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

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

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

Algorithmic Aspects of Some Problems in Computational Biology

Given a sequence of pairs of numbers ( a i , l i ), i = 1, 2, ..., n , with l i \u3e 0, and another pair of numbers L and U , the length-constrained maximum density segment problem is to find a subsequence [ a i , a j ]whose density is the maximum under the constraint L ≤ [Special characters omitted.] Sjs=i l s ≤ U . It has application to DNA sequence analysis in Computational Biology, particularly in the determination of the percentage of CG contents in a DNA sequence. A linear time geometric algorithm is presented that is more powerful than the existing linear time algorithms. The method is extended to solve the k length-constrained maximum density segments problem. Previously, there was no known algorithm with non-trivial time complexity for this problem. We present a linear time algorithm to solve the length-constrained maximum sum segment problem. It is extended to solve the k length-constrained maximum sum segments problem in O(n+k) time. The algorithms are extended to solve the problem of finding all the length-constrained segments satisfying user specified sum or density lower bound in O(n+h) time, where h is the size of the output. The point placement problem is to determine the positions of a linear set of points uniquely up to translation and reflection from the fewest possible distance queries between pairs of points. The motivation comes from a problem known as the restriction site mapping. We present 2-round algorithms with queries 10 n /7+ O (1), 4 n /3+ O (1) and 9 n /7+ O (1) respectively. The lower bound for 2 rounds is improved from 17 n /16 to 9 n /8. We also present a modification of a geometric method called MSPocket for detection of ligand binding sites on protein surfaces. Experimentation using 48 benchmark dataset of bound protein structures shows that the success rate of our method is slightly better than that of MSPocket. (Abstract shortened by UMI.

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

The Role of Microcredit Program on Women Empowerment: Empirical Evidence from Rural Bangladesh

The empowerment of women is the burning issues in developing countries. This study examined the impact of micro-credit on the empowerment of rural women in Bangladesh. A total of 120 respondents were selected as sample using stratified random sampling technique on Tuker bazar Union Parishad under Sylhet Sadar Upazilla in Sylhet district, Bangladesh and data was collected through face to face interview by using survey method. The women empowerment was measured by five dimensions .These dimension were (1) economic decision making, (2) household decision making,(3) freedom of  physical movement, (4) ownership of property,(5) political and social awareness. OLS (Ordinary Least Squares) regression was applied to understand the effects of microcredit program on each dimension of women empowerment and aggregate women empowerment. The results showed that microcredit program was positively associated with each dimension of women empowerment as well as aggregate measure of Empowerment. So, this study reveals that microcredit program improves the women empowerment in Bangladesh. Keywords: Microcredit, Empowerment, Effects, Rural Women, Bangladesh

Software Development Standard and Software Engineering Practice: A Case Study of Bangladesh

Improving software process to achieve high quality in a software development organization is the key factor to success. Bangladeshi software firms have not experienced much in this particular area in comparison to other countries. The ISO 9001 and CMM standard has become a basic part of software development. The main objectives of our study are: 1) To understand the software development process uses by the software developer firms in Bangladesh 2) To identify the development practices based on established quality standard and 3) To establish a standardized and coherent process for the development of software for a specific project. It is revealed from this research that software industries of Bangladesh are lacking in target set for software process and improvement, involvement of quality control activities, and standardize business expertise practice. This paper investigates the Bangladeshi software industry in the light of the above challenges.Comment: 13 pages, 3 figures, 11 table