In this article, we offer a detailed study of two important episodes in the early history of high-energy physics, namely the development of the Chew and the Nambu-Jona-Lasinio models. Our study reveals that both models resulted from the combination of an old Hamiltonian, which had been introduced by earlier researchers, and two new approximation methods developed by Chew and by Nambu and Jona-Lasinio. These new approximation methods, furthermore, were the key component behind the models’ success. We take this historical investigation (...) to support two philosophical theses about the manner in which scientific modelling operates in high-energy physics. Both of these theses run counter to a view that is commonly accepted among philosophers of science: the view that all approximations can be embedded within an equivalent idealized system, and that whatever role the former might play in scientific modelling is therefore parasitic on the much more substantial work performed by the latter. Our first thesis, which we call “Distinctness,” states that approximation methods constitute an independent category of theoretical output from idealized systems. We thus believe that approximations and idealized systems constitute two independent types of objects, both of which are essential to the practice of modelling. Our second, more radical thesis is called “Content Determination.” Our claim here is that approximation methods can in fact be essential to assigning determinate physical content to the idealized systems with which they jointly operate. As we show, this is due to the fact that quantum field theory allows for a very thin characterization of idealized systems only, making the use of approximations necessary to supply additional content. We conclude the paper with a few reflections about the manner in which our two theses can be used to articulate David Kaiser’s views on the “vanishing of scientific theory” in physics after WWII. (shrink)

Machine learning (ML) models are increasingly discussed in the philosophy of science in terms of idealization and even by analogy with toy models. I argue that this framing conflates idealization with approximation. Once the relevant ML target is specified as relations among features represented in data---relative to a target system---the claim that ML models are dissimilar to their targets becomes too coarse. Scientific ML models can and often must be approximately similar to their targets in the relevant respects. Approximation failure (...) therefore provides the more direct standard of assessment, and ML models do not function as toy models. (shrink)

The qualitative theory of nomic truth approximation, presented in Kuipers in his (from instrumentalism to constructive realism, 2000), in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption, viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. Fully recognizing two different functions of theories, viz. excluding and representing, this paper drops this assumption by conceiving theories in development as tuples of postulates and models, where the (...) postulates claim to exclude nomic impossibilities and the (not-excluded) models claim to represent nomic possibilities. Revising theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress in this way provides good reasons for the abductive conclusion that truth approximation has been achieved as well. Here, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted and decreased rejected content in the light of increasing evidence. These definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” (Cevolani et al. in Erkenntnis 75(2):183–222, 2011). (shrink)

In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is (...) then made in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it. (shrink)

This paper develops new closed form normal approximations for the ergodic distribution of a renewal–reward process $X(t)$ describing a semi-Markovian inventory model of type $(s, S)$. When demand sizes follow a Weibull distribution with shape parameter $\alpha \ge 3$, the renewal function can be well approximated by that of a normal distribution, as shown by Cui and Xie. We use this observation to derive a new numerical method for computing the ergodic distribution $Q_{X}(x)$ of the process $X(t)$. The resulting (...) formulas are easy to evaluate and avoid repeated numerical computation of the Weibull renewal function. Numerical examples show that the approximations are accurate over a wide range of parameter values and that, as the replenishment threshold increases, the ergodic distribution of the inventory level approaches a uniform distribution. (shrink)

We outline fresh findings that show that our macroscopic electrocorticographic (ECoG) simulations can account for synchronous multiunit pulse oscillations at separate, simultaneously activated cortical sites and the associated gamma-band ECoG activity. We clarify our views on the approximations of dynamic class applicable to neural events at macroscopic and microscopic scales, and the analogies drawn to classes of ANN behaviour. We accept the need to introduce memory processes and detailed anatomical and physiological information into any future developments of our simulations. On (...) the issue of intrinsic cortical stability and the role of extrinsic fibre systems in maintaining stability, we argue that this position is not in extreme contradiction to those of our commentators, and that the mechanisms implicit in our simulations' properties imply rich computational possibilities. We discuss some of the reasons for and against the existence of significant global resonances in the brain and explain why such behaviour appears absent in our simulations. Last, we discuss other phenomena, such as rhythmic driving of the cortex, which have not yet been introduced into our models, and indicate lines for future development of the simulations. (shrink)

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented, in my article entitled “Models, postulates, and generalized nomic truth approximation” :3057–3077, 2016. 10.1007/s11229-015-0916-9), the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (...) the traditional view: theories are postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and the model view: theories are sets of models that claim to represent certain realizable possibilities. Nomic truth approximation, i.e. increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence. The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, it does not take into account that one conceptual possibility may be more similar to another than a third one. However, for example, one theory may include a possibility that is more similar to a wrongly not included possibility than another theory can offer. Similarly, for wrongly not excluded possibilities. In this article it will be shown that such ‘refined’ considerations can be taken into account by adapted clauses based on a ternary similarity relation between possibilities. This allows again abductive conclusions about refined truth approximation if a theory is persistently more successful in the refined sense than another. It will also be indicated and illustrated that this refined approach enables a specification to the effect that refined truth approximation can be obtained by the method of idealization and subsequent concretization. Finally, the basic and the refined approach will be evaluated with regard to some general principles and objections that have been discussed in the literature. (shrink)

Approximations have come to occupy a central role within Bayesian cognitive science. Many cognitive scientists view current approximation-based models as showing that the mind approximates Bayesian inference. In this paper I interrogate this idea, asking what it means to claim that the mind approximates one computation by executing another. I look at three possible interpretations of such claims, finding problems with each. I argue that this poses challenges to one central rationale for the Bayesian approach, and to its top-down methodology.

Approximations form an essential part of scientific activity and they come in different forms: conceptual approximations (simplifications in models), mathematical approximations of various types (e.g. linear equations instead of non-linear ones, computational approximations), experimental approximations due to limitations of the instruments and so on and so forth. In this paper, we will consider one type of approximation, namely numerical approximations involved in the comparison of two results, be they experimental or theoretical. Our goal is to lay down the conceptual and (...) formal foundations of a local theory of partial truth. This is done by introducing and exploring the concept of truth space. (shrink)

In this note, I apply Norton’s (Philos Sci 79(2):207–232, 2012) distinction between idealizations and approximations to argue that the epistemic and inferential advantages often taken to accrue to minimal models (Batterman in Br J Philos Sci 53:21–38, 2002) could apply equally to approximations, including “infinite” ones for which there is no consistent model. This shows that the strategy of capturing essential features through minimality extends beyond models, even though the techniques for justifying this extended strategy remain similar. As an (...) application I consider the justification and advantages of the approximation of a inertial reference frame in Norton’s dome scenario (Philos Sci 75(5):786–798, 2008), thereby answering a question raised by Laraudogoitia (Synthese 190(14):2925–2941, 2013). (shrink)

Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal model (...) offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction. (shrink)

The relevance of exchange effects for the stability of superheavy nuclei is examined within a linear QHD-II model by comparing Hartree-Fock with meanfield results. To allow a scan of the complete superheavy regime the recently developed local density approximation (LDA) for the exchange potential is employed for the Hartree-Fock level calculations. It turns out that, while many nuclear properties obtained with the LDA approach differ significantly from the corresponding mean-field results, the predictions of the two methods for shell closures (...) are very similar. Furthermore, a comparison with a nonlinear variant of QHD-II shows that many nuclear properties obtained with the LDA in the framework of linear QHD-II are somewhere in-between the corresponding linear and nonlinear mean-field results. This indicates that the LDA exchange partially includes nonlinear contributions, which supports the interpretation of the meson self-coupling as a parametrization of many-body effects. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

This paper, which is based on recent empirical research at the University of Leeds, the University of Edinburgh, and the University of Bristol, presents two difficulties which arise when condensed matter physicists interact with molecular biologists: the former use models which appear to be too coarse-grained, approximate and/or idealized to serve a useful scientific purpose to the latter; and the latter have a rather narrower view of what counts as an experiment, particularly when it comes to computer simulations, than (...) the former. It argues that these findings are related; that computer simulations are considered to be undeserving of experimental status, by molecular biologists, precisely because of the idealizations and approximations that they involve. The complexity of biological systems is a key factor. The paper concludes by critically examining whether the new research programme of ‘systems biology’ offers a genuine alternative to the modelling strategies used by physicists. It argues that it does not. (shrink)

In a supply chain system, the prices with which the suppliers supply its local commodity to the retailers should satisfy the requirements of the retailers and the consumers. The supply and demand scheme satisfying these requirements is reduced into fuzzy relation inequalities with min-product composition. Due to the difference between the min-product composition and the classical max-t-norm one, we first study the resolution of such min-product FRI system. For optimization management in the supply chain system, we further investigate a maximin (...) programming problem subject to the min-product FRIs. An algorithm is proposed to obtain the optimal solution based on the quasi-maximal matrix and corresponding index set. To illustrate the efficiency of our proposed algorithm, we provide a simple numerical example. The obtained optimal solution reflects an optimal pricing scheme, which maximizes the minimum prices of the commodity from the suppliers. (shrink)

Exact solutions of epidemic models are critical for identifying the severity and mitigation possibility for epidemics. However, solving complex models can be difficult when interfering conditions from the real-world are incorporated into the models. In this paper, we focus on the generally unsolvable adaptive susceptible-infected-susceptible epidemic model, a typical example of a class of epidemic models that characterize the complex interplays between the virus spread and network structural evolution. We propose two methods based on mean-field approximation, i.e., the first-order (...) mean-field approximation and higher-order mean-field approximation, to derive the exact solutions to ASIS models. Both methods demonstrate the capability of accurately approximating the metastable-state statistics of the model, such as the infection fraction and network density, with low computational cost. These methods are potentially powerful tools in understanding, mitigating, and controlling disease outbreaks and infodemics. (shrink)

A single abstract from the DHd-2020 Book ofs.

Everybody knows the phenomena summarized with the term attention: concentration, focalization, limitation, selection, and intensification . The explanation of these phenomena is, however, a different matter. Problems easily arise with regard towhathas to be explained and with regard to thestyleof explanation. A problem of the first kind is the “methodology of ‘bad focus’”: the explanation starts with and is fixated on an intuitively striking but nonessential behavioral feature or cognitive achievement. A problem of the second kind is a “virtus dormitiva” (...) explanation: the explanation starts with emphasizing one aspect of the observed phenomena, the emphasized aspect receives an interesting and suggestive name, and that name with its connotations is used as a concept in the explanation. At the start of contemporary, behavior-based, information processing psychology, avirtus dormitivaexplanation infiltrated the functional accounts of the phenomena of attention; the empirical observation that people show performance limitations was translated into the theoretical concept of a communication channel with a limited capacity. That limited capacity notion became the core concept in what can be called the standard theory of attention. This standard theory of attention faced severe difficulties in explaining the guidance of attention by the information processor's goals and intentions. Subsequent modifications, concerned with removing these difficulties, revealed that selection, guided by goals and intentions, is the essential behavioral feature and that the observed performance limitations are a result of this selection. So, the limited capacity theorizing was not only plagued by avirtus dormitivaexplanation, it also suffered from the methodology of bad focus. (shrink)

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a (...) four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold. (shrink)

De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also established.

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory [math] of [E. Jeřábek, Approximate counting by hashing in bounded arithmetic, J. Symb. Log. 74(3) (2009) 829–860]. In particular, the Ramsey and weak pigeonhole search problems lie in the new class. We give (...) a purely computational characterization of this class and show that, relative to an oracle, it does not contain the problem CPLS, a strengthening of PLS. As CPLS is provably total in the theory [math], this shows that [math] does not prove every [math] sentence which is provable in bounded arithmetic. This answers the question posed in [S. Buss, L. A. Kołodziejczyk and N. Thapen, Fragments of approximate counting, J. Symb. Log. 79(2) (2014) 496–525] and represents some progress in the program of separating the levels of the bounded arithmetic hierarchy by low-complexity sentences. Our main technical tool is an extension of the “fixing lemma” from [P. Pudlák and N. Thapen, Random resolution refutations, Comput. Complexity, 28(2) (2019) 185–239], a form of switching lemma, which we use to show that a random partial oracle from a certain distribution will, with high probability, determine an entire computation of a [math] oracle machine. The introduction to the paper is intended to make the statements and context of the results accessible to someone unfamiliar with NP search problems or with bounded arithmetic. (shrink)

Given a rough definably amenable rough approximate subgroup A of a group in some first-order structure there is a type-definable subgroup N normalized by A and contained in A4 of bounded index in the subgroup ⟨A⟩ generated by A.

Let G be a group with a metric invariant under left and right translations, and let ?r be the ball of radius r around the identity. A (k,r)-metric approximate subgroup is a symmetric subset X of G...

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales are very (...) different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one. (shrink)

This paper addresses a common challenge with computational cognitive models: identifying parameter values that are both theoretically plausible and generate predictions that match well with empirical data. While computational models can offer deep explanations of cognition, they are computationally complex and often out of reach of traditional parameter fitting methods. Weak methodology may lead to premature rejection of valid models or to acceptance of models that might otherwise be falsified. Mathematically robust fitting methods are, therefore, essential to the progress of (...) computational modeling in cognitive science. In this article, we investigate the capability and role of modern fitting methods—including Bayesian optimization and approximate Bayesian computation—and contrast them to some more commonly used methods: grid search and Nelder–Mead optimization. Our investigation consists of a reanalysis of the fitting of two previous computational models: an Adaptive Control of Thought—Rational model of skill acquisition and a computational rationality model of visual search. The results contrast the efficiency and informativeness of the methods. A key advantage of the Bayesian methods is the ability to estimate the uncertainty of fitted parameter values. We conclude that approximate Bayesian computation is (a) efficient, (b) informative, and (c) offers a path to reproducible results. (shrink)

We explore approximate categoricity in the context of distortion systems, introduced in our previous paper (Hanson in Math Logic Q 69(4):482–507, 2023), which are a mild generalization of perturbation systems, introduced by Yaacov (J Math Logic 08(02):225–249, 2008). We extend Ben Yaacov’s Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley’s theorem for inseparable approximate categoricity, showing that if there (...) is some uncountable cardinal $$\kappa $$ such that every model of size $$\kappa $$ is ‘approximately saturated,’ in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity. (shrink)

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and possibly new (...) generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix''. (shrink)

We explore approximate categoricity in the context of distortion systems, introduced in our previous paper (Hanson in Math Logic Q 69(4):482–507, 2023), which are a mild generalization of perturbation systems, introduced by Yaacov (J Math Logic 08(02):225–249, 2008). We extend Ben Yaacov’s Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley’s theorem for inseparable approximate categoricity, showing that if there (...) is some uncountable cardinal $$\kappa $$ such that every model of size $$\kappa $$ is ‘approximately saturated,’ in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity. (shrink)

What is the relation between what is good for you and how well you are doing? It is common and natural to think that the latter asymmetrically depends upon the former. I call this the molecular model of well-being, which holds that how well you are doing depends directly upon the presence of independently specifiable welfare goods in your life. Just about every contemporary theory of well-being embodies the form specified by the molecular model. Here I articulate and (...) defend an alternative way to think about well-being, a way based upon the notion of approximation. According to the approximation model of well-being, how well you are doing directly instead depends upon how closely you resemble an ideal way to live. One person is doing better than another just in case the life of the first more closely approximates the ideal life. To make this case I briefly sketch a substantive theory of well-being that employs it: what I take to be Aristotle’s view of well-being, which works as a proof of concept. We see that the approximation model of well-being can explain some patterns of value better than the molecular model can. (shrink)

In this paper we start from the assumption that in a metaphor, or an analogy, some terms belonging to one domain (source domain) are used to refer to objects other than their conventional referents belonging to a possibly different domain (target domain). We describe a formalism, which is based on the First Order Predicate Calculus, for representing the knowledge structure associated with a domain and then develop a theory of Constrained Semantic Transference [CST] which allows the terms and the structural (...) relationships of the source domain to be transferred coherently across to the target domain. We show how metaphors and analogies can be characterized in CST in such a way that many of their cognitive properties con be explained.We then propose a theory of Approximate Semantic Transference [AST] which is a computational version of CST and is derived from it by replacing the coherency requirement with approximate coherency. We show how AST can be used as a basis for designing models of cognitive processes involved in comprehending metaphors and analogies. (shrink)

A theory of approximation to measurable sets and measurable functions based on the concepts of recursion theory and discrete complexity theory is developed. The approximation method uses a model of oracle Turing machines, and so the computational complexity may be defined in a natural way. This complexity measure may be viewed as a formulation of the average-case complexity of real functions—in contrast to the more restrictive worst-case complexity. The relationship between these two complexity measures is further studied and compared (...) with the notion of the distribution-free probabilistic computation. The computational complexity of the Lebesgue integral of polynomial-time approximable functions is studied and related to the question “FP = ♯P?”. (shrink)

We study metric valued fields in continuous logic, following Ben Yaacov’s approach, thus working in the metric space given by the projective line. As our main result, we obtain an approximate Ax–Kochen–Ershov principle in this framework, completely describing elementary equivalence in equicharacteristic 0 in terms of the residue field and value group. Moreover, we show that, in any characteristic, the theory of metric valued difference fields does not admit a model-companion. This answers a question of Ben Yaacov.

An important assumption underlying meaningful comparisons of scores in rater-mediated assessments is that measurement is commensurate across raters. When raters differentially apply the standards established by an instrument, scores from different raters are on fundamentally different scales and no longer preserve a common meaning and basis for comparison. In this study, we developed a method to accommodate measurement noninvariance across raters when measurements are cross-classified within two distinct hierarchical units. We conceptualized random item effects cross-classified graded response models and used (...) random discrimination and threshold effects to test, calibrate, and account for measurement noninvariance among raters. By leveraging empirical estimates of rater-specific deviations in the discrimination and threshold parameters, the proposed method allows us to identify noninvariant items and empirically estimate and directly adjust for this noninvariance within a cross-classified framework. Within the context of teaching evaluations, the results of a case study suggested substantial noninvariance across raters and that establishing an approximately invariant scale through random item effects improves model fit and predictive validity. (shrink)

Everybody knows the phenomena summarized with the term attention: concentration, focalization, limitation, selection, and intensification. The explanation of these phenomena is, however, a different matter. Problems easily arise with regard towhathas to be explained and with regard to thestyleof explanation. A problem of the first kind is the “methodology of ‘bad focus’”: the explanation starts with and is fixated on an intuitively striking but nonessential behavioral feature or cognitive achievement. A problem of the second kind is a “virtus dormitiva” explanation: (...) the explanation starts with emphasizing one aspect of the observed phenomena, the emphasized aspect receives an interesting and suggestive name, and that name with its connotations is used as a concept in the explanation. At the start of contemporary, behavior-based, information processing psychology, avirtus dormitivaexplanation infiltrated the functional accounts of the phenomena of attention; the empirical observation that people show performance limitations was translated into the theoretical concept of a communication channel with a limited capacity. That limited capacity notion became the core concept in what can be called the standard theory of attention. This standard theory of attention faced severe difficulties in explaining the guidance of attention by the information processor's goals and intentions. Subsequent modifications, concerned with removing these difficulties, revealed that selection, guided by goals and intentions, is the essential behavioral feature and that the observed performance limitations are a result of this selection. So, the limited capacity theorizing was not only plagued by avirtus dormitivaexplanation, it also suffered from the methodology of bad focus. (shrink)

The standard theory for belief revision provides an elegant and powerful framework for reasoning about how a rational agent should change its beliefs when confronted with new information. However, the agents considered are extremely idealized. Some recent models attempt to tackle the problem of plausible belief revision by adding structure to the belief bases and using nonstandard inference operations. One of the key ideas is that not all of an agent's beliefs are relevant for an operation of belief change.In this (...) paper we incorporate the insights pertaining to local change and relevance sensitivity with the use of approximate inference relations. These approximate inference relations offer us partial solutions at any stage of the revision process. The quality of the approximations improves as we allow for more and more resources to be used. We are provided with upper and lower bounds to what would be obtained with the use of classical inference. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations (...) of pure magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

Whooping cough is a highly transmitted disease around the world. According to the World Health Organization, 0.15 million cases had reported globally in 2018. Most of the Asian and African states are infected regions. Through the study, we investigated the whole population into the four classes susceptible, exposed, infected, and vaccinated or recovered. The transmission dynamics of whooping cough disease are studied analytically and numerically. Analytical analyses are positivity, boundedness, reproduction number, equilibria, and local and global stabilities. In numerical analysis, (...) we developed an implicit numerical integration scheme consistent with the biological problem’s properties. The analysis of the implicit method for the said model is dynamically consistent, positive, and bounded. Furthermore, an implicit numerical integration scheme is suitable for studying a particular epidemic model such as the whooping cough disease. (shrink)