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In bistable perception, observers experience alternations between two interpretations of an unchanging stimulus. Neurophysiological studies of bistable perception typically partition neural measurements into stimulus-based epochs and assess neuronal differences between epochs based on subjects' perceptual reports. Computational studies replicate statistical properties of percept durations with modeling principles like competitive attractors or Bayesian inference. However, bridging neuro-behavioral findings with modeling theory requires the analysis of single-trial dynamic data. Here, we propose an algorithm for extracting nonstationary time series features from single-trial electrocorticography (ECoG) data. We applied the proposed algorithm to 5-min ECoG recordings from human primary auditory cortex obtained during perceptual alternations in an auditory triplet streaming task (six subjects: four male, two female). We report two ensembles of emergent neuronal features in all trial blocks. One ensemble consists of periodic functions that encode a stereotypical response to the stimulus. The other comprises more transient features and encodes dynamics associated with bistable perception at multiple time scales: minutes (within-trial alternations), seconds (duration of individual percepts), and milliseconds (switches between percepts). Within the second ensemble, we identified a slowly drifting rhythm that correlates with the perceptual states and several oscillators with phase shifts near perceptual switches. Projections of single-trial ECoG data onto these features establish low-dimensional attractor-like geometric structures invariant across subjects and stimulus types. These findings provide supporting neural evidence for computational models with oscillatory-driven attractor-based principles. The feature extraction techniques described here generalize across recording modality and are appropriate when hypothesized low-dimensional dynamics characterize an underlying neural system. [ABSTRACT FROM AUTHOR]

Byline: Remus OAan (1), Rodica Curtu (1), Jonathan Rubin (1), Bard Ermentrout (1) Abstract: This paper builds on the past study of single-spike waves in one-dimensional integrate-and-fire networks to provide a framework for the study of waves with arbitrary (finite or countably infinite) collections of spike times. Based on this framework, we prove an existence theorem for single-spike traveling waves, and we combine analysis and numerics to study two-spike traveling waves, periodic traveling waves, and general infinite spike trains. For a fixed wave speed, finite-spike waves, periodic waves, and other infinite-spike waves may all occur, and we discuss the relationships among them. We also relate the waves considered analytically to waves generated in numerical simulations by the transient application of localized excitation. Author Affiliation: (1) Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA Article History: Registration Date: 01/01/2003 Received Date: 07/08/2002 Online Date: 20/08/2003 Article note: Key words or phrases:aTraveling waves, Integrate-and-fire network, Excitatory synaptic coupling

A repeating triplet-sequence ABA− of non-overlapping brief tones, A and B, is a valued paradigm for studying auditory stream formation and the cocktail party problem. The stimulus is "heard" either as a galloping pattern (integration) or as two interleaved streams (segregation); the initial percept is typically integration then followed by spontaneous alternations between segregation and integration, each being dominant for a few seconds. The probability of segregation grows over seconds, from near-zero to a steady value, defining the buildup function, BUF. Its stationary level increases with the difference in tone frequencies, DF, and the BUF rises faster. Percept durations have DF-dependent means and are gamma-like distributed. Behavioral and computational studies usually characterize triplet streaming either during alternations or during buildup. Here, our experimental design and modeling encompass both. We propose a pseudo-neuromechanistic model that incorporates spiking activity in primary auditory cortex, A1, as input and resolves perception along two network-layers downstream of A1. Our model is straightforward and intuitive. It describes the noisy accumulation of evidence against the current percept which generates switches when reaching a threshold. Accumulation can saturate either above or below threshold; if below, the switching dynamics resemble noise-induced transitions from an attractor state. Our model accounts quantitatively for three key features of data: the BUFs, mean durations, and normalized dominance duration distributions, at various DF values. It describes perceptual alternations without competition per se, and underscores that treating triplets in the sequence independently and averaging across trials, as implemented in earlier widely cited studies, is inadequate. Author summary: Segregation of auditory objects (auditory streaming) is widely studied using ambiguous stimuli. A sequence of repeating triplets ABA− of non-overlapping brief pure tones, A and B, frequency-separated, is a valued stimulus. Studies typically focus on one of two behavioral phases: the early (say, ten seconds) buildup of segregation from the default integration or later spontaneous alternations (bistability) between seconds-long integration and segregation percepts. Our experiments and modeling encompass both. Our novel, data-driven, evidence-accumulation model accounts for key features of the observations, taking as input recorded spiking activity from primary auditory cortex (as opposed to most existing, more abstract, models). Our results underscore that assessing individual triplets independently and averaging across trials, as in some earlier studies, is inadequate (lacking neuronal-accountability for percept duration statistics, the underlying basis of buildup). Further, we identify fresh parallels between evidence accumulation and competition as potential dynamic processes for choice in the brain. [ABSTRACT FROM AUTHOR]

A key challenge in neuroscience is understanding how sensory stimuli give rise to perception, especially when the process is supported by neural activity from an extended network of brain areas. Perception is inherently subjective, so interrogating its neural signatures requires, ideally, a combination of three factors: (1) behavioral tasks that separate stimulus-driven activity from perception per se; (2) human subjects who self-report their percepts while performing those tasks; and (3) concurrent neural recordings acquired at high spatial and temporal resolution. In this study, we analyzed human electrocorticographic recordings obtained during an auditory task which supported mutually exclusive perceptual interpretations. Eight neurosurgical patients (5 male; 3 female) listened to sequences of repeated triplets where tones were separated in frequency by several semitones. Subjects reported spontaneous alternations between two auditory perceptual states, 1-stream and 2-stream, by pressing a button. We compared averaged auditory evoked potentials (AEPs) associated with 1-stream and 2-stream percepts and identified significant differences between them in primary and nonprimary auditory cortex, surrounding auditory-related temporoparietal cortex, and frontal areas. We developed classifiers to identify spatial maps of percept-related differences in the AEP, corroborating findings from statistical analysis. We used one-dimensional embedding spaces to perform the group-level analysis. Our data illustrate exemplar high temporal resolution AEP waveforms in auditory core region; explain inconsistencies in perceptual effects within auditory cortex, reported across noninvasive studies of streaming of triplets; show percept-related changes in frontoparietal areas previously highlighted by studies that focused on perceptual transitions; and demonstrate that auditory cortex encodes maintenance of percepts and switches between them. [ABSTRACT FROM AUTHOR]

Several authors have reported diel oscillations in streamflow records and have hypothesized that these oscillations are linked to evapotranspiration cycles in the watershed. The timing of oscillations in rivers, however, lags behind those of temperature and evapotranspiration in hillslopes. Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low-flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical model to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for the case of uniform velocities in space over all river links. We then use our analytic solution to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, we have tested our theoretical formulation in the Dry Creek Experimental Watershed, where oscillations are clearly observed in streamflow records. We find that our solution produces streamflow values and fluctuations that are similar to those observed in the summer of 2011. [ABSTRACT FROM AUTHOR]

We present a system of ordinary differential equations (ODEs) capable of reproducing simultaneously the aggregated behavior of changes in water storage in the hillslope surface, the unsaturated and the saturated soil layers and the channel that drains the hillslope. The system of equations can be viewed as a two-state integral-balance model for soil moisture and groundwater dynamics. Development of the model was motivated by the need for landscape representation through hillslopes and channels organized following stream drainage network topology. Such a representation, with the basic discretization unit of a hillslope, allows ODEs-based simulation of the water transport in a basin. This, in turn, admits the use of highly efficient numerical solvers that enable space-time scaling studies. The goal of this paper is to investigate whether a nonlinear ODE system can effectively replicate observations of water storage in the unsaturated and saturated layers of the soil. Our first finding is that a previously proposed ODE hillslope model, based on readily available data, is capable of reproducing streamflow fluctuations but fails to reproduce the interactions between the surface and subsurface components at the hillslope scale. However, the more complex ODE model that we present in this paper achieves this goal. In our model, fluxes in the soil are described using a Taylor expansion of the underlying storage flux relationship. We tested the model using data collected in the Shale Hills watershed, a 7.9-ha forested site in central Pennsylvania, during an artificial drainage experiment in August 1974 where soil moisture in the unsaturated zone, groundwater dynamics and surface runoff were monitored. The ODE model can be used as an alternative to spatially explicit hillslope models, based on systems of partial differential equations, which require more computational power to resolve fluxes at the hillslope scale. Therefore, it is appropriate to be coupled to runoff routing models to investigate the effect of runoff and its uncertainty propagation across scales. However, this improved performance comes at the expense of introducing two additional parameters that have no obvious physical interpretation. We discuss the implications of this for hydrologic studies across scales. [ABSTRACT FROM AUTHOR]

A bifurcation analysis of a simplified model for excitatory and inhibitory dynamics is presented. Excitatory cells are endowed with a slow negative feedback and inhibitory cells are assumed to act instantly. This results in a generalization of the Hansel­Sompolinsky model for orientation selectivity. Normal forms are computed for the Turing­Hopf instability, where a new class of solutions is found. The transition from stationary patterns to traveling waves is analyzed by deriving the normal form for a Takens­Bogdanov bifurcation. Comparisons between the normal forms and numerical solutions of the full model are presented. [ABSTRACT FROM AUTHOR]

The singularity theorem is used to derive the deformations of the static bifurcation diagram of the Gray-Scott model. [ABSTRACT FROM AUTHOR]

Abstract: This paper documents our development and evaluation of a numerical solver for systems of sparsely linked ordinary differential equations in which the connectivity between equations is determined by a directed tree. These types of systems arise in distributed hydrological models. The numerical solver is based on dense output Runge–Kutta methods that allow for asynchronous integration. A partition of the system is used to distribute the workload among different processes, enabling a parallel implementation that capitalizes on a distributed memory system. Communication between processes is performed asynchronously. We illustrate the solver capabilities by integrating flow transport equations for a ∼17,000km2 river basin subdivided into 305,000 sub-watersheds that are interconnected by the river network. Numerical experiments for a few models are performed and the runtimes and scalability on our parallel computer are presented. Efficient numerical integrators such as the one demonstrated here bring closer to reality the goal of implementing fully distributed real-time flood forecasting systems supported by physics based hydrological models and high-quality/high-resolution rainfall products. [Copyright &y& Elsevier]

The role of striatal pathways in cognitive processing is unclear. We studied dorsomedial striatal cognitive processing during interval timing, an elementary cognitive task that requires mice to estimate intervals of several seconds and involves working memory for temporal rules as well as attention to the passage of time. We harnessed optogenetic tagging to record from striatal D2-dopamine receptor-expressing medium spiny neurons (D2-MSNs) in the indirect pathway and from D1-dopamine receptor-expressing MSNs (D1-MSNs) in the direct pathway. We found that D2-MSNs and D1-MSNs exhibited distinct dynamics over temporal intervals as quantified by principal component analyses and trial-by-trial generalized linear models. MSN recordings helped construct and constrain a four-parameter drift-diffusion computational model. This model predicted that disrupting either D2-MSNs or D1-MSNs would increase interval timing response times and alter MSN firing. In line with this prediction, we found that optogenetic inhibition or pharmacological disruption of either D2-MSNs or D1-MSNs increased interval timing response times. Pharmacologically disrupting D2-MSNs or D1-MSNs also changed MSN dynamics and degraded trial-by-trial temporal decoding. Together, our findings demonstrate that D2-MSNs and D1-MSNs make complementary contributions to interval timing despite opposing dynamics, implying that striatal direct and indirect pathways work together to shape temporal control of action. These data provide novel insight into basal ganglia cognitive operations beyond movement and have implications for human striatal diseases and therapies targeting striatal pathways.

The vertebrate unfolded protein response (UPR) is characterized by multiple interacting nodes among its three pathways, yet the logic underlying this regulatory complexity is unclear. To begin to address this issue, we created a computational model of the vertebrate UPR that was entrained upon and then validated against experimental data. As part of this validation, the model successfully predicted the phenotypes of cells with lesions in UPR signaling, including a surprising and previously unreported differential role for the eIF2α phosphatase GADD34 in exacerbating severe stress but ameliorating mild stress. We then used the model to test the functional importance of a feedforward circuit within the PERK/CHOP axis and of cross-regulatory control of BiP and CHOP expression. We found that the wiring structure of the UPR appears to balance the ability of the response to remain sensitive to endoplasmic reticulum stress and to be deactivated rapidly by improved protein-folding conditions. This model should serve as a valuable resource for further exploring the regulatory logic of the UPR.

The accumulation of unfolded proteins in the endoplasmic reticulum (ER) activates a mechanism whose primary functions are to sense any perturbation in the protein-folding capacity of the cell, and correct the situation to restore homeostasis. This cellular mechanism is called the unfolded protein response (UPR). We propose a biologically plausible computational model for the UPR under ER stress in mammalian cells. The model accounts for the signaling pathways of PERK, ATF6, and IRE1 and has the advantage of simulating the dynamical (timecourse) changes in the relative concentrations of proteins without any a priori steady-state assumption. Several types of ER stress can be assumed as input, including long-term (eventually periodic) stress. Moreover, the model allows for outcomes ranging from cell survival to cell apoptosis.

We investigate analytically a firing rate model for a two-population network based on mutual inhibition and slow negative feedback in the form of spike frequency adaptation. Both neuronal populations receive external constant input whose strength determines the system's dynamical state-a steady state of identical activity levels or periodic oscillations or a winner-take-all state of bistability. We prove that oscillations appear in the system through supercritical Hopf bifurcations and that they are antiphase. The period of oscillations depends on the input strength in a nonmonotonic fashion, and we show that the increasing branch of the period versus input curve corresponds to a release mechanism and the decreasing branch to an escape mechanism. In the limiting case of infinitely slow feedback we characterize the conditions for release, escape, and occurrence of the winner-take-all behavior. Some extensions of the model are also discussed.

Models implementing neuronal competition by reciprocally inhibitory populations are widely used to characterize bistable phenomena such as binocular rivalry. We find common dynamical behavior in several models of this general type, which differ in their architecture in the form of their gain functions, and in how they implement the slow process that underlies alternating dominance. We focus on examining the effect of the input strength on the rate (and existence) of oscillations. In spite of their differences, all considered models possess similar qualitative features, some of which we report here for the first time. Experimentally, dominance durations have been reported to decrease monotonically with increasing stimulus strength (such as Levelt's "Proposition IV"). The models predict this behavior; however, they also predict that at a lower range of input strength dominance durations increase with increasing stimulus strength. The nonmonotonic dependency of duration on stimulus strength is common to both deterministic and stochastic models. We conclude that additional experimental tests of Levelt's Proposition IV are needed to reconcile models and perception.

We explore the mechanism of synchronized bursting activity with frequency of approximately 10 Hz that appears in cortical tissues at low extracellular magnesium concentration [Mg2+]o. We hypothesize that this activity is persistent, namely coexists with the quiescent state and depends on slow N-methyl-D-aspartate (NMDA) conductances. To explore this hypothesis, we construct and investigate a conductance-based model of excitatory cortical networks. Population bursting activity can persist for physiological values of the NMDA decay time constant (approximately 100 ms). Neurons are synchronized at the time scale of bursts but not of single spikes. A reduced model of a cell coupled to itself can encompass most of this highly synchronized network behavior and is analyzed using the fast-slow method. Synchronized bursts appear for intermediate values of the NMDA conductance g(NMDA) if NMDA conductances are not too fast. Regular spiking activity appears for larger g(NMDA). If the single cell is a conditional burster, persistent synchronized bursts become more robust. Weakly synchronized states appear for zero AMPA conductance g(AMPA). Enhancing g(AMPA) increases both synchrony and the number of spikes within bursts and decreases the bursting frequency. Too strong g(AMPA), however, prevents the activity because it enhances neuronal intrinsic adaptation. When [Mg2+]o is increased, higher g(NMDA) values are needed to maintain bursting activity. Bursting frequency decreases with [Mg2+]o, and the network is silent with physiological [Mg2+]o. Inhibition weakly decreases the bursting frequency if inhibitory cells receive enough NMDA-mediated excitation. This study explains the importance of conditional bursters in layer V in supporting epileptiform activity at low [Mg2+]o.