Pritha Mahata

Regular Tree Model Checking

In this paper, we present an approach for algorithmic verification of infinite-state systems with a parameterized tree topology. Our work is a generalization of regular model checking, where we extend the work done with strings toward trees. States are represented by trees over a finite alphabet, and transition relations by regular, structure preserving relations on trees. We use an automata theoretic method to compute the transitive closure of such a transition relation. Although the method is incomplete, we present sufficient conditions to ensure termination.We have implemented a prototype for our algorithm and show the result of its application on a number of examples.

Multi-clock timed networks

We consider verification of safety properties for parameterized systems of timed processes, so called timed networks. A timed network consists of a finite state process, called a controller, and an arbitrary set of identical timed processes. In a previous work, we showed that checking safety properties is decidable in the case where each timed process is equipped with a single real-valued clock. It was left open whether the result could be extended to multi-clock timed networks. We show that the problem becomes undecidable when each timed process has two clocks. On the other hand, we show that the problem is decidable when clocks range over a discrete time domain. This decidability result holds when processes have any finite number of clocks.

DENSE-TIMED PETRI NETS: CHECKING ZENONESS, TOKEN LIVENESS AND BOUNDEDNESS

We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which each token is equipped with a real-valued clock and where the semantics is lazy (i.e., enabled transitions need not fir ...

Forward Reachability Analysis of Timed Petri Nets

We consider verification of safety properties for concurrent real-timed systems modelled as timed Petri nets, by performing symbolic forward reachability analysis. We introduce a formalism, called region generators for representing sets of markings of timed Petri nets. Region generators characterize downward closed sets of regions, and provide exact abstractions of sets of reachable states with respect to safety properties. We show that the standard operations needed for performing symbolic reachability analysis are computable for region generators. Since forward reachability analysis is necessarily incomplete, we introduce an acceleration technique to make the procedure terminate more often on practical examples. We have implemented a prototype for analyzing timed Petri nets and used it to verify a parameterized version of Fischer’s protocol and a producer-consumer protocol. We also used the tool to extract finite-state abstractions of these protocols.

Selecting differentially expressed genes using minimum probability of classification error

Discovery of differentially expressed genes between normal and diseased patients is a central research problem in bioinformatics. It is specially important to find few genetic markers which can be explored for diagnostic purposes. The performance of a set of markers is often measured by the associated classification accuracy. This motivates our ranking of genes depending on the minimum probability of classification errors (MPE) for each gene. In this work, we use Bayesian decision-making algorithm to compute MPE. A quantile-based probability density estimation technique is used for generating probability density functions of genes. The method is tested on three datasets: colon cancer, leukaemia, and hereditary breast cancer. The quality of the selected markers is evaluated by the classification accuracy obtained using support-vector-machine and a modified naive Bayes classifier. We obtain 96.77% accuracy in colon cancer and 97.06% accuracy in leukaemia, using only five genes in each case. Finally, using just three genes we get 100% accuracy in hereditary breast cancer. We also compare our results with those using the genes ranked by p-value and show that the genes ranked by MPE perform better or equal to those ranked by p-value.

Hierarchical clustering, languages and cancer

In this paper, we introduce a novel objective function for the hierarchical clustering of data from distance matrices, a very relevant task in Bioinformatics. To test the robustness of the method, we test it in two areas: (a) the problem of deriving a phylogeny of languages and (b) subtype cancer classification from microarray data. For comparison purposes, we also consider both the use of ultrametric trees (generated via a two-phase evolutionary approach that creates a large number of hypothesis trees, and then takes a consensus), and the best-known results from the literature. We used a dataset of measured ’separation time’ among 84 Indo-European languages. The hierarchy we produce agrees very well with existing data about these languages across a wide range of levels, and it helps to clarify and raise new hypothesis about the evolution of these languages. Our method also generated a classification tree for the different cancers in the NCI60 microarray dataset (comprising gene expression data for 60 cancer cell lines). In this case, the method seems to support the current belief about the heterogeneous nature of the ovarian, breast and non-small-lung cancer, as opposed to the relative homogeneity of other types of cancer. However, our method reveals a close relationship of the melanoma and CNS cell-lines. This is in correspondence with the fact that metastatic melanoma first appears in central nervous system (CNS).

Decidability of zenoness, syntactic boundedness and token-liveness for dense-timed petri nets

We consider Timed Petri Nets (TPNs): extensions of Petri nets in which each token is equipped with a real-valued clock. We consider the following three verification problems for TPNs. (i) Zenoness: whether there is an infinite computation from a given marking which takes only a finite amount of time. We show decidability of zenoness for TPNs, thus solving an open problem from [dFERA00]. (ii) Token Liveness: whether a token is alive in a marking, i.e., whether there is a computation from the marking which eventually consumes the token. We show decidability of the problem by reducing it to the coverability problem, which is decidable for TPNs. (iii) Boundedness: whether the size of the reachable markings is bounded. We consider two versions of the problem; namely semantic boundedness where only live tokens are taken into consideration in the markings, and syntactic boundedness where also dead tokens are considered. We show undecidability of semantic boundedness, while we prove that syntactic boundedness is decidable through an extension of the Karp-Miller algorithm.

Hierarchical Clustering Using the Arithmetic-Harmonic Cut: Complexity and Experiments

Clustering, particularly hierarchical clustering, is an important method for understanding and analysing data across a wide variety of knowledge domains with notable utility in systems where the data can be classified in an evolutionary context. This paper introduces a new hierarchical clustering problem defined by a novel objective function we call the arithmetic-harmonic cut. We show that the problem of finding such a cut is -hard and -hard but is fixed-parameter tractable, which indicates that although the problem is unlikely to have a polynomial time algorithm (even for approximation), exact parameterized and local search based techniques may produce workable algorithms. To this end, we implement a memetic algorithm for the problem and demonstrate the effectiveness of the arithmetic-harmonic cut on a number of datasets including a cancer type dataset and a corona virus dataset. We show favorable performance compared to currently used hierarchical clustering techniques such as -Means, Graclus and Normalized-Cut. The arithmetic-harmonic cut metric overcoming difficulties other hierarchal methods have in representing both intercluster differences and intracluster similarities.

Maximizing Correlation for Supervised Classification

In this paper, we develop a novel feature selection and classification approach using the correlation maximization paradigm. This approach is particularly interesting when the number of features is very large in comparison to the number of samples, as in the datasets arising in the bioinformatics applications. We illustrate our method by showing 100 genetic markers which act together in separating ovarian endometroid tumors from other ovarian epithelial tumors. Notice that in the previous works, there was no single marker gene found for this purpose.

Periodicity Detection in Small-Sample Gene-Expression Data

Analysis of cell-cycle regulation, circadian rhythms, ovarian cycle, etc, demands finding periodicity in the biological data. In this work, we will consider gene expression data, which is usually quite noisy and comprise of small number of samples from very few periods (2 - 3). We propose a n on-parametric method for detecting the period and shape of the periodic signals (e.g., gene expressions for cell-cycles). We use a quadratic-optimization problem formulation in order to find the shape of the signal and the properties of periodicity to find the exact period. Finally, we show the results of applying this method on the gene expression data for human fibroblast cell cycles.