Real subset sums and posets with an involution

In this paper, we carry out in an abstract order context some real subset combinatorial problems. Specifically, let [Formula: see text] be a finite poset, where [Formula: see text] is an order-reversing and involutive map such that [Formula: see text] for each [Formula: see text]. Let [Formula: see text] be the Boolean lattice with two elements and [Formula: see text] the family of all the order-preserving 2-valued maps [Formula: see text] such that [Formula: see text] if [Formula: see text] for all [Formula: see text]. In this paper, we build a family [Formula: see text] of particular subsets of [Formula: see text], that we call [Formula: see text]-bases on [Formula: see text], and we determine a bijection between the family [Formula: see text] and the family [Formula: see text]. In such a bijection, a [Formula: see text]-basis [Formula: see text] on [Formula: see text] corresponds to a map [Formula: see text] whose restriction of [Formula: see text] to [Formula: see text] is the smallest 2-valued partial map on [Formula: see text] which has [Formula: see text] as its unique extension in [Formula: see text]. Next we show how each [Formula: see text]-basis on [Formula: see text] becomes, in a particular context, a sub-system of a larger system of linear inequalities, whose compatibility implies the compatibility of the whole system.

Trading accuracy for speed over the course of a decision

Humans and other animals often need to balance the desire to gather sensory information (to make the best choice) with the urgency to act, facing a speed-accuracy tradeoff (SAT). Given the ubiquity of SAT across species, extensive research has been devoted to understanding the computational mechanisms allowing its regulation at different timescales, including from one context to another, and from one decision to another. However, animals must frequently change their SAT on even shorter timescales - i.e., over the course of an ongoing decision - and little is known about the mechanisms that allow such rapid adaptations. The present study aimed at addressing this issue. Human subjects performed a decision task with changing evidence. In this task, subjects received rewards for correct answers but incurred penalties for mistakes. An increase or a decrease in penalty occurring halfway through the trial promoted rapid SAT shifts, favoring speeded decisions either in the early or in the late stage of the trial. Importantly, these shifts were associated with stage-specific adjustments in the accuracy criterion exploited for committing to a choice. Those subjects who decreased the most their accuracy criterion at a given decision stage exhibited the highest gain in speed, but also the highest cost in terms of performance accuracy at that time. Altogether, the current findings offer a unique extension of previous work, by suggesting that dynamic changes in accuracy criterion allow the regulation of the SAT within the timescale of a single decision.

On the Radon-Nikodym Property for Vector Measures and Extensions of Transfunctions

If \left( {{\mu _n}} \right)_{n = 1}^\infty are positive measures on a measurable space (X, Σ) and \left( {{v_n}} \right)_{n = 1}^\infty are elements of a Banach space 𝔼 such that \sum\nolimits_{n = 1}^\infty {\left\| {{v_n}} \right\|{\mu _n}\left( X \right)} < \infty, then \omega \left( S \right) = \sum\nolimits_{n = 1}^\infty {{v_n}{\mu _n}\left( S \right)} defines a vector measure of bounded variation on (X, Σ). We show 𝔼 has the Radon-Nikodym property if and only if every 𝔼-valued measure of bounded variation on (X, Σ) is of this form. This characterization of the Radon-Nikodym property leads to a new proof of the Lewis-Stegall theorem.We also use this result to show that under natural conditions an operator defined on positive measures has a unique extension to an operator defined on 𝔼-valued measures for any Banach space 𝔼 that has the Radon-Nikodym property.

Dynamic changes in urgency over the course of a decision

While making decisions, humans and other animals always need to balance the desire to gather sensory information (to make the best choice) with the urge to act, facing a speed-accuracy tradeoff (SAT). Given the ubiquity of the SAT across species, extensive research has been devoted to understanding the computational mechanisms allowing its regulation at different timescales, including from one context to another, and from one decision to another. However, in dynamic environments, animals often need to change their SAT on even shorter timescales – i.e., over the course of an ongoing decision – and very little is known about the mechanisms that allow such rapid adaptations. The present study aimed at addressing this issue. Human subjects performed a modified version of the tokens task, where an increase or a decrease in penalty occurring halfway through the trial promoted rapid SAT shifts, favoring speeded decisions either in the early or in the late stage of the trial. Importantly, these shifts were associated with stage-specific adjustments in the accuracy criterion exploited for committing to a choice and relatedly, with dynamic, non-linear changes in urgency. Those subjects who decreased the most their accuracy criterion at a given decision stage presented the highest gain in speed, but also the highest cost in terms of accuracy at that time. Altogether, the current findings offer a unique extension of former work, by revealing that dynamic changes in urgency allow the regulation of the SAT within the timescale of a single decision.

MILES: a Java tool to extract node-specific enriched subgraphs in biomolecular networks

Summary The growing availability of biomolecular networks has led to a need for analysis methods that are able to extract biologically meaningful information from these complex data structures. Here we present MILES (MIning Labeled Enriched Subgraphs), a Java-based subgraph mining tool for discovering motifs that are associated to a given set of nodes of interest, such as a list of genes or proteins, in biomolecular networks. It provides a unique extension to the widely used enrichment analysis methodologies by integrating network structure and functional annotations in order to discern novel biological subgraphs which are enriched in the targets of interest. The tool can handle various types of input data, including (un)directed, (un)connected and multi-label networks, and is thus compatible with most types of biomolecular networks. Availability and implementation MILES is available as a platform-independent Java application at https://github.com/pmoris/miles-subgraph-miner alongside a user manual, example datasets and the source code. Supplementary information Supplementary data are available at Bioinformatics online.

Probability Integral as a Linearization

In fuzzified probability theory, a classical probability space (Ω, A, p) is replaced by a generalized probability space (Ω, ℳ(A), ∫(.) dp), where ℳ(A) is the set of all measurable functions into [0,1] and ∫(.)dp is the probability integral with respect to p. Our paper is devoted to the transition from p to ∫(.) dp. The transition is supported by the following categorical argument: there is a minimal category and its epireflective subcategory such that A and ℳ(A) are objects, probability measures and probability integrals are morphisms, ℳ(A) is the epireflection of A, ∫(.) dp is the corresponding unique extension of p, and ℳ(A) carries the initial structure with respect to probability integrals. We discuss reasons why the fuzzy random events are modeled by ℳ(A) equipped with pointwise partial order, pointwise Łukasiewicz operations (logic) and pointwise sequential convergence. Each probability measure induces on classical random events an additive linear preorder which helps making decisions. We show that probability integrals can be characterized as the additive linearizations on fuzzy random events, i.e., sequentially continuous maps, preserving order, top and bottom elements.