External control in Markovian genetic regulatory networks
Probabilistic Boolean networks (PBN's) have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. Such networks, which form a subclass of Markovian genetic regulatory networks, provide a convenient tool for studying interactions between different genes while allowing for uncertainty in the knowledge of these relationships. This paper deals with the issue of control in probabilistic Boolean networks. More precisely, given a general Markovian genetic regulatory network whose state transition probabilities depend on an external (control) variable, the paper develops a procedure by which one can choose the sequence of control actions that minimize a given performance index over a finite number of steps. The procedure is based on the theory of controlled Markov chains and makes use of the classical technique of dynamic programming. The choice of the finite horizon performance index is motivated by cancer treatment applications where one would ideally like to intervene only over a finite time horizon, then suspend treatment and observe the effects over some additional time before deciding if further intervention is necessary. The undiscounted finite horizon cost minimization problem considered here is the simplest one to formulate and solve, and is selected mainly for clarity of exposition, although more complicated costs could be used, provided appropriate technical conditions are satisfied.

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: Generating Boolean networks with a prescribed attractor structure
abstract: 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: 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: Publish/subscribe scheme for mobile networks
abstract: The information dissemination in mobile networks is an important but complex and challenging problem. Designing suitable communication primitives for these systems is critical. One of these primitives is the publish/subscribe paradigm. The publish/subscribe is a strategy to establish communication between the information providers (publishers) and information consumers (subscribers) in a distributed system. Our work focuses on an appropriate distributed infrastructure suitable for a scalable implementation of a publish/subscribe system. We present a formal model which is adapted for the peer-based particular subscription criteria of publish/subscribe systems. Moreover, we propose a general deterministic information diffusion scheme for mobile systems. The three main features of our communication scheme are the following: First, our scheme is well-adapted to scalable systems without compromising any subscription criteria or network reorganization. Second, we maintain the anonymity of the distributed system --- in order to maintain the network structure, we need only local information. Third, our solution is fully decentralized and modular, thus making it appropriate for practical implementations.

title: Abstraction and refinement in protocol derivation
abstract: Protocols may be derived from initial components by composition, refinement, and transformation. Adding function variables to a previous protocol logic, we develop an abstraction-instantiation method for reasoning about a class of protocol refinements. The main idea is to view changes in a protocol as a combination of finding a meaningful "protocol template" that contains function variables in messages, and producing the refined protocol as an instance of the template. Using higher-order protocol logic, we can develop a single proof for all instances of a template. A template can also be instantiated to another template, or a single protocol may be an instance of more than one template, allowing separate protocol properties to be proved modularly. These methods are illustrated using some challenge-response and key exchange protocol templates and an exploration of the design space surrounding JFK (just fast keying) and related protocols from the IKE (Internet key exchange) family, which produces some interesting protocols not previously studied in the open literature.

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.

title: Handling Sensor Data in Rapidly Changing Environments to Support Soft Real-Time Requirements
abstract: Databases have been mandated as the chosen platform to develop automated control systems for environments where the state of the system changes rapidly and actions need to be taken with timing constraints, for example, stock trading, air traffic control, network management, and process control to name a few. Input data in such systems come from sensors distributed throughout the physical environment being monitored. As the system state changes rapidly, the sensors report information fast and with high volumes. Control decisions in such systems are highly dependent on the accuracy and timeliness of such recorded sensor-reported data. In this paper we suggest ways to algorithmically maintain the accuracy and timeliness of sensor data by enforcing two properties termedrecency andtemporal consistency. Simultaneously, our algorithms also attempt to satisfyquality of service requirements on response times of queries submitted in such systems. The performance of these algorithms is validated through an extensive simulation.