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In this the first of an anticipated four paper series, fundamental results of quantitative genetics are presented from a first principles approach. While none of these results are in any sense new, they are presented in extended detail to precisely distinguish between definition and assumption, with a further emphasis on distinguishing quantities from their usual approximations. Terminology frequently encountered in the field of human genetic disease studies will be defined in terms of their quantitive genetics form. Methods for estimation of both quantitative genetics and the related human genetics quantities will be demonstrated. While practitioners in the field of human quantitative disease studies may find this work pedantic in detail, the principle target audience for this work is trainees reasonably familiar with population genetics theory, but with less experience in its application to human disease studies. We introduce much of this formalism because in later papers in this series, we demonstrate that common areas of confusion in human disease studies can be resolved be appealing directly to these formal definitions. The second paper in this series will discuss polygenic risk scores. The third paper will concern the question of "missing" heritability and the role interactions may play. The fourth paper will discuss sexually dimorphic disease and the potential role of the X chromosome.

The covering number, $\sigma(G)$, of a finite, noncyclic group $G$ is the least positive integer $n$ such that $G$ is the union of $n$ proper subgroups. Here we investigate the covering numbers of the projective special unitary groups $U_3(q)$, give upper and lower bounds for $\sigma(U_3(q))$ when $q \geq 7$, and show that $\sigma(U_3(q))$ is asymptotic to $q^6/3$ as $q \rightarrow \infty$.

A \emph{finite cover} of a group $G$ is a finite collection $\mathcal{C}$ of proper subgroups of $G$ with the property that $\bigcup \mathcal{C} = G$. A finite group admits a finite cover if and only if it is noncyclic. More generally, it is known that a group admits a finite cover if and only if it has a finite, noncyclic homomorphic image. If $\mathcal{C}$ is a finite cover of a group $G$, and no cover of $G$ with fewer subgroups exists, then $\mathcal{C}$ is said to be a \emph{minimal cover} of $G$, and the cardinality of $\mathcal{C}$ is called the \emph{covering number} of $G$, denoted by $\sigma(G)$. Here we investigate the covering numbers of the McLaughlin sporadic simple group and some low degree primitive groups.

To each generic complex polynomial $p(z)$ there is associated a labeled binary tree (here referred to as a "lemniscate tree") that encodes the topological type of the graph of $|p(z)|$. The branching structure of the lemniscate tree is determined by the configuration (i.e., arrangement in the plane) of the singular components of those level sets $|p(z)|=t$ passing through a critical point. In this paper, we address the question "How many branches appear in a typical lemniscate tree?" We answer this question first for a lemniscate tree sampled uniformly from the combinatorial class and second for the lemniscate tree arising from a random polynomial generated by i.i.d. zeros. From a more general perspective, these results take a first step toward a probabilistic treatment (within a specialized setting) of Arnold's program of enumerating algebraic Morse functions., Comment: 18 pages, 6 figures

This paper reports on the development of a scale to identify a child's emotional and behavioral skills, competencies, and characteristics, the Behavioral and Emotional Rating Scale: A Strength-Based Approach to Assessment (BERS). The BERS is a 52-item scale that identifies strengths in five areas: interpersonal strengths, family involvement, intrapersonal strengths, school functioning, and affective strengths. This paper describes development of norms for children without disabilities as well as for children with emotional or behavioral disorders, results of factor analyses, studies of the scale's concurrent and construct validity, and reliability studies. The paper suggests that the BERS is suitable for five uses: (1) to identify children with limited emotional and behavioral strengths; (2) to target goals for an individual treatment plan or individual educational plan; (3) to identify strengths and weaknesses for treatment; (4) to document progress in a strength area as a consequence of specialized treatment or services; and (5) to measure strengths in research and evaluation projects. (DB)

The Scale for Assessing Emotional Disturbances (SAED) is a standardized, norm-referenced scale used to identify children who qualify for the federal special education category of "emotional disturbance". It uses the five conditions on which identification of emotional disturbance is based under the Individuals with Disabilities Education Act as amended in 1997. This study presents data from norming, factor analysis, and construct validity studies. The measure's subscales examine: (1) inability to learn; (2) relationship problems; (3) inappropriate behavior; (4) unhappiness or depression; (5) physical symptoms or fears; (6) social maladjustment; and (7) overall competence. The paper concludes that the SAED is well constructed and has excellent psychometric properties. It recommends the measure to: identify students with emotional disturbances; aid in the prereferral screening of large groups of students; clarify the "socially maladjusted" and "adversely affects educational performance" conditions of decision-making about emotional disturbances under the law; and select appropriate education goals for an individualized education program. (DB)

This conference paper discusses the results of a study that investigated how the clients of the Chicago-based Satellite Family Outreach program are served by the social workers and family workers of Satellite. The Satellite Program is offered by Kaleidoscope, Inc., a child welfare agency that provides unconditional, individualized and, when necessary, wraparound services to more than 600 children and families. The Satellite Program is designed to help maintain referred children, parents, and siblings as an intact family unit. Specifically, this study investigated the type of activities performed by the four social workers and 13 family workers of the Satellite Program, the frequency of the occurrence of these activities, with whom the staff members are engaged in each activity, where each activity occurred, and the duration of each activity. Results indicated the most frequently occurring professional activities were writing reports, individual counseling, collateral contacts, and transportation. The least frequently occurring professional activities per day were employment/vocational activities, relationship counseling, housing, and training. (CR)

This paper describes the development of the Behavioral and Emotional Strengths Scale (BESS), developed as part of a program which focuses on strengths of children usually seen as having severe emotional and/or behavioral disorders. The BESS is a 68-item scale that identifies children's behavioral strengths on five dimensions: (1) self-control; (2) affective development; (3) family involvement; (4) school performance; and (5) self-confidence. The paper reports the results of efforts that establish the scale's content validity, item discrimination, and factor structure. It also notes current efforts to establish norms for the BESS. (DB)

A review of 20 independent samples found a wide range of school and student variables influence the use of administrative discipline contacts, whereas administrator/teacher and family variables have less influence. Relevant variables include participation in athletics, child neglect, antisocial behavior, and anecdotal suspension report. (Contains references.) (Author/CR)

This article reviewed 55 studies to examine trends in interventions to improve the academic functioning of students with emotional disturbance. Results of descriptive analysis indicated: lack of demographic information; settings usually special education classrooms; predominantly single-subject designs; lack of treatment fidelity data; lack of studies on females or minorities; and a recent decline in relevant studies. (Contains references.) (Author/DB)

Systematic review of 26 studies on language deficits in children with emotional and behavioral disorders (EBD) found 71 percent of EBD children had clinically significant broad-based language deficits including pragmatic, receptive, and expressive deficits. Longitudinal studies suggested that the rate of comorbidity between language deficits and EBD tends to either be stable or to increase over time. (Contains references.) (Author/DB)

Outlines steps in simultaneous treatment design: (1) carefully describe different treatments so that each is a separate and distinct intervention; (2) define target behavior and develop assessment instrument; (3) order treatments so that conditions other than treatments can be ruled out; (4) implement treatments and allow enough time to indicate which is more powerful. (CMG)

Contrasts the "ability training" and "task-analytic" approaches in teaching learning disabled children. Describes the use of the task-analytic behavioral model in Project EXCEL, a Child Service Demonstration Center. Summarizes guiding principles of this approach, and indicates that participating students have shown dramatic improvement. (CJM)

Two hundred sixty-five subjects learned a mixed list of paired associates in an AB, AD and AB, CD transfer paradigm. Two levels of semantic processing were factorially varied across original and interpolated pairs. Recall of original pairs was shown to be directly related to the processing depth of original pairs in both paradigms and inversely related to the processing depth of interpolated pairs in the AB, AD paradigm, but not in the AB, CD paradigm. Twenty additional subjects intentionally learned and recalled the same list and showed significant retroactive inhibition for original pairs in the AB, AD paradigm. The findings indicate that interference does not occur in a mechanical fashion, but is sensitive to subjects' level of perceptual analysis of the pairs. (Author)

Teachers and classroom aides of learning disabled pupils were asked to complete the Conners Abbreviated Teacher Rating Scale (CATRS) on two separate occasions, one month apart. Inter-rater reliability for teachers (.866) and for aides (.602), and reliability across time for teachers (.866) and aides (.603) achieved acceptable levels. (Author/BW)