Discrepancy and Signed Domination in Graphs and Hypergraphs

For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to combinatorial discrepancy theory as shown by Fueredi and Mubayi [J. Combin. Theory, Ser. B 76 (1999) 223-239]. The signed domination number of G is the minimum of the sum of colours for all vertices, taken over all signed domination functions of G. In this paper, we present new upper and lower bounds for the signed domination number. These new bounds improve a number of known results.Comment: 12 page

Upper domination and upper irredundance perfect graphs

Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. A graph G is called IR-perfect if Γ(H) = IR(H), for every induced subgraph H of G. In this paper, we present a characterization of Γ-perfect graphs in terms of a family of forbidden induced subgraphs, and show that the class of Γ-perfect graphs is a subclass of IR-perfect graphs and that the class of absorbantly perfect graphs is a subclass of Γ-perfect graphs. These results imply a number of known theorems on Γ-perfect graphs and IR-perfect graphs. Moreover, we prove a sufficient condition for a graph to be Γ-perfect and IR-perfect which improves a known analogous result. © 1998 Elsevier Science B.V. All rights reserved

An enhanced model for portfolio choice with SSD criteria: a constructive approach

We formulate a portfolio planning model which is based on Second-order Stochastic Dominance as the choice criterion. This model is an enhanced version of the multi-objective model proposed by Roman, Darby-Dowman, and Mitra (2006); the model compares the scaled values of the different objectives, representing tails at different confidence levels of the resulting distribution. The proposed model can be formulated asrisk minimisation model where the objective function is a convex risk measure; we characterise this risk measure and the resulting optimisation problem. Moreover, our formulation offers a natural generalisation of the SSD-constrained model of Dentcheva and Ruszczynski (2006). A cutting plane-based solution method for the proposed model is outlined. We present a computational study showing: (a) the effectiveness of thesolution methods and (b) the improved modelling capabilities: the resulting portfolios have superior return distributions

Extending indoor open street mapping environments to navigable 3D citygml building models: Emergency response assessment

© Authors 2018. Disaster scenarios in high-rise buildings such as the Address Downtown, Dubai or Grenfell Tower, London have showed ones again the importance of data information availability for emergency management in buildings. 3D visualization of indoor routing services using extensive and high quality geographic data sources is essential for spatial analysis in emergency responses. In order to facilitate emergency response simulations, a combination of geometrical, graphical and semantic information is essential. Successful and efficient emergency evacuation responses is facilitated by the availability of both digital static and dynamic information of the incident site. However, interruptions may be encountered with the availability of dynamic data, where static data developed using indoor navigation ontologies serve as an alternative to inform the first responders. Thus, it is necessary to obtain a firm, interactive and quasi-realistic virtual simulation of the building environments. Voxelized CityGML models imported into voxel based hazard simulation systems fits well into the simulation algorithm requirements (Groger et al., 2008; Moreno et.al, 2010). Therefore, the research investigates an alternative platform for generating CityGML spatial analysis models. LoD4 models are developed using Computer Aided Design (Auto CAD) 2D files, crowdsourced geo-data (OpenStreetMap) and open source tools. A combination of software packages is utilized for 3D reconstruction of building interiors. This process is achieved through a Java application developed by researchers at Heidelberg University. Conclusions drawn from the research validate the 3D CityGML model generation process as an international standard to effectively enhance the outcome of emergency evacuation simulations of high rise buildings

TWO-GRAPH BUILDING INTERIOR REPRESENTATION for EMERGENCY RESPONSE APPLICATIONS

Nowadays, in a rapidly developing urban environment with bigger and higher public buildings, disasters causing emergency situations and casualties are unavoidable. Preparedness and quick response are crucial issues saving human lives. Available information about an emergency scene, such as a building structure, helps for decision making and organizing rescue operations. Models supporting decision-making should be available in real, or near-real, time. Thus, good quality models that allow implementation of automated methods are highly desirable. This paper presents details of the recently developed method for automated generation of variable density navigable networks in a 3D indoor environment, including a full 3D topological model, which may be used not only for standard navigation but also for finding safe routes and simulating hazard and phenomena associated with disasters such as fire spread and heat transfer.This research/publication was made possible by a National Priority Research Program NPRP award [NPRP-06-1208-2-492] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.Scopu

Нахождение областей сходимости и вычисление сумм степенных рядов от h-комплексного переменного

Herein, taking power series from a real variable that converge on a certain interval to known sums, the authors consider the power series with the same coefficients from an h-complex variable. For such series, the interiors of the regions of convergence are found, and their sums are explicitly expressed in terms of the sums of the original series. Along the way, the problem of isolation conditions for the zeros of the sums of such series is solved.Взяв степенные ряды от вещественного переменного, сходящиеся на некотором интервале к известным суммам, авторы рассматривают степенные ряды с теми же коэффициентами от h-комплексного переменного. Для таких рядов найдены внутренности областей сходимости, а их суммы явно выражены через суммы исходных рядов. Попутно решен вопрос об условиях изолированности нулей сумм таких рядов

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces

Thomae type formulae for singular Z_N curves

We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 page