On the Exploratory Function of Agent-Based Modeling

Agent-based models (ABM) derive the behavior of artificial socio-economic entities computationally from the actions of a large number of agents. One objection is that highly idealized ABMs fail to represent the real world in any reasonable sense. Another objection is that they at best show how observed patterns may have come about, because simulations are easy to produce and there is no evidence that this is really what happens. Moreover, different models may well yield the same result. I will rebut these objections by focusing on an often neglected, but crucial function of ABMs. Building on Gelfert’s (2016) account of the exploratory uses of scientific models I show that, in the absence of an accepted underlying theory, successful ABMs lend inductive support to assumptions concerning certain structural feutures of the behavioral rules employed. One core step towards this goal is what I call multiple-model robustness analysis.

Ill-posedness of the Maxwell–Dirac system below charge in space dimension three and lower

The Maxwell–Dirac system describes the interaction of an electron with its self-induced electromagnetic field. In space dimension $$d=3$$ d = 3 the system is charge-critical, that is, $$L^2$$ L 2 -critical for the spinor with respect to scaling, and local well-posedness is known almost down to the critical regularity. In the charge-subcritical dimensions $$d=1,2$$ d = 1 , 2 , global well-posedness is known in the charge class. Here we prove that these results are sharp (or almost sharp, if $$d=3$$ d = 3 ), by demonstrating ill-posedness below the charge regularity. In fact, for $$d \le 3$$ d ≤ 3 we exhibit a spinor datum belonging to $$H^s(\mathbb {R}^d)$$ H s ( R d ) for $$s<0$$ s < 0 , and to $$L^p(\mathbb {R}^d)$$ L p ( R d ) for $$1 \le p < 2$$ 1 ≤ p < 2 , but not to $$L^2(\mathbb {R}^d)$$ L 2 ( R d ) , which does not admit any local solution that can be approximated by smooth solutions in a reasonable sense.

Why Dilated Convolutional Neural Networks: A Proof of Their Optimality

One of the most effective image processing techniques is the use of convolutional neural networks, where we combine intensity values at grid points in the vicinity of each point. To speed up computations, researchers have developed a dilated version of this technique, in which only some points are processed. It turns out that the most efficient case is when we select points from a sub-grid. In this paper, we explain this empirical efficiency proving that the sub-grid is indeed optimal – in some reasonable sense. To be more precise, we prove that all reasonable optimality criteria, the optimal subset of the original grid is either a sub-grid, or a sub-grid-like set.

Métodos para Avaliação Global de Risco em Saúde Ocupacional: sabemos o suficiente?

Introduction / background / objectives Risk assessment in the workplace is a fundamental step towards obtaining safer and healthier jobs. The Security Technicians are generally the most experienced in this context; however, not all the professionals that carry out Occupational Health activities present well-structured and/ or practical knowledge about most of these methods. The purpose of this review was to summarize the main techniques used in this context. Methodology This is a review, initiated through a survey conducted in April 2020, in the RCAAP database (Open Access Scientific Repositories in Portugal). Content The author made some practical considerations about MARAT (Methodology for Risk Assessment and Accidents at Work), William Fine, MIAR (Integrated Methodology for Risk Assessment) and FMEA (Failure Mode and Effect Analysis), valuing with explanatory tables and highlighted the slight discrepancies between the documents consulted. Conclusions The key-words used were related to the methods that the author briefly know; in the documents found, sometimes, other techniques have been included; this obviously implies a bias selection. We easily find articles in indexed databases that mention these methods, but due to the limits imposed by most journals, relating to the size of the document, almost all authors only mention the name of the method or, at most, use a very synthetic description of it. In turn, in some Master’s or Doctorate Theses (where this problem does not exist) we can find a more methodological description, but still, sometimes you cannot always get the practice knowledge of how to use all methods or if the items are slightly different, result of adaptations, consideration of different subtypes or a mixture of methods, carried out over the decades. Any professional on an Occupational Health Team will have a reasonable sense of what the most damaging tasks will be; however, presenting this evidence, attenuating subjectivity and making use of the hierarchy that mathematical scales can offer, it becomes more accepted as valid by employers/ representatives/ workers and, consequently, increase the receptivity to proposed measures to mitigate/ correct the problem and reassess it, after introducing corrective measures. It would be desirable for all professionals in the field to have (at least) a generic idea of ​​the existing methods and where they can seek more information, in order to execute these techniques, when necessary.

The Hegemony of the Reasonable Person in Anglo-American Tort Law

Tort law has increasingly employed the rubric of the reasonable person in a variety of doctrinal domains. Many jurisdictions have rejected a differentiation of landowner duties according to the status of the entrant as trespasser, licensee, or invitee, and substituted a “reasonable person” test. Assumption of risk has been eliminated or greatly narrowed in favor of comparative fault, which asks simply whether the plaintiff failed to act as a reasonable person. The reasonable person plays a significant role even in intentional torts: apparent consent precludes liability when the defendant reasonably (though mistakenly) believes that plaintiff consented; putative self-defense precludes liability when the defendant reasonably (though mistakenly) believes facts that would establish that privilege; and offensive battery requires that the contact be offensive to a “reasonable” sense of dignity. What explains this widespread use of “reasonable person” tests? A desire for simplicity? The normative appeal of such a standard? Normative modesty about adopting a more controversial standard or about specifying more detailed rules? A concern to empower juries? Inertia or lazy thinking? Are such tests mainly descriptive (of ordinary conduct) or mainly idealized and prescriptive? In answering these questions, this paper argues that the hegemony of the reasonable person is sometimes a welcome but often an unwelcome development.

Admissibility conditions for Riemann data in shallow water theory

Consideration is given to the shallow-water equations, a hyperbolic system modeling the propagation of long waves at the surface of an incompressible inviscible fluid of constant depth. It is well known that the solution of the Riemann problem associated to this system may feature dry states for some configurations of the Riemann data. This article will discuss various scenarios in which the Riemann problem for the shallow water system arises in a physically reasonable sense. In particular, it will be shown that if certain physical assumptions on the disposition of the Riemann data are made, then dry states can be avoided in the solution of the Riemann problem.

Noncommutative coverings of quantum tori

We investigate a framework for coverings of noncommutative spaces. Furthermore, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.

Now & Then: Community Planning through Data Analysis, John Graunt: The Founder of Statistics

Now… A NEW HOUSING DEVELOPMENT IS BEING BUILT ON THE outskirts of town. Is the closest elementary school large enough to accommodate the expected influx of new students? Members of local and regional planning commissions consider such questions and help communities adapt to growth and change. Andrew Singelakis is the head of the Regional Planning Commission in south-central New Hampshire. He uses mathematics to help towns and cities in his part of the state plan and evaluate community services, from bus routes and new schools to traffic lights and tollbooths. To help communities plan for the future, Andrew uses mathematics to analyze data from the past and present. He also relies on a reasonable sense of both current trends and human nature.

Unique factorization in the ring R[x]

If R is a commutative unique factorization domain (UFD) then so is the ring R[x]. If R is not commutative then no such result is possible. An example is given of a bounded principal right and left ideal domain R, hence a similarity-UFD, for which the polynomial ring R[x] in a central indeterminate x is not a UFD in any reasonable sense. On the other hand, it is shown that if R is an invariant UFD then R[x] is a UFD in an appropriate sense.