Quantitative Biology

Within computational neuroscience, informal interactions with modelers often reveal wildly divergent goals. In this opinion piece, we explicitly address the diversity of goals that motivate and ultimately influence modeling efforts. We argue that a wide range of goals can be meaningfully taken to be of highest importance. A simple informal survey conducted on the Internet confirmed the diversity of goals in the community. However, different priorities or preferences of individual researchers can lead to divergent model evaluation criteria. We propose that many disagreements in evaluating the merit of computational research stem from differences in goals and not from the mechanics of constructing, describing, and validating models. We suggest that authors state explicitly their goals when proposing models so that others can judge the quality of the research with respect to its stated goals.

The human brain exhibits large-scale spontaneous fluctuations that account for most of its total energy metabolism. Independent of any overt function, this immense ongoing activity likely creates or maintains a potential functional brain reserve to facilitate normal brain function. An important property of spontaneous brain activity is the long-range temporal coherence, which can be characterized by resting state fMRI-based brain entropy mapping (BEN), a relatively new method that has gained increasing research interest. The purpose of this study was to leverage the large resting state fMRI and behavioral data publicly available from the human connectome project to address three important but still unknown questions: temporal stability of rsfMRI-derived BEN; the relationship of resting BEN to latent functional reserve; associations of resting BEN to neurocognition. Our results showed that rsfMRI-derived BEN was highly stable across time; resting BEN in the default mode network (DMN) and executive control network (ECN) was related to brain reserve in a negative correlation to education years; and lower DMN/ECN BEN corresponds to higher fluid intelligence and better task performance. These results suggest that resting BEN is a temporally stable brain trait; BEN in DMN/ECN may provide a means to measure the latent functional reserve that bestows better brain functionality and may be enhanced by education.

This document gives a specification for the model used in [1]. It presents a simple way of optimizing mutual information between some input and the attractors of a (noisy) network, using a genetic algorithm. The nodes of this network are modeled as simplified versions of the structures described in the "interface theory of perception" [2]. Accordingly, the system is referred to as a "perceptual network". The present paper is an edited version of technical parts of [1] and serves as accompanying text for the Python implementation PerceptualNetworks, freely available under [3]. 1. Prentner, R., and Fields, C.. Using AI methods to Evaluate a Minimal Model for Perception. OpenPhilosophy 2019, 2, 503-524. 2. Hoffman, D. D., Prakash, C., and Singh, M.. The Interface Theory of Perception. Psychonomic Bulletin and Review 2015, 22, 1480-1506. 3. Prentner, R.. PerceptualNetworks. this https URL. (accessed September 17 2020)

Adolescents with Attention-deficit/hyperactivity disorder (ADHD) have difficulty processing speech with background noise due to reduced inhibitory control and working memory capacity (WMC). This paper presents a pilot study of an audiovisual Speech-In-Noise (SIN) task for young adults with ADHD compared to age-matched controls using eye-tracking measures. The audiovisual SIN task consists of varying six levels of background babble, accompanied by visual cues. A significant difference between ADHD and neurotypical (NT) groups was observed at 15 dB signal-to-noise ratio (SNR). These results contribute to the literature of young adults with ADHD.

Neural Ordinary Differential Equations replace the right-hand side of a conventional ODE with a neural net, which by virtue of the universal approximation theorem, can be trained to the representation of any function. When we do not know the function itself, but have state trajectories (time evolution) of the ODE system we can still train the neural net to learn the representation of the underlying but unknown ODE. However if the state of the system is incompletely known then the right-hand side of the ODE cannot be calculated. The derivatives to propagate the system are unavailable. We show that a specially augmented Neural ODE can learn the system when given incomplete state information. As a worked example we apply neural ODEs to the Lotka-Voltera problem of 3 species, rabbits, wolves, and bears. We show that even when the data for the bear time series is removed the remaining time series of the rabbits and wolves is sufficient to learn the dynamical system despite the missing the incomplete state information. This is surprising since a conventional ODE system cannot output the correct derivatives without the full state as the input. We implement augmented neural ODEs and differential equation solvers in the julia programming language.

Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of stochastic ordinary differential equations. A solution to these equations is the joint probability density function (PDF) of neuron states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for stochastic leaky integrate-and-fire (LIF) and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron.

Magnetic field sensing, with its recent advances, is emerging as a viable alternative to measure functional activity of single neurons in the brain by sensing action potential associated magnetic fields (APMFs). Measurement of APMFs of large axons of worms have been possible due to their size. In the mammalian brain, axon sizes, their numbers and routes, restricts using such functional imaging methods. With segmented model of mammalian pyramidal neurons, we show that the APMF of intra-axonal currents in the axon hillock are two orders of magnitude larger than other neuronal locations. Expected 2-dimensional vector magnetic field maps of naturalistic spiking activity of a volume of neurons via widefield diamond-nitrogen-vacancy-center-magnetometry (DNVM) were simulated. A dictionary based matching pursuit type algorithm applied to the data using the axon-hillock's APMF signature allowed spatiotemporal reconstruction of APs in the volume of brain tissue at single cell resolution. Enhancement of APMF signals coupled with NVMM advances thus can potentially replace current functional brain mapping techniques.

Background: Direct electrical stimulation of the brain through intracranial electrodes is currently used to probe the epileptic brain as part of pre-surgical evaluation, and it is also being considered for therapeutic treatments through neuromodulation. It is still unknown, however, how consistent intracranial direct electrical stimulation responses are across sessions, to allow effective neuromodulation design. Objective: To investigate the cross-session consistency of the electrophysiological effect of electrical stimulation delivered through intracranial EEG. Methods: We analysed data from 79 epilepsy patients implanted with intracranial EEG who underwent brain stimulation as part of a memory experiment. We quantified the effect of stimulation in terms of band power modulation and compared this effect from session to session. As a reference, we applied the same measures during baseline periods. Results: In most sessions, the effect of stimulation on band power could not be distinguished from baseline fluctuations of band power. Stimulation effect was also not consistent across sessions; only a third of the session pairs had a higher consistency than the baseline standards. Cross-session consistency is mainly associated with the strength of positive stimulation effects, and it also tends to be higher when the baseline conditions are more similar between sessions. Conclusion: These findings can inform our practices for designing neuromodulation with greater efficacy when using direct electrical brain stimulation as a therapeutic treatment.

The free energy principle (FEP) in the neurosciences stipulates that all viable agents induce and minimize informational free energy in the brain to fit their environmental niche. In this study, we continue our effort to make the FEP a more physically principled formalism by implementing free energy minimization based on the principle of least action. We build a Bayesian mechanics (BM) by casting the formulation reported in the earlier publication (Kim 2018) to considering active inference beyond passive perception. The BM is a neural implementation of variational Bayes under the FEP in continuous time. The resulting BM is provided as an effective Hamilton's equation of motion and subject to the control signal arising from the brain's prediction errors at the proprioceptive level. To demonstrate the utility of our approach, we adopt a simple agent-based model and present a concrete numerical illustration of the brain performing recognition dynamics by integrating BM in neural phase space. Furthermore, we recapitulate the major theoretical architectures in the FEP by comparing our approach with the common state-space formulations.

Emotions are a central key for understanding human beings and of fundamental importance regarding their impact in human and animal behaviors. They have been for a long time a subject of study for various scholars including in particular philosophers and mystics. In modern science, the emotional phenomenon has attracted for a few decades an increasing number of studies, notably in the fields of Psychology, Psychiatry, Neuroscience and Biochemistry. However, since our perception of emotions is not, so far, directly detectable nor recordable by our measure instruments, Physics and Mathematics have not been so far used academically to provide a precise description of the phenomenon of feeling an emotion. Relying upon the works of O. Elahi and on the hypothesis that the human soul and its psyche may manifest in ourselves (in both conscious and unconscious manner) in an analog way as electromagnetic waves, we propose here a few mathematical descriptions consistent with the human personal experience, of the feeling and cognition of emotions. As far as we know, such a mathematical description has never been provided before. It allows a quantitative (intensity) and qualitative (nature of feelings/frequency) of the emotional phenomenon which provides a novel scientific approach of the nature of the mind, complementary to the on going research of physiological manifestation of emotions. We anticipate such an approach and the associated mathematical modeling to become an important tool to describe emotions and their subsequent behavior. In complement of the modeling of oscillations and brain dynamics, it provides a fruitful direction of research with potentially broad and deep impacts in both applied mathematics, physics, cognitive and behavioral sciences.