Dissecting CTCF site function in a tense HoxD locus

In this issue of Genes & Development, Amândio and colleagues (pp. 1490–1509) dissect the function of a cluster of several CTCF binding sites in the HoxD cluster by iterative deletions in mice. They found additive functions for some, and intriguingly found that some sites function as insulators, while others function as anchors for enhancer–promoter interactions. These functions vary depending on developmental context. The work provides new insights into the roles played by CTCF in regulating developmental patterns and 3D chromatin organization.

A Unified General Class of Interdistributional Income Inequality Measures Based on Weighted Incomplete Moments

Many authors have proposed measures for between groups income inequalities. Mostly, these measures are based on functional of the income distribution. Others are based on Gini index, measures of entropies or additive functions. Butler and McDonald (1987) developed a class of between groups income inequality measures based on incomplete moments and showed its applicability. In this article, A unified class of interdistributional inequality measures are introduced. Most of previous measures are special cases from the new class, such as Butler-McDonald measures. These new measures are estimated and studied. Also, the new general class is based on probability weighted moments which can be given any values as the upper value. A real data application is presented to compare among all these measures and show the benefits of the new measures.

Meaningful interpretation of algebraic inequalities to achieve uncertainty and risk reduction

The paper develops an important method related to using algebraic inequalities for uncertainty and risk reduction and enhancing systems performance. The method consists of creating relevant meaning for the variables and different parts of the inequalities and linking them with real physical systems or processes. The paper shows that inequalities based on multivariable sub-additive functions can be interpreted meaningfully and the generated new knowledge used for optimising systems and processes in diverse areas of science and technology. In this respect, an interpretation of the Bergström inequality, which is based on a sub-additive function, has been used to increase the accumulated strain energy in components loaded in tension and bending. The paper also presents an interpretation of the Chebyshev’s sum inequality that can be used to avoid the risk of overestimation of returns from investments and an interpretation of a new algebraic inequality that can be used to construct the most reliable series-parallel system. The meaningful interpretation of other algebraic inequalities yielded a highly counter-intuitive result related to assigning devices of different types to missions composed of identical tasks. In the case where the probabilities of a successful accomplishment of a task, characterising the devices, are unknown, the best strategy for a successful accomplishment of the mission consists of selecting randomly an arrangement including devices of the same type. This strategy is always correct, irrespective of existing uknown interdependencies among the probabilities of successful accomplishment of the tasks characterising the devices.

Tight Approximation for Unconstrained XOS Maximization

A set function is called XOS if it can be represented by the maximum of additive functions. When such a representation is fixed, the number of additive functions required to define the XOS function is called the width. In this paper, we study the problem of maximizing XOS functions in the value oracle model. The problem is trivial for the XOS functions of width 1 because they are just additive, but it is already nontrivial even when the width is restricted to 2. We show two types of tight bounds on the polynomial-time approximability for this problem. First, in general, the approximation bound is between O(n) and [Formula: see text], and exactly [Formula: see text] if randomization is allowed, where n is the ground set size. Second, when the width of the input XOS functions is bounded by a constant k ≥ 2, the approximation bound is between k − 1 and k − 1 − ɛ for any ɛ > 0. In particular, we give a linear-time algorithm to find an exact maximizer of a given XOS function of width 2, whereas we show that any exact algorithm requires an exponential number of value oracle calls even when the width is restricted to 3.

Strategyproof Mechanisms for Additively Separable and Fractional Hedonic Games

Additively separable hedonic games and fractional hedonic games have received considerable attention in the literature. They are coalition formation games among selfish agents based on their mutual preferences. Most of the work in the literature characterizes the existence and structure of stable outcomes (i.e., partitions into coalitions) assuming that preferences are given. However, there is little discussion of this assumption. In fact, agents receive different utilities if they belong to different coalitions, and thus it is natural for them to declare their preferences strategically in order to maximize their benefit. In this paper we consider strategyproof mechanisms for additively separable hedonic games and fractional hedonic games, that is, partitioning methods without payments such that utility maximizing agents have no incentive to lie about their true preferences. We focus on social welfare maximization and provide several lower and upper bounds on the performance achievable by strategyproof mechanisms for general and specific additive functions. In most of the cases we provide tight or asymptotically tight results. All our mechanisms are simple and can be run in polynomial time. Moreover, all the lower bounds are unconditional, that is, they do not rely on any computational complexity assumptions.

On the relation between length functions and exact Sylvester rank functions

Inspired by the work of Crawley-Boevey on additive functions in locally finitely presented Grothendieck categories, we describe a natural way to extend a given exact Sylvester rank function on the category of finitely presented left modules over a given ring R, to the category of all left R-modules.