Generating Boolean networks with a prescribed attractor structure
Dynamical modeling of gene regulation via network models constitutes a key problem for genomics. The long-run characteristics of a dynamical system are critical and their determination is a primary aspect of system analysis. In the other direction, system synthesis involves constructing a network possessing a given set of properties. This constitutes the inverse problem. Generally, the inverse problem is ill-posed, meaning there will be many networks, or perhaps none, possessing the desired properties. Relative to long-run behavior, we may wish to construct networks possessing a desirable steady-state distribution. This paper addresses the long-run inverse problem pertaining to Boolean networks (BNs).



The long-run behavior of a BN is characterized by its attractors. The rest of the state transition diagram is partitioned into level sets, the j-th level set being composed of all states that transition to one of the attractor states in exactly j transitions. We present two algorithms for the attractor inverse problem. The attractors are specified, and the sizes of the predictor sets and the number of levels are constrained. Algorithm complexity and performance are analyzed. The algorithmic solutions have immediate application. Under the assumption that sampling is from the steady state, a basic criterion for checking the validity of a designed network is that there should be concordance between the attractor states of the model and the data states. This criterion can be used to test a design algorithm: randomly select a set of states to be used as data states; generate a BN possessing the selected states as attractors, perhaps with some added requirements such as constraints on the number of predictors and the level structure; apply the design algorithm; and check the concordance between the attractor states of the designed network and the data states.


AVAILABILITY
The software and supplementary material is available at http://gsp.tamu.edu/Publications/BNs/bn.htm

title: Intervention in context-sensitive probabilistic Boolean networks
abstract: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a context-sensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper extends the methods of external control to context-sensitive PBNs.



This paper treats intervention via external control variables in context-sensitive PBNs by extending the results for instantaneously random PBNs in several directions. First, and most importantly, whereas an instantaneously random PBN yields a Markov chain whose state space is composed of gene vectors, each state of the Markov chain corresponding to a context-sensitive PBN is composed of a pair, the current gene vector occupied by the network and the current constituent Boolean network. Second, the analysis is applied to PBNs with perturbation, meaning that random gene perturbation is permitted at each instant with some probability. Third, the (mathematical) influence of genes within the network is used to choose the particular gene with which to intervene. Lastly, PBNs are designed from data using a recently proposed inference procedure that takes steady-state considerations into account. The results are applied to a context-sensitive PBN derived from gene-expression data collected in a study of metastatic melanoma, the intent being to devise a control strategy that reduces the WNT5A gene's action in affecting biological regulation, since the available data suggest that disruption of this influence could reduce the chance of a melanoma metastasizing.

title: Multiclass Transaction Scheduling and Overload Management in Firm Real-Time Database Systems
abstract: Real-Time Database Systems (RTDBSs), have attracted considerable amount of research attention in the recent past and a number of important applications have been identified for such systems, such as telecommunications network management, automated air traffic control, automated financial trading, process control and military command and control systems. Due to the rapidity of change of the system state in such applications, as well as the inherent complexities in controlling such systems (which result in frequent violation of consistency requirements and consequent repeated firings of control actions), it is likely that the transaction load in these systems would be fairly high. Thus RTDBSs need to be equipped with overload management mechanisms. Unfortunately overload management has been a fairly neglected area in real-time systems research in general and real-time database research in particular. In this paper we introduce Adaptive Access Parameter (AAP), a scheduling mechanism for multiclass transactions in real-time database systems that employs an explicit admission control policy to manage overload as well as system bias towards particular transaction classes. We show the theoretical underpinnings behind AAP and then report a thorough performance study that demonstrates AAP's substantial superiority over current algorithms with regard to performance metrics as well as computational overhead.

title: MANDATE: MAnaging Networks Using DAtabase TEchnology
abstract: There has been a growing demand for the development of tools to manage enterprise communication networks. A management information database is the heart of a network management system-it provides the interface between all functions of the network management system and, therefore, has to provide sophisticated functionality allied with high performance. The authors introduce the design of MANDATE (MAnaging Networks using DAtabase TEchnology), a proposed database system for effectively supporting the management of large enterprise networks. The MANDATE design makes a conscious attempt to take advantage of the special characteristics of network data and transactions, and of advances in database technology, to efficiently derive some of the required management functionality.

title: Internet-Scale Storage Systems under Churn -- A Study of the Steady-State using Markov Models
abstract: Content storage in a distributed collaborative environment uses redundancy for better resilience and thus provides good availability and durability. In a peer-to-peer environment, where peers continuously leave and rejoin the network, various lazy strategies can be employed to maintain a minimal redundancy of stored content in the system. Existing static resilience analyses fail to capture in detail the system's behavior over time, particularly the probability mass function of the actual available redundancy, since it ignores the crucial interplay between churn and maintenance operations, and looks only at the average system property. We perform a Markovian time-evolution analysis of the system specified by probability mass function of each possible system state, and establish that given a fixed rate of churn and a specific maintenance strategy, the system operates in a corresponding steady-state (dynamic equilibrium). Understanding the behavior of the system under such a dynamic equilibrium is a fundamental ingredient to precisely evaluate analytically the system's performance and availability as well as to determine the required operational maintenance cost. We also propose a new randomized variant of a lazy-maintenance scheme which has significant performance benefits in comparison to the existing deterministic procrastination based maintenance. We demonstrate the use of our analysis methodology in comparing performance of maintenance schemes using the examples of the new maintenance scheme we propose and the erstwhile best known existing lazy maintenance scheme. The comparative study shows that our randomized lazy maintenance strategy has substantially better resilience at same maintenance cost

title: Self-stabilizing mutual exclusion using unfair distributed scheduler
abstract: A self-stabilizing algorithm, regardless of the initial system state, converges infinite time to a set of states that satisfy a legitimacy predicate without the need for explicit exception handler of backward recovery. Mutual exclusion is fundamental in the area of distributed computing, by serializing the accesses to a common shared resource. All existing probabilistic self-stabilizing mutual exclusion algorithms designed to work under an unfair distributed scheduler suffer from the following common drawback: Once stabilized, there exists no upper bound of time between two executions of the critical section at a given node. We present the first probabilistic self-stabilizing algorithm that guarantees such a bound (O(n/sup 3/), where n is the network size) while working using an unfair distributed scheduler. As the scheduling adversary gets weaker the bound gets better. Our algorithm works in an anonymous unidirectional ring of any size and has a O(n/sup 3/) expected stabilization time.

title: Anonymous publish/subscribe in P2P networks
abstract: One of the most important issues to deal with in peer-to-peer networks is how to disseminate information. In this paper, we use a completely new approach to solving the information dissemination problem. Our approach uses the publish/subscribe paradigm. The publish/subscribe method is the most inclusive strategy to establish communication between the information providers (publishers) and the information consumers (subscribers). We give a formal definition of publish/subscribe systems. We then use the publish/subscribe communication paradigm to design deterministic protocols (topic and content-based) for peer-to-peer networks. Our protocols are designed on top of an innovative information dissemination scheme, and can cope with the anonymity and mobility of both publishers and subscribers, weak-connectivity, and polarization, which are some of the characteristics of peer-to-peer networks. Moreover, in our solutions, every node could play a role of both publisher and subscriber The algorithms are designed completely independent of the underlying routing substrates. The key advantage of our protocols is that they are scalable without additional re-organization cost. To the best of our knowledge, this is the first time the content-based subscription has been addressed in peer-to-peer networks.