Efficient algorithms for single- and two-layer linear placement of parallel graphs

This paper outlines an algorithm for optimum linear ordering (OLO) of a weighted parallel graph with O(n log k) worst-case time complexity, and O(n + k log(n/k) log k) expected-case time complexity, where n is the total number of nodes and k is the number of chains in the parallel graph. Next, the two-layer OLO problem is considered, where the goal is to place the nodes linearly in two routing layers minimizing the total wire length. The two-layer problem is shown to subsume the maxcut problem and a befitting heuristic algorithm is proposed. Experimental results on randomly generated samples show that the heuristic algorithm runs very fast and outputs optimum solutions in more than 90% instances.     

A New Classification of Path-Delay Fault Testability in Terms of Stuck-at Faults

A new classification of path-delay fault testability in a combinational circuit is presented in terms of testability of stuck-at faults in an equivalent circuit. Earlier results describing correlation of path-delay and stuck-at faults are either incomplete, or use a complex model of equivalent circuit based on timing parameters. It is shown here that a path-delay fault (rising or falling) is testable if and only if certain single or multiple stuck-at fault in the equivalent circuit is testable. Thus, all aspects of path-delay faults related to testability under various classification schemes can be interpreted using the stuck-at fault model alone. The results unify most of the existing concepts and provide a better understanding of path-delay faults in logic circuits.     

Spatial consistency of dense features within interest regions for efficient landmark recognition

Recently, feature grouping has been proposed as a method for improving retrieval results for logos and web images. This relies on the idea that a group of features matching over a local region in an image is more discriminative than a single feature match. In this paper, we evolve this concept further and apply it to the more challenging task of landmark recognition. We propose a novel combination of dense sampling of SIFT features with interest regions which represent the more salient parts of the image in greater detail. In place of conventional dense sampling used in category recognition that computes features on a regular grid at a number of fixed scales, we allow the sampling density and scale to vary based on the scale of the interest region. We develop new techniques for exploring stronger geometric constraints inside the feature groups and computing the match score. The spatial information is stored efficiently in an inverted index structure. The proposed approach considers part-based matching of interest regions instead of matching entire images using a histogram under bag-of-words. This helps reducing the influence of background clutter and works better under occlusion. Experiments reveal that directing more attention to the salient regions of the image and applying proposed geometric constraints helps in vastly improving recognition rates for reasonable vocabulary sizes.     

Forecasting the trend of international scientific collaboration

The study demonstrates an integrated method of forecasting the trend of a country’s publications. In this context the paper examines international collaboration in a country’s overall publication and forecasts its future trend. The integrated method is based on regression and scaling relationship. India is taken as a case study for this examination. The study shows some interesting features of India’s publication pattern based on time-series data. One observes exponential nature of her publication growth from 2002 onwards. International collaboration also exhibits exponential growth roughly from the same period. Also one observes the faster growth of international collaborative papers than the overall growth of research papers. The study predicts values of number of internationally collaborative papers for the years 2015 and 2020. The robustness of the method is also demonstrated.     

Remote sensing and GIS for locating favourable zones of lead-zinc-copper mineralization in Rajpura-Dariba area,Rajasthan, India

This paper reports the results of a pilot study carried out in RajpuraDariba area, Rajasthan, for locating favourable zones of lead-zinc-copper (Pb-Zn-Cu) mineralization using remote sensing, Geographical Information System (GIS) and geostatistical modelling techniques. Remotely sensed data, both aerial and satellite, were used to update the existing geological map. ATLAS GIS software and multivariate geostatistical techniques were used to analyse and integrate different types of geological and geophysical datasets. The Favourability Index (FI) maps prepared during this study show the occurrence of three favourable zones for Pb-Zn-Cu mineralization. They are: (i) around and north of Rawan ka Khera; (ii) isolated spots between Ruppura and Bhupalsagar; and (iii) north of Dhani. Selective geochemical sampling and resistivity profiling carried out in these favourable zones indicated the presence of geochemical anomalies (anomalous concentrations of Zn and Cu) and low/moderate resistivity zones, respectively. Recent drilling carried out by the Department of Mines and Geology (DMG), Rajasthan, at about 2.5 km north of Rawan ka Khera (one of the predicted favourable zones) indicated evidence of Cu mineralization at a depth of about 70 m.     

Collective foraging in heterogeneous landscapes

Animals foraging alone are hypothesized to optimize the encounter rates with resources through Lévy walks. However, the issue of how the interactions between multiple foragers influence their search efficiency is still not completely understood. To address this, we consider a model to study the optimal strategy for a group of foragers searching for targets distributed heterogeneously. In our model, foragers move on a square lattice containing immobile but regenerative targets. At any instant, a forager is able to detect only those targets that happen to be in the same site. However, we allow the foragers to have information about the state of other foragers. A forager who has not detected any target walks towards the nearest location, where another forager has detected a target, with a probability exp(−αd), where d is the distance between the foragers and α is a parameter characterizing the propensity of the foragers to aggregate. The model reveals that neither overcrowding (α → 0) nor independent searching (α → ∞) is beneficial for the foragers. For a patchy distribution of targets, the efficiency is maximum for intermediate values of α. In addition, in the limit α → 0, the length of the walks can become scale-free.     

Development of real-time reference evapotranspiration at the regional scale using satellite-based observations

Real-time data of reference evapotranspiration (ET₀) at different space-time scales are essential to regional agricultural drought assessment, water accounting at the watershed to basin scale, and provide irrigation advisory to farmers. Here, we present a data-fusion approach that integrates satellite-based insolation product (8 km) from an Indian geostationary satellite (Kalpana-1) sensor (VHRR; Very High Resolution Radiometer) and high-resolution (~ 5 km) short-range weather forecast into an FAO56 model based on the classical Penman–Monteith (P-M) formulation. Five year (2009–2013) mean monthly estimates from the daily ET₀ product over the Indian landmass were found to vary between 10 and 350 mm. It increased from January to May (70–350 mm), followed by a decrease to reach the lowest in November (10–140 mm), thus typically showing unimodal distribution. The comparison of daily space-based and station-based estimates (at six ground stations) produced a root mean square deviation (RMSD) ranging from 21% to 38% for 977 paired data sets with the correlation coefficient (r) varying from 0.32 to 0.82. The error was reduced from 25% to 10% with an increase in ‘r’ from 0.43 to 0.98 for daily to 10 day summation period. Spatial grid-to-grid comparison of monthly ET₀ estimates with Global Data Assimilation System (GDAS) potential evapotranspiration (PET) showed RMSD within a range of 1.4–18.4% for most of the months, except for two. Further ET₀ analysis over normal and drought years showed that it could be used for comprehensive drought assessment with other existing indicators.     

Optimizing microstructure for toughness: the model problem of peeling

We consider the problem of peeling an adhesive thin film from a substrate that has a non-uniform distribution of adhesive. When the length scale of the non-uniformity is small compared to the overall dimensions of the film being peeled, it is possible to describe the overall peeling behavior with an effective adhesive strength. In this paper, we seek to find the distributions of adhesive strength at the microscale that optimize various aspects of the effective adhesive strength at the macroscale. We do so using both analytic bounds and topology optimization. We formulate the problem of peeling as a free boundary problem, and the effective strength as a maximum principle over the trajectory. For topology optimization, we replace the maximum with an integral norm, and use an adjoint method for the sensitivity. The problem of peeling may be viewed as a model problem in fracture mechanics where the crack (peel) front is confined to a plane, and thus our analysis as a first step toward studying the more general problem of optimizing microstructure for toughness.     

Fifth sustainable development goal gender equality in India: analysis by mathematics of uncertainty and covering of fuzzy graphs

Neural Computing and Applications - In the present situation, the sustainable development goal on “Gender Equality” (SDG 5) is a challenging problem over the entire globe, also in...