Wallace's unfinished business: The “Other Man” in evolutionary theory

After a century in the shadows, Alfred Russel Wallace (1823–1913) has recently become the subject of increasing attention. It is suggested here, expanding on observations made by anthropologist Gregory Bateson some years ago, that Wallace's cybernetics‐like view of the operation of natural selection—as a governor‐like principle tending to keep species unvarying—can be expanded to a more complete evolutionary understanding by exploring in modern context Wallace's idea that “more recondite forces” are driving the process. Specifically, when the environment is regarded as a final cause (but not a deterministic force), individual adaptations may be viewed as entropy‐relaying structures (acting in response to, and as a part of, larger scale biogeochemical agenda), whereas negentropy is accumulated by nonrandomly directed organism‐ and population‐level forms of ecological engagement. Thus, range change in particular is viewed as a process that is both driven and nonrandom, and ultimately connected to the derivation of more and more organized individual, population, and community structures. © 2004 Wiley Periodicals, Inc. Complexity 10:25–32, 2004     

On a vector-valued integral in the “noncommutative” statistical decision theory

A generalization of a vector-valued integral arising in the noncommutative (quantum) statistical decision theory is considered.     

Robustness in complex information systems: The role of information “barriers” in Boolean networks

In this supposed “information age,” a high premium is put on the widespread availability of information. Access to as much information as possible is often cited as key to the making of effective decisions. While it would be foolish to deny the central role that information and its flow has in effective decision‐making processes, this chapter explores the equally important role of “barriers” to information flows in the robustness of complex systems. The analysis demonstrates that (for simple Boolean networks at least) a complex system's ability to filter out, i.e., block, certain information flows is essential if it is not to be beholden to every external signal. The reduction of information is as important as the availability of information. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Proposal and implementation of the “science SQC” quality control principle

In forecasting the operation of the manufacturing industry in the 21^st century, the authors recently proposed “science SQC” as a demonstrative-scientific methodology and discussed its effectiveness on the basis of verification studies conducted by Toyota Motor Corporation. This study outlines a new SQC principle “science SQC”, as a demonstrative-scientific methodology, which enables the principle of TQM to be improved systematically.     

Perfect simulation of processes with long memory: A “coupling into and from the past” algorithm

We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling into and from the past. It improves on existing algorithms by relaxing the conditions on the kernel and by accelerating convergence, even in the simple case of finite order Markov chains. Although chains of variable or infinite order have been widely investigated for decades, their use in applied probability, from information theory to bio‐informatics and linguistics, has recently led to considerable renewed interest. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 46, 300–319, 2015     

Correction to: “Exponential bounds on the number of designs with affine parameters”

It is well known that the number of designs with the parameters of a classical design having as blocks the hyperplanes in PG(n, q) or AG(n, q), n?3, grows exponentially. This result was extended recently [5] to designs having the same parameters as a projective geometry design whose blocks are the d‐subspaces of PG(n, q), for any 2?d?n ? 1. In this paper, exponential lower bounds are proved on the number of non‐isomorphic designs having the same parameters as an affine geometry design whose blocks are the d‐subspaces of AG(n, q), for any 2≤d≤n ? 1. Exponential bounds are also proved for the number of resolvable designs with these parameters. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:156‐166, 2011     

How Students “Unpack” the Structure of a Word Problem: Graphic Representations and Problem Solving

This research investigated how fourth and fifth grade students spontaneously ‘unpacked’ a word problem when generating a graphic representation to aid in problem solution. Relationships among the type of graphic representation produced, spatial visualization, drawing ability, gender, and problem solving also were examined and described. Instrumentation developed for the study included several math challenge tasks, a spatial visualization task, and a drawing task. For one of the math challenge tasks, students were instructed to draw a picture to assist them with problem solution. These graphic representations generated by students were rated as pictorial or as displaying some level of schematic representation. Schematic representations included germane information from the problem supportive of problem solution. Pictorial representations included expressive and extraneous elements not necessary for problem solution, with no schematic elements. Findings indicated that the majority of students rendered schematic representations, with girls more likely than boys to use schematic representations at a statistically significant level. Students who used schematic visual representations were more successful problem solvers than those pictorially representing problem elements. The more “schematic‐like” the visual representation, the more successful students were at problem solution. Drawing a pictorial representation in the math challenge task also was negatively correlated to drawing skill.     

The 3‐connectivity of a graph and the multiplicity of zero “2” of its chromatic polynomial

Let G be a graph of order n, maximum degree Δ, and minimum degree δ. Let P(G, λ) be the chromatic polynomial of G. It is known that the multiplicity of zero “0” of P(G, λ) is one if G is connected, and the multiplicity of zero “1” of P(G, λ) is one if G is 2‐connected. Is the multiplicity of zero “2” of P(G, λ) at most one if G is 3‐connected? In this article, we first construct an infinite family of 3‐connected graphs G such that the multiplicity of zero “2” of P(G, λ) is more than one, and then characterize 3‐connected graphs G with Δ + δ?n such that the multiplicity of zero “2” of P(G, λ) is at most one. In particular, we show that for a 3‐connected graph G, if Δ + δ?n and (Δ, δ₃)≠(n?3, 3), where δ₃ is the third minimum degree of G, then the multiplicity of zero “2” of P(G, λ) is at most one. © 2011 Wiley Periodicals, Inc. J Graph Theory     

Discussion of “Birnbaum‐Saunders distribution: A review of models,analysis and applications”

This paper provides the distribution of order statistics from a multivariate Birnbaum‐Saunders (GMBS) distribution which can be used in the reliability and lifetime analyses. Proposing a new generalization of Birnbaum‐Saunders distribution based on the unified skew‐elliptical model, some properties of the order statistics are also studied.     

On the invertibility of “rectangular” bi-infinite matrices and applications in time–frequency analysis

Finite dimensional matrices with more columns than rows have no left inverses while those with more rows than columns have no right inverses. We give generalizations of these simple facts to bi–infinite matrices. Our results are then used to obtain density results for p-frames of time–frequency molecules in modulation spaces and identifiability results for operators with bandlimited Kohn–Nirenberg symbols.     

Comment on “On the Neumann function and the method of images in spherical and ellipsoidal geometry”

In this note, we point out two errors in the article “On the Neumann function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed.     

Corrigendum to “A note on the Loewenstein–Prelec theory of intertemporal choice” [Math. Social Sci. 52 (1) (2006) 99–108]

In a critique of the Loewenstein and Prelec [Loewenstein G., Prelec D., 1992. Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics 107, 573–597] theory of intertemporal choice, [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] point out four errors. One of the alleged errors was that the elasticity of the value function in prospect theory is decreasing. But it is in fact increasing. We provide a correction and a formal proof. As a corollary, we show that the elasticity of the value function is bounded between zero and one. Nevertheless, all the remaining points in [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] remain valid     

Erratum to: “A linear vizing‐like relation relating the size and total domination number of a graph”

The proof of the main theorem in the paper [1] is incorrect as it is missing an important case. Here we complete the proof by giving the missing case. © 2007 Wiley Periodicals, Inc. J Graph Theory 54: 350–353, 2007     

Erratum to: “The Gromov norm of the product of two surfaces” [Topology 44 (2005) 321–339]

We report an error in the proof of Lemma 2.7 of the original article. This invalidates one direction of our main theorem.     

Models are a “metaphor in your brain”: How potential and preservice teachers understand the science and engineering practice of modeling

We investigated beginning secondary science teachers’ understandings of the science and engineering practice of developing and using models. Our study was situated in a scholarship program that served two groups: undergraduate STEM majors interested in teaching, or potential teachers, and graduate students enrolled in a teacher education program to earn their credentials, or preservice teachers. The two groups completed intensive practicum experiences in STEM‐focused academies within two public high schools. We conducted a series of interviews with each participant and used grade‐level competencies outlined in the Next Generation Science Standards to analyze their understanding of the practice of developing and using models. We found that potential and preservice teachers understood this practice in ways that both aligned and did not align with the NGSS and that their understandings varied across the two groups and the two practicum contexts. In our implications, we recommend that teacher educators recognize and build from the various ways potential and preservice teachers understand this complex practice to improve its implementation in science classrooms. Further, we recommend that a variety of practicum contexts may help beginning teachers develop a greater breadth of understanding about the practice of developing and using models.     

Comments on “Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method”

Tari et al. [A. Tari, M.Y. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comput. Appl. Math. 228 (2009) 70–76], presented some fundamental properties of TDTM for the kernel functions in two-dimensional Volterra integral equations. Here, we suggest simple proofs of those fundamental properties by using the basic properties of TDTM. Furthermore, we present some fundamental properties of TDTM for the kernel functions of a quotient type in two-dimensional Volterra integral equations. Numerical illustrations are demonstrated to show the effectiveness of the TDTM for solving two-dimensional Volterra integral equations.     

The Effects of Project‐Based Learning on Students' Academic Achievement,Attitude, and Retention of Knowledge: The Subject of “Electricity in Our Lives”

The aim of this study is to analyze the effects of project‐based learning on students' academic achievement, attitude, and retention of knowledge in relation to the subject of “Electricity in Our Lives” in a fourth‐grade science course. The study was conducted in a quasi‐experimental design as a “pre‐test, post‐test with control group.” In the experimental group, the unit was taught through the project‐based learning method. The measuring tools were administered to both groups before and after the applications. To perfectly analyze the “process” of the method, seven different learning assessment “forms” were administered to the students. The findings of the forms indicated that the students learn to construct their own learning and to evaluate changes in their own behavior through the application of the method. The application of different methods between both groups had a statistically significant effect in terms of academic achievement, (F(1,112) = 46.78, p = .000) and of retention of knowledge (F(1,112) = 35.24, p = .000). However, there were no statistically significant effects from being in different groups for the attitudes of students (F(1,112) = .99, p = .321). For the students, being in the project‐based learning groups resulted in better academic achievement and retention of knowledge than being in the traditional teaching group.     

A Padé family of iterations for the matrix sign function and related problems

In this paper we consider the Pad'e family of iterations for computing the matrix sign function and the Padé family of iterations for computing the matrix p‐sector function. We prove that all the iterations of the Padé family for the matrix sign function have a common convergence region. It completes a similar result of Kenney and Laub for half of the Padé family. We show that the iterations of the Padé family for the matrix p‐sector function are well defined in an analogous common region, depending on p. For this purpose we proved that the Padé approximants to the function (1?z)^?σ, 0<σ<1, are a quotient of hypergeometric functions whose poles we have localized. Furthermore we proved that the coefficients of the power expansion of a certain analytic function form a positive sequence and in a special case this sequence has the log‐concavity property. Copyright © 2011 John Wiley & Sons, Ltd.