There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

http://user.it.uu.se/~jarst116/slides/week4.pdf

Graph-Based Algorithms for Boolean Function Manipulation

A survey on fall detection: Principles and approaches

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

A Theory of Graphs

In this paper, we present an approach for human fall detection, which has important applications in the field of safety and security. The proposed approach consists of two parts: object detection and the use of a fall model. We use an adaptive background subtraction method to detect a moving object and mark it with its minimum-bounding box. The fall model uses a set of extracted features to analyze, detect and confirm a fall. We implement a two-state finite state machine (FSM) to continuously monitor people and their activities. Experimental results show that our method can detect most of the possible types of single human falls quite accurately.

/pdf/automatic-detection-of-human-fall-in-video-2qsph6gnr8.pdf

Automatic detection of human fall in video

A minimum connected dominating set (MCDS) is used as virtual backbone for efficient routing and broadcasting in ad hoc sensor networks. The minimum CDS problem is NP-complete even in unit disk graphs. Many heuristics-based distributed approximation algorithms for MCDS problems are reported and the best known performance ratio has (4.8 + 1n 5). We propose a new heuristic called collaborative cover using two principles: 1) domatic number of a connected graph is at least two and 2) optimal substructure defined as subset of independent dominator preferably with a common connector. We obtain a partial Steiner tree during the construction of the independent set (dominators). A final postprocessing step identifies the Steiner nodes in the formation of Steiner tree for the independent set of G. We show that our collaborative cover heuristics are better than degree-based heuristics in identifying independent set and Steiner tree. While our distributed approximation CDS algorithm achieves the performance ratio of (4.8 + 1n 5) opt + 1.2, where opt is the size of any optimal CDS, we also show that the collaborative cover heuristic is able to give a marginally better bound when the distribution of sensor nodes is uniform permitting identification of the optimal substructures. We show that the message complexity of our algorithm is O(n?2), ? being the maximum degree of a node in graph and the time complexity is O(n).

Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks

Data aggregation is an essential paradigm for energy efficient routing in energy constraint wireless sensor networks. The complexity of optimal data aggregation is NP-hard. Ant colony system, a population-based algorithm, provides natural and intrinsic way of exploration of search space in optimization settings in determining optimal data aggregation. The simulation results shows improvement in energy efficiency depending on the number of source nodes in the sensor network which is 45% energy efficiency using optimal aggregation compared to approximate aggregation schemes in moderate number of source whereas 20% energy efficiency in large number of source nodes. The proposed ant-aggregation algorithm is simulated in MATLAB.

Ant-aggregation: ant colony algorithm for optimal data aggregation in wireless sensor networks

A formal method for checking equivalence between a given behavioral specification prior to scheduling and the one produced by the scheduler is described. Finite state machine with data path (FSMD) models have been used to represent both the behaviors. The method consists of introducing cutpoints in one FSMD, visualizing its computations as concatenation of paths from cutpoints to cutpoints, and identifying equivalent finite path segments in the other FSMD; the process is then repeated with the FSMDs interchanged. Unlike many other reported techniques, this method is strong enough to work when path segments in the original behavior are merged, a common feature of scheduling. It is also capable of verifying several arithmetic transformations and many code-motion techniques employed during scheduling. Correctness and complexity of the method have been dealt with. Experimental results for several high-level synthesis benchmarks demonstrate the effectiveness of the method.

An Equivalence-Checking Method for Scheduling Verification in High-Level Synthesis

Wireless ad hoc and sensor networks (WSNs) often require a connected dominating set (CDS) as the underlying virtual backbone for efficient routing. Nodes in a CDS have extra computation and communication load for their role as dominator, subjecting them to an early exhaustion of their battery. A simple mechanism to address this problem is to switch from one CDS to another fresh CDS, rotating the active CDS through a disjoint set of CDSs. This gives rise to the connected domatic partition (CDP) problem, which essentially involves partitioning the nodes V(G) of a graph G into node disjoint CDSs. We have developed a distributed algorithm for constructing the CDP using our maximal independent set (MlS)-based proximity heuristics, which depends only on connectivity information and does not rely on geographic or geometric information. We show that the size of a CDP that is identified by our algorithm is at least [delta+1/beta(c+1)] - f, where delta is the minimum node degree of G, beta les 2, c les 11 is a constant for a unit disk graph (UDG), and the expected value of f is epsidelta|V|, where epsi Lt 1 is a positive constant, and delta ges 48. Results of varied testing of our algorithm are positive even for a network of a large number of sensor nodes. Our scheme also performs better than other related techniques such as the ID-based scheme.

Chittaranjan Mandal

Papers

Automatic detection of human fall in video

Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks

Ant-aggregation: ant colony algorithm for optimal data aggregation in wireless sensor networks

An Equivalence-Checking Method for Scheduling Verification in High-Level Synthesis

Rotation of CDS via Connected Domatic Partition in Ad Hoc Sensor Networks