Minimal unsatisfiable sets: Classification and bounds

Proving the unsatisfiability of propositional Boolean formulas has applications in a wide range of fields. Minimal Unsatisfiable Sets (MUS) are signatures of the property of unsatisfiability in formulas and our understanding of these signatures can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this paper, we explore some combinatorial properties of MUS and use them to devise a classification scheme for MUS. We also derive bounds on the sizes of MUS in Horn, 2-SAT and 3-SAT formulas.

Minimal triangulation, complementarity and projective planes

Brehm and Kuhnel proved that if M-d is a combinatorial d-manifold with 3d/2 + 3 vertices and \ M-d \ is not homeomorphic to Sd then the combinatorial Morse number of M-d is three and hence d is an element of {0, 2, 4, 8, 16} and \ M-d \ is a manifold like a projective plane in the sense of Eells and Kuiper. We discuss the existence and uniqueness of such combinatorial manifolds. We also present the following result: ''Let M-n(d) be a combinatorial d-manifold with n vertices. M-n(d) satisfies complementarity if and only if d is an element of {0, 2, 4, 8, 16} with n = 3d/2 + 3 and \ M-n(d) \ is a manifold like a projective plane''.

Contractive Hilbert modules and their dilations

In this note, we show that a quasi-free Hilbert module R defined over the polydisk algebra with kernel function k(z,w) admits a unique minimal dilation (actually an isometric co-extension) to the Hardy module over the polydisk if and only if S (-1)(z, w)k(z, w) is a positive kernel function, where S(z,w) is the Szego kernel for the polydisk. Moreover, we establish the equivalence of such a factorization of the kernel function and a positivity condition, defined using the hereditary functional calculus, which was introduced earlier by Athavale [8] and Ambrozie, Englis and Muller [2]. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. The proof works for a wider class of Hilbert modules in which the Hardy module is replaced by more general quasi-free Hilbert modules such as the classical spaces on the polydisk or the unit ball in a'', (m) . Some consequences of this more general result are then explored in the case of several natural function algebras.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Tight co-degree condition for perfect matchings in 4-graphs

We will give a tight minimum co-degree condition for a 4-uniform hypergraph to contain a perfect matching.

Minimal residual method provides optimal regularization parameter for diffuse optical tomography

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). DOI: 10.1117/1.JBO.17.10.106015]

Leptonic minimal flavour violation in warped extra dimensions

Lepton mass hierarchies and lepton flavour violation are revisited in the framework of Randall-Sundrum models. Models with Dirac-type as well as Majorana-type neutrinos are considered. The five-dimensional c-parameters are fit to the charged lepton and neutrino masses and mixings using chi(2) minimization. Leptonic flavour violation is shown to be large in these cases. Schemes of minimal flavour violation are considered for the cases of an effective LLHH operator and Dirac neutrinos and are shown to significantly reduce the limits from lepton flavour violation.

Stability of Adult Emergence and Activity/Rest Rhythms in Fruit Flies Drosophila melanogaster under Semi-Natural Condition

Here we report the results of a study aimed at examining stability of adult emergence and activity/rest rhythms under seminatural conditions (henceforth SN), in four large outbred fruit fly Drosophila melanogaster populations, selected for emergence in a narrow window of time under laboratory (henceforth LAB) light/dark (LD) cycles. When assessed under LAB, selected flies display enhanced stability in terms of higher amplitude, synchrony and accuracy in emergence and activity rhythms compared to controls. The present study was conducted to assess whether such differences in stability between selected and control populations, persist under SN where several gradually changing time-cues are present in their strongest form. The study revealed that under SN, emergence waveform of selected flies was modified, with even more enhanced peak and narrower gate-width compared to those observed in the LAB and compared to control populations in SN. Furthermore, flies from selected populations continued to exhibit enhanced synchrony and accuracy in their emergence and activity rhythms under SN compared to controls. Further analysis of zeitgeber effects revealed that enhanced stability in the rhythmicity of selected flies under SN was primarily due to increased sensitivity to light because emergence and activity rhythms of selected flies were as stable as controls under temperature cycles. These results thus suggest that stability of circadian rhythms in fruit flies D. melanogaster, which evolved as a consequence of selection for emergence in a narrow window of time under weak zeitgeber condition of LAB, persists robustly in the face of day-to-day variations in cycling environmental factors of nature.

OTCYMIST: Otsu-Canny minimal spanning tree for born-digital images

Text segmentation and localization algorithms are proposed for the born-digital image dataset. Binarization and edge detection are separately carried out on the three colour planes of the image. Connected components (CC's) obtained from the binarized image are thresholded based on their area and aspect ratio. CC's which contain sufficient edge pixels are retained. A novel approach is presented, where the text components are represented as nodes of a graph. Nodes correspond to the centroids of the individual CC's. Long edges are broken from the minimum spanning tree of the graph. Pair wise height ratio is also used to remove likely non-text components. A new minimum spanning tree is created from the remaining nodes. Horizontal grouping is performed on the CC's to generate bounding boxes of text strings. Overlapping bounding boxes are removed using an overlap area threshold. Non-overlapping and minimally overlapping bounding boxes are used for text segmentation. Vertical splitting is applied to generate bounding boxes at the word level. The proposed method is applied on all the images of the test dataset and values of precision, recall and H-mean are obtained using different approaches.

Accelerated multistress aging of polymer nanocomposites and its condition monitoring

In recent years, the time dependant maintenance of expensive high voltage power equipments is getting replaced by condition based maintenance so as to detect apriori an impending failure of the equipment. For condition based maintenance, most monitoring systems concentrate on the electrical quantities such as measurement and evaluation of partial discharges, tan delta, tip-up test, dielectric strength, insulation resistance, polarization and depolarization current. However, in the case of equipments being developed with novel nanodielectric insulating materials, the variation in these parameters before an impending failure is not available. Hence in this work, accelerated electrothermal aging studies have been conducted on unfilled epoxy as well as epoxy nanocomposite samples of 5 wt% filler loading, and the tan d values were continuously monitored to obtain the condition of the samples under study. It was observed that those samples whose tan d increased at a rapid rate failed first.

Antioxidant and oxidative stress parameters in brain of Heteropneustes fossilis under air exposure condition; role of mitochondrial electron transport chain

Many fishes are exposed to air in their natural habitat or during their commercial handling. In natural habitat or during commercial handling, the cat fish Heteropneustes fossilis is exposed to air for > 24 h. Data on its oxidative metabolism in the above condition are not available. Oxidative stress (OS) indices (lipid and protein oxidation), toxic reactive oxygen species (ROS: H2O2) generation, antioxidative status (levels of superoxide dismutase, catalase, glutathione peroxidase and reductase, ascorbic acid and nonprotein sulfhydryl) and activities of electron transport chain (ETC) enzymes (complex I-IV) were investigated in brain tissue of H. fossilis under air exposure condition (0, 3, 6, 12 and 18 h at 25 degrees C). Decreased activities of antioxidant (except catalase) and ETC enzymes (except complex II) with increased H2O2 and OS levels were observed in the tissue under water deprivation condition. Positive correlation was observed for complex II activity and non-protein thiol groups with time period of air exposure. The critical time period to induce OS and to reduce most of the studied antioxidant level in brain was found to be 3-6 h air exposure. The data can be useful to minimize the stress generated during commercial handling of the live fishes those exposed to air in general and H. fossilis in particular. (C) 2013 Elsevier Inc. All rights reserved.

Rotating beams and non-rotating beams with shared eigenpair for pinned-free boundary condition

In this paper we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF's in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams.

Condition R and proper holomorphic maps between equidimensional product domains

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as a product of proper mappings between the factor domains. (C) 2013 Elsevier Inc. All rights reserved.

A multi-level multi-scale approach to study essential genes in Mycobacterium tuberculosis

Background: The set of indispensable genes that are required by an organism to grow and sustain life are termed as essential genes. There is a strong interest in identification of the set of essential genes, particularly in pathogens, not only for a better understanding of the pathogen biology, but also for identifying drug targets and the minimal gene set for the organism. Essentiality is inherently a systems property and requires consideration of the system as a whole for their identification. The available experimental approaches capture some aspects but each method comes with its own limitations. Moreover, they do not explain the basis for essentiality in most cases. A powerful prediction method to recognize this gene pool including rationalization of the known essential genes in a given organism would be very useful. Here we describe a multi-level multi-scale approach to identify the essential gene pool in a deadly pathogen, Mycobacterium tuberculosis. Results: The multi-level workflow analyses the bacterial cell by studying (a) genome-wide gene expression profiles to identify the set of genes which show consistent and significant levels of expression in multiple samples of the same condition, (b) indispensability for growth by using gene expression integrated flux balance analysis of a genome-scale metabolic model, (c) importance for maintaining the integrity and flow in a protein-protein interaction network and (d) evolutionary conservation in a set of genomes of the same ecological niche. In the gene pool identified, the functional basis for essentiality has been addressed by studying residue level conservation and the sub-structure at the ligand binding pockets, from which essential amino acid residues in that pocket have also been identified. 283 genes were identified as essential genes with high-confidence. An agreement of about 73.5% is observed with that obtained from the experimental transposon mutagenesis technique. A large proportion of the identified genes belong to the class of intermediary metabolism and respiration. Conclusions: The multi-scale, multi-level approach described can be generally applied to other pathogens as well. The essential gene pool identified form a basis for designing experiments to probe their finer functional roles and also serve as a ready shortlist for identifying drug targets.

Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.