In teaching statistics in secondary schools and at university, two visualizations are primarily used when situations with two dichotomous characteristics are represented: 2×2 tables and tree diagrams. Both visualizations can be depicted either with probabilities or with frequencies. Visualizations with frequencies have been shown to help students significantly more in Bayesian reasoning problems than probability visualizations do. Because tree diagrams or double-trees (which are largely unknown in school) are node-branch-structures, these two visualizations (compared to the 2×2 table) can even simultaneously (...) display probabilities on branches and frequencies inside the nodes. This is a teaching advantage as it allows the frequency concept to be used to better understand probabilities. However, 2×2 tables and (double-) trees have a decisive disadvantage: While joint probabilities (e.g., P(AB)) are represented in 2×2 tables but no conditional probabilities (e.g., P(A|B)), it is exactly the other way around with (double-) trees. Therefore, a visualization that is equally suitable for the representation of joint probabilities and conditional probabilities is desirable. In this article, we present a new visualization—the frequency net—in which all absolute frequencies and all types of probabilities can be depicted. In addition to a detailed theoretical analysis of the frequency net, we report the results of a study with 249 university students that shows that “net diagrams” can improve reasoning without previous instruction to a similar extent as 2×2 tables and double-trees. Regarding questions about conditional probabilities, frequency visualizations (2×2 table, double-tree, or net diagram with natural frequencies) are consistently superior to probability visualizations. The frequency net performs as well as the frequency double-tree. Only the 2×2 table with frequencies—the only visualization that participants were already familiar with —led to higher performance rates. If, on the other hand, a question about a joint probability had to be answered, all implemented visualizations clearly supported participants’ performance, and no uniform format effect becomes visible. Participants reached the highest performance in the versions with probability 2×2 tables and probability net diagrams. Furthermore, after conducting a detailed error analysis, we report interesting error shifts between the two information formats and the different visualizations and give recommendations for teaching probability. (shrink)

We concentrate on two aspects of the article by Pothos & Busemeyer (P&B): the relationship between classical and quantum probability and quantum probability as a basis for rational decisions. We argue that the mathematical relationship between classical and quantum probability is not quite what the authors claim. Furthermore, it might be premature to regard quantum probability as the best practical rational scheme for decision making.

There is currently a debate over whether cognitive architecture is classical or connectionist in nature. One finds the following three comparisons between classical architecture and connectionist architecture made in the pro-connectionist literature in this debate: (1) connectionist architecture is neurally plausible and classical architecture is not; (2) connectionist architecture is far better suited to model pattern recognition capacities than is classical architecture; and (3) connectionist architecture is far better suited to model the acquisition of pattern recognition capacities by learning than (...) is classical architecture. If true, (1)-(3) would yield a compelling case against the view that cognitive architecture is classical, and would offer some reason to think that cognitive architecture may be connectionist. We first present the case for (1)-(3) in the very words of connectionist enthusiasts. We then argue that the currently available evidence fails to support any of (1)-(3). (shrink)

This essay explores some concerns about the quality of informed consent in patients whose autonomy is diminished by fatal illness. It argues that patients with diminished autonomy cannot give free and voluntary consent, and that recruitment of such patients as subjects in human experimentation exploits their vulnerability in a morally objectionable way. Two options are given to overcome this objection: (i) recruit only those patients who desire to contribute to medical knowledge, rather than gain access to experimental treatment, or (ii) (...) provide prospective subjects the choice to participate in standard doubleblind study or receive the experimental treatment. Either option would guarantee that patients in desperate conditions are given a more meaningful choice and a richer freedom, and thus a higher quality of informed consent, than under standard randomized trials. (shrink)

The United States District Court of Kansas, in Gudenkauf v. Stauffer, Znc., granted the defendants motion for summary judgment for the plaintiff's claims of pregnancy-related discrimination under the Americans with Disabilities Act and the Family and Medical Leave Act of 1993, but the court denied a similar motion for the plaintiff's claim under the Pregnancy Discrimination Act. The court found summary judgment to be appropriate for the ADA claim based on its finding that the plaintiff's pregnancy did not constitute an (...) impairment as required by the statute; as for the FMLA claim, it determined that the defendants failure to grant the plaintiff's leave request did not violate the statute. However, the court determined that summary judgment was inappropriate for the PDA claim because of material questions of fact about whether the defendant had acted with discriminatory intent.In considering the motions for summary judgment, the court accepted the following facts as incontrovertible. Plaintiff Michaela Gudenkauf worked for the defendant Stauffer, Inc. (shrink)

Predation and escaping from predation through hiding are two fundamental phenomena in ecology. The most common approach to reducing the chance of predation is to use a refuge. Here, we consider a three species fishery model system with prey refuge induced by a Holling type-II functional response. These three species of fish populations are named prey, middle predator, and top predator. Harvesting is employed in most fishery models to achieve both ecological and commercial benefits. Research proves that non-linear harvesting (Michaelis–Menten (...) type) returns more realistic outcomes. So, we have combined the Michaelis–Menten type of harvesting efforts for all populations. Uniform boundedness conditions for the solutions of the model are discussed. The existence conditions for possible equilibrium points with stability are presented. We explain the dynamical behavior at each equilibrium point through bifurcation analysis. The persistent criteria of the system are examined. Bionomic equilibrium and optimal harvesting control using Pontryagin’s maximum principle are calculated. For validation of the model in the real world, we have implemented this in the freshwater ecosystem of Lake Victoria. Extraction of native fish species and ecological balances are the foremost solicitude of Lake Victoria. We may resolve this concern partially by implementing prey refuge, since it may sustain the ecology of Lake Victoria, and therefore also its economical importance. Lake Victoria is acclaimed worldwide for the trade of fishing. Also, it provides the largest employment in east-central Africa and is beneficial to fishing equipment manufacturers. So, the bionomic equilibrium and harvesting control have significant applications in the fisheries. All the analytical studies are verified by numerical simulations. We have plotted phase portraits, bifurcation diagrams, Lyapunov exponents to explore the dynamics of the proposed model. (shrink)

The central idea of this paper is that forming the black hole horizon is attended with the transition from the classical regime of evolution to the quantum one. We offer and justify the following criterion for discriminating between the classical and the quantum: creations and annihilations of particle-antiparticle pairs are impossible in the classical reality but possible in the quantum reality. In flat spacetime, we can switch from the classical picture of field propagation to the quantum picture by changing the (...) overall sign of the spacetime signature. To describe a self-gravitating object at the final stage of its classical evolution, we propose to use the Foldy–Wouthuysen representation of the Dirac equation in curved spacetimes, and the Gozzi classical path integral. In both approaches, maintaining the dynamics in the classical regime is controlled by supersymmetry. (shrink)

A generally clear and well-written introduction to Thomistic natural theology which, like most such "textbook" treatments, suffers from too much commentary and too little Aquinas. The nature and existence of God are dealt with in some detail, and two interesting sections on "Invalid Reasons for Holding the Existence of God" and "Some Controverted Arguments" are included.--B. P. H.

Nurses and midwives are the majority of healthcare professionals globally, including Africa, and they provide care at all levels of the health system including community levels. Nurses and midwives contribute to the care of patients with rigid or dogmatic religious beliefs or those with suicidal ideations. This review paper discusses acute and chronic diseases that have suicidal tendencies such as terminal cancer, diseases with excruciating pain, physical disability, stroke, end-stage renal failure, and diabetics who are amputated. It was reiterated that (...) nurses and midwives taking care of these patients should be alert and observant to identify their suicidal tendencies. The paper also discusses religious or spiritual inclinations that negatively affect healthcare access and adherence, especially to biomedical or western medicine. It was emphasized that some religious beliefs do not allow their followers to employ biomedical treatment and nurses and midwives should not impose their faith on patients and their families. The paper ends with a discussion on the specific roles of nurses and midwives in the care of patients with suicidal ideations such as assessment, counseling, administering medication, observation, social interaction, ensuring safety measures, and providing an enabling environment for the family to part of the care and for the observation of religious coping strategies. Nurses and midwives should enhance their knowledge and skills on suicide and increase public education on suicide prevention and identification of those at risk. (shrink)

We interpret the concept of determinism for a classical system as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally believed to hold for all autonomous classical systems. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension provides counterexamples of this belief. Given the initial conditions of a particular type, the Cauchy problem may have an infinite set of solutions. Therefore, (...) random behavior of closed classical systems is indeed possible. With this finding, we give a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems. (shrink)

As John Henry Newman reflected on 'The Idea of a University' more than a century and a half ago, Bradley C. S. Watson brings together some of the nation's most eminent thinkers on higher education to reflect on the nature and purposes of the American university today. Their mordant reflections paint a picture of the American university in crisis. This book is essential reading for thoughtful citizens, scholars, and educational policymakers.