Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres

It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.

A Partition Metric for Clustering Features Analysis

A new distance function to compare arbitrary partitions is proposed. Clustering of image collections and image segmentation give objects to be matched. Offered metric intends for combination of visual features and metadata analysis to solve a semantic gap between low-level visual features and high-level human concept.

A Sensitive Metric of Class Cohesion

Metrics estimate the quality of different aspects of software. In particular, cohesion indicates how well the parts of a system hold together. A metric to evaluate class cohesion is important in object-oriented programming because it gives an indication of a good design of classes. There are several proposals of metrics for class cohesion but they have several problems (for instance, low discrimination). In this paper, a new metric to evaluate class cohesion is proposed, called SCOM, which has several relevant features. It has an intuitive and analytical formulation, what is necessary to apply it to large-size software systems. It is normalized to produce values in the range [0..1], thus yielding meaningful values. It is also more sensitive than those previously reported in the literature. The attributes and methods used to evaluate SCOM are unambiguously stated. SCOM has an analytical threshold, which is a very useful but rare feature in software metrics. We assess the metric with several sample cases, showing that it gives more sensitive values than other well know cohesion metrics.

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

AMS Subj. Classification: 83C15, 83C35

Quality-driven resource utilization methods for video streaming in wireless communication networks

This research is focused on the optimisation of resource utilisation in wireless mobile networks with the consideration of the users’ experienced quality of video streaming services. The study specifically considers the new generation of mobile communication networks, i.e. 4G-LTE, as the main research context. The background study provides an overview of the main properties of the relevant technologies investigated. These include video streaming protocols and networks, video service quality assessment methods, the infrastructure and related functionalities of LTE, and resource allocation algorithms in mobile communication systems. A mathematical model based on an objective and no-reference quality assessment metric for video streaming, namely Pause Intensity, is developed in this work for the evaluation of the continuity of streaming services. The analytical model is verified by extensive simulation and subjective testing on the joint impairment effects of the pause duration and pause frequency. Various types of the video contents and different levels of the impairments have been used in the process of validation tests. It has been shown that Pause Intensity is closely correlated with the subjective quality measurement in terms of the Mean Opinion Score and this correlation property is content independent. Based on the Pause Intensity metric, an optimised resource allocation approach is proposed for the given user requirements, communication system specifications and network performances. This approach concerns both system efficiency and fairness when establishing appropriate resource allocation algorithms, together with the consideration of the correlation between the required and allocated data rates per user. Pause Intensity plays a key role here, representing the required level of Quality of Experience (QoE) to ensure the best balance between system efficiency and fairness. The 3GPP Long Term Evolution (LTE) system is used as the main application environment where the proposed research framework is examined and the results are compared with existing scheduling methods on the achievable fairness, efficiency and correlation. Adaptive video streaming technologies are also investigated and combined with our initiatives on determining the distribution of QoE performance across the network. The resulting scheduling process is controlled through the prioritization of users by considering their perceived quality for the services received. Meanwhile, a trade-off between fairness and efficiency is maintained through an online adjustment of the scheduler’s parameters. Furthermore, Pause Intensity is applied to act as a regulator to realise the rate adaptation function during the end user’s playback of the adaptive streaming service. The adaptive rates under various channel conditions and the shape of the QoE distribution amongst the users for different scheduling policies have been demonstrated in the context of LTE. Finally, the work for interworking between mobile communication system at the macro-cell level and the different deployments of WiFi technologies throughout the macro-cell is presented. A QoEdriven approach is proposed to analyse the offloading mechanism of the user’s data (e.g. video traffic) while the new rate distribution algorithm reshapes the network capacity across the macrocell. The scheduling policy derived is used to regulate the performance of the resource allocation across the fair-efficient spectrum. The associated offloading mechanism can properly control the number of the users within the coverages of the macro-cell base station and each of the WiFi access points involved. The performance of the non-seamless and user-controlled mobile traffic offloading (through the mobile WiFi devices) has been evaluated and compared with that of the standard operator-controlled WiFi hotspots.

On a Class Almost Contact Manifolds with Norden Metric

Certain curvature properties and scalar invariants of the mani- folds belonging to one of the main classes almost contact manifolds with Norden metric are considered. An example illustrating the obtained results is given and studied.

Linear Connections on Normal Almost Contact Manifolds with Norden Metric

Families of linear connections are constructed on almost con- tact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connec- tion are studied on two basic classes of normal almost contact manifolds with Norden metric.

Lie Groups as Four-Dimensional Special Complex Manifolds with Norden Metric

Марта Теофилова - Конструиран е пример на четиримерно специално комплексно многообразие с норденова метрика и постоянна холоморфна секционна кривина чрез двупара-метрично семейство от разрешими алгебри на Ли. Изследвани са кривинните свойства на полученото многообразие. Дадени са необходими и достатъчни усло-вия за разглежданото многообразие да бъде изотропно келерово.

Every N-Dimensional Separable Metric Space Contains a Totally Disconnected (n-1)-Dimensional Subset with no True Quasi-Components

Владимир Тодоров, Петър Стоев - Тази бележка съдържа елементарна конструкция на множество с указаните в заглавието свойства. Да отбележим в допълнение, че така полученото множество остава напълно несвързано дори и след като се допълни с краен брой елементи.

On Affine Connections in a Riemannian Manifold with a Circulant Metric and two Circulant Affinor Structures

Ива Р. Докузова, Димитър Р. Разпопов - В настоящата статия е разгледан клас V оттримерни риманови многообразия M с метрика g и два афинорни тензора q и S. Дефинирана е и друга метрика ¯g в M. Локалните координати на всички тези тензори са циркулантни матрици. Намерени са: 1) зависимост между тензора на кривина R породен от g и тензора на кривина ¯R породен от ¯g; 2) тъждество за тензора на кривина R в случая, когато тензорът на кривина ¯R се анулира; 3) зависимост между секционната кривина на прозволна двумерна q-площадка {x, qx} и скаларната кривина на M.

Regrouping metric-space search index for search engine size adaptation

This work contributes to the development of search engines that self-adapt their size in response to fluctuations in workload. Deploying a search engine in an Infrastructure as a Service (IaaS) cloud facilitates allocating or deallocating computational resources to or from the engine. In this paper, we focus on the problem of regrouping the metric-space search index when the number of virtual machines used to run the search engine is modified to reflect changes in workload. We propose an algorithm for incrementally adjusting the index to fit the varying number of virtual machines. We tested its performance using a custom-build prototype search engine deployed in the Amazon EC2 cloud, while calibrating the results to compensate for the performance fluctuations of the platform. Our experiments show that, when compared with computing the index from scratch, the incremental algorithm speeds up the index computation 2–10 times while maintaining a similar search performance.

Model and performance of a no-reference quality assessment metric for video streaming

Video streaming via Transmission Control Protocol (TCP) networks has become a popular and highly demanded service, but its quality assessment in both objective and subjective terms has not been properly addressed. In this paper, based on statistical analysis a full analytic model of a no-reference objective metric, namely pause intensity (PI), for video quality assessment is presented. The model characterizes the video playout buffer behavior in connection with the network performance (throughput) and the video playout rate. This allows for instant quality measurement and control without requiring a reference video. PI specifically addresses the need for assessing the quality issue in terms of the continuity in the playout of TCP streaming videos, which cannot be properly measured by other objective metrics such as peak signal-to-noise-ratio, structural similarity, and buffer underrun or pause frequency. The performance of the analytical model is rigidly verified by simulation results and subjective tests using a range of video clips. It is demonstrated that PI is closely correlated with viewers' opinion scores regardless of the vastly different composition of individual elements, such as pause duration and pause frequency which jointly constitute this new quality metric. It is also shown that the correlation performance of PI is consistent and content independent. © 2013 IEEE.

Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.