Where do preferences come from?

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice (Dietrich and List, Nous, forthcoming), we describe a framework for conceptualizing preference formation and preference change. In our model, an agent’s preferences are based on certain ‘motivationally salient’ properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice.     

What do the Chinese value in (mathematics) education?

The achievement in mathematics among the Chinese has aroused the interest of educationalists, sociologists and psychologists worldwide. The coining of the term Confucian Heritage Culture learner??s phenomenon mistakenly led researchers to look for direct attributions from Confucianism, without realizing that Confucianism is just one Chinese school of thought, and it is over-simplistic to draw causal relationships between schools of thought and social phenomena. This paper begins by introducing three major Chinese schools of thought??Confucianism, Daoism and Buddhism??and their views on education. The discussion will then focus on how these schools of thought might impact education in general and mathematics education in particular.     

Approach to mathematics in textbooks at tertiary level – exploring authors’ views about their texts

The aim of this article is to present and discuss some results from an inquiry into mathematics textbooks authors’ visions about their texts and approaches they choose when new concepts are introduced. Authors’ responses are discussed in relation to results about students’ difficulties with approaching calculus reported by previous research. A questionnaire has been designed and sent to seven authors of the most used calculus textbooks in Norway and four authors have responded. The responses show that the authors mainly view teaching in terms of transmission so they focus mainly on getting the mathematical content correct and ‘clear’. The dominant view is that the textbook is intended to help the students to learn by explaining and clarifying. The authors prefer the approach to introduce new concepts based on the traditional way of perceiving mathematics as a system of definitions, examples and exercises. The results of this study may enhance our understanding of the role of the textbook at tertiary level. They may also form a foundation for further research.     

Can remembering history from predecessor promote cooperation in the next generation?

People usually think that helping the next generation to remember history can promote cooperation in dilemma games. We show that is not always the case when agents have memory. Agents play with each neighbor by game history and strategies (such as TFT and WSLS), and the next generation inherits good strategies from the predecessor. We analyze the system’s cooperation ratio by comparing the 2 sources of history at the beginning of each generation: (a) inherited from the predecessor; (b) randomly initialized with different cooperation ratio. We find that with unconditional imitation update rule, agents who remember history get lower cooperation ratio than those who randomly initialize the history; while with replicator rule, higher initial cooperation ratio promotes higher final cooperation. We also do additional experiments to investigate the R, ST, P reciprocity and strategies distribution of the systems.     

Possibilities of introducing different functional circuits on top of a structural neuron triplet: Where do the gains lie?

Instigated by the research on clusterization phenomena in complex neural networks, we study a triplet of bursting Rulkov map neurons connected via inhibitory synapses with delay. It is demonstrated how on a background of structural motif one can build different types of functional circuits. The approach is based on utilizing the properties of the chemical synapses, whose gating is modeled by the fast threshold modulation, in conjunction with the phase plane analysis, allowing the system state to be represented in terms of maps the neurons reside on. For both the dynamical configurations, monitoring the layout of active neurons, and the functional motifs, following the maps where the synchronized neurons lie, we establish a one-on-one correspondence between sequences in the time series and the triads, making up the subgraphs of the original graph. By introducing the appropriate sets of quantities, one obtains not only the distributions of triads as a function of synaptic parameters, but is also able to identify a distinct triad whose presence may be viewed as a signature of the burst synchronization process. In another setup, the regularization of burst cycles for an arbitrary neuron is explained by classifying all the bursts as long or short, with their fractions linked to the abundances of triads under variation of synaptic parameters.     

Low discrepancy sequences in high dimensions: How well are their projections distributed?

Quasi-Monte Carlo (QMC) methods have been successfully used to compute high-dimensional integrals arising in many applications, especially in finance. To understand the success and the potential limitation of QMC, this paper focuses on quality measures of point sets in high dimensions. We introduce the order-?$?$, superposition and truncation discrepancies, which measure the quality of selected projections of a point set on lower-dimensional spaces. These measures are more informative than the classical ones. We study their relationships with the integration errors and study the tractability issues. We present efficient algorithms to compute these discrepancies and perform computational investigations to compare the performance of the Sobol’ nets with that of the sets of Latin hypercube sampling and random points. Numerical results show that in high dimensions the superiority of the Sobol’ nets mainly derives from the one-dimensional projections and the projections associated with the earlier dimensions; for order-2 and higher-order projections all these point sets have similar behavior (on the average). In weighted cases with fast decaying weights, the Sobol’ nets have a better performance than the other two point sets. The investigation enables us to better understand the properties of QMC and throws new light on when and why QMC can have a better (or no better) performance than Monte Carlo for multivariate integration in high dimensions.     

What do the arithmetic,geometric and harmonic means tell us in length-biased sampling?

Properties of the A.M., G.M. and H.M. for length-biased distributions are studied in a nonparametric fashion. Unbiased estimation of the coefficient of variation is considered, and a characterization of length-biased distributions is also made in this light.     

Can home-owners benefit from stochastic programming models? A study of mortgage choice in Denmark

The Danish mortgage market is large and sophisticated. However, most Danish mortgage banks advise private home-owners based on simple, if sensible, rules of thumb. In recent years a number of papers (from Nielsen and Poulsen in J Econ Dyn Control 28:1267–1289, 2004 over Rasmussen and Zenios in J Risk 10:1–18, 2007 to Pedersen et al. in Ann Oper Res, 2013) have suggested a model-based, stochastic programming approach to mortgage choice. This paper gives an empirical comparison of performance over the period 2000–2010 of the rules of thumb to the model-based strategies. While the rules of thumb slightly outperform a passive benchmark on average and are less risky than pure adjustable rate loans, we find considerable gains from using the model-based strategies. Using a strategy that minimizes conditional-value-at-risk lowers average effective yearly interest rate over a 10-year horizon by 0.3–0.9 %-points (depending on the borrower’s level of conservatism) compared to the rules of thumb without increasing the risk. The answer to the question in the title is thus affirmative.     

Can matching improve the performance of boosting for identifying important genes in observational studies?

When two groups of individuals are to be compared with respect to gene expression there will often be some potentially confounding variables that differ between the groups. Matching is an established approach for obtaining comparable groups and enabling subsequent univariate tests for each gene. Alternatively, the confounders might be incorporated directly into a multivariable regression model for adjustment. In contrast to univariate tests, such models can consider all genes simultaneously. Aiming to combine the advantages of both approaches, matching and multivariable modeling, we consider a matching-based boosting procedure for fitting risk prediction models in two-group settings. This possibly allows to identify and automatically remove problematic observations that might negatively affect the regression model. Therefore, we compare the ability to identify important covariates for this combination of matching and boosting with only boosting for different covariate correlation structures in a simulation study. Furthermore, we analyze the prediction performance of these approaches on two gene expression microarray studies. The first study comprises patients with B-cell and T-cell type acute lymphoblastic leukemia and the second patients with acute megakaryoblastic leukemia. While the matching component can in principle guard against problematic observations, the combined approach is seen to neither improve identification of important covariates nor to improve prediction performance. Therefore, a combination of the two approaches cannot be recommended. Adjustment for potential confounders is seen to provide the best performance, i.e. a pure multivariable regression modeling strategy seems to be promising even in presence of considerable heterogeneity.     

How do open-ended problems promote indirect argumentation? Conceptual replications in a Japanese secondary school

The possibility of connecting spontaneous indirect argumentation to indirect mathematical proof has been investigated for decades. It may be effective to use open-ended problems based on the notion of cognitive unity to promote indirect argumentation. Moreover, it also appears useful to analyze students’ indirect argumentation through a model based on the logical structure of indirect proof. However, several convincing critiques of these proposals exist. This study aimed to resolve this dispute and obtain a deeper understanding of indirect argumentation in the process. To achieve this, conceptual replications of previous research were conducted at a Japanese secondary school. The results demonstrated that the exploration of various cases in the situation of an open-ended problem could promote indirect argumentation. Furthermore, the findings indicate that indirect argumentation exhibits diverse characteristics that can be omitted if the analysis is conducted only from a logical perspective.     

Can asset allocation limits determine portfolio risk–return profiles in DC pension schemes?

In defined contribution (DC) pension schemes, the regulator usually imposes asset allocation constraints (minimum and maximum limits by asset class) in order to create funds with different risk–return profiles. In this article, we challenge this approach and show that such funds can exhibit erratic risk–return profiles that deviate significantly from the intended design. We propose to replace all minimum and maximum asset allocation constraints by a single risk metric (or measure) that controls risk directly. Thus, funds with different risk–return profiles can be immediately created by adjusting the risk tolerance parameter accordingly. Using data from the Chilean DC pension system, we show that our approach generates funds whose risk–return profiles are consistently ordered according to the intended design, and outperforms funds created by means of asset allocation limits.     

What generalizations do students achieve with respect to trigonometric functions in the transition from angles in degrees to real numbers?

The aim of this study is to examine prospective mathematics teachers’ generalizations of trigonometric functions from the unit circle to the Cartesian coordinate system. The researcher developed a test that aimed to reveal students’ generalizations, as well as the possible differences between them. The test was administered to 30 students who were near completion of their university degree program. The findings showed that the students were unable to establish the link between the unit circle and the Cartesian coordinate representation system; and therefore, they were not able to interpret the outputs of trigonometric functions with input of a real number that is not a multiple of π. The researcher also found that the students had developed certain misconceptions regarding the properties of trigonometric functions. To improve the teaching of trigonometric functions an instructional sequence and an alternative definition for trigonometric functions is proposed.     

How do inhibitors and modifiers of individual enzymes affect steady-state fluxes and concentrations in metabolic systems?

By using metabolic control theory we show how one can calculate the effect on steady-state metabolite concentrations and steady-state fluxes of small amounts of inhibitors or activators of individual enzymes in a metabolic system of arbitrary complexity. It turns out that only limited knowledge of the kinetics of the enzymes in the systems, summarized in their “Elasticity Coefficients,” is needed. An example of an actual calculation is given.