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Metastability and Eye Movements: A Dynamical‑Systems Interpretation

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  1. Why metastability is a natural language for gaze behavior The idea that perception, attention, and neural activity evolve through transiently stable states has deep roots in cognitive science and neuroscience. Concepts such as attractors , basins , noise‑induced transitions , and escape times appear in work on perceptual switching, decision‑making, and neural population dynamics (Kelso, 1995; Rabinovich et al., 2008; Deco & Jirsa, 2012). Eye movements, especially the alternation between fixations and saccades ,   fit remarkably well into this metastable picture. The Freidlin–Wentzell theory of rare events (Freidlin & Wentzell, 2012) provides a rigorous mathematical language for these intuitions. 2. Fixations as metastable states  Consider the gaze position X t as the state of a stochastic dynamical system. During a fixation the  gaze remains confined to a small region, microsaccades and noise generate small fluctuations, and the gaze tends to return...
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THE NEUROECONOMICS IN THE CONTEXT OF INTEGRATIVE NEUROSCIENCE

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The brain's large-scale organizational principles are elucidated by many fields, including the neurophysiology, clinical practice, biology, cognitive sciences.   Integrative neuroscience   attempts to consolidate these observations through unified descriptive models and databases of behavioral measures and recordings. These are the basis for some quantitative modeling of large-scale brain activity [1] . Statistics and computational neuroscience form the bases of the quantitative analysis for those models. Actually, computational neuroscience is an approach to understanding the information content of neural signals by modeling the nervous system at many different structural scales, including the biophysical, the circuit and the system levels. Computer simulations of neurons and neural networks are complementary to traditional techniques in neuroscience. Computational modeling of higher cognitive functions has only recently begun with experimental data that comes primarily fr...
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Statistics: the basic tool of scientific research

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Complexity is an ubiquitous condition. We all make decisions of varying importance every day, so one may find strange that decision making involves rather sophisticated mechanisms. However, studies have shown that most people are much poorer at decision making than they think. The understanding of the decision making processes has been the aim of scientific research for many years.  Decision making rules act not only at a macro-level, whose results we can observe  as economic aggregates, but take a major role also at the micro-level in terms of interactions among neuronal populations.  In both cases the comprehension of the phenomena relies on robust computational approach. In this sense, statistics offers the tools for modelling and understanding  economic (i.e., social) behaviors and neuronal activities. 
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Diagnosing Singular Fits in Linear Mixed Models: Practical Examples, Code, and Alternatives

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  Introduction This post is the practical follow‑up to When Linear Mixed Models Don’t Converge , where I discussed the theoretical reasons why convergence issues often arise in linear mixed models. Here, we move from theory to practice: simulated examples, diagnostic tools, interpretation of singular fits, and practical modeling alternatives. If you haven’t read the first part yet, you may want to start there for the conceptual foundations. Figure. Conceptual map showing how model complexity and available information interact Legend of Figure 1. Green = identifiable models; yellow = risk of singularity; red = non‑identifiable models. A Concrete Example Using R: When a Random-Slope Model Becomes Singular Let’s simulate a simple dataset with only 8 groups and a very small random‑slope variance. This is a classic scenario where the model converges numerically but is statistically non‑identifiable. ```r set.seed(123) n_groups <- 8 n_per_group <- 20 group <- factor(rep(1:n_gro...
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Understanding Anaerobic Threshold (VT2) and VO2 Max in Endurance Training

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  Introduction: The Science Behind Ventilatory Thresholds VT1 vs. VT2: Defining Energy Transitions p (Aerobic Threshold) : The transition from lipid metawwwpp (fat-burning) to a mixed metabolism, where both carbohydrates and fats fuel muscle activity. V0T2 (Anaerobic Threshold) : The point where the  shifts to a predominantly carbohydrate-based wmetabolism , leading to rapid lactate waccumpulation and increased reliance on anaerobic energy pathways. www w In p VT1 and VT2 Wwww ewAgep & Sex Younger athletes generally exhibit higher VT2 values , while aging naturally reduces aerobicw capacity. Men tend to have a higher VO2 Max due to greater lung capacity and muscle mass, but women can achieve similar endurance levels through optimized training. Body Composition & Health Status High body fat percentage may reduce VT2 efficiency, as excess weight increases ...
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Unit Root Testing in Practice: A Tutorial on ADF–KPSS, Specification, and Diagnostics

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  Stationary Signals   A stationary signal is defined by the stability of its statistical properties over time. Specifically, this implies that the signal’s mean, variance, and autocorrelation function remain consistent, regardless of the time in which the signal is evaluated. There are two main types of stationarity: ·        Strict-sense stationarity refers to the property of a signal in which all statistical characteristics remain unchanged over time. This encompasses all moments of the distribution, indicating that the entire probability distribution remains constant throughout the observed period. ·        Wide-sense stationarity requires that the first two moments, specifically the mean and variance, remain constant over time. The autocorrelation function is dependent only on the time difference between two points, not on the exact time points themselves.   Importance in Signal...
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