P. S. Thiagarajan

We introduce a framework for analyzing ordinary differential equation (ODE) models of biological networks using statistical model checking (SMC). A key aspect of our work is the modeling of single-cell variability by assigning a probability distribution to intervals of initial concentration values and kinetic rate constants. We propagate this distr...

Identifying non-trivial requirements for large complex dynamical systems is a challenging but fruitful task. Once identified such requirements can be used to validate updated versions of the system and verify functionally similar systems. Here we present a technique for discovering behavioural properties of bio-pathway models whose dynamics is mode...

Glioblastoma (GBM) is a deadly brain cancer that suppresses cellular immunity through the production of anti-inflammatory cytokines/catabolites, expression of immune checkpoint molecules, and induction of tolerogenic immune cell subsets. While preclinical models have shown each of these mechanisms to negatively impact survival outcome, it remains u...

Toll-like receptors (TLRs) recognize pathogen-associated molecular patterns (PAMPs) and stimulate the innate immune response through the production of cytokines. The innate immune response depends on the timing of encountering PAMPs, suggesting a short-term "memory." In particular, activation of TLR3 appears to prime macrophages for the subsequent...

Software is often governed by and thus adapts to phenomena that occur at runtime. Unlike traditional decision problems, where a decision-making model is determined for reasoning, the adaptation logic of such software is concerned with empirical data and is subject to practical constraints. We present an Iterative Decision-Making Scheme (IDMS) that...

We develop a GPU based technique to analyze bio-pathway models consisting of systems of ordinary differential equations (ODEs). A key component in our technique is an online procedure for verifying whether a numerically generated trajectory of a model satisfies a property expressed in bounded linear temporal logic. Using this procedure, we construc...

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability...

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are difficult to analyze. To address this, we develop an approximate probabilistic analysis method. We do so by approximating the mode transitions as stochastic events. More precisely, we assume that the probability of making a mode transition is pr...

The formal verification of large probabilistic models is challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a class of communicating probabilistic agents in which the synchronizations determine the probability distribution for the next moves of the participating agents. The key property o...

Rabin's theorem says that the monadic second order theory of the infinite binary tree is decidable. This result has had a far reaching influence in the theory of branching time temporal logics. A simple consequence of Rabin's theorem is that for every finite state transition system, the monadic second order theory of its computation tree is decidab...

The TGF-β/Smad signaling system decreases its activity through strong negative regulation. Several molecular mechanisms of negative regulation have been published, but the relative impact of each mechanism on the overall system is unknown. In this work, we used computational and experimental methods to assess multiple negative regulatory effects on...

Reactive species such as free radicals are constantly generated in vivo and DNA is the most important target of oxidative stress. Oxidative DNA damage is used as a predictive biomarker to monitor the risk of development of many diseases. The comet assay is widely used for measuring oxidative DNA damage at a single cell level. The analysis of comet...

We present a novel code generation scheme for GPUs. Its key feature is the platform-aware generation of a heterogeneous pool of threads. This exposes more data-sharing opportunities among the concurrent threads and reduces the memory requirements that would otherwise exceed the capacity of the on-chip memory. Instead of the conventional strategy of...

We present a novel code generation scheme for GPUs. Its key feature is the platform-aware generation of a heterogeneous pool of threads. This exposes more data-sharing opportunities among the concurrent threads and reduces the memory requirements that would otherwise exceed the capacity of the on-chip memory. Instead of the conventional strategy of...

We present a statistical model checking (SMC) based framework for studying ordinary differential equation (ODE) models of bio-pathways. We address cell-to-cell variability explicitly by using probability distributions to model initial concentrations and kinetic rate values. This implicitly defines a distribution over a set of ODE trajectories, the...

We present a novel class of distributed stochastic systems called deterministically communicating Markov Decision Processes (DMDPs). A DMDP is a network of communicating agents in which the local prob-abilistic choices available to each agent are influenced by information obtained from partners during synchronizations. The identity of the communica...

Carl Adam Petri was a visionary who founded an extraordinarily fruitful domain of study in the field of distributed discrete event systems. He was the first computer scientist to identify concurrency as a fundamental aspect of computing. He did so in his seminal PhD thesis from 1962 where in fact he outlined a whole new foundations for computer sci...

Statistical model checking techniques have been shown to be effective for approximate model checking on large stochastic systems, where explicit representation of the state space is impractical. Importantly, these techniques ensure the validity of results with statistical guarantees on errors. There is an increasing interest in these classes of alg...

The modeling and analysis of probabilistic dynamical systems is becoming a central topic in the formal methods community. Usually, Markov chains of various kinds serve as the core mathematical formalism in these studies. However, in many of these settings, the probabilistic graphical model called dynamic Bayesian networks (DBNs) [4] can be amore ap...

Cellular processes are governed and coordinated by a multitude of biopathways. A pathway can be viewed as a complex network of biochemical reactions. The dynamics of this network largely determines the functioning of the pathway. Hence the modeling and analysis of biochemical networks dynamics is an important problem and is an active area of resear...

We summarize some previous results on the discrete time behaviour of a class of restricted linear hybrid automata. Specifically, we show the regularity of the discrete time behaviour of hybrid automata in which the rates of continuous variables are governed by linear operators in a diagonal form and in which the values of the continuous variables c...

A finite-state Markov chain M can be regarded as a linear transform operating on the set of probability distributions over its node set. The iterative applications of M to an initial probability distribution μ0 will generate a trajectory of probability distributions. Thus, a set of initial distributions will induce a set of trajectories. It is an i...

Dynamic Bayesian Networks (DBNs) can serve as succinct probabilistic dynamic models of biochemical networks. To analyze these models, one must compute the probability distribution over system states at a given time point. Doing this exactly is infeasible for large models; hence one must use approximate algorithms. The Factored Frontier algorithm (F...

Biopathways are often modeled as systems of ordinary differential equations (ODEs). Such systems will usually have many unknown parameters and hence will be difficult to calibrate. Since the data available for calibration will have limited precision, an approximate representation of the ODEs dynamics should suffice. One must, however, be able to ef...

Dynamic Bayesian Networks (DBNs) can serve as succinct models of large biochemical networks [19]. To analyze these models, one must compute the probability distribution over system states at a given time point. Doing this exactly is infeasible for large models and hence approximate methods are needed. The Factored Frontier algorithm (FF) is a simpl...

Constructing and analyzing large biological pathway models is a significant challenge. We propose a general approach that exploits the structure of a pathway to identify pathway components, constructs the component models, and finally assembles the component models into a global pathway model. Specifically, we apply this approach to pathway paramet...

equations (ODEs). The equations describe specific bio-chemical reactions, while the variables typically represent concentration levels of molecular species (genes, RNAs, proteins). Bio-pathways usually involve a large number of molecular species and bio-chemical reactions. Hence the corresponding ODE model will involve many variables and parameters...

DBN Structure of PC-initiated classical complement pathway. (0.08 MB PDF)

Prior (initial) probability distribution of variables. (0.09 MB PDF)

The ODE Model. (0.08 MB PDF)

The CRP level in the blood of patients diagnosed with infection compared to normal healthy individuals. (A) The CRP concentration in normal individuals and patients included in this study. (B) The average CRP levels from five healthy volunteers and nine patients were measured by Bioassay ELISA kit (BD Biosciences, San Jose, CA) and calculated to re...

DBN Structure of GlcNAc-initiated classical complement pathway. (0.08 MB PDF)

In vitro bacteria killing assay. (A) Bright field of bacterial killing effect image (Figure 1A) indicated that the bacteria were within the field of view. 108 cfu bacteria with GFP fluorescence were incubated with sera or buffers under normal or infection-inflammation conditions. Images were taken at 15 s intervals for 30 min (magnification: 63×1.6...

C4BP levels measured by C4BP sandwich ELISA for both treated and untreated serum samples. (0.10 MB TIF)

The initial concentrations. (0.05 MB PDF)

Parameter values. Known parameters are marked with *. (0.09 MB PDF)

Prior (initial) probability distribution of parameters. (0.09 MB PDF)

The complement system is key to innate immunity and its activation is necessary for the clearance of bacteria and apoptotic cells. However, insufficient or excessive complement activation will lead to immune-related diseases. It is so far unknown how the complement activity is up- or down- regulated and what the associated pathophysiological mechan...

Good scheduling policies for distributed embedded applications are required for meeting hard real time constraints and for optimizing the use of computational resources. We study the quasi-static scheduling problem in which (uncontrollable) control flow branchings can influence scheduling decisions at run time. Our abstracted distributed task model...

Constructing quantitative dynamic models of signaling pathways is an important task for computational systems biology. Pathway model construction is often an inherently incremental process, with new pathway players and interactions continuously being discovered and additional experimental data being generated. Here we focus on the problem of perfor...

We consider a network of hybrid automata that observe and control a plant whose state space is determined by a finite set of continuous variables. We assume that at any instant, these variables are evolving at (possibly different) constant rates. Each automaton in the network controls-i.e. can switch the rates of-a designated subset of the continuo...

Systems of ordinary differential equations (ODEs) are often used to model the dynamics of complex biological pathways. We construct a discrete state model as a probabilistic approximation of the ODE dynamics by discretizing the value space and the time domain. We then sample a representative set of trajectories and exploit the discretization and th...

The Real-Time Calculus (RTC) framework proposed in [Chakraborty et al., DATE 2003] and subsequently extended in [Wandeler et al., Real-Time Systems 29(2-3), 2005] and a number of other papers is geared towards the analysis of real-time systems that process various types of streaming data. The main strength of RTC is a count-based abstraction, where...

Good scheduling policies for distributed embedded applications are required for meeting hard real time constraints and for optimizing the use of computational resources. We study the quasi-static scheduling problem in which (uncontrollable) control flow branchings can influence scheduling decisions at run time. Our abstracted task model consists of...

Time-triggered architectures (TTAs) are strong candidate platforms for safety-critical real-time applications. A typical time-triggered architecture is constituted by one or more clusters. Each cluster consists of nodes communicating with one another via a time-triggered communication protocol. Designing applications to run on such a platform is a...

We present a performance analysis technique for dis- tributed real-time systems in a setting where certain com- ponents are modeled in a purely functional manner, while the remaining components require additional modeling of state information. The functional models can be efficiently analyzed but have restricted expressiveness. On the other hand, s...

Parameter estimation of large bio-pathway models is an important and difficult problem. To reduce the prohibitive computational cost, one approach is to decompose a large model into components and estimate their parameters separately. However, the decomposed components often share common parts that may have conflicting parameter estimates, as they...

Scenario languages based on Message Sequence Charts (MSCs) have been widely studied in the last decade. The high expressive power of MSCs renders many basic problems concerning these languages undecidable. However, several of these problems are decidable for languages that possess a behavioral property called “existentially bounded”. Unfortunately,...

Message sequence charts (MSCs) constitute an attractive visual formalism that is widely used to capture system requirements during the early design stages in domains such as telecommunication software. A version of MSCs called sequence diagrams is one of the behavioral diagram types adopted in the UML. In this chapter we survey MSCs and their exten...

A Communicating Transaction Process (CTP) is a computational model that serves as a high level specification language for reactive embedded system components and their interactions. It consists of a network of communicating processes coordinating their behaviors via common actions and the common actions are refined as a set of guarded Message Seque...

Our aim will be to introduce and discuss the basic system model of net theory called Condition/Event Systems. We shall start with a brief discussion of the twin notions of states and transitions as viewed within net theory. This will motivate the restrictions placed on the Condition/Event System model. We shall then introduce nets and construct Con...

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Parameter estimation is a critical problem in modeling biological pathways. It is difficult because of the large number of parameters to be estimated and the limited experimental data available. In this paper, we propose a decompositional approach to parameter estimation. It exploits the structure of a large pathway model to break it into smaller c...

We present a system level description mechanism based on UML notations from which one can automatically extract SystemC code. Our modelling framework is based on a restricted set of UML diagram types together with some extensions developed using stereotypes. As a result, applications as well as platform features can be captured at this level. Our s...

We study collections of Message Sequence Charts (MSCs) defined by High-level MSCs (HMSCs) under a new type of concatenation operation called anchored concatenation. We show that there is no decision procedure for determining if the MSC language defined by an HMSC is regular and that it is undecidable if an HMSC admits an implied scenario. Fur-ther,...

Many reactive control systems consist of classes of active objects involving both intraclass interactions (i.e., objects belonging to the same class interacting with each other) and interclass interactions. Such reactive control systems appear in domains such as telecommunication, transportation and avionics. In this article, we propose a modeling...

We investigate the problem of designing interface circuits for rationally clocked modules in GALS systems. As a key contribution, we show that knowledge of flow-control protocols can be used to significantly optimize synchronization mechanisms. We present delay-augmented netcharts as a formalism for representing communication protocols and describe...

We present here a linear time temporal logic which simultaneously extends LTL, the propositional temporal logic of linear time, along two dimensions. Firstly, the until operator is strengthened by indexing it with the regular programs of propositional dynamic logic (PDL). Secondly, the core formulas of the logic are decorated with names of sequenti...

We give a sketch of the theory of Petri nets. The aspects that we concentrate on are the basic notions of the theory and the interplay between the structure and behaviour of distributed systems as modelled by Petri nets. The theory we present is confined to a restricted class of Petri nets called safe Petri nets which correspond essentially to syst...

We present a logical characterization of a particular aspect of concurrency called the concurrent step notion. We do so by providing a sound and complete axiomatization of models called distributed transition systems. In a distributed transition system an old state is transformed into a new state through a set of actions occurring concurrently. Our...

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We show the regularity of the discrete time behaviour of hybrid automata in which the rates of continuous variables are governed by linear differential operators in a diagonal form and in which the values of the continuous variables can be observed only with finite precision. We do not demand resetting of the values of the continuous variables duri...

We investigate the problem of designing interface circuits for rationally clocked modules in GALS systems. As a key contribution, we show that knowledge of flow-control protocols can be used to significantly optimize synchronization mechanisms. We present delay-augmented netcharts as a formalism for representing communication protocols and describe...

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Recently there has been a growing interest in models and methods targeted towards the (co)design of stream processing applications; e.g. those for audio/video processing. Streams processed by such applications tend to be highly bursty and exhibit a high data-dependent variability in their processing requirements. As a result, classical event and se...

Embedded computing systems have started to carry out the key control functions in diverse domains such as telecommunications, automotive electronics, avionics and even complete industrial manufacturing lines. Traditionally, such embedded control systems have been implemented in a monolithic, centralized manner. However, distributed and parallel sol...

We identify a network of sequential processes that commu- nicate by synchronizing frequently on common actions. More precisely, we demand that there is a bound k such that if the process p executes k steps without hearing from process q—directly or indirectly—then it will never hear fromq again. The non-interleaved branching time behavior of a syst...

We study the class of lazy linear hybrid automata with finite precision. The key features of this class are: The observation of the continuous state and the rate changes associated with mode switchings take place with bounded delays. The values of the continuous variables can be observed with only finite precision. The guards controlling the transi...

We present a system level description mechanism based on UML-notations from which one can automatically extract SystemC code. Our modelling framework is based on a restricted set of UML diagram types and some standard extensions influenced by the communication infrastructure of SystemC. The system specifications are developed using the UML-compatib...

To establish a semantic foundation for the synthesis of executable programs from timed models, we study in what sense the timed language (i.e. sequences of events with real-valued time-stamps) of a timed automaton is recognized by a digital machine. Based on the non-instant observability of events, we propose an alternative semantics for timed auto...

Introduction We present preliminary results concerning a translation that generates SystemC code from designs developed in UML using the Rational Rose RT tool. For suitably restricted designs, the generated SystemC code is synthesizable in that it is accepted by the Synopsis CoCentric compiler. The construction of this translator is a part of our o...

Message Sequence Charts (MSC) have been traditionally used to depict execution scenarios in the early stages of design cycle. MSCs portray inter-object interactions. Synthesizing intra-object executable specifications from an MSC-based description is a non-trivial task. Here we present a model of computation called Communicating Transaction Process...

Message Sequence Charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose,...

We introduce the class of lazy rectangular hybrid automata. The key feature of this class is that both the observation of the continuous state and the rate changes associated with mode switchings take place with bounded delays. We show that the discrete time dynamics of this class of automata can be effectively analyzed without requiring resetting...

Reuse of IP blocks is an important design philosophy for embedded systems. This allows shorter design cycles under tight time-to-market constraints. However, reusing IP blocks often requires designing converters (glue logic) to enable their communication. In this paper, we study the problem of automatically generating a protocol converter which ena...

We define a new notation called netcharts for describing sets of message sequence chart scenarios (MSCs). Netcharts correspond to a distributed version of High-level Message Sequence Charts (HMSCs). Netcharts improve on HMSCs in two respects. Netcharts admit a natural and direct translation into communicating finite-state machines, unlike HMSCs, fo...

Message sequence charts (MSC) have been traditionally used to depict execution scenarios in the early stages of design cycle. MSCs portray inter-process (inter-object) interactions. Synthesizing intra-process (intra-object) executable specifications from an MSC-based description is a nontrivial task. Here we present a model called communicating tra...

We advocate Cyclic Communicating Processes (CCPs) as a viable and tractable model of computation for reactive systems. As the name suggests, the model consists of a network of sequential agents that communicate with each other. The crucial restriction is that the control flow of each agent is cyclic. The communication mechanism consists of the agen...

Message Sequence Charts (MSC) have been traditionally used to depict execution scenarios in the early stages of design cycle. MSCs portray inter-process ( inter-object) interactions. Synthesizing intra-process (intra-object) executable specifications from an MSC-based description is a non-trivial task. Here we present a model called Communicating T...

Message Sequence Charts (MSCs) are an appealing visual formalism that play a useful role in the early design stages of reactive systems such as telecommunication protocols. They also constitute one of the behavioral diagram types in the UML framework [4]. MSCs are usually intended to capture system requirements. However there is no standard relatio...

Message Sequence Charts (MSC) have been traditionally used to depict execution scenarios in the early stages of design cycle. MSCs portray inter-object interactions. Synthesizing intra-object executable specifications from an MSC-based description is a non-trivial task. Here we present a model of computation called Communicating Transaction Process...

We present the notion of regular event structures and conjecture that they correspond exactly to finite 1-safe Petri nets. We show that the conjecture holds for the conflict-free case. Even in this restricted setting, the proof is non-trivial and involves a natural subclass of regular event structures that admit a sensible labeling with Mazurkiewic...

We identify a subclass of timed automata called product interval automata and develop its theory. These automata consist of a network of timed agents with the key restriction being that there is just one clock for each agent and the way the clocks are read and reset is determined by the distribution of shared actions across the agents. We show that...

We study the problem of synthesizing controllers for discrete event systems in a branching time framework. We use a class of labelled transition systems to model both plants and specifications. We use first simulations and later bisimulations to capture the role of a controller; the controlled behaviour of the plant should be related via a simulati...