In this paper, we discuss the problem of optimizing a multi-level logic combinational Boolean network. Our techniques apply a sequence of local perturbations and modifications of the network which are guided by the automatic test pattern... more
In this paper, we discuss the problem of optimizing a multi-level logic combinational Boolean network. Our techniques apply a sequence of local perturbations and modifications of the network which are guided by the automatic test pattern generation ATPG based reasoning. In particular, we propose several new ways in which one or more redundant gates or wires can be added to
Though there is agreement in the literature that juvenile delinquency is a group phenomenon, there is controversy regarding the explanation of this finding. Subcultural theorists argue that youths become delinquent through peer... more
Though there is agreement in the literature that juvenile delinquency is a group phenomenon, there is controversy regarding the explanation of this finding. Subcultural theorists argue that youths become delinquent through peer socialization in gangs, while control theorists contend that adolescents become delinquent & associate with delinquent others because they have weakened bonds to the conventional social order. Here, data collected via participant observation of a gang of 35 "punks" in a western Canadian city are drawn on to examine the role of social bonds & group structure in the generation of delinquency through the application of social network analysis. Results support the control explanation: those members who have the weakest bonds, regardless of gang participation, have the most delinquent attitudes. Though companionship alone does not lead youths to become delinquent, it should still be considered important in the explanation of delinquency.
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that... more
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that control the dynamics of the entire network and thus determine the attractors. Assuming that the attractor period is equal to the least common multiple of the size of all relevant components, we show that the distribution in large networks is well approximated by a power-law with an exponent of -1. Numerical evidence based on sampling of attractors supports the conclusions of our analytic arguments.
We propose a new power consumption model that accounts for the power consumption at the internal nodes of a CMOS gate. Next, we address the problem of minimizing the average power consumption during the technology dependent phase of logic... more
We propose a new power consumption model that accounts for the power consumption at the internal nodes of a CMOS gate. Next, we address the problem of minimizing the average power consumption during the technology dependent phase of logic synthesis. Our approach consists of two steps. In the first step, we generate a NAND decomposition of an optimized Boolean network such that the sum of average switching rates for all nodes in the network is minimum. In the second step, we perform a power efficient technology mapping that finds a minimal power mapping for given timing constraints (subject to the unknown load problem)
Abstract. Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of S. cerevisiae and S. pombe. Threshold... more
Abstract. Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of S. cerevisiae and S. pombe. Threshold networks assume that gene regulation processes are additive. This, however, contrasts with the mechanism proposed by S. Kauffman in which each of the logic functions must be carefully con-structed to accurately take into account the combinatorial nature of gene regulation. While Kauffman Boolean networks have been extensively studied and proved to have the necessary properties required for model-ing the fundamental characteristics of genetic regulatory networks, not much is known about the essential properties of threshold networks. Here we study the dynamical properties of these networks with different con-nectivities, activator-repressor proportions, activator-repressor strengths and different thresholds. Special attention is paid to the way in w...
With cellular reprogramming it is possible to convert a cell from one phenotype to another without necessarily passing through a pluripotent state. This perspective is opening many interesting fields in the world of research and... more
With cellular reprogramming it is possible to convert a cell from one phenotype to another without necessarily passing through a pluripotent state. This perspective is opening many interesting fields in the world of research and biomedical applications. This essay provides a concise description of the subject by describing the purpose of this technique, its evolution, mathematical models used and applied methodologies. As example, four areas in the biomedical field where cellular reprogramming can be applied with interesting perspectives are illustrated: diseases modeling, drug discovery, precision medicine and regenerative medicine. Furthermore, the use of ordinary differential equations, Bayesian network and Boolean network are described in these contexts. These strategies of mathematical modeling are the three main types that are applied in gene regulatory networks to analyze the dynamic interaction between a network of nodes. Ultimately, their application in disease research is discussed considering their benefits and limitations.
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory... more
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. In the same context, polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks. Finally, unate cascade functions have been studied in the design of logic circuits and binary decision diagrams. This paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions. Furthermore, it provides a description of nested canalyzing functions as a certain type of Boolean polynomial function. Using the polynomial framework one can show that the class of nested canalyzing functions, or, equivalently, the class of unate cascade functions, forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and com...
Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distance-to-positive-feedback which, in essence, captures the... more
Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distance-to-positive-feedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distance-to-positive-feedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean... more
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean network, and demonstrate how the sole requirement of sequential matching of attractors may open for an evolution that exhibits punctuated equilibrium.
Cells in an organism interact with each other and with the environment through a complex set of signals, which triggers responses and activate cellular regulation mechanisms. Models obtained by computational mathematics for cellular... more
Cells in an organism interact with each other and with the environment through a complex set of signals, which triggers responses and activate cellular regulation mechanisms. Models obtained by computational mathematics for cellular signaling dynamics are used to understand factors and causes of deregulation of internal biological processes, which is a relevant knowledge in a disease such as cancer. Gene regulatory networks describe gene interactions and how these relationships control cellular processes such as growth and cell division, which relate this disease to the regulatory network. Despite its simplicity, Boolean networks may accurately model some biological phenomena, such as gene regulatory network dynamics. Indeed, several reports in the literature show that they are accurate enough to build models of regulatory networks of cell lines related to breast cancer. In this chapter, we present a methodology for building cellular regulatory networks based on the Boolean paradigm...
Many interesting properties of Boolean networks, cellular automata, and other models of complex systems rely heavily on the use of synchronous updating of the individual elements. This has motivated some researchers to claim that, if the... more
Many interesting properties of Boolean networks, cellular automata, and other models of complex systems rely heavily on the use of synchronous updating of the individual elements. This has motivated some researchers to claim that, if the natural systems being modelled lack any clear evidence of synchronously driven elements, then asynchronous rules should be used by default. Given that standard asynchronous updating precludes the possibility of strictly cyclic attractors, does this mean that asynchronous Boolean networks, ...
We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic... more
We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic behaviour or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power law. In an experiment, the non-ideal behaviour of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and asymmetry between the logic states tend to engender periodic behaviour, at least for the simplest networks. On the other hand, we find that a memory effect termed ‘degradation’ can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices ...
