretches of A+Trich sequence, interspersed with potentially transposable GC clusters. The usual mould mt genetic code is used. Interestingly, there is no tRNA able to read CGN (arginine) codons. CGN codons could not be found in exonic open reading frames, whereas they do occur in intronic open reading frames. However, several of the intronic open reading frames have accumulated mutations and must be regarded as pseudogenes. We propose that this may have been triggered by the presence of untranslatable CGN codons. This sequence is available under EMBL Accession No. AJ307410

Detecting Multiple Change Points Using Adaptive Regression Splines With Application to Neural Recordings

Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such change points in time series statistics have been developed over the years, in addition to test criteria to evaluate their significance. Issues to consider when developing change point analysis methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many changes as contained in potentially high-dimensional time series. Here, a general method called Paired Adaptive Regressors for Cumulative Sum is developed for detecting multiple change points in the mean of multivariate time series. The method's advantages over alternative approaches are demonstrated through a series of simulation experiments. This is followed by a real data application to neural recordings from rat medial prefrontal cortex during learning. Finally, the method's flexibility to incorporate useful features from state-of-the-art change point detection techniques is discussed, along with potential drawbacks and suggestions to remedy them

Psychiatric Illnesses as Disorders of Network Dynamics

This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we will focus on the idea that cognitive and emotional functions are implemented in terms of dynamical systems phenomena in the brain, a common assumption in theoretical and computational neuroscience. Specific computational models, anchored in biophysics, for generating different types of network dynamics, and with a relation to psychiatric symptoms, will be briefly reviewed, as well as methodological approaches for reconstructing the system dynamics from observed time series (like fMRI or EEG recordings). We then attempt to outline how psychiatric phenomena, associated with schizophrenia, depression, PTSD, ADHD, phantom pain, and others, could be understood in dynamical systems terms. Most importantly, we will try to convey that the dynamical systems level may provide a central, hub-like level of convergence which unifies and links multiple biophysical and behavioral phenomena, in the sense that diverse biophysical changes can give rise to the same dynamical phenomena and, vice versa, similar changes in dynamics may yield different behavioral symptoms depending on the brain area where these changes manifest. If this assessment is correct, it may have profound implications for the diagnosis, prognosis, and treatment of psychiatric conditions, as it puts the focus on dynamics. We therefore argue that consideration of dynamics should play an important role in the choice and target of interventions

A biophysical model of decision making in an antisaccade task through variable climbing activity

We present a biophysical model of saccade initiation based on competitive integration of planned and reactive cortical saccade decision signals in the intermediate layer of the superior colliculus. In the model, the variable slopes of the climbing activities of the input cortical decision signals are produced from variability in the conductances of Na+, K+, Ca2+ activated K+, NMDA and GABA currents. These cortical decision signals are integrated in the activities of buildup neurons in the intermediate layer of the superior colliculus, whose activities grow nonlinearly towards a preset criterion level. When the level is crossed, a movement is initiated. The resultant model reproduces the unimodal distributions of saccade reaction times (SRTs) for correct antisaccades and erroneous prosaccades as well as the variability of SRTs (ranging from 80ms to 600ms) and the overall 25% of erroneous prosaccade responses in a large sample of 2006 young men performing an antisaccade task