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Measures and Limits of Models of Fixation Selection
Niklas Wilming, Torsten Betz, Tim C. Kietzmann, Peter K?nig
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0024038
Abstract: Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection . We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced.
Disequilibrium Pricing Theory—Bubbles and Recessions  [PDF]
Frederick Betz
Theoretical Economics Letters (TEL) , 2014, DOI: 10.4236/tel.2014.41009

How can one track a financial bubble as a likely precursor to bank panics and subsequent recessions? We model the Minsky-Keynes depiction of a financial marketby extending the “equilibrium-price” model to a “disequilibrium-price” model, through adding a third dimension of time. In this way, we use a topological graphic approach to see how the models from the two schools of economics, exogenous and endogenous, relate to each other as complementary models of production and financial sub-systems. These economic models are partial models in an economynot a model of the whole economy. However, such partial models can be used to anticipate financial bubbleshence bank runs and recessions due to bank runswhich typically follow.

Disequilibrium Pricing—Greek Euro Crisis  [PDF]
Frederick Betz
Theoretical Economics Letters (TEL) , 2014, DOI: 10.4236/tel.2014.49113
Abstract: Financial instability in Greece began in 2009 when the interest rates on Greek sovereign bonds surged; and this can be graphed in a “price disequilibrium” model. To explain how this came about, we create a systems-dynamics model of the Greek fiscal system. Government fiscal systems are not a kind of a “causal” system, but a “structural-functional” system instead. This approach is in the spirit of the Keynes-Minsky model of a financial market as a “dynamic” of the value of capital assets. Financial bubbles occur from “perceptions”—cognitive “reflexivity” in Soros’ term—as expectations of the future values in a financial market. The Greek government fiscal crisis is a “Minsky moment”, which occurs at a time when traders in a financial market have moved from speculative finance to the unstable reflexivity in Ponzi finance. The governments in Greece had indulged in the dynamics of a budget policy of “Ponzi finance”. Unsound fiscal policy over many years had accumulated a very large and increasing government debt—until bond market “reflexive cognition” triggered the Greek fiscal crisis in 2010. The “reflexive perception” of bond traders was that either the Greek government must “default” or be “bailed out”.
Private and Public Debt Markets in Disequilibrium Theory  [PDF]
Frederick Betz
Theoretical Economics Letters (TEL) , 2015, DOI: 10.4236/tel.2015.55073
Abstract: In disequilibrium pricing of financial markets, excesses in either public debt or private debt can trigger a financial crisis, with attendant bank panics and recessions. For example, in the Euro crisis beginning in 2010, financial contagion in the sovereign bond market has spread among five nations: Greece, Ireland, Cyprus, Portugal, and Spain. But the reasons for the contagion was initially different for the countries, due to either disequilibrium pricing in public debt markets or disequilibrium pricing in private debt markets. In previous papers, we introduced a time-independent supply-demand model (three-dimensional model) for disequilibrium pricing in financial markets [1] and a steady-state disequilibrium systems model for the run-up of a financial crisis in a public debt market [2]. In this paper we construct a time-dependent disequilibrium systems model for the run-up of financial crises in a private debt market. We analyze the empirical case of the 2010-12 Euro crisis in Spain (private debt crisis) and then compare this to the empirical case of the 2010-2015 Euro crisis in Greece (public debt crisis).
Disequilibrium Systems Representation of Growth Models—Harrod-Domar, Solow, Le-ontief, Minsky, and Why the U.S. Fed Opened the Discount Window to Money-Market Funds  [PDF]
Frederick Betz
Modern Economy (ME) , 2015, DOI: 10.4236/me.2015.612113
Abstract: One of the intriguing puzzles from the Global Financial Crisis of 2007-08 was this one: To save the U.S. economy, why did the U.S. Federal Reserve System (under the chair, Ben Bernanke) open its central bank discount window to the unregulated money-market funds? The discount window of a central bank is usually only open to legitimate banks; and money-market funds are not banks. But the action proved correct, and the crisis slipped into an economic recession and not a depression. Yet how can one theoretically explain Bernanke’s economic reasoning underlying this critical decision? For explanation of that event, we integrate several traditional economic models: 1) the growth models of Harrod-Domar and of Solow, 2) the production-consumption model of Leontief, and 3) Minsky’s price-disequilibrium model. The integration of these models is methodologically possible through a system dynamics representation of the algebraic forms of the traditional economic models. In a system dynamics model, economic flows become explicit, as well as do the connections between institutions. In this explanation, we see evidence for the economic postulate that: it is financial crises which trigger depressions and not production business-cycles. Production business-cycles trigger recessions.
Model of the International Financial Grid and the Panama Papers  [PDF]
Frederick Betz
Theoretical Economics Letters (TEL) , 2017, DOI: 10.4236/tel.2017.74056
Abstract: One of the advantages of empirically-grounded theory is to provide a deeper understanding of natural events. This is true both of the physical and social sciences, and especially of economic theory. We examine an empirical event in economics in 2016, called the “Panama Papers. Reports on the event provide material for an empirical case study about the international financial grid, focused upon the use of dummy corporations in “dark money” international-capital-flows. We analyze the case though a topological model of the international financial grid.
Capital Structures: Vectorizing the Harrod-Domar Model in Macro-Economics  [PDF]
Frederick Betz
Theoretical Economics Letters (TEL) , 2018, DOI: 10.4236/tel.2018.812170
Abstract: The epistemological status of economic theory is either as an idealistic pre-scription or a depiction of a factual reality in context. We examine the reality of the macro-economic model of Harrod-Domar in the context of the Japa-nese, Korean and American economic history. Empirically, one sees that the model remained ideal but incomplete in fact. The capital structures in an economy determined whether capital flowed ideally or otherwise. This is a cross-disciplinary research approach combining the economic perspective with the management perspective in the disciplines of the social sciences.
Theoretical Metric of Civilization: The Case of the International Court of Justice  [PDF]
Frederick Betz
Open Journal of Social Sciences (JSS) , 2019, DOI: 10.4236/jss.2019.71001
Abstract: The usefulness of a theoretical metric for civilization is that it can help to identify the kinds of progress which society can make that is universalized for all humanity. Societal systems perform the functions which provide the values and performance of the society, and wherein societal problems occur. In the concept of the level of “civilization” of a society, four kinds of measures can assess the progress of a society in attaining universalized values: Truth, Good, Beautiful, and Wealth. The value of Truth in our civilization is methodologically investigated by science. The value of Good in our civilization is politically pursued through democracy. The value of Beautiful in our civilization is seen in the preservation of the environment of the Earth. The value of Wealth in our civilization is generated through industrialization of societal production. We apply the theory to the historical case of the International Court of Justice and Yugoslav War Crimes to examine empirical evidence about the validity of a theoretical metric.
Beyond Correlation: Do Color Features Influence Attention in Rainforest?
Hans-Peter Frey,Verena Willenbockel,Torsten Betz,Tomasz Troscianko,Peter K?nig
Frontiers in Human Neuroscience , 2011, DOI: 10.3389/fnhum.2011.00036
Abstract: Recent research indicates a direct relationship between low-level color features and visual attention under natural conditions. However, the design of these studies allows only correlational observations and no inference about mechanisms. Here we go a step further to examine the nature of the influence of color features on overt attention in an environment in which trichromatic color vision is advantageous. We recorded eye-movements of color-normal and deuteranope human participants freely viewing original and modified rainforest images. Eliminating red–green color information dramatically alters fixation behavior in color-normal participants. Changes in feature correlations and variability over subjects and conditions provide evidence for a causal effect of red–green color-contrast. The effects of blue–yellow contrast are much smaller. However, globally rotating hue in color space in these images reveals a mechanism analyzing color-contrast invariant of a specific axis in color space. Surprisingly, in deuteranope participants we find significantly elevated red–green contrast at fixation points, comparable to color-normal participants. Temporal analysis indicates that this is due to compensatory mechanisms acting on a slower time scale. Taken together, our results suggest that under natural conditions red–green color information contributes to overt attention at a low-level (bottom-up). Nevertheless, the results of the image modifications and deuteranope participants indicate that evaluation of color information is done in a hue-invariant fashion.
Why “Austerity” Failed in Greece: Testing the Validity of Macro-Economic Models  [PDF]
Frederick Betz, Elias Carayannis
Modern Economy (ME) , 2015, DOI: 10.4236/me.2015.66063
Abstract: During the Euro Crisis which began in 2009 and is still continuing in 2015, Greece provided an interesting case of an empirical test of some macro-economic theories—particularly the theory underpinning the European Union (EU) policy of “austerity”. Fiscal austerity had been imposed upon the Greek governments as the price of EU bailout of bankrupt Greece. But after five years, the EU austerity policy was judged by many as a failure, and Greece continued to struggle at the bottom of a depression. Underlying the austerity policies, there was a macro-economic model called the Polak model. We examine whether or not this model was valid in the Greek economic context. Identifying the conceptual model underlying economic policy is important to clarify the validity or the invalidity of the model assumptions upon which a policy rests. We compare the macro-economic Polak model to an alternative model of the Greek fiscal crisis as “disequilibrium-pricing” in financial markets. An empirically invalid model can suggest bad policy, which may not solve an economic problem but can even deepen a crisis. An empirically valid model can provide a realistic basis for formulating effective policy.
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