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.

Hong-Ou-Mandel interference with a single atom

The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thus argue that the presence of such nonlinearity would reduce the visibility in the standard HOM setup, offering some explanation for the diminution of the HOM visibility observed in many experiments. We use the same model to show that the nonlinearity affects a resonant two-photon propagation through a two-level impurity in a waveguide due to a " weak photon blockade" caused by the impossibility of double-occupancy and argue that this effect might be stronger for multi-photon propagation.

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.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Soliton mode locking fiber laser with an all-fiber polarization interference filter

An erbium doped fiber ring laser achieving soliton mode locking by the use of an intra-cavity all-fiber polarization interference filter (AFPIF) has been demonstrated. To incorporate an AFPIF with relative narrow transmission bandwidth, the laser has produced clean soliton pulses of 1.2 ps duration at a repetition rate of 14.98 MHz with a polarization extinction ratio up to 25.7 dB. Moreover, we have demonstrated that the operating wavelength of the mode locking laser can be tuned over 20 nm range from 1545 to 1565 nm by thermally tuning the AFPIF cavity. © 2012 Optical Society of America.

Pause intensity:a no-reference quality assessment metric for video streaming in TCP networks

In this paper a full analytic model for pause intensity (PI), a no-reference metric for video quality assessment, is presented. The model is built upon the video play out buffer behavior at the client side and also encompasses the characteristics of a TCP network. Video streaming via TCP produces impairments in play continuity, which are not typically reflected in current objective metrics such as PSNR and SSIM. Recently the buffer under run frequency/probability has been used to characterize the buffer behavior and as a measurement for performance optimization. But we show, using subjective testing, that under run frequency cannot reflect the viewers' quality of experience for TCP based streaming. We also demonstrate that PI is a comprehensive metric made up of a combination of phenomena observed in the play out buffer. The analytical model in this work is verified with simulations carried out on ns-2, showing that the two results are closely matched. The effectiveness of the PI metric has also been proved by subjective testing on a range of video clips, where PI values exhibit a good correlation with the viewers' opinion scores. © 2012 IEEE.

Reductions of peak-to-average power ratio and optical beat interference in cost-effective OFDMA-PONs

The peak-to-average power ratio (PAPR) and optical beat interference (OBI) effects are examined thoroughly in orthogonal frequency-division multiplexing access (OFDMA)-passive optical networks (PONs) at a signal bit rate up to ∼ 20 Gb/s per channel using cost-effective intensity-modulation and direct-detection (IM/DD). Single-channel OOFDM and upstream multichannel OFDM-PONs are investigated for up to six users. A number of techniques for mitigating the PAPR and OBI effects are presented and evaluated including adaptive-loading algorithms such as bit/power-loading, clipping for PAPR reduction, and thermal detuning (TD) for the OBI suppression. It is shown that the bit-loading algorithm is a very efficient PAPR reduction technique by reducing it at about 1.2 dB over 100 Km of transmission. It is also revealed that the optimum method for suppressing the OBI is the TD + bit-loading. For a targeted BER of 1 × 10-3, the minimum allowed channel spacing is 11 GHz when employing six users. © 2013 Springer Science+Business Media New York.

Nonlinear refraction in optical lattices induced by the wave-soliton interference

In the framework of 1D Nonlinear Shrödinger Equation (NSE) we demonstrate how one can control the refractive angle of a fundamental soliton beam passing through an optical lattice, by adjusting either the shape of an individual waveguide or the relative positions of waveguides. Even for a single scatterer its shape has a nontrivial effect on the refraction direction. In the case of shallow modulation we provide an analytical description based of the effect on the soliton perturbation theory. When one considers a lattice of scatterers, there emanates an additional form factor in the radiation density (RD) of emitted waves referring to the wave-soliton beating and interference inside the lattice. We concentrate on the results for two cases: periodic lattice and disordered lattice of scattering shapes. © 2011 IEEE.

Self-adapting parallel metric-space search engine for variable query loads

This research focuses on automatically adapting a search engine size in response to fluctuations in query workload. Deploying a search engine in an Infrastructure as a Service (IaaS) cloud facilitates allocating or deallocating computer resources to or from the engine. Our solution is to contribute an adaptive search engine that will repeatedly re-evaluate its load and, when appropriate, switch over to a dierent number of active processors. We focus on three aspects and break them out into three sub-problems as follows: Continually determining the Number of Processors (CNP), New Grouping Problem (NGP) and Regrouping Order Problem (ROP). CNP means that (in the light of the changes in the query workload in the search engine) there is a problem of determining the ideal number of processors p active at any given time to use in the search engine and we call this problem CNP. NGP happens when changes in the number of processors are determined and it must also be determined which groups of search data will be distributed across the processors. ROP is how to redistribute this data onto processors while keeping the engine responsive and while also minimising the switchover time and the incurred network load. We propose solutions for these sub-problems. For NGP we propose an algorithm for incrementally adjusting the index to t the varying number of virtual machines. For ROP we present an ecient method for redistributing data among processors while keeping the search engine responsive. Regarding the solution for CNP, we propose an algorithm determining the new size of the search engine by re-evaluating its load. We tested the solution performance using a custom-build prototype search engine deployed in the Amazon EC2 cloud. Our experiments show that when we compare our NGP solution with computing the index from scratch, the incremental algorithm speeds up the index computation 2{10 times while maintaining a similar search performance. The chosen redistribution method is 25% to 50% faster than other methods and reduces the network load around by 30%. For CNP we present a deterministic algorithm that shows a good ability to determine a new size of search engine. When combined, these algorithms give an adapting algorithm that is able to adjust the search engine size with a variable workload.