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Showing posts from February, 2013

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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DECISION MAKING PROCESS: COMPONENTS AND TIME EFFECT

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We have seen  [ here ]  that the decision making activates a circuit, where the  evaluation  of the alternative solutions to a given problem and the  choice  of the best one would give rise to a learning mechanism for error reduction.   Now let's talk about the main components which influence the decision making (see Figure 1). We can consider the combination of three factors over the decision making process: the  decision environment ; the  quantity of information ; the  decision stream . Figure 1. The components of decision making and the role of the time Decision making is a process which requires the definition of the informative set (environment) by which select and implement the best solution to a given problem. During the decisional process the quantity of information is cumulated until a certain time (t') beyond which the gathering of more information overload the decision maker. That is, the quan...
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ITALY'S FOREIGN TRADE 2012

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The performance of the foreign trade of Italy during the last part of year 2012 has been exhibited in positive   terms  by the majority of the mass media and politicians in Italy. In particular the  alleged "good" performance has been attributed (at least indirectly) to the financial measures adopted by the government led by Mr. Monti.  But the value of the trade expressed in monetary units can be better understood if we consider the two factors that compose them: the amount ( volume )  the average unit value ( AUV ) which is an estimate of the average prices of products exported (imported) in a certain period. By looking at the data presented by the  Istat ( Italian  National Institute of Statistics ) on Italy's foreign trade as well as unit value and volume indices (base year 2005=100) referring to October 2012 results in a useful argument for analyzing the foreign trade.  In the following plots there are shown the results of so...
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EURO ZONE GDP DOWN BY 0.6%

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GDP fell by 0.6% in the euro area (EA17) and by 0.5% in the EU27 during the fourth quarter of 2012, compared with the previous quarter, according to flash estimates published by EUROSTAT , the statistical office of the  European Union.  In the third quarter of 2012, growth rates were -0.1% and +0.1% respectively. This is the synthesis on the (bad) status of the Q4 GDP released today by EUROSTAT [read  document ].  Figure1. The time course of GDP: Q1 2006 - Q4 2012 Table1. Quarterly growth rates of GDP in Europe. The data confirmed the downward trend in both the EA17 and the EA27 areas. What worries the market analysts is that the worsening of the Q4 GDP is larger than it was unexpected . Only for Germany seems likely to observe during the rest of 2013 a GDP growth.  Meanwhile France has announced that in 2013 the target of the 3% GDP deficit will be dissatisfied.  Things are expected to get even worse for the other Euro peripher...
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Neuromarketing World Forum 2013

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Breaking all Marketing Standards! Neuromarketing World Forum 2013  During the Neuromarketing World Forum, 6-8 March in São Paulo (Brazil), the latest news from the brain is shared and the top of the marketing and advertisement industry gathers to take advantage of these new insights. This annual event merges science and business from all over the world and leads marketing managers into the new reality of how we do business. A business man summarized: “No more pain of a failing campaign”. Link to the web site [ neuromarketingworldforum2013 ] for info and registration 
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A Continuous Semantic Space Describes the Representation of Thousands of Object and Action Categories across the Human Brain

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"Humans can recognize thousands of categories. Given the limited size of the human brain, it seems unreasonable to expect that every category is represented in a distinct brain area,” says first author Alex Huth, a graduate student working in Dr. Jack Gallant’s laboratory at the University of California, Berkeley. In a video diplayed at the web page of NEURON   [l ink to the   article ] , the author reports how  objects and action categories are organized within the brain according to a continuous    semantic space  throughout the cortical surface. Dr. A.P. Masucci ( Research fellow at the Centre for Advanced Spatial Analysis CASA, University College of London. ) defines [ here ] the semantic space as:    "the space of meaning, where the dynamics of meaning keep place. Where is it? It is in our heads!! Language is a collective phenomena and it resides in all our heads. As a natural phenomena language follows its natural laws and...
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The Drift Diffusion Model (DDM) for Decision Making in the TAFC task

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In applying the diffusion model to the TAFC, it is assumed that the accrual of noisy evidence corresponding to the two alternatives (e1, e2) is carried on until their difference (e1–e2) reaches a decisional threshold at the upper value (Th) or at the lower value 0. The attainment of one of these critical values indicates where the preference is directed: the upper threshold relates to the positive sign of the difference (e1–e2), while the lower thresholds corresponds to the negative value of (e1–e2).  The time necessary to reach one of the boundaries, i.e. the response time RT, depends on: a) the distance between the boundaries and the starting point;  b) the drift , i.e., the rate at which the average (trend) of the random variable (e1–e2) changes;  c) the diffusion , i.e., the variability of the path from the trend (Figure 1).  These elements characterizes the so called drift diffusion model (DDM) . The accumulation of evidence is driven both by...
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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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