Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Qualitative Air Flow Modelling and Analysis of Data Centre Air Conditioning as Multiple Jet Array

Data centre is a centralized repository,either physical or virtual,for the storage,management and dissemination of data and information organized around a particular body and nerve centre of the present IT revolution.Data centre are expected to serve uniinterruptedly round the year enabling them to perform their functions,it consumes enormous energy in the present scenario.Tremendous growth in the demand from IT Industry made it customary to develop newer technologies for the better operation of data centre.Energy conservation activities in data centre mainly concentrate on the air conditioning system since it is the major mechanical sub-system which consumes considerable share of the total power consumption of the data centre.The data centre energy matrix is best represented by power utilization efficiency(PUE),which is defined as the ratio of the total facility power to the IT equipment power.Its value will be greater than one and a large value of PUE indicates that the sub-systems draw more power from the facility and the performance of the data will be poor from the stand point of energy conservation. PUE values of 1.4 to 1.6 are acievable by proper design and management techniques.Optimizing the air conditioning systems brings enormous opportunity in bringing down the PUE value.The air conditioning system can be optimized by two approaches namely,thermal management and air flow management.thermal management systems are now introduced by some companies but they are highly sophisticated and costly and do not catch much attention in the thumb rules.

Qualitative air flow modelling and analysis of data centre air conditioning as multiple jet array

This work identifies the importance of plenum pressure on the performance of the data centre. The present methodology followed in the industry considers the pressure drop across the tile as a dependant variable, but it is shown in this work that this is the only one independent variable that is responsible for the entire flow dynamics in the data centre, and any design or assessment procedure must consider the pressure difference across the tile as the primary independent variable. This concept is further explained by the studies on the effect of dampers on the flow characteristics. The dampers have found to introduce an additional pressure drop there by reducing the effective pressure drop across the tile. The effect of damper is to change the flow both in quantitative and qualitative aspects. But the effect of damper on the flow in the quantitative aspect is only considered while using the damper as an aid for capacity control. Results from the present study suggest that the use of dampers must be avoided in data centre and well designed tiles which give required flow rates must be used in the appropriate locations. In the present study the effect of hot air recirculation is studied with suitable assumptions. It identifies that, the pressure drop across the tile is a dominant parameter which governs the recirculation. The rack suction pressure of the hardware along with the pressure drop across the tile determines the point of recirculation in the cold aisle. The positioning of hardware in the racks play an important role in controlling the recirculation point. The present study is thus helpful in the design of data centre air flow, based on the theory of jets. The air flow can be modelled both quantitatively and qualitatively based on the results.

“Qualitative Air Flow Modelling And Analysis Of Data Centre Air Conditioning As Multiple Jet Array

In the present study the effect of hot air recirculation is studied with suitable assumptions. It identifies that, the pressure drop across the tile is a dominant parameter which governs the recirculation. The rack suction pressure of the hardware along with the pressure drop across the tile determines the point of recirculation in the cold aisle. The positioning of hardware in the racks play an important role in controlling the recirculation point. The present study is thus helpful in the design of data centre air flow, based on the theory of jets. The air flow can be modelled both quantitatively and qualitatively based on the results

Nitrification in a packed bed bioreactor integrated into amarine recirculating maturation system under different substrate concentrations and flow rates

BACKGROUND: A packed bed bioreactor (PBBR) activated with an indigenous nitrifying bacterial consortia was developed and commercialized for rapid establishment of nitrification in brackish water and marine hatchery systems in the tropics. The present study evaluated nitrification in PBBR integrated into a Penaeus monodon recirculating maturation system under different substrate concentrations and flow rates. RESULTS:Instantnitrificationwasobservedafter integration ofPBBRinto thematuration system.TANandNO2-Nconcentrations were always maintained below0.5 mg L−1 during operation. The TANandNO2-N removalwas significant (P < 0.001) in all the six reactor compartments of the PBBR having the substrates at initial concentrations of 2, 5 and 10 mg L−1. The average volumetric TAN removal rates increased with flow rates from 43.51 (250 L h−1) to 130.44 (2500 L h−1) gTAN m−3 day−1 (P < 0.05). FISH analysis of the biofilms after 70 days of operation gave positive results with probes NSO 190 ((β ammonia oxidizers), NsV 443 (Nitrosospira spp.) NEU (halophilic Nitrosomonas), Ntspa 712 (Phylum Nitrospira) indicating stability of the consortia. CONCLUSION: The PBBR integrated into the P. monodon maturation system exhibited significant nitrification upon operation for 70 days as well as at different substrate concentrations and flow rates. This system can easily be integrated into marine and brackish water aquaculture systems, to establish instantaneous nitrification

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Betweenness Centrality in Some Classes of Graphs

There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest path between them. In this paper we present betweenness centrality of some important classes of graphs.

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Content aggregation on knowledge bases using graph clustering

Recently, research projects such as PADLR and SWAP have developed tools like Edutella or Bibster, which are targeted at establishing peer-to-peer knowledge management (P2PKM) systems. In such a system, it is necessary to obtain provide brief semantic descriptions of peers, so that routing algorithms or matchmaking processes can make decisions about which communities peers should belong to, or to which peers a given query should be forwarded. This paper proposes the use of graph clustering techniques on knowledge bases for that purpose. Using this clustering, we can show that our strategy requires up to 58% fewer queries than the baselines to yield full recall in a bibliographic P2PKM scenario.

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.

Stereo-Based Head Pose Tracking Using Iterative Closest Point and Normal Flow Constraint

In this text, we present two stereo-based head tracking techniques along with a fast 3D model acquisition system. The first tracking technique is a robust implementation of stereo-based head tracking designed for interactive environments with uncontrolled lighting. We integrate fast face detection and drift reduction algorithms with a gradient-based stereo rigid motion tracking technique. Our system can automatically segment and track a user's head under large rotation and illumination variations. Precision and usability of this approach are compared with previous tracking methods for cursor control and target selection in both desktop and interactive room environments. The second tracking technique is designed to improve the robustness of head pose tracking for fast movements. Our iterative hybrid tracker combines constraints from the ICP (Iterative Closest Point) algorithm and normal flow constraint. This new technique is more precise for small movements and noisy depth than ICP alone, and more robust for large movements than the normal flow constraint alone. We present experiments which test the accuracy of our approach on sequences of real and synthetic stereo images. The 3D model acquisition system we present quickly aligns intensity and depth images, and reconstructs a textured 3D mesh. 3D views are registered with shape alignment based on our iterative hybrid tracker. We reconstruct the 3D model using a new Cubic Ray Projection merging algorithm which takes advantage of a novel data structure: the linked voxel space. We present experiments to test the accuracy of our approach on 3D face modelling using real-time stereo images.

Output from the 1998 Product Development Value Stream Workshop: A Framework for Understanding Information Flow in the Product Development Process

The descriptions below and the attached diagrams are outputs of the 1998 LAI Product Development Focus Team workshop on the Value Chain in Product Development. A working group at that workshop was asked to model the product development process: in terms of the phases of product development and their interfaces, boundaries and outputs. Their work has proven to be generally useful to LAI researchers and industry members, and so is formalized here.