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Prenatal screening poses specific challenges in multiple pregnancies but is in growing demand due to their increasing prevalence. Both ultrasound and biochemical screening methods are available, although they are less accurate than in singleton pregnancies. The introduction of non-invasive prenatal testing has been a big step forward with higher sensitivities and lower false-positive rates. In this chapter, we present an overview of the methods and implications of screening in multiple pregnancies, which will aid in the counseling of prospective parents.

Large-for-gestational-age (LGA), defined as foetal weight above the 90th percentile, is an adverse pregnancy outcome associated with increased delivery complications such as shoulder dystocia and caesarean deliveries. Standard prediction methods have been reported to be generally poor predictors of LGA. This study uses ethnically diverse data from the Born In Bradford dataset to predict LGA using machine learning algorithms. Data from 13,194 pregnant women with singleton infants was used, 43% of which were South Asian women and 35% White women. Within this dataset, 5% of the infants born to South Asian women were LGA compared to 11% of infants born to White women. Models built with resampled White and South Asian data had improved sensitivity (19–92%), and low precision (7–28%). Therefore, additional class balancing techniques are required to achieve more precise prediction models.

International audience; Evidential preference based on belief function theory has been proposed recently, simultaneously characterizing preference information with uncertainty and imprecision. However, traditional distances on belief functions do not adapt to some intrinsic properties of preference relations, especially when indifference relation is taken into comparison, therefore may cause inconsistent results in preference-based applications. In order to solve this issue, Unequal Singleton Pair (USP) distance has been proposed previously, with applications limited in preference aggregation. This paper explores forward the effectiveness of USP distance in preference clustering, especially confronting multiple conflicting sources. Moreover, a combination strategy for multiple conflicting sources of preference is proposed. The experiments on synthetic data show that USP distance can effectively improve the clustering results in Adjusted Rand Index (ARI).

A basic technique used in algorithms for constraint satisfaction problems (CSPs) is removing values that are locally inconsistent, since they cannot form part of a globally consistent solution. The best-known algorithms of this type establish arc consistency (AC), where every value has support in neighbouring domains. Here, we consider algorithms that use AC repeatedly under severe local assumptions to achieve higher overall levels of consistency. These algorithms establish (neighbourhood) singleton arc consistency ((N)SAC). Most of these use simple AC interleaved with the basic (N)SAC procedure. To date, however, this strategy of interleaving weaker and stronger forms of reasoning has not received much attention in and of itself. Moreover, one of the best (N)SAC algorithms (called (N)SACQ) does not use this method. This paper investigates the effects of interleaving and presents new methods based on this idea. We show that different kinds of problems vary greatly in their amenability to AC interleaving; while in most cases it is beneficial, with some algorithms and problem types it can be harmful. More significantly, when this feature is added to (N)SACQ algorithms, the latter’s superiority to other (N)SAC algorithms becomes more consistent and decisive. We also consider an AC-4 based approach to interleaving as well as interleaving with stronger methods than AC.

The concepts we have seen in the previous chapter can also be applied to scalar objective optimization problems (SOPs). Unlike for MOPs, where one expects an entire manifold of solutions, the solution of a SOP is typically given by a singleton. That is, if one is “only” interested in the best solution for a given SOP, one can simply keep and update the best found solution during the run of the algorithm. For instance, within an evolutionary algorithm, the best found solution in each step will always be kept in the current population, and there is no need for an additional archiver.

We study the subclass of singleton congestion games in which there are identical resources with increasing cost functions. In this domain, we prove that there always exists an outcome that is resilient to weakly-improving deviations by singletons (i.e., the outcome is a Nash equilibrium), by the grand coalition (i.e., the outcome is Pareto efficient), and by coalitions with respect to an a priori given partition coalition structure (i.e., the outcome is a partition equilibrium). To our knowledge, this is the strongest existence guarantee in the literature on congestion games when weakly-improving deviations are considered. Our proof technique gives the false impression of a potential function argument but it is a novel application of proof by contradiction.

In the authors’ previous research the possible usage of correlation clustering in rough set theory was investigated. Correlation clustering is based on a tolerance relation that represents the similarity among objects. Its result is a partition which can be treated as the system of base sets. However, singleton clusters represent very little information about the similarity. If the singleton clusters are discarded, then the approximation space received from the partition is partial. In this way, the approximation space focuses on the similarity (represented by a tolerance relation) itself and it is different from the covering type approximation space relying on the tolerance relation. In this paper, the authors examine how the partiality can be decreased by inserting the members of some singletons into base sets and how this annotation affects the approximations. This process can be performed by the user of system. However, in the case of a huge number of objects, the annotation can take a tremendous amount of time. This paper shows an alternative solution to the issue using neural networks.

Many of the world’s most outstanding theater plays derive their dramatic effect from the fact that the hero does not follow the path of action that corresponds to what the audience considers the dominant strategy. This holds for Brutus in Shakespeare’s Julius Cesar as well as for Schiller’s Wallenstein, both characters who hesitate to grab power and thereby make use of the possibility to escape their fate. However, if players do not have dominant strategies and there are more than one Nash equilibria so that players control alternative equilibrium strategies, then the decision problem becomes even more challenging. Selten’s trembling hand perfectness can be applied to select equilibrium strategies which are still adequate even when it is assumed that the other players deviate from their equilibrium strategies in the form of small e trembles. Often this reduces the set of Nash equilibria and in some cases a singleton is left. In contrast to this operation, the concept of rationalizable strategies leads to an expansion of the set of justifiable strategy choices. A strategy x is rationalizable if it is a best reply to strategy y and y is a best reply to a strategy z. In a Nash equilibrium (x, y), x and y are mutually best replies. It is immediately understood that Nash equilibrium strategies are rationalizable, but not all rationalizable strategies are Nash equilibrium strategies.

Job scheduling on parallel machines is a well-studied singleton congestion game. We consider a variant of this game in which the jobs are partitioned into competition sets, and the goal of every player is to minimize the completion time of his job relative to his competitors. Specifically, the primary goal of a player is to minimize the rank of its completion time among his competitors, while minimizing the completion time itself is a secondary objective. This fits environments with strong competition among the participants, in which the relative performance of the players determine their welfare.

Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the “splicing operation”, a cut-and-paste binary string operation defined by a set of “splicing rules”, quadruples \(r = (u_1, u_2 ; u_3, u_4)\) where \(u_1, u_2, u_3, u_4\) are words over an alphabet \(\varSigma \). For two strings \( x_1 u_1 u_2 y_1\) and \( x_2 u_3 u_4 y_2\), applying the splicing rule r produces the string \( x_1 u_1 u_4 y_2\). In this paper we focus on a particular type of splicing systems, called (i, j) semi-simple splicing systems, \(i = 1,2\) and \(j = 3, 4\), wherein all splicing rules r have the property that the two strings in positions i and j in r are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called “axiom set”, by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.

In this paper we address a fundamental combinatorial optimization problem in communication systems. A fully-connected system is modeled by a complete graph, where all nodes have identical capacities. A message is owned by a singleton. If he/she decides to forward the message simultaneously to several nodes, he/she will take longer, with respect to a one-to-one forwarding scheme. The only rule in this communication system is that a message can be forwarded by a node that owns the message. The makespan is the time when the message is broadcasted to all the nodes. The problem under study is to select the communication strategy that minimizes both the makespan and the average waiting time among all the nodes. A previous study claims that a sequential or one-to-one forwarding scheme minimizes the average waiting time, but they do not offer a proof. Here, a formal proof is included. Furthermore, we show that the sequential strategy minimizes the makespan as well. A discussion of potential applications is also included.

We consider computability-theoretic aspects of the algebraic and definable closure operations for formulas. We show that for \(\varphi \) a Boolean combination of \(\varSigma _n\)-formulas and in a given computable structure, the set of parameters for which the closure of \(\varphi \) is finite is \(\varSigma ^0_{n+2}\), and the set of parameters for which the closure is a singleton is \(\varDelta ^0_{n+2}\). In addition, we construct examples witnessing that these bounds are tight.

We introduce a concept of a binary-direct implicational basis and show that the shortest binary-direct basis exists and it is known as the D-basis introduced in Adaricheva, Nation, Rand [4]. Using this concept we approach the algorithmic solution to the Singleton Horn Extension problem, as well as the one set removal problem, when the closure system is given by the canonical direct or binary-direct basis. In this problem, a new closed set is added to or removed from the closure system forcing the re-write of a given basis. Our goal is to obtain the same type of implicational basis for the new closure system as was given for original closure system and to make the basis update an optimal process.

In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of axis in metric spaces, which are not necessarily compact. For these optimal control problems the turnpike is not a singleton. We also study the existence of solutions of the corresponding infinite horizon optimal control problems.

In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of half-axis in infinite dimensional spaces. For these optimal control problems, the turnpike is not a singleton. We also study the existence of solutions of the corresponding infinite horizon optimal control problems. The results of this chapter will be obtained for two large classes of problems which will be treated simultaneously.

The gap between a definite and an indefinite is reduced in the case of specific indefinites, in the sense that they both have determined reference. This fact is reflected in most accounts, particularly so in the analysis of Schwarzschild (2002) where specific indefinites are argued to quantify over singleton sets. If definites and specific indefinites share the singleton domain property, how are we to separate the two? The Privacy Principle, which is cued to the information state of discourse participants, is argued to apply to definites as well as indefinites (among other quantifiers), making it even harder to draw the line between definites and specific indefinites. We look at issues surrounding the distinction between definiteness and specificity through the lens of two empirical phenomena, bare nominals and specificity markers. Bare nominals in languages with determiners, for example, English, and bare nominals in languages without determiners, for example, Hindi, highlight different aspects of the problem. English bare plurals are known to have indefinite readings but not specific indefinite readings. Hindi bare nominals are thought to have definite and indefinite readings but can be shown not to have specific indefinite readings. The second empirical phenomenon we consider are specificity markers like certain. In many languages, they require a determiner in the singular but not in the plural, raising questions about their syntactic status as determiners or modifiers. They also do not occur in certain constructions, for example, imperatives. Probing such restrictions provides a window into their semantic profile. This paper thus presents some puzzles that center around the creation of singleton sets and its relation to the Privacy Principle.

In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces, which are not necessarily compact. For these optimal control problems, the turnpike is not a singleton. We also study the existence of solutions of the corresponding infinite horizon optimal control problems.

In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems in infinite dimensional spaces. For these optimal control problems the turnpike is a singleton. We also study the structure of approximate solutions on large intervals in the regions close to the endpoints and the existence of solutions of the corresponding infinite horizon optimal control problems. The results of this chapter will be obtained for two large classes of problems which will be treated simultaneously.

Sorting permutations by block moves is a fundamental combinatorial problem in genome rearrangements. The classic block move operation is called transposition, which switches two consecutive blocks, or equivalently, moves a block to some other position. But large blocks movement rarely occurs during real evolutionary events. A natural restriction of transposition is to bound the length of the blocks to be switched. In this paper, we investigate the problem called sorting by bounded singleton moves, where one block is exactly a singleton while the other is of length at most c. This problem generalizes the sorting by short block moves problem proposed by Heath and Vergara [10], which requires the total length of blocks switched bounded by 3. By exploring some properties of this problem, we devise a \(\frac{9}{5}\)-approximation algorithm for \(c=3\). Our algorithm can be extended to any constant \(c\ge 3\), guaranteeing an approximation factor of \(\frac{3c}{5}\).

In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for discrete-time optimal control problems in metric spaces, which are not necessarily compact. For these optimal control problems, the turnpike is a singleton. We also study the structure of approximate solutions on large intervals in the regions close to the endpoints and the existence of solutions of the corresponding infinite horizon optimal control problems.

Andrew Singleton received his B.Sc. from the University of Sunderland, UK and his Ph.D. from the University of Newcastle upon Tyne, UK. His postdoctoral studies were spent at the Mayo Clinic in Jacksonville Florida. He then moved to the National Institute on Aging at NIH Bethesda, MD. In 2008 he became the Chief of the Laboratory of Neurogenetics, and in 2016 he was named an NIH Distinguished Investigator. He has published more than 550 articles on a wide variety of topics. His laboratory comprises ~60 staff, including six principal investigators and three group leaders, working on the genetic basis of neurological disorders including Parkinson’s disease, Alzheimer’s disease, dystonia, ataxia, dementia with Lewy bodies, and amyotrophic lateral sclerosis.

In this chapter we establish sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of axis in infinite dimensional spaces. For these optimal control problems, the turnpike is not a singleton. We also study the existence of solutions of the corresponding infinite horizon optimal control problems.

Architectural design patterns capture architectural design experience and provide abstract solutions to recurring architectural design problems. Their description is usually expressed informally and it is not verified whether the proposed specification indeed solves the original design problem. As a consequence, an architect cannot fully rely on the specification when implementing a pattern to solve a certain problem. To address this issue, we propose an approach for the specification and verification of architectural design patterns. Our approach is based on interactive theorem proving and leverages the hierarchical nature of patterns to foster reuse of verification results. The following paper presents FACTum, a methodology and corresponding specification techniques to support the formal specification of patterns. Moreover, it describes an algorithm to map a given FACTum specification to a corresponding Isabelle/HOL theory and shows its soundness. Finally, the paper demonstrates the approach by verifying versions of three widely used patterns: the singleton, the publisher-subscriber, and the blackboard pattern.

Multi-criteria decision making (MCDM) is a category of techniques for solving decision making problems based on the performance of multiple criteria. One shortcoming of the existing MCDM techniques is that they rarely consider the relations among decision criteria. Nevertheless, different types of criterion relations significantly impact the results of the decision making problem. In this paper, we solve this problem by establishing and measuring different types of relations among decision criteria. We propose a MCDM framework, named InterDM, to rank a set of alternatives based on the utilities of both singleton criteria and criterion coalitions, in which we design an Interactive Interpretive Structural Modeling technique to construct consistent criterion relations. We use a case study of ranking cloud services to demonstrate the efficiency of InterDM.

This article proposes a new method to calculate the distance between fuzzy singleton variables. It uses a measure of generalized fuzzy numbers based on the center of gravity. The fuzzy signals are transformed by applying convolution. To prove the effectiveness of this method, it is applied to a pattern recognition problem that deals with stock markets. Comparison with other classical distance measurements shows that this approach provides a consistent and reliable distance measure for the stock market scenario and can be generalized for any pattern recognition problem.

Recall that if x is a member of a set X and \(t\in [0,1],\) then we define the fuzzy subset \(x_{t}\) of X by \(x_{t}(x)=t\) and \(x_{t}(y)=0\) for all \(y\in X\backslash \{x\}.\) We call \(x_{t}\) a fuzzy singleton

In the authors’ previous research the possible usage of the correlation clustering in rough set theory was investigated. Correlation clustering relies on a tolerance relation. Its result is a partition. From the similarity point of view singleton clusters have no information. A system of base sets can be generated from the partition, and if the singleton clusters are left out, then it is a partial approximation space. This way the approximation space focuses on the similarity (the tolerance relation) itself and it is different from the covering type approximation space relying on the tolerance relation. In this paper the authors examine how the partiality can be decreased by inserting the members of some singletons into an arbitrary base set and how this annotation affects the approximations. The authors provide software that can execute this process and also helps to select the destination base set and it can also handle missing data with the help of the annotation.

Boolean network is a discrete mathematical model of gene regulatory networks. In this short article, we briefly review algorithmic results on finding attractors in Boolean networks. Since it is known that the problem of finding a singleton attractor is NP-hard and the problem can be trivially solved in \(O^{*}(2^n)\) time (under a reasonable assumption), we focus on special cases in which the problem can be solved in \(O((2-\delta )^n)\) time for some constant \(\delta >0\). We also briefly review algorithmic results on control of Boolean networks.

Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). The goal of this chapter is to introduce the reader to matroids and polymatroids, and illustrate their relation to distributed storage systems. While many of the results are rather technical in nature, effort is made to increase accessibility via simple examples. The chapter embeds all the essential features of LRCs, namely locality, availability, and hierarchy alongside with related generalised Singleton bounds.

Opinion spam is a well-recognized threat to the credibility of online reviews. Existing approaches to detecting spam reviews or spammers examine review content, reviewer behavior and reviewer-product network, and often operate on the assumption that spammers write at least several if not many fake reviews. On the other hand, spammers setup multiple sockpuppet IDs and write one-time, singleton spam reviews to avoid detection. It is reported that for most review sites, a large portion, sometimes over 90%, of reviewers are singletons (identified by the reviewer ID). Singleton spammers are difficult to catch due to the scarcity of behavioral clues. In this paper, we argue that the key to detect singleton spammers (and their fake reviews) is to detect group spam attacks by inferring the hidden collusiveness among them. To address the challenge of lack of explicit behavioral signals for singleton reviewers, we propose to infer the hidden reviewer-product associations by completing the review-product matrix by leveraging the product and review metadata and text. Experiments on three real-life Yelp datasets established that our approach can effectively detect singleton spammers via group detection, which are often missed by existing approaches.

Learning meaningful and effective representations for transaction data is a crucial prerequisite for transaction classification and clustering tasks. Traditional methods which use frequent itemsets (FIs) as features often suffer from the data sparsity and high-dimensionality problems. Several supervised methods based on discriminative FIs have been proposed to address these disadvantages, but they require transaction labels, thus rendering them inapplicable to real-world applications where labels are not given. In this paper, we propose an unsupervised method which learns low-dimensional continuous vectors for transactions based on information of both singleton items and FIs. We demonstrate the superior performance of our proposed method in classifying transactions on four datasets compared with several state-of-the-art baselines.

A singleton abstraction occurs in a program analysis when some results of the analysis are known to be exact: an abstract binding corresponds to a single concrete binding. In this paper, we develop a novel approach to constructing singleton abstractions via relative store fragments. Each store fragment is a locally exact store abstraction in that it contains only those abstract variable bindings necessary to address a particular question at a particular program point; it is relative to that program point and the point of view may be shifted. We show how an analysis incorporating relative store fragments achieves flow-, context-, path- and must-alias sensitivity, and can be used as a basis for environment analysis, without any machinery put in place for those specific aims. We build upon recent advances in demand-driven higher-order program analysis to achieve this construction as it is fundamentally tied to demand-driven lookup of variable values.

In the field of Fuzzy Set Theory, special attention has been paid to the problem of determining whether a fuzzy set is a singleton, by means of the well-known measures of specificity. This has been done, for example, to be able to measure the level of uncertainty associated with the fuzzy set or, also, to be able to determine the discriminatory power of the property associated with the fuzzy set in a given context. This concept was extended to that of k-specificity in order to determine the difficulty of choosing k objects in a fuzzy set. In this paper we study bounding properties for k-specificity measures, and we introduce their use in flexible querying, analyzing their computation, and comparing the information provided by these measures with the tightly related fuzzy cardinality measures.

Objective: To explore potential risk factors for the emergency caesarean section in term, singleton pregnancies. Methods: A retrospective population based case-control study in term deliveries from the University Hospital in Brno, Czech Republic collected between 2014 and 2016. Cases were deliveries by emergency caesarean section; controls were all others modes of delivery. We excluded elective caesarean from the populations.

This paper is an exposition, with some new applications, of our results from Hochman (Ann Math (2) 180(2):773–822, 2014; preprint, 2015, http://arxiv.org/abs/1503.09043) on the growth of entropy of convolutions. We explain the main result on \(\mathbb{R}\), and derive, via a linearization argument, an analogous result for the action of the affine group on \(\mathbb{R}\). We also develop versions of the results for entropy dimension and Hausdorff dimension. The method is applied to two problems on the border of fractal geometry and additive combinatorics. First, we consider attractors X of compact families \(\Phi\) of similarities of \(\mathbb{R}\). We conjecture that if \(\Phi\) is uncountable and X is not a singleton (equivalently, \(\Phi\) is not contained in a 1-parameter semigroup) then dimX = 1. We show that this would follow from the classical overlaps conjecture for self-similar sets, and unconditionally we show that if X is not a point and \(\dim \Phi> 0\) then dimX = 1. Second, we study a problem due to Shmerkin and Keleti, who have asked how small a set \(\emptyset \neq Y \subseteq \mathbb{R}\) can be if at every point it contains a scaled copy of the middle-third Cantor set K. Such a set must have dimension at least dimK and we show that its dimension is at least dimK + δ for some constant δ > 0.

This chapter explores many aspects of the type-1 fuzzy system that was introduced in Chap. 1. It provides a very comprehensive and unified description of the two major kinds of type-1 fuzzy systems that are widely used in real-world applications—Mamdani and TSK fuzzy systems. The coverage of this chapter includes rules, singleton, and non-singleton fuzzifiers, input–output formulas for the fuzzy inference engine, type-1 first- and second-order rule partitions, the effects of the two kinds of fuzzifiers on the input–output formulas, combining or not combining fired-rule output sets on the way to defuzzification, defuzzifiers (centroid, height, and center-of-sets), fuzzy basis functions which provide a mathematical description of a fuzzy system from its input to its output, remarks and insights about a type-1 fuzzy system (including layered architecture interpretations for it, universal approximation by it, continuity of it, rule explosion and some ways to control it, and rule interpretability for it). Eighteen examples are used to illustrate the important concepts and there is also a comprehensive numerical example in Sect. 3.7 that is continued in later chapters. Chap. 9 builds upon the material that is in this chapter.

There are differences in the resultant of extracting the relations between social actors based on two streams of approaches in principle. However, one of the methods like the superficial methods can upgraded to make the information extraction by using the principles of the other methods, and this needs proof systematically. This paper serves to reveal some formulations have the function for resolving this issue. Based on the results of experiments conducted the expanded method is the adequate.

Recently, it has been shown that interval type-2 fuzzy sets (IT2FSs) are more general than interval-valued fuzzy sets (IVFSs), and some of these IT2FSs can actually be non-convex. Although these IT2FSs could be considered within the general type-2 fuzzy sets’ (GT2FSs) scope, this latter have always been studied and developed under certain conditions considering the convexity and normality of their secondary grades. In recent works the operations of intersection and union for GT2FSs have been extended to include non-convex secondary grades. Hence, there is a need to develop the theory for those general forms of interval type-2 fuzzy logic systems (gfIT2FLSs) which use IT2FSs that are not equivalent to IVFSs and can have non-convex secondary grades. In this chapter, we will present the mathematical tools to define the inference engine for singleton gfIT2FLSs. This work aims to introduce the basic structure of such singleton gfIT2FLSs, paying special attention to those blocks presenting significant differences with the already well known type-2 FLSs which employ IT2FSs which are equivalent to IVFSs (we will term IVFLSs).

At fuzzy modelling the inputs of fuzzy systems being modeled can receive both crisp and fuzzy information. The methods of fuzzy logical inference known for fuzzy input values have either low calculation efficiency, or do not allow the use the whole variety of fuzzy logical operations. The paper describes a new method of logical inference based on fuzzy truth value for Multi-Input Single-Output (MISO) systems, which receive non-singleton input values. It gives a comparison of the method with the original method of Zadeh and popular method of Mamdani, and shows high computational efficiency of the method proposed. The method is generalized to systems with rule blocks.

In this paper we present experimental results on rule sets induced from 12 data sets with many missing attribute values. We use two interpretations of missing attribute values: lost values and attribute-concept values. Our main objective is to check which interpretation of missing attribute values is better from the view point of complexity of rule sets induced from the data sets with many missing attribute values. The better interpretation is the attribute-value. Our secondary objective is to test which of the three probabilistic approximations used for the experiments provide the simplest rule sets: singleton, subset or concept. The subset probabilistic approximation is the best, with 5 % significance level.

In this paper we present results of novel experiments conducted on 12 data sets with many missing attribute values interpreted as attribute-concept values and “do not care” conditions. In our experiments complexity of rule sets, in terms of the number of rules and the total number of conditions induced from such data, are evaluated. The simpler rule sets are considered better. Our first objective was to check which interpretation of missing attribute values should be used to induce simpler rule sets. There is some evidence that the “do not care” conditions are better. Our secondary objective was to test which of the three probabilistic approximations: singleton, subset or concept, used for rule induction should be used to induce simpler rule sets. The best choice is the subset probabilistic approximation and the singleton probabilistic approximation is the worst choice.

Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which completeness is not possible. An important element in concrete SL is the points-to predicate which denotes a singleton heap. SL with the points-to predicate has been shown to be non-recursively enumerable. In this paper, we develop a first-order SL, called FOASL, with an abstracted version of the points-to predicate. We prove that FOASL is sound and complete with respect to an abstract semantics, of which the standard SL semantics is an instance. We also show that some reasoning principles involving the points-to predicate can be approximated as FOASL theories, thus allowing our logic to be used for reasoning about concrete program verification problems. We give some example theories that are sound with respect to different variants of separation logics from the literature, including those that are incompatible with Reynolds’s semantics. In the experiment we demonstrate our FOASL based theorem prover which is able to handle a large fragment of separation logic with heap semantics as well as non-standard semantics.

Low-weight births have long occupied the American health disparities research agenda because African-American mothers have a much higher risk of a low-weight baby than do white mothers. Struening et al. (Bull N Y Acad Med 66:463–478, 1990) examined the effect of 1970–1980 change in number of housing units on frequency distribution of low weight births in the 380 health areas of New York City. Although the average and median proportion of live singleton babies weighing less than 2500 g declined between 1970 and 1980 and between 1980 and 1986, variance and range increased greatly, as did the maximum. Well over half of the variability in proportion of births below 2500 g in the health areas with over 90 % of the population African-American and with increases in LOB over 1 % between 1970 and 1980 was explained by the decrease in number of housing units between 1970 and 1980. Struening et al. reviewed the literature on factors fostering high proportions of LOB: housing overcrowding, family instability, family income, and neighborhood socioeconomic status.

This paper starts with a brief critical overview of the hypothesis—often elevated in popular discourse to ‘theory’—that language learning is subject to maturational constraints of a kind which beyond a certain age preclude the complete acquisition of the language in question (Munoz & Singleton, 2011). It goes on to relate this ‘theory’ to the practical question of when the teaching of languages should begin in schools, and concludes that the relationship between the two is extremely problematic (Singleton, 2012). In conclusion the paper points out that some of the age-related issues that can be identified as relevant to language learning are not in fact strictly related to maturation (Moyer, 2013) and could be seen having the capacity to manifest themselves pedagogically in something like an age-neutral manner.