Algorithms for the Problems of Length-Constrained Heaviest Segments

We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a sequence of n real numbers and two real parameters L and U (L <= U), the maximum sum segment problem is to find a consecutive subsequence, called a segment, of length at least L and at most U such that the sum of the numbers in the subsequence is maximum. The maximum density segment problem is to find a segment of length at least L and at most U such that the density of the numbers in the subsequence is the maximum. For the first problem with non-uniform width there is an algorithm with time and space complexities in O(n). We present an algorithm with time complexity in O(n) and space complexity in O(U). For the second problem with non-uniform width there is a combinatorial solution with time complexity in O(n) and space complexity in O(U). We present a simple geometric algorithm with the same time and space complexities. We extend our algorithms to respectively solve the length-constrained k maximum sum segments problem in O(n+k) time and O(max{U, k}) space, and the length-constrained $k$ maximum density segments problem in O(n min{k, U-L}) time and O(U+k) space. We present extensions of our algorithms to find all the length-constrained segments having user specified sum and density in O(n+m) and O(nlog (U-L)+m) times respectively, where m is the number of output. Previously, there was no known algorithm with non-trivial result for these problems. We indicate the extensions of our algorithms to higher dimensions. All the algorithms can be extended in a straight forward way to solve the problems with non-uniform width and non-uniform weight.Comment: 21 pages, 12 figure

Control of constraint weights for an autonomous camera

Constraint satisfaction based techniques for camera control has the flexibility to add new constraints easily to increase the quality of a shot. We address the problem of deducing and adjusting constraint weights at run time to guide the movement of the camera in an informed and controlled way in response to the requirement of the shot. This enables the control of weights at the frame level. We analyze the mathematical representation of the cost structure of the domain of constraint search so that the constraint solver can search the domain efficiently. We start with a simple tracking shot of a single target. The cost structure of the domain of search suggests the use of a binary search which searches along a curve for 2D and on a surface for 3D by utilizing the information about the cost structure. The problems of occlusion and collision avoidance have also been addressed

Scalable base station switching framework for green cellular networks

With the recent unprecedented growth in the wireless market, network operators are obliged not only to find new techniques including dense deployment of base stations (BSs) in order to support high data rate services and high user density, but also to reduce the operating costs and energy consumption of various network elements. To solve these challenges, powering down certain BSs during low-traffic periods, so-called BS sleeping, has emerged as an effective green communications paradigm. While BS sleeping offers the potential to significantly lower energy consumption, it also raises many challenges, since when a BS is switched off, this can lead to, for example, coverage holes, sudden degradation in quality of service (QoS), higher transmit power dissipation in off-cell mobile stations (MSs), an inability to rapidly power up/down equipment and finally, a failure to uphold regulatory requirements. In order to realise greener network designs which both maximise energy savings whilst guaranteeing QoS, innovative BS switching mechanisms need to be developed. This thesis presents a novel BS switching framework which improves energy efficiency (EE) in comparison with existing approaches, while guaranteeing the minimum QoS and seamless services. The major technical contributions in this framework are: i) a new BS to relay station (RS) switching model where certain BSs are switched to RS mode rather than being turned off, firstly using a fixed threshold based switching algorithm utilizing temporal traffic diversity, and ii) then subsequently by means of an adaptive threshold by exploiting the inherently asymmetric traffic profile between cells, i.e., by exploiting both the temporal and spatial traffic diversity; iii) a traffic-and-interference-aware BS switching strategy that considers the impact of inter-cell interference in the decision making process to dynamically determine the best BS set to be kept active for improved EE; and finally iv) a novel scalable multimode BS switching model which enables each BS to operate in different power modes i.e., macro/micro/sleep to explore energy savings potential even at higher traffic conditions. The thesis findings conclusively confirm this new BS switching framework provides significant EE improvements from both BS and MS perspectives, under diverse network conditions and represents a notable step towards greener communications

ORIENTED MANIFOLDS WITH COMPACT SUPPORT AND COHOMOLOGY ALGEBRA

The cohomology of with compact supports is the graded algebra....... Keywords: Compact manifold, cohomology, graded algebra, isomorphism, bilinear map

ORIENTATION OF MANIFOLDS AND SMOOTH FIBRE BUNDLES

For a smooth fibre bundle ......More details can be found in the full paper. Keywords: Smooth fibre bundle, manifold, vector bundle, bundle isomorphism, bundle orientation, graded subalgebra

Determinants of Male Internal Migration in Bangladesh: Is Due to Services Matter?

Migration is a common process where people move rural to urban area for better livelihood. The aim of this study is exploring the factors of rural to urban migration in Bangladesh. A cross-sectional study was conducted in Sylhet City Corporation and 120 migrants were selected through two stage cluster sampling technique. Social survey method was used to collect the data from the respondents. Binary logistic regression was applied to determine the factors related to male migration due to services. The results show that level of education is positively associated with male migration due to services. The results also show that income, occupation before migration, family types also effects cause of migration due to services. Keywords: Rural-urban migration, Determinants, Migration status, Banglades

Energy savings using an adaptive base station-to-relay station switching paradigm

Applying a Base Station (BS) sleep approach during low traffic periods has recently been advocated as a strategy for reducing energy consumption in cellular networks. The complete switching off of certain BS however, can lead to coverage holes and severe performance degradation in terms of off-cell user throughput, greater transmit power dissipation in both the up and downlinks, and more complex interference management. This paper presents a novel cellular network energy saving model in which certain BS rather being turned off are switched to Relay Station (RS) mode during low traffic periods. The switched RS and other shared RS deployed at the cross border of each cell are responsible for upholding the same quality of service (QoS) provision as when all BS are active. A centralised adaptive switching threshold algorithm is also introduced to undertake the switching decision, instead of using a fixed threshold. Simulation results confirm the new BS-RS Switching model using an adaptive threshold can reduce network energy consumption by more than half, as well as improving off-cell users’ throughput

ラマヌジャンのモジュラー方程式とヘッケ群に関する幾何学的研究

Tohoku University須川敏幸課