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Showing posts from March, 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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EUROPEAN DEBT CRISIS: THE CURRENT ACCOUNT BALANCE IS AN EARLY WARNING SIGNAL

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Often the financial/economic crises  in the Euro-zone are attributed to government budget deficits in excess of the values stated in the Stability and Growth Pact (SGP)  [ SGP regulation ] , and the Maastricht Treaty  [ see the EU document ], but we'd better take  the external debts of the European countries as at the core of the current crises.  " Because they carry obligations to make future payments, external debt liabilities have the potential to create circumstances that render an economy vulnerable to solvency and liquidity problems. Moreover, as experience has shown, external vulnerability can have widespread economic costs, and not just for the initially affected economy. It is clear, therefore, that external debt needs to be measured and monitored. "  [ see here the IMF guide on external debt ]  Under this perspective, it will turn easy to realize that the most important variable to assess the financial health of a country is given by t...
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EURO CRISIS: THE CYPRUS PLOT TWIST

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And so, finally the financial system of Cyprus , has been secured. Or not?  The current Eurogroup President, Mr Jeroen Dijsselbloem, who is also the Minister of Finance of the Netherlands , hailed the agreement between the government of Cyprus and the troika (EU-ECB-IMF) about the bank rescue as a template for bank restructurings:  "The agreement reached tonight puts an end to the uncertainties of Cyprus and the euro zone, "said the President of the Eurogroup, who explained that" the agreement avoids the tax, and allows a thorough restructuring of the banking sector in Cyprus."   According to the understanding reached between the troika and prime minister Anastasiades, the Laiki Bank will be closed through a controlled process and its assets will fall into a "good bank" and a "bad bank." The good assets will end up in Bank of Cyprus, as well as emergency liquidity from the ECB, which must be returned.   The threshold of € 100000 ha...
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DECISION UNDER UNCERTAINTY AND THE BAYESIAN BRAIN: A NOTE ON THE CONCEPT OF DETERMINISM

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In a previous post  [ here ] it was addressed the issue of bayesian modality of information processing into the brain.  The main purpose was focused on the biological palusibility of the bayesian approach in decision making under uncertainty as reported by several authors in books and in leading journals of neuroscience.  Now let's see an elucidation on   the concept of  determinism . It has different meanings [ see also ]: Causal Determinism   (or   Nomological Determinism ) states that  all events have a   cause   and   effect  therefore  future events are explained (caused) by   past   and present events   combined with the   laws of nature .   Logical Determinism   is the notion that all   propositions   (i.e. assertions or declarative sentences), whether about the past, present or future, are either   true   or   false .  Environmental Determ...
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GOVERNMENT DEBT, PRIVATE DEBT & CURRENT ACCOUNT BALANCE IN EURO ZONE: A MANIFESTATION OF THE CYCLE OF FRENKEL

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The balance of payments is the statistical statement that systematically summarises, for a specific time period, the economic transactions of an economy with the rest of the world. The Balance of Payments is broken down into three broad sub-balances: the current account, the capital account, and the financial account.  Current account is the major driver of net lending/net borrowing of an economy; it provides important information about the economic relations of a country with the rest of the world. It covers all transactions (other than those in financial items) that involve economic values and occur between resident and non-resident units.  By analyzing [ source of data ] the performances of some countries in the euro area (Germany, Italy, Spain, France, Greece and the Nederlands) in three different periods (1995:2000; 2001:2007; 2008:2011) we can note that:  A) the northern countries (Germany and the Nederlands) have had significant benefits from the introduc...
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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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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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Owen's Function: A Simple Solution to Complex Problems

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Definition   If you are interested in statistics or probability, you may have encountered the Owen's function , a special function that arises in various applications involving bivariate normal distributions. Let’s explain what Owen's function is, how it is defined and notated, and why it is useful.  The Owen's function is defined as follows: for any real numbers h and a, Owen's function T(h,a) is given by T ( h , a ) = 1 2 π · ∫ 0 a exp ( - h 2 2 · ( 1 ...
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