Disjunctive Networks Research Articles

Dynamically equivalent disjunctive networks

The study of the dynamical behavior of Boolean networks with different update schedules has so far focused primarily on the possible dynamics and equivalent networks that can be obtained. However, few studies have been done about which networks can be obtained from another network with a non-parallel schedule.In this article, we define the problem of finding a Boolean network that is dynamically equivalent to another network. For the general case, it is shown that the problem is NP-Hard. However, if the problem is restricted to disjunctive Boolean networks, it can be solved in polynomial time.

Crime Fiction as World Literature ed. by Louise Nilsson, David Damrosch, and Theo D’haen

Reviewed by: Crime Fiction as World Literature ed. by Louise Nilsson, David Damrosch, and Theo D’haen Eric Sandberg Nilsson, Louise, David Damrosch, and Theo D’haen, eds. Crime Fiction as World Literature. New York: Bloomsbury Academic, 2017. Pp. vii+301. US$135.00 hardcover, US$32.35 paperback, US$28.88 ebook. It is something of a critical commonplace-or perhaps it would be better to say a rhetorical flourish-to bemoan the scholarly neglect of crime fiction. This is a genre that is, as the editors of Crime Fiction as World Literature, Louise Nilsson, David Damrosch, and Theo D’haen, point out, “a significant participant in the international sphere of world literature” (2), and one that is both hugely popular and tightly entangled with elite literary production (3). Crime fiction, on the one hand, accounts for seven of the top ten most frequently borrowed authors in the British Public library system, at least of works intended for adult consumption, such as James Patterson and Agatha Christie, both of whom appear on the list (“Most Borrowed”). It is, on the other hand, closely associated with high-culture figures such as Umberto Eco, whose 1983 The Name of the Rose is an overt detective novel with a protagonist, William of Baskerville, directly linked to the most famous figure in the genre, and Jorge Luis Borges, who continued and extended Edgar Allan Poe’s groundbreaking exploration of the genre’s potentials in stories such as “Death and the Compass.” Crime fiction thus clearly deserves the sustained attention of literary scholars. To be fair, despite the ritualistic complaints of crime fiction scholars-and I am as guilty as any in this regard-the genre has received a fair measure of attention. On “crime-novel-ridden campuses,” as the editors note, scholars are working hard, and have been for some years now, to understand the genre’s popularity (2–3), not to mention its particular aesthetic effects, its entanglement with modern technologies [End Page 433] and ideologies, its relationship to questions of race, gender, and sexuality, and much more. There are now several scholarly journals dedicated to the study of crime fiction, including the venerable McFarland publication Clues and the newly-launched Crime Fiction Studies from Edinburgh University Press, and the number of monographs and edited collections published annually in the field easily reaches double digits. This is, admittedly, a sparse academic crop when compared to the superabundance of work dedicated to, say, Virginia Woolf-or, of course, modernism more generally -but it certainly represents more scholarly interest than is accorded to some other forms of popular fiction-romance, for instance, or the spy novel. The editors of Crime Fiction as World Literature have, however, identified an important exception to this rule. “To date,” they note, “studies of crime fiction have largely been confined to individual national or at most regional traditions” (3). This means that the “complex, overlapping disjunctive networks and sub-networks” (3) within which crime fiction is created and read in a global context tend to be ignored. Consider, for example, the way a Japanese police procedural, inspired both by American generic models and an indigenous crime writing tradition, might be influenced, both in terms of composition, distribution, and reception, by the global success of, say, Scandinavian Noir, yet remain in other ways a resolutely local cultural artefact responding to and shaped by Japanese linguistic and cultural norms. This process of intersecting local and global factors gains another level of complexity when the resulting work is translated into English or another global language, and marketed internationally. Nilsson, Damrosch, and D’haen also point to the undue prominence regularly, indeed almost inevitably, given to British and American crime writing. Peter Messent’s The Crime Fiction Handbook, mentioned here in this context, may well be, as I believe, the single best introductory volume on the subject currently available, but it is true that of the fourteen key works to which Messent dedicates an individual chapter, all but two are from Britain and America. Maj Sjöwall and Per Wahlöö’s The Laughing Policeman and Stieg Larsson’s The Girl with the Dragon Tattoo are the exceptions-both...

Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks

In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, ie any Boolean network with firing memory composed of $m$ vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, \ie the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the $\lambda$-phage and that of the genetic control of the floral morphogenesis of the plant \emph{Arabidopsis thaliana}.

Disjunctive networks and update schedules

In this paper, we present a study of the dynamics of disjunctive networks under all block-sequential update schedules. We also present an extension of this study to more general fair periodic update schedules, that is, periodic update schedules that do not update some elements much more often than some others. Our main aim is to classify disjunctive networks according to the robustness of their dynamics with respect to changes of their update schedules. To study this robustness, we focus on one property, that of being able to cycle dynamically.

An integrated selection and scheduling for disjunctive network problems

In network optimization problems, the application of conventional integrated selection and scheduling solution methods becomes complicated when the size of the problems, such as real life project management, assembly and transportation problems, get bigger. These kinds of problems often consist of disjunctive networks with alternative subgraphs. Traditionally, in order to handle alternative subgraphs in a disjunctive network, researchers consider first selection and then solution (scheduling) of the problem sequentially. However, the use of traditional approaches result in the loss of the problem structural integrity. When the approach losses its integrated structure, the network problem also losses its integrity. Therefore, these two issues, i.e. selection and scheduling, have to be considered together. To provide a new approach to maintain the problem integrity, we proposed an integrated genetic algorithm for solving this selection and scheduling problems together using a multi-stage decision approach. In this study, two newly defined problems with different disjunctive networks and different characteristics, i.e. resource constrained multiple project scheduling (rc-mPSP) models with alternative projects and variable activity times, and U-shaped assembly line balancing (uALB) models with alternative subassemblies, have been solved using the proposed solution approach to highlight the applicability and performance of the proposed solution approach.

On the Number of Functions Realized by Cascades and Disjunctive Networks

In this paper, the number of functions realized by certain networks of two-input one-output gates are presented. Two networks are considered; one is the disjunctive network, which is characterized by the restriction that each gate output and each network input connect to exactly one gate input. The other network, the cascade, is the special case of the disjunctive networks in which each gate has at least one input which connects to a network input. For both networks, a recursion relation is derived for the number of realized switching functions dependent on exactly k variables. Both expressions have been solved by computer for k up to 15. Also, expressions are derived for the number of functions realized by cascades and disjunctive networks of two-input one-output cells, where each cell realizes any of the 16 functions on two variables.