Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).

Optimizing the Dynamic Distribution of Data-stream for High Speed Communications

The performances of high-speed network communications frequently rest with the distribution of data-stream. In this paper, a dynamic data-stream balancing architecture based on link information is introduced and discussed firstly. Then the algorithms for simultaneously acquiring the passing nodes and links of a path between any two source-destination nodes rapidly, as well as a dynamic data-stream distribution planning are proposed. Some related topics such as data fragment disposal, fair service, etc. are further studied and discussed. Besides, the performance and efficiency of proposed algorithms, especially for fair service and convergence, are evaluated through a demonstration with regard to the rate of bandwidth utilization. Hoping the discussion presented here can be helpful to application developers in selecting an effective strategy for planning the distribution of data-stream.

On optimal computation of MPLS label binding for multipoint-to-point connections

Most network operators have considered reducing Label Switched Routers (LSR) label spaces (i.e. the number of labels that can be used) as a means of simplifying management of underlaying Virtual Private Networks (VPNs) and, hence, reducing operational expenditure (OPEX). This letter discusses the problem of reducing the label spaces in Multiprotocol Label Switched (MPLS) networks using label merging - better known as MultiPoint-to-Point (MP2P) connections. Because of its origins in IP, MP2P connections have been considered to have tree- shapes with Label Switched Paths (LSP) as branches. Due to this fact, previous works by many authors affirm that the problem of minimizing the label space using MP2P in MPLS - the Merging Problem - cannot be solved optimally with a polynomial algorithm (NP-complete), since it involves a hard- decision problem. However, in this letter, the Merging Problem is analyzed, from the perspective of MPLS, and it is deduced that tree-shapes in MP2P connections are irrelevant. By overriding this tree-shape consideration, it is possible to perform label merging in polynomial time. Based on how MPLS signaling works, this letter proposes an algorithm to compute the minimum number of labels using label merging: the Full Label Merging algorithm. As conclusion, we reclassify the Merging Problem as Polynomial-solvable, instead of NP-complete. In addition, simulation experiments confirm that without the tree-branch selection problem, more labels can be reduced

A proposal for the diagnosis of uncertain dynamic systems based on interval models

The performance of a model-based diagnosis system could be affected by several uncertainty sources, such as,model errors,uncertainty in measurements, and disturbances. This uncertainty can be handled by mean of interval models.The aim of this thesis is to propose a methodology for fault detection, isolation and identification based on interval models. The methodology includes some algorithms to obtain in an automatic way the symbolic expression of the residual generators enhancing the structural isolability of the faults, in order to design the fault detection tests. These algorithms are based on the structural model of the system. The stages of fault detection, isolation, and identification are stated as constraint satisfaction problems in continuous domains and solved by means of interval based consistency techniques. The qualitative fault isolation is enhanced by a reasoning in which the signs of the symptoms are derived from analytical redundancy relations or bond graph models of the system. An initial and empirical analysis regarding the differences between interval-based and statistical-based techniques is presented in this thesis. The performance and efficiency of the contributions are illustrated through several application examples, covering different levels of complexity.

Sonic to ultrasonic Q of sandstones and limestones: Laboratory measurements at in situ pressures

Laboratory measurements of the attenuation and velocity dispersion of compressional and shear waves at appropriate frequencies, pressures, and temperatures can aid interpretation of seismic and well-log surveys as well as indicate absorption mechanisms in rocks. Construction and calibration of resonant-bar equipment was used to measure velocities and attenuations of standing shear and extensional waves in copper-jacketed right cylinders of rocks (30 cm in length, 2.54 cm in diameter) in the sonic frequency range and at differential pressures up to 65 MPa. We also measured ultrasonic velocities and attenuations of compressional and shear waves in 50-mm-diameter samples of the rocks at identical pressures. Extensional-mode velocities determined from the resonant bar are systematically too low, yielding unreliable Poisson's ratios. Poisson's ratios determined from the ultrasonic data are frequency corrected and used to calculate the sonic-frequency compressional-wave velocities and attenuations from the shear- and extensional-mode data. We calculate the bulk-modulus loss. The accuracies of attenuation data (expressed as 1000/Q, where Q is the quality factor) are +/- 1 for compressional and shear waves at ultrasonic frequency, +/- 1 for shear waves, and +/- 3 for compressional waves at sonic frequency. Example sonic-frequency data show that the energy absorption in a limestone is small (Q(P) greater than 200 and stress independent) and is primarily due to poroelasticity, whereas that in the two sandstones is variable in magnitude (Q(P) ranges from less than 50 to greater than 300, at reservoir pressures) and arises from a combination of poroelasticity and viscoelasticity. A graph of compressional-wave attenuation versus compressional-wave velocity at reservoir pressures differentiates high-permeability (> 100 mD, 9.87 X 10(-14) m(2)) brine-saturated sandstones from low-permeability (< 100 mD, 9.87 X 10 (14) m(2)) sandstones and shales.

Simulating global properties of electroencephalograms with minimal random neural networks

The human electroencephalogram (EEG) is globally characterized by a 1/f power spectrum superimposed with certain peaks, whereby the "alpha peak" in a frequency range of 8-14 Hz is the most prominent one for relaxed states of wakefulness. We present simulations of a minimal dynamical network model of leaky integrator neurons attached to the nodes of an evolving directed and weighted random graph (an Erdos-Renyi graph). We derive a model of the dendritic field potential (DFP) for the neurons leading to a simulated EEG that describes the global activity of the network. Depending on the network size, we find an oscillatory transition of the simulated EEG when the network reaches a critical connectivity. This transition, indicated by a suitably defined order parameter, is reflected by a sudden change of the network's topology when super-cycles are formed from merging isolated loops. After the oscillatory transition, the power spectra of simulated EEG time series exhibit a 1/f continuum superimposed with certain peaks. (c) 2007 Elsevier B.V. All rights reserved.

Verification and FPGA circuits of a block-2 fast path-based predictor

This paper formally derives a new path-based neural branch prediction algorithm (FPP) into blocks of size two for a lower hardware solution while maintaining similar input-output characteristic to the algorithm. The blocked solution, here referred to as B2P algorithm, is obtained using graph theory and retiming methods. Verification approaches were exercised to show that prediction performances obtained from the FPP and B2P algorithms differ within one mis-prediction per thousand instructions using a known framework for branch prediction evaluation. For a chosen FPGA device, circuits generated from the B2P algorithm showed average area savings of over 25% against circuits for the FPP algorithm with similar time performances thus making the proposed blocked predictor superior from a practical viewpoint.

Using the web graph to influence application behaviour

The Web's link structure (termed the Web Graph) is a richly connected set of Web pages. Current applications use this graph for indexing and information retrieval purposes. In contrast the relationship between Web Graph and application is reversed by letting the structure of the Web Graph influence the behaviour of an application. Presents a novel Web crawling agent, AlienBot, the output of which is orthogonally coupled to the enemy generation strategy of a computer game. The Web Graph guides AlienBot, causing it to generate a stochastic process. Shows the effectiveness of such unorthodox coupling to both the playability of the game and the heuristics of the Web crawler. In addition, presents the results of the sample of Web pages collected by the crawling process. In particular, shows: how AlienBot was able to identify the power law inherent in the link structure of the Web; that 61.74 per cent of Web pages use some form of scripting technology; that the size of the Web can be estimated at just over 5.2 billion pages; and that less than 7 per cent of Web pages fully comply with some variant of (X)HTML.

On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

Maximum induced subgraph of a recursive circulant

The recursive circulant RC(2(n), 4) enjoys several attractive topological properties. Let max_epsilon(G) (m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. In this paper, we show that max_epsilon(RC(2n,4))(m) = Sigma(i)(r)=(0)(p(i)/2 + i)2(Pi), where p(0) > p(1) > ... > p(r) are nonnegative integers defined by m = Sigma(i)(r)=(0)2(Pi). We then apply this formula to find the bisection width of RC(2(n), 4). The conclusion shows that, as n-dimensional cube, RC(2(n), 4) enjoys a linear bisection width. (c) 2005 Elsevier B.V. All rights reserved.

Fault tolerance of Mobius cubes under two forbidden fault set models

An n-dimensional Mobius cube, 0MQ(n) or 1MQ(n), is a variation of n-dimensional cube Q(n) which possesses many attractive properties such as significantly smaller communication delay and stronger graph-embedding capabilities. In some practical situations, the fault tolerance of a distributed memory multiprocessor system can be measured more precisely by the connectivity of the underlying graph under forbidden fault set models. This article addresses the connectivity of 0MQ(n)/1MQ(n), under two typical forbidden fault set models. We first prove that the connectivity of 0MQ(n)/1MQ(n) is 2n - 2 when the fault set does not contain the neighborhood of any vertex as a subset. We then prove that the connectivity of 0MQ(n)/1MQ(n) is 3n - 5 provided that the neighborhood of any vertex as well as that of any edge cannot fail simultaneously These results demonstrate that 0MQ(n)/1MQ(n) has the same connectivity as Q(n) under either of the previous assumptions.

A lower bound on the size of k-neighborhood in generalized cubes

The determination of the minimum size of a k-neighborhood (i.e., a neighborhood of a set of k nodes) in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems. The generalized cubes include the hypercube and most hypercube variants as special cases. In this paper, we present a lower bound on the size of a k-neighborhood in n-dimensional generalized cubes, where 2n + 1 <= k <= 3n - 2. This lower bound is tight in that it is met by the n-dimensional hypercube. Our result is an extension of two previously known results. (c) 2005 Elsevier Inc. All rights reserved.