Much of scientific inference involves fitting numerical data with a curve, or functional relation. The received view is that the fittest curve is the curve which best balances the conflicting demands of simplicity and accuracy, where simplicity is measured by the number ofparameters in the curve. The problem with this view is that there is no commonly accepted justification for desiring simplicity. This paper presents a measure of the stability of equations. It is argued that (...) the fittest curve is the curve which best balances stability and accuracy. The received view is defended with a proof that simplicity corresponds to stability, for linear regression equations. 1This paper is based on part of my doctoral dissertation. My thanks go to my thesis supervisor Professor Alasdair Urquhart for his encouragement, constructive criticism, and for directing me to several relevant articles: to my advisor Professor Ian Hacking for reminding me to concentrate on results that might have some application in the real world; and to my friend Wendy Brandts for sharing her ideas on a closely related problem. My thanks also to an anonymous referee of The British Journal of the Philosophy of Science for several helpful comments, to my friends and family for unfailing support, and to the Social Sciences and Humanities Research Council (awards 452-86-5885 and 453-87-0513) and the University of Toronto for financial assistance. (shrink)

Much of scientific inference involves fitting numerical data with a curve, or functional relation. The received view is that the fittest curve is the curve which best balances the conflicting demands of simplicity and accuracy, where simplicity is measured by the number ofparameters in the curve. The problem with this view is that there is no commonly accepted justification for desiring simplicity.This paper presents a measure of the stability of equations. It is argued that the (...) fittest curve is the curve which best balances stability and accuracy. The received view is defended with a proof that simplicity corresponds to stability, for linear regression equations. (shrink)

A modal accessibility relation is just a transition relation, and so can be represented by a {0, 1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in terms of transformations on Boolean vector spaces. The resulting theory is a curious hybrid, fitting between conventional modal semantics (...) and conventional linear algebra. I don’t know where the investigations begun here will ultimately wind up, but in the meantime the approach has a kind of curious charm that others may find appealing. (shrink)

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework.

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. Further, it is often claimed that the Bayesian framework automatically implements Occam's razor—that conditionalizing on data consistent with both a simple theory and a complex theory more or less inevitably favours the simpler theory. But it is shown here that there are simplicity-driven approaches to curve-fitting (...) problems that cannot be captured within the orthodox Bayesian framework and that the automatic razor does not function for such problems. (shrink)

Expiratory flow limitation (EFL) can occur in mechanically ventilated patients with chronic obstructive pulmonary disease and other disorders. It leads to dynamic hyperinflation with ensuing deleterious consequences. Detecting EFL is thus clinically relevant. Easily applicable methods however lack this detection being routinely made in intensive care. Using a simple mathematical model, we propose a new method to detect EFL that does not require any intervention or modification of the ongoing therapeutic. The model consists in a monoalveolar representation of the respiratory (...) system, including a collapsible airway that is submitted to periodic changes in pressure at the airway opening: EFL provokes a sharp expiratory increase in the resistance Rc of the collapsible airway. The model parameters were identified via the Levenberg-Marquardt method by fitting simulated data on the airway pressure and the flow signals recorded in 10 mechanically ventilated patients. A sensitivity study demonstrated that only 8/11 parameters needed to be identified, the remaining three being given reasonable physiological values. Flow-volume curves built at different levels of positive expiratory pressure, PEEP, during PEEP trials (stepwise increases in positive end-expiratory pressure to optimize ventilator settings) have shown evidence of EFL in three cases. This was concordant with parameter identification (high Rc during expiration for EFL patients). We conclude from these preliminary results that our model is a potential tool for the non-invasive detection of EFL in mechanically ventilated patients. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose (...) the relationship between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that (...) AIC approach has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)

Model simplicity in curve fitting is the fewness of parameters estimated. I use a vector model of least squares estimation to show that degrees of freedom, the difference between the number of observed parameters fit by the model and the number of explanatory parameters estimated, are the number of potential dimensions in which data are free to differ from a model and indicate the disconfirmability of the model. Though often thought to control for parameter estimation, the AIC and (...) similar indices do not do so for all model applications, while goodness of fit indices like chi-square, which explicitly take into account degrees of freedom, do. Hypothesis testing with prespecified values for parameters is based on a metaphoric regulative subject/object schema taken from object perception and has as its goal the accumulation of objective knowledge. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose (...) the relationship between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose (...) the relationship between simplicity of a theory and its predictive accuracy. (shrink)

The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the (...) problem. Using goodness-of-fit as the primary criterion for ‘best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. ‡I am grateful to Deborah Mayo and Clark Glymour for many valuable suggestions and comments on an earlier draft of the paper; estimating the Ptolemaic model was the result of Glymour's prompting and encouragement. †To contact the author, please write to: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

The aim of this study was to examine whether the relationship between the ratio of job-related positive to negative emotions and job burnout is best described as linear or curvilinear. Participants were 89 police officers and 86 firefighters. The positivity ratio was evaluated using the Job-related Affective Wellbeing Scale. Exhaustion and disengagement, two components of job burnout, were measured using the Oldenburg Burnout Inventory. The results of regression analysis revealed that curvilinear relationships between the positivity ratio and two components (...) of job burnout appeared to better fit the data than linear relationships. The relationship between the positivity ratio and exhaustion was curvilinear with a curve point at around 2.1. A similar curvilinear relationship, but with a lower curve point, i.e., around 1.8, was observed for disengagement. It seems that beyond certain values there may be hidden costs of maintaining positive emotions at work. Also, the unequal curve points for subscales suggest that different dimensions of work-related functioning are variously prone to such costs. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

The philosophical significance of the procedure of applying Akaike Information Criterion (AIC) to curve-fitting problems is evaluated. The theoretical justification for using AIC (the so-called Akaike's theorem) is presented in a rigorous way, and its range of validity is assessed by presenting both instances in which it is valid and counter-examples in which it is invalid. The philosophical relevance of the justification that this result gives for making one particular choice between simple and complicated hypotheses is emphasized. In (...) addition, recent claims that the methods based on Akaike's theorem are relevant to other philosophical problems associated with the notion of simplicity are presented and evaluated. (shrink)

The developing body of empirical work on the "Gettier effect" indicates that, in general, the presence of a Gettier-type structure in a case makes participants less likely to attribute knowledge in that case. But is that a sufficient reason to diverge from a JTB theory of knowledge? I argue that considerations of good model selection, and worries about noise and overfitting, should lead us to consider that a live, open question. The Gettier effect is perhaps so transient, and so sensitive (...) to other, epistemologically-inappropriate factors, that it raises the question of whether it ought to be counted as something to include in our theories -- or as a piece of noise to be excluded from them. (shrink)

The number of adjustable parameters in a model or hypothesis is often taken as the formal expression of its simplicity. I take issue with this `definition´ and argue that comparative simplicity has a quasi-empirical measure, reflecting experts’ judgements who track past use of a model-type in or across domains. Since models are represented by restricted sets of functions in a suitable space, formally speaking, a general `measure of simplicity´ may be defined implicitly for the elements of a function space. This (...) paper sketches such a framework starting from intuitive constraints. It is shown how experts’ judgements feed into this framework and how the usual definition can be recovered. A theorem by H. Akaike in the theory of model-choice has recently been used to shine new light on the relationship between the demand for simplicity and empirical success, or even `truth´. The approach favored here permits an alternative answer based on a reliabilist account of justification: if judgements of simplicity track past successful use of a model-type comparative simplicity is evidential and inductive. (shrink)

Curve-fitting typically works by trading off goodness-of-fit with simplicity, where simplicity is measured by the number of adjustable parameters. However, such methods cannot be applied in an unrestricted way. I discuss one such correction, and explain why the exception arises. The same kind of probabilistic explanation offers a surprising resolution to a common-sense dilemma.

This paper is a response to Forster and Sober's [1994] solution to the curve-fitting problem. If their solution is correct, it will provide us with a solution to the New Riddle of Induction as well as provide a basis for choosing realism over conventionalism. Examining this solution is also important as Forster and Sober incorporate it in much of their other philosophical work (see Forster [1995a, b, 1994] and Sober [1996, 1995, 1993]). I argue that Forster and Sober's (...) solution is subject precisely to the problem they seek to solve. They provide a method of choosing among hypotheses but only at the cost of requiring that we have a method of choosing between different ways of conceptualizing the world. Thus the solution raises a new problem--the world-fitting problem. (shrink)

Forster and Sober present a solution to the curve-fitting problem based on Akaike's Theorem. Their analysis shows that the curve with the best epistemic credentials need not always be the curve that most closely fits the data. However, their solution does not, without further argument, avoid the two difficulties that are traditionally associated with the curve-fitting problem: that there are infinitely many equally good candidate-curves relative to any given set of data, and that these (...) best candidates include curves with indefinitely many bumps. (shrink)

A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are usually represented as vertices, while their bonding or interaction is shown by edges in a molecular graph. In this paper, we computed various connectivity indices based on degrees of vertices of a chemical graph of indium phosphide. Afterward, we found the physical measures like entropy and heat of formation of InP. Then, we fitted curves between different indices and the thermodynamical properties, namely, heat (...) of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and nonlinearity. Furthermore, we depicted our results numerically and graphically. These numerical systems may give an approach to concentrate on the thermodynamical properties of the compound design of InP at an exceptional level that will help understand the connection between framework measurement and these actions. (shrink)

We present a formal derivation of the Mino–Sasaki–Tanaka–Quinn–Wald (MSTQW) equation describing the self-force on a (semi-) classical relativistic point mass moving under the influence of quantized linear metric perturbations on a curved background space–time. The curvature of the space–time implies that the dynamics of the particle and the field is history-dependent and as such requires a non-equilibrium formalism to ensure the consistent evolution of both particle and field, viz., the worldline influence functional and the closed- time-path (CTP) coarse-grained effective (...) action. In the spirit of effective field theory, we regularize the formally divergent self-force by smearing the local part of the retarded Green’s function and employing a quasi-local expansion. We derive the MSTQW–Langevin equations describing the perturbations of the particle’s worldline about its semi-classical trajectory resulting from interactions with the quantum fluctuations of the linear metric perturbations. Finally, we demonstrate that the quantum fluctuations of the field could, in principle, leave imprints on gravitational waveforms expected to be observed by gravitational interferometers, thereby encoding information about tree-level perturbative quantum gravity. (shrink)

Temporal justification logic is a new family of temporal logics of knowledge in which the knowledge of agents is modelled using a justification logic. In this paper, we present various temporal justification logics involving both past and future time modalities. We combine Artemov’s logic of proofs with linear temporal logic with past, and we also investigate several principles describing the interaction of justification and time. We present two kinds of semantics for our temporal justification logics, one based on interpreted (...) systems and Fitting models and the other based on Mkrtychev models, and further, we establish soundness and completeness. We show that the internalization property holds in some of the temporal justification logics. We further investigate the two well-known epistemic-temporal notions of no forgetting and no learning in the framework of justification logics. Finally, we present temporal justification logics that avoid the logical omniscience problem. (shrink)

The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties can easily be transferred into (...) a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space. (shrink)

Can green growth policies help protect the environment while keeping the industry growing and infrastructure expanding? The City of Kitakyushu, Japan, has actively implemented eco-friendly policies since 1967 and recently inspired the pursuit of sustainable development around the world, especially in the Global South region. However, empirical studies on the effects of green growth policies are still lacking. This study explores the relationship between road infrastructure development and average industrial firm size with air pollution in the city through the Environmental (...) Kuznets Curve (EKC) hypothesis. Auto-Regressive Distributed Lag (ARDL) and Non-linear Auto-Regressive Distributed Lag (NARDL) methods were applied on nearly 50-years’ time series data, from 1967 to 2015. The results show that the shape of the EKC of industrial growth, measured by average firm size, depends on the type of air pollution: inverted N-shaped relationships with NO2 and CO, and the U-shaped relationships with falling dust particle and Ox. Regarding infrastructure development, on the one hand, our analysis shows a positive effect of road construction on alleviating the amount of falling dust and CO concentration. On the other hand, the emissions of NO2 and Ox are shown to rise when plotted against road construction. The decline of CO emission, when plotted against both industrial growth and road development, indicates that the ruthlessness of the local government in pursuing green growth policies is effective in this case. However, the story is not straightforward when it comes to other air pollutants, which hint at limits in the current policies. The case of Kitakyushu illustrates the complex dynamics of the interaction among policy, industry, infrastructure, and air pollution. It can serve as an important reference point for other cities in the Global South when policies are formed, and progress is measured in the pursuit of a green economy. Finally, as an OECD SDGs pilot city and the leading Asian green-growth city, policymakers in Kitakyushu city are recommended to revise the data policy to enhance the findability and interoperability of data as well as to invest in the application of big data. (shrink)

Our proposal is concerned with the relation between an aspect of phonology (linearization) and syntax.1 In the picture that we had in mind, the syntax is autonomous — "it does what it does" — but sometimes the result maps to an unusable phonological representation. In this sense, linearization acts logically as a filter on derivations. We know of no evidence that the syntax can predict which syntactic objects will be usable by the phonology, and we know of no clear evidence (...) that the phonology communicates this information to the syntax. In this sense, our proposal fits squarely into the tradition that Svenonius characterizes as the "mainstream".2 We thus attempted to identify certain deviant configurations that are not plausibly excluded for syntax-internal reasons, but are filtered out in the linearization process. (shrink)

We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted (...) as the operations on games introduced for entirely different purposes by Blass . We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Gödel's Dialectica interpretation , which was connected to linear logic by de Paiva , fits with game semantics. (shrink)

This article provides an overview of recent results on lexicographic, linear, and Bayesian models for paired comparison from a cognitive psychology perspective. Within each class, we distinguish subclasses according to the computational complexity required for parameter setting. We identify the optimal model in each class, where optimality is defined with respect to performance when fitting known data. Although not optimal when fitting data, simple models can be astonishingly accurate when generalizing to new data. A simple heuristic belonging (...) to the class of lexicographic models is Take The Best (Gigerenzer & Goldstein (1996) Psychol. Rev. 102: 684). It is more robust than other lexicographic strategies which use complex procedures to establish a cue hierarchy. In fact, it is robust due to its simplicity, not despite it. Similarly, Take The Best looks up only a fraction of the information that linear and Bayesian models require; yet it achieves performance comparable to that of models which integrate information. Due to its simplicity, frugality, and accuracy, Take The Best is a plausible candidate for a psychological model in the tradition of bounded rationality. We review empirical evidence showing the descriptive validity of fast and frugal heuristics. (shrink)

Linear regression and its variants have been widely used for classification problems. However, they usually predefine a strict binary label matrix which has no freedom to fit the samples. In addition, they cannot deal with complex real-world applications such as the case of face recognition where samples may not be linearly separable owing to varying poses, expressions, and illumination conditions. Therefore, in this paper, we propose the kernel negative ε dragging linear regression method for robust classification on noised (...) and nonlinear data. First, a technique called negative ε dragging is introduced for relaxing class labels and is integrated into the LR model for classification to properly treat the class margin of conventional linear regressions for obtaining robust result. Then, the data is implicitly mapped into a high dimensional kernel space by using the nonlinear mapping determined by a kernel function to make the data more linearly separable. Finally, our obtained KNDLR method is able to partially alleviate the problem of overfitting and can perform classification well for noised and deformable data. Experimental results show that the KNDLR classification algorithm obtains greater generalization performance and leads to better robust classification decision. (shrink)

Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett (...) and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them, regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers. (shrink)

Corradi's book is a detailed account of modernization in Argentina. There has been considerable urbanization and industrialization. There is a highly organized work force and a large educated middle class. Yet, Argentina is not all that different from other Latin American countries, and remains a peripheral capitalist society characterized by “dependency, stagnation, political decay and violence” (p. 2). Although Corradi does not indulge in theoretical debates, his insistence on the analysis of the conscious subjects who have made Argentinian history challanges (...) all linear theories of development, including Wallerstein's world system perspective since it assumes a mechanical hierarchy of economic growth in different regions of the world. (shrink)

Growth modelling is of interest to scientists in various disciplines. In our article, we will collect 17 models designed for growth modelling, appraise these models and contribute to the discussion of their applicability. The merit of the paper lies in studying the convergence properties of nonlinear regression in selected models. Our studies will be performed mainly concerning the quality of the obtained estimates, which are closely related to the intrinsic curvature of the model according to Bates and Watts. This curvature (...) determines the size of the linearization domains. Only if the initial solution is in this domain, then the convergence of the estimate in nonlinear regression is guaranteed. The primary goal is to design a methodology for selecting a growth model. We will demonstrate fruitfulness of our methodology on the weight measurements of 10 calves under 25 months of age from cowsheds in the village Záluží in the Czech Republic. Estimated parameters of growth curves, sizes of linearization domain, calculated residues and coefficients of determination indices will be the subject of discussion. (shrink)

We give the precise correspondence between polarized linear logic and polarized classical logic. The properties of focalization and reversion of linear proofs are at the heart of our analysis: we show that the tq-protocol of normalization for the classical systems and perfectly fits normalization of polarized proof-nets. Some more semantical considerations allow us to recover LC as a refinement of multiplicative.

Harmonic Grammar (HG) is a model of linguistic constraint interaction in which well-formedness is calculated as the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the HG framework and comparing the results with those of OT. We describe (...) the translation from Harmonic Grammars to systems solvable by linear programming, and we illustrate the usefulness of OT-Help with a set of studies of the predictions HG makes for phonological typology. (shrink)

Over the past three decades, the discourse on the mechanistic approach to scientific modelling and explanation has notably sidestepped the topic of simplicity and fit within the process of model selection. This paper aims to rectify this disconnect by delving into the topic of simplicity and fit within the context of mechanistic explanations. More precisely, our primary objective is to address whether simplicity metrics hold any significance within mechanistic explanations. If they do, then our inquiry extends to the suitability of (...) the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and related criteria in determining the optimal balance of fit and simplicity of mechanistic models. As our main claims, we argue that mechanistic models inherently lend themselves to considerations of simplicity, and that the AIC and BIC and related criteria are applicable to some submodels of certain kinds of mechanistic models. However, these criteria and related criteria designed for curve fitting and causal modelling are of little help for a comparative assessment of full mechanistic models, and a fundamentally different approach is needed to make determinations of this kind. (shrink)

The hypothesis that excessive early infant crying evolved to reduce the risk of withdrawal of parental care is disputed on the grounds that excessive infant crying is irritating and imposes fitness losses rather than gains. Alternative explanations for the early crying curve that take into account development on the part of the infant and the emerging infant-caregiver bond are proposed.

BackgroundSubjective wellbeing is a research topic of growing interest for different disciplines. Based on a cross-sectional survey with 1,597 participants aged 12–94, this study investigated life satisfaction and momentary happiness, two important dimensions of SWB. We examined their relationship, shape, and correlates across individuals of different ages and interpreted the results in the light of a neurobiological model of motivation systems.MethodsStatistical analyses were performed using multiple linear regression. First, we examined how life satisfaction is associated with selected socio-demographic variables (...) across four age groups. Second, we analyzed the association between life satisfaction and age, and lastly, we examined the extent to which happiness is a prerequisite for life satisfaction in each age group.ResultsOur analyses show that life satisfaction correlates negatively with poor health and financial worries, and positively with partnership, grandchildren, and religiosity. However, the inverse relationship with poor health is stronger in younger than in older individuals, while the inverse association with financial worries is strongest in late midlife. We identified gender-specific differences concerning the relationship between life satisfaction and age, with males displaying a U-shape trend with its lowest point between the ages of 30 and 49, whereas females’ life satisfaction increases stepwise with age. Although momentary happiness correlates strongly with life satisfaction, this relationship decreases with age.ConclusionThe results suggest that individuals adjust or even grow beyond their perceptions of a “good life” over time. Neurobiological processes of adaptation and personal growth could play an important role in these developments. (shrink)

The parameters governing our behavior are in constant flux. Accurately capturing these dynamics in cognitive models poses a challenge to modelers. Here, we demonstrate a mapping of ACT-R's declarative memory onto the linear ballistic accumulator (LBA), a mathematical model describing a competition between evidence accumulation processes. We show that this mapping provides a method for inferring individual ACT-R parameters without requiring the modeler to build and fit an entire ACT-R model. Existing parameter estimation methods for the LBA can be (...) used, instead of the computationally expensive parameter sweeps that are traditionally done. We conduct a parameter recovery study to confirm that the LBA can recover ACT-R parameters from simulated data. Then, as a proof of concept, we use the LBA to estimate ACT-R parameters from an empirical dataset. The resulting parameter estimates provide a cognitively meaningful explanation for observed differences in behavior over time and between individuals. In addition, we find that the mapping between ACT-R and LBA lends a more concrete interpretation to ACT-R's latency factor parameter, namely as a measure of response caution. This work contributes to a growing movement towards integrating formal modeling approaches in cognitive science. (shrink)

This paper introduce a new variant of the Genetic Algorithm whichis developed to handle multivariable, multi-objective and very high search space optimization problems like the solving system of non-linear equations. It is an integer coded Genetic Algorithm with conventional cross over and mutation but with Inverse algorithm is varying its search space by varying its digit length on every cycle and it does a fine search followed by a coarse search. And its solution to the optimization problem will converge (...) to precise value over the cycles. Every equation of the system is considered as a single minimization objective function. Multiple objectives are converted to a single fitness function by summing their absolute values. Some difficult test functions for optimization and applications are used to evaluate this algorithm. The results prove that this algorithm is capable to produce promising and precise results. (shrink)

Self-efficacy is an important predictor of learning and achievement. By definition, self-efficacy requires a task-specific assessment, in which students are asked to evaluate whether they can solve concrete tasks. An underlying assumption in previous research into such assessments was that self-efficacy is a one-dimensional construct. However, empirical evidence for this assumption is lacking, and research on students’ performance suggests that it depends on various task characteristics. The present study explores the potential multi-dimensionality of self-efficacy in the topic of linear (...) functions. More specifically, we investigate how three task characteristics – the representational format, embedding in a real-life context, or the required operation – are related to students’ self-efficacy. We asked 8th and 9th graders to evaluate their self-efficacy on specific linear function tasks which systematically varied along the three dimensions of task characteristics. Using confirmatory factor analysis, we found that a two-dimensional model which includes the task characteristic of real-life context fitted the data better than other two-dimensional models or a one-dimensional model. These results suggest that self-efficacy with linear functions is empirically separable with respect to tasks with vs. without a real-life context. This means that in their self-evaluation of linear function tasks students particularly rely on whether or not the linear function task is embedded in a real-life context. This study highlights the fact that even within a specific content domain students’ self-efficacy can be considered a multi-dimensional construct. (shrink)