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International Journal of Distributed Sensor Networks
Volume 2012 (2012), Article ID 135054, 9 pages
Holes Detection in Anisotropic Sensornets: Topological Methods
1School of Computer Science and Engineering, Xi'an University of Technology, Xi'an 710048, China
2College of Management Science, Chengdu University of Technology, Chengdu 610059, China
3National School of Software, Xidian University, Xi'an 710071, China
4College of Science, Xi'an University of Science and Technology, Xi'an 710054, China
Received 11 May 2012; Revised 2 September 2012; Accepted 12 September 2012
Academic Editor: Chuan Foh
Copyright © 2012 Wei Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Wireless sensor networks (WSNs) are tightly linked with the practical environment in which the sensors are deployed. Sensor positioning is a pivotal part of main location-dependent applications that utilize sensornets. The global topology of the network is important to both sensor network applications and the implementation of networking functionalities. This paper studies the topology discovery with an emphasis on boundary recognition in a sensor network. A large mass of sensor nodes are supposed to scatter in a geometric region, with nearby nodes communicating with each other directly. This paper is thus designed to detect the holes in the topological architecture of sensornets only by connectivity information. Existent edges determination methods hold the high costs as assumptions. Without the help of a large amount of uniformly deployed seed nodes, those schemes fail in anisotropic WSNs with possible holes. To address this issue, we propose a solution, named PPA based on Poincare-Perelman Theorem, to judge whether there are holes in WSNs-monitored areas. Our solution can properly detect holes on the topological surfaces and connect them into meaningful boundary cycles. The judging method has also been rigorously proved to be appropriate for continuous geometric domains as well as discrete domains. Extensive simulations have been shown that the algorithm even enables networks with low density to produce good results.
1. Introduction and Motivation
Sensornets are appearing as promising techniques for pervasive data exchange and information sharing. Sensornets are tightly linked with the geometric environment in which they are deployed. Detecting topological holes is a very important task in wireless sensor networks [1]. In many crucial safe-related scenarios, such as earthwork construction and mine exploitation cases, we need to determine whether topological holes in space topological structure exist, thus, we can send the urgent warning for users so as to prevent the disasters that happen suddenly and have enough time to deal with the accidents in time. Many existing countermeasures usually do strong assumptions. As we know, all of mathematical theorems have their own used field. That is to say, before we use these mathematical methods to solve the practical problems, we need to proof at least explain that these mathmatic ways can be used in the specialized domain. Simultaneously, those current methods either enquire customerized hardware devices or have strong assumptions on the network environment, leading to low efficiency and applicability. In this work, we fundamentally analyze the detecting mind of space holes issue by topology methodology and by observing the inevitable topology deviations introduced by holes. We generalize the definition of space holes in practical scenarios and propose a topological approach. Mathmatical proof and simulation results show that our approach can detect and locate various holes and relies solely on topological information of the network. To the best of our knowledge, we try our best to make the first attempt towards a purely topological approach to detect holes distributedly without any rigorous requirements and assumptions. At the same time, we also solve the applied domain problem of mathmaitical theorem by removing the theoretical barriers to finish it. Our approach achieves superior performance and applicability with the least limitations.
On one hand, sensor network applications for example environment monitoring and data collection demand wealthy coverage over the region of interest. On the other hand, the global topology of a WSN has a great influence on the design of basic networking functionalities, for example, point-to-point routing and data collecting mechanisms. In this paper we study the problem of discovering the global geometry of the sensornets field, especially, inspecting sensor nodes on the boundaries (both inner and outer boundaries). The standpoint we take is to regard the sensornet as a discrete sampling of the underlying geometric environment. This is inspired by the fact that sensornets are to offer dense monitoring of the potential space. Therefore, the shape of the sensor field, that is, the boundaries, indicates significant characters of the underlying environment. These boundaries usually have physical correspondences, such as a building floor plan, a map of a transit network, topography changes, and barriers (skyscrapers, subsidence areas, etc). Holes can also map to events that are being monitored by the sensornet. If we consider the sensors with readings above a threshold to be "invalid", then the hole borders are essentially iso-contours of the landscape of the property of interest.
Cases include the identification of regions with overheated sensors or abnormal chemical contamination. Holes are also important indicators of the universal health of a sensornet, for example insufficient coverage and connectivity. The detection of holes divulges groups of destroyed sensors because of physical destruction or power consumption, where additional sensor deployment is demanded. Besides the real scenario mentioned above, understanding the global geometry and topology of the sensor field is of great importance in the design of basic networking operations. For example, in the sensor deployment problem, if we are desirous to spread some mobile sensors in an unknown region formed by static sensor nodes, knowing the border of the region permits us to guarantee that newly added sensors are deployed only in the expected region.
A number of networking protocols also exploit geometric intuitions for simplicity and scalability, for instance geographical greedy forwarding [2, 3]. Such algorithms based on local greedy advances may fail at local minima if the sensor networks have nontrivial topology. Backup methods, for instance face, routing on a explanate subgraph, can assist packets avoid local minima, but build high traffic on hole boundaries, and eventually destroy the network lifetime [2, 3]. This artificial product is not amazing because any algorithm with a strong geometrical application, for example geographical forwarding, ought to stick to the genuine shape of the sensor field. Currently, there are lots of routing schemes that address explicitly the importance of topological properties and propose routing with virtual coordinates that are adaptive to the inner geometric features [4, 5]. The construction of these virtual coordinate systems needs the identification of topological features. We focus on developing a judgment method that detects hole boundaries based on the Poincare Conjecture theory.
The rest of this paper is organized as follows. We first give a brief overview of this scheme in Section 2. And then, we present the PPA design principle in a continuous domain and offer the solid and complete theoretical proof to describe how the traditional and continuous topological theory (Poincare-Perelman Theorem) can be suitably (appropriately) applied to discrete and practical scenarios. As a result, we utilize the Poincare-Perelman Theorem to judge (determine) whether there are existing holes in real topological spaces. Namely, the constructing topological structure of continuous deployment of sensors over the Euclidean plane can also be used to justify whether holes in practical applications exist. We can efficiently detect holes danger and therefore send alert notice in real and safe field applications. In Section 3, we perform the problem formulation and holes detection in discrete environments. Section 4 extends the discussion into the practical discrete context. Section 5 evaluates the proposed scheme through comprehensive simulations and compares it with state of the art-area-based approaches localization schemes. We conclude the work in Section 5.
2. Prior Works
A lot of methods have been presented to judge sensor locations in WSNs. A universal overview of the state-of-the-art localization schemes is available in [6].
Existing researches on edges recognition can be separated into three classifications: geometric, statistical, and topological methods. Geometric methods that were proposed by Fang et al. [1] for boundary detection use geographical location information. This method assumes that the sensor nodes can sense their geographical locations and that the communication graph follows the UDG (Unit Disk Graph) assumption, when two nodes are connected by an edge if and only if their interval is at most 1. The description of holes in [1] is closely interrelated with geographical forwarding so that a packet can only get stuck at a node of hole edges. Fang et al. also presented a simple algorithm that greedily sweeps along hole boundaries and eventually discovers boundary cycles. Statistical methods for boundary detection usually make assumptions about the probability distribution of the sensor deployment. Fekete et al. [7] proposed a border detection algorithm for sensors (uniformly) randomly deployed inside a geometric region. The primary idea is that boundaries nodes have much lower average degrees than nodes in the "interior" of the network. Statistical arguments cause an appropriate degree threshold to differentiate border nodes. An statistical way is to calculate the "restricted stress centrality" of a vertex , which measures the quantity of shortest paths going through with a bounded length [7]. Nodes in the interior tend to have a higher centrality than nodes on the boundary. With a sufficient nodes density, the centrality of the nodes holds dual features so that it can be used to detect boundaries. The dominating weak points of these two algorithms are the idealized request on sensor deployment and density: the mean density needs to be 100 at least. In real scenario, the sensors are not as dense and they are unnecessarily arranged uniformly and randomly. There are also topological methods to prime deficient sensor coverage and holes. Ghrist and Muhammad [8] presented an algorithm that detects holes via homology with no knowledge of sensor locations; on the contrary, the algorithm is centralized, with assumptions that both the sensing range and communication range are disks with radii carefully tuned. Kröller et al. [9] presented an algorithm by probing for combinatorial structures called flowers and augmented cycles. They make less restrictive assumptions on the problem setup, modeling the communication graph by a quasi UDG, with nodes and demonstrably linked by an edge if and not connected if . The success of this algorithm critically depends on the identification of at least one flower structure, which might not often be the case specially in a sparse network. For a real scenario, Funke [10] developed a simple heuristic with only connectivity information. The essential idea is to build iso contours with hop count from a root node and identify where the contours are broken. Under the unit-disk graph assumption and adequate sensor density, the algorithm outputs nodes marked as border with certain guarantees. Definitely, for each node of the geometry boundary, the algorithm enables to mark a corresponding sensor node within distance 4.8, and each node marked as boundary is within distance 2.8 from the actual geometry boundary [11]. The simplicity of the algorithm is appealing; however, the algorithm only identifies nodes that are near the boundaries but does not show how they are connected in a meaningful way. The density requirement of the algorithm is also rather high; so as to obtain good results, the average degree generally needs to be at least 16.
From mathematics aspect, the Poincare Conjecture [12] is a theorem about the specification of the three-dimensional sphere among three-dimensional manifolds. Original conjectured is proposed by Henri Poincare, the claim considers a space that locally resembles ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed three-dimensional manifold). The Poincare Conjecture states that if each loop in such a space can be continuously tightened to a point, then it must be a three-dimensional sphere. An similar result has been proved in higher dimensions. (Some related content is partially referred to the Wikipedia information).
2.1. Definitions of Manifold
A manifold is a space made by conglutinating together pieces of Euclidean space, which is called charts. For example you could take two-dimensional disks and bend them around two hemispheres and then stick them together to form a two-dimensional sphere. (See also in Figure 1(d)).
A torus (the surface of a donut) can be established utilizing a rectangular diagram as shown in this image. The colored parallelograms explain how a pattern on the associated surface would arise in case the edges were once again disconnected. (See also in Figures 1(b) and 1(c)). A pair of solid balls can made a three-dimensional sphere. It should be required to discern every point of the first ball boundary with the corresponding point of the second one. Other kinds of manifolds can be established by the mimetic ways.
2.2. Explanations of Homeomorphic
Generally, two shapes are homeomorphic if one of these shapes can be transformed into the other without pause or discontinuity. homeomorphism is a function of continuous domain that maps points of one object into another.
Two spaces are regarded as homeomorphic if a homeomorphism between them exists. Such as, a two-dimensional sphere is homeomorphic to the surface of a cube; homoplastically, a three-dimensional sphere is homeomorphic to the three-dimensional boundary of a four-dimensional hypercube. In the above-mentioned primary concepts, they can aid to comprehend the specification of the Poincare-Perelman Theorem: the Poincare-Perelman Theorem says that a three-dimensional manifold which is compact, has no boundary and is simply connected must be homeomorphic to a three dimensional-sphere. The original phrasing was as follows: consider a compact three dimensional manifold without boundary. Is it possible that the fundamental group of could be trivial, even though is not homeomorphic to the three-dimensional sphere? This centurial challenging problem is proofed by Grigori Perelman [12] in 2006.
Here is the standard form of the conjecture: every simply connected, closed tridimensional manifold is homeomorphic to the triaxial sphere. Therefore, a centralized method of collecting all of the information to a central server is not feasible for large sensor networks.
2.3. Preliminaries
Materials for topology theory. The following definitions in topology theory can be found in [13].
Let be a set. is called a topology on if (1) ; (2) if , then ; (3) if , then . The pair is called a topological space. The members of are called open sets. If is a subset of , then is a topology on and called the induced topology of . A bijection between two topological spaces is called a homeomorphism if iff for any . In this case, and are said to be homeomorphic to each other.
Dense Set
Let be a topological space and . A point is called a cluster of if any with . Denote as the set of all cluster of , called the closure of . The set is called a closed set if . A set is called a clopen set if it is simultaneously open and closed. A set is called dense of if . Dense set is an important and useful concept in topology. For example, every continuous map from a dense set of a topological space to another topological space can be extended onto the whole topological space. Thus dense sets in a topological space may share some same topological properties as the whole topological space, for example the connectedness as Theorem 1 shows.
The specification of partition for a set , a family of subsets is called a partition of , if and for all with .
2.4. Our Contributions
We develop a practical and efficient determination solution for boundary detection in sensor networks, using only the communication graph and not making unrealistic assumptions. We do not assume any location information, angular information, or distance information. More importantly, we do not request that the communication graph obeys the unit disk graph model or the quasi-unit disk graph model. Actual communication ranges are not circular disks and are often quite irregularly shaped [14]. Algorithms that depend on the unit disk graph model fail in practice (e.g., the extraction of a planar subgraph by the relative neighborhood graph or Gabriel graph [15].
Our PPA method also readily provides other topological and geometric information, such as the number of holes (genus), the nearest hole to any given sensor, and the sensor field's medial axis (the collection of nodes with at least two closest boundary nodes), which is useful for virtual coordinate systems for load-balanced routing [4]. Simulation results show that our algorithm correctly determines useful borders for sensor networks with rational node density (average degree 10 and above) and distribution (e.g., uniform). The algorithm also works well for nonuniform distributions. The algorithm is efficient. The entire procedure involves only three network flooding procedures and greedy shrinkage of paths or cycles. Further, as a theoretical ensure, we prove that for a continuous geometric space bounded by polygonal obstacles, the case in which node density approaches infinity, the algorithm correctly discovers all of the boundaries. More definitely, we investigate the fact that a legitimate multihop sensor network deployed on the surface of a geometric terrain, (even possibly including irregular boundaries, inner obstacles, or even on a non-2D plain) PPA solution is able to accurately estimate the node-to-node distances and calculate node locations with only 3 seeds, thus increasing system scalability and usage as well as lowering hardware costs. In addition, PPA does not presume the superior communication capability of seeds, that is, with much larger radio range than those of the ordinary nodes [16].
Due to all mentioned above assumptions based on UDG graph model and its basis on the symptom of packing number, it is thus inaccurate under non-UDG graphs. Indeed, there are still no perfect symptoms found to establish an all-round method in the resource-limited sensornets. Our design is originated from the perspective of topological observation and is based on the theory of Poincare Conjecture, our solution is orthogonal to existing approaches and takes a step towards relaxing these assumptions and expanding the applicability of methods.
3. Problem Formulation and Holes Detection
The definition has been given under the constraints of the UDG communication graph model, which has been proven far from practical in many analytical and experimental works. Second, the distance-based definition in Euclidean space naturally binds the hole features with external geometric environments and thus neglects the inherent topological impacts introduced by holes. We hereby present a more general and fundamental definition of the hole based only on network topologies and aim to present the inherent characteristics of holes. According to the Poincare-Perelman Theorem, in the three dimensions space, the donut topology is homeomorphous to the coffee cup topology (see also Figure 2(b)). As shown in Figure 2(a), since these two topologies are not equivalent (namely, not homeomorphism), we can determine that the holes in the monitored areas based on the Poincare-Perelman Theorem exist (see also Figures 2(a) and 2(b)). Since these two topologies are not equivalent (namely, not homeomorphism), we can determine that the holes in the monitored areas based on the Poincare-Perelman Theorem exist.
In real scenario, we will treat the multihole condition. But in this proposed solution, we currently do not differentiate the numbers of holes. In future work, we will discuss and deal with this condition.
Owing to constructing the network topological structure of monitored areas, in given the surface , we first select an arbitrary point in as the root and run a continuous Dijkstra shortest path algorithm [17, 18] to construct the topology structure (manifold) of monitored areas. As shown in Figure 3(a) and Figure 3. Consequently, we can determine whether any closed and simply connected manifold is homeomorphic to the three dimensions sphere. If it is not homeomorphic to the three dimensions sphere. It refers to there is/are hole(s) in the monitored areas. (See also in Figure 3(b)).
3.1. Holes Detection in Discrete Environments
We have characterized the impact of holes and described the principles of holes detection under continuous settings in the previous section. In a real multihop network, however, nodes are deployed discretely on the field. In this section, we focus on solving the mapping question from the discrete domain to continuous geometric domain. Since the theory of Poincare-Perelman Theorem belongs to the judgement of continuous geometric domain, we need to proof the correctness and applicability of this topological judgement. By means of the following solid proof, we can transfer the discrete topological space to the continuous geometric domains. Namely, we utilize the partial discrete topology structure to substitute the whole continuous geometric topology. As a result, we can apply the theory of Poincare-Perelman Theorem to judge the existence of holes in the monitored areas by WSNs.
Let be a topology on a set and . Then is a topology on , called the induced topology on and in this case is always called a subspace of and an extension of from to . We confirm that these two topological spaces and have the same topological properties. In a topological space , a subset is called dense if , where is the closure of in . A topological space is called connected if there exists no clopen (simultaneously closed and open) subset except empty and whole set .
Theorem 1. Suppose that is a dense subspace , then is connected if and only if is connected.
Proof. Suppose that is connected. If is not connected, then there exists a clopen set in and . Put , we have that is a clopen set in , which implies that and (obviously, ). Since is dense in , we have , which contradicts to . Conversely, suppose that is connected. If is not connected, then it contains a clopen set which is neither nor . For this , there exist a clopen set in such that . In order to induce a contradiction, we only need to show that . If , then , which is another contradiction to . The proof is complete.
Remark 2. If a topological space is -connected topological space (), then can exactly be separated into connected subspace such that is a partition of . By Theorem 1, if is a dense subspace , then is -connected if and only if is -connected. As mentioned in the above Remark, the definition of concept partition for a set , a family of subsets is called a partition of , if and for all with .
The following verdict is usually held for any set that satisfies the requirement of the theory. Whatever the set is finite or infinite. We assume that a certain area deployed the WSNs. This area can be considered as a smooth curve equipped with the traditional Euclidean topology, the set of all sensors equipped with their own topology can be considered as a subspace of the former one. Furthermore, we assume that the set of all sensors is dense in this area.
We assume that the whole sensor nodes set, which completely cover the monitored area, constructs a dense set. A dense set is the monitored area which is abundantly and completely covered by the large quantities of sensor nodes. Therefore, the network topology can be continuously expanded to the monitored area. Specially, some part of sensornets can be destroyed by some accidents so that it will lead to form a hole in the architecture of topology. As a result, there exists a hole in the corresponding practical area. The sensornets corresponding geometric structure is a universal Euclid topology, particularly, if a hole in this monitoring area exists. If and only if the topology of sensornets is sub dense space of area topology space. Furthermore, If and only if the geometric topology of monitored area is connected completely, consequently, the constructing topology of sensornets is interconnected. Simultaneously, if and only if there exists holes in the geometric topology of monitored area, as a result, there exists holes in the constructing topology of sensornets.
Thus detecting whether there are holes existing in sensornets topology is equivalent to detecting whether there are holes in the monitored area.
Symbolic Interpretation. Area , is the Euclidean topology of . The set denotes the sensornets while denotes the efficient sensornets. Precondition: set is dense in .
(1) Let be the closure of on . If it exists holes, then . (2) Obtaining while the topology of is constrained in the . Therefore, is a subspace of . (3) In the above mentioned, is continuous set. Consequently, we can depend on the Poincare Conjecture theory to determine whether there are holes that existed in monitoring area. If there are holes in the topology structure of , then there are holes in the topology structure of . The above-mentioned theory can guarantee this determination.
3.2. Topological Boundary Recognition
Suppose a large number of sensor nodes are scattered in a geometric region with nearby nodes communicating with each other directly. Our goal is to discover the nodes on the boundary of the sensor field, using only local connectivity information. We propose a solution that identifies boundary cycles for the sensor field. For compact 2-dimensional surfaces without boundary, if every loop can be continuously tightened to a point, then the surface is topologically homeomorphic to a 2 spheres, usually just called a sphere. The Poincare Conjecture asserts that the same is true for 3-dimensional surfaces. (See also in Figure 1(a)). Practically, for obtaining the topology of monitored areas, we firstly use the Dijkstra Shortest Path algorithm [17] to construct the topology (manifold) of monitored areas. Consequently, we can determine whether any closed and simply connected manifold is homeomorphic to the three dimensions sphere. If it is not homeomorphic to the three dimensions sphere, it refers to there is/are hole(s) in the monitored areas (see also Figure 3(b)).
In the following, we first outline the Dijkstra Shortest Path algorithm and then explain each step in detail.
Algorithm allows the node at which we are starting to be called the initial node. Let the distance of node be the distance from the initial node to . Dijkstra's algorithm that allocates some initial distance values and will try to increase them step-by-step. Assign to every node a distance value. Set it to zero for our initial sensor node and to infinity for all other nodes. Mark all nodes as unvisited. Set initial sensor node as current. For current node, consider all its unvisited neighbors and calculate their distance (from the initial node). For instance, if current node () has distance of 6, and an edge connecting it with another node () is 2, the distance to through will be . If this distance is less than the previously recorded distance (infinity in the beginning, zero for the initial node), overwrite the distance. When we are done considering all neighbors of the current node, mark it as visited. A visited node will not be checked ever again; its distance recorded now is final and minimal. If all nodes have been visited, finish. Otherwise, set the unvisited node with the smallest distance (from the initial node) as the next "current node". Suppose you want to find the shortest path between two intersections on a map, a starting point and a destination. To accomplish this, you could highlight the streets (tracing the streets with a marker) in a certain order, until you have a route highlighted from the starting point to the destination. The order is conceptually simple: at each iteration, create a set of intersections consisting of every unmarked intersection that is directly connected to a marked intersection, and this will be your set of considered intersections. From that set of considered intersections, find the closest intersection to the destination (this is the "greedy" part, as described above) and highlight it and mark that street to that intersection, draw an arrow with the direction, then repeat. In each stage mark just one new intersection. As getting to the destination, follow the arrows backwards. There will be only one path back against the arrows, the shortest one. The basic idea is to detect the existence of holes by judging whether if the existing topology is equivalent to sphere in the three-dimension space. Based on the mentioned above, we can construct a topology of monitored areas. Intuitively, it is very hard to determine the existence of holes by the two-topology structure. We assume our method can obtain the whole monitored topology, and then we can compare this obtained topology with sphere topology. Finally, we can determine whether holes in the monitored area exist.
4. Simulations
We performed extensive simulations in various scenarios, with the goal to evaluate the performance of the algorithm with respect to the network topology, node density and distribution, so on. We particularly note that our method works well even in cases of very low average degree, such as less than 10, or even as low as 10 in some models. Its ability is also similar to average degree 20 condition. Degree 6 has been shown to be optimal for mobile networks [19]. For each figure in this part, we assume a root node in the upper left corner and middle to illustrate the communication range of the sensor field.
4.1. Random Distribution of Sensors
In this experiment, we first assume that the network connectivity and link quality are good enough. In terms of a uniform distribution, we randomly deploy 1600 nodes in a square region with one hole. The average degree of the graph is discriminated by regulating the communication radius. As expected, Figures 4(a) and 4(b) show the results of our method. We can efficiently judge the hole existing in the monitored area. Connectivity is necessary for computing the shortest path tree. Practically, this low-degree graph with insufficient connectivity is the major troubling issue for prior boundary detection methods. Since our method only requires the communication graph, we can use several simple policies to raise artificially the average degree. For a disconnected network, we use the largest connected component of the graph to build our shortest path tree. Then we artificially enlarge the communication radius by taking two/three hops neighbors as fake one-hop neighbors. According to this means, the connectivity of the graph will be made better, and the results will be improved correspondingly by this simple strategy. The result using three hops neighbors has fewer incorrectly marked extremal nodes, and the final judgement is in good result except that the boundary cycle is not very tense. This is understandable since we make the communication range artificially larger, so that more nodes could be equivalently to distribute on the boundary now. Therefore, based on our solution, we can efficiently find holes in the supervised area.
4.2. Grid with Random Perturbation
In this simulation, we put about 1600 nodes on a grid and then perturbed each point by a random shift. Especially, for each original grid node we create two random numbers modulo the length and the width of each block of the grid and use these two small numbers to perturb the positions of the nodes. This distribution may be a good approximation of manual deployments of sensors; it also gives an alternative means of modeling "uniform" distributions, while avoiding clusters and holes that can arise from the usual continuous uniform distribution or Poisson process. As the theoretic verification considering, our method generates very good results, while average degree of graphs is ten or more.
4.3. Low Density, Sparse Graphs
In the experiments, we spread sensor nodes in a square region with one hole. In order to guarantee good connectivity, the nodes are distributed on a randomly perturbed grid. Our experiments show that if we amend the communication radius and decrease the density of nodes, our solution is performed very well, even for low density or sparse condition, as long as the average degree is at about ten or more. See also Figure 4(c).
5. Conclusion and Discussion
We devote our most efforts to explore the application of Poincare Conjecture to resolve the holes detection of safety-monitored areas in WSNs. Based on the theoretic specification, we can judge whether there are holes in the detected area. Because the detected network topology is not homeomorphous to the three dimensions sphere, it can be confirmed to have holes in the detected topology architecture. Therefore, we can accomplish the detecting holes purposes. The proposed new detection solution enables us to find holes in the continuous case, in discrete sensors networks several implementation issues arise. First, even for a given homotopy type, there needs not be a unique shortest path between two nodes. Thus, the boundary topology discovered by our solution, as shown in the simulations, may not tightly surround the real boundaries. Currently, we have two approaches to improve it. One is to make use of the fact that the nodes with lower degree are more likely to be on the boundary; thus, we implemented a preferential scheme for low-degree nodes when computing shortest paths. Another approach is to use an iterative method to find more extremal nodes and then refine the topology; this can also help to address the issue that several extremal points may have the same positions because we use hop counts to approximate true distances. Second, deciding the correct orderings of the extremal nodes requires some care. In the continuous case, extremal nodes project to their nearest node. In the discrete case, since we employ hop counts to approximate the true distance, it is possible that different extremal points are mapped to the same position on the inner boundary, obscuring their ordering. Again, by using an iterative procedure, we delete all the extremal nodes with duplicate positions except one and then iteratively find more extremal points and refine the boundary gradually. In real scenarios, the sensor nodes often know some partial location information or relative angular information. Such positional information can help to improve the performance of our holes detection solution, for example, when we utilize the shortest path algorithm to construct the topology of monitored areas. If the nodes have knowledge of a general arctic direction, it is easier to distinguish the extremal nodes in the interior and exterior of rough boundary. Also, if we have estimated distance or other rough localization information, other than pure hop count, the procedure to find shortest paths will become more reliable. Finally, our method discussed until now assumes a sensor field with holes. We remark that the case with no holes can be solved as well.
Finally, our method discussed until now assumes a sensor field with holes. We remark that the case with no holes can be solved as well. If a network topology is equivalent to (homeomorphous) the three dimensions sphere, then it have no holes on the monitored areas based on the proofed of Poincare Conjecture, vice versa.
6. Conclusion
In this paper, a novel CT reconstruction model is proposed based on the approximate inverse where the kernel of the FDK method is derived and is used to complete the reconstruction. In order to eliminate the imposed ring artifacts, the kernel is truncated with proper radius. Reconstruction results show that the compact support FDK kernel reconstruction model can suppress the ring artifacts. The proposed reconstruction model preserves the simplicity of the FDK reconstruction method and also provides an alternative to realize the approximate inverse method for circular trajectory. And when the kernel of an algorithm is modified, the corresponding reconstruction formula is also modified accordingly. And this give us another way to improve the existing reconstruction methods.
The authors would like to thank the anonymous reviewers for their constructive feedback and valuable input. Thanks are due for the supports to our program from the TI, the XILINX, and the Software School of Xidian University. This program is partially supported by NSFC (Grant no. 61072105, 61007011) and also supported by the Open Projects Program of National Laboratory of Pattern Recognition. The project is also partially supported by Natural Science Basic Research Plan in Shaanxi Province of China (Program no. 2010JM8005) and Scientific Research Program Funded by Shaanxi Provincial Education Department (Program no. 11JK0504).
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- S. Funke, "Topological hole detection in wireless sensor networks and its applications," in Proceedings of the Joint Workshop on Foundations of Mobile Computing, pp. 44–53, 2005.
- S. Funke and C. Klein, "Hole detection or: 'how much geometry hides in connectivity?'," in Proceedings of the 22nd Annual Symposium on Computational Geometry (SCG '06), pp. 377–385, June 2006. View at Scopus
- Poincare and Jules Henri, The American Heritage Dictionary of the English Language, Houghton Mifflin Company, Boston, Mass, USA, 4th edition, 2000.
- J. L. Kelly, General Topology, D. Van Nostrand, Princeton, NJ, USA, 1955.
- D. Ganesan, B. Krishnamachari, A. Woo, D. Culler, D. Estrin, and S. Wicker, "Complex behavior at scale: an experimental study of low-power wireless sensor networks," Tech. Rep. UCLA/CSD-TR 02-0013, UCLA, 2002. View at Google Scholar
- Y. J. Kim, R. Govindan, B. Karp, and S. Shenker, "Geographic routing made practical," in Proceedings of the 2nd USENIX/ACM Symposium Networked System Design and Implementation, pp. 217–230, 2005.
- T. He, C. Huang, B. M. Blum, J. A. Stankovic, and T. Abdelzaher, "Range-Free Localization Schemes for Large Scale Sensor Networks," in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking (MobiCom '03), pp. 81–95, September 2003. View at Scopus
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- E. M. Royer, P. M. Melliar-Smith, and L. E. Moser, "An analysis of the optimum node density for ad hoc mobile networks," in International Conference on Communications (ICC '01), pp. 857–861, June 2000. View at Scopus


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- Business News
- Trading And Investing
- sectors
- special features
- MV Education center
- Video
- t3 live subscriptions
In light of the Department of Justice's complaint, AT&T is very willing to sweeten the deal.
In a rare display of actual justice, the US Department of Justice attempts to block the worst merger in tech.
New conditions on phone exchanges could have customers accruing hefty fees.
Everyone can agree that the AT&T, T-Mobile merger is bad for customers. But just how bad?
It's never good for consumers to have fewer choices in a powerful market.

subset: commoncrawl


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That's one heck of a nonsense headline, and yet it is correct. Read on…
Abby Lowell / Juneau Empire
A trio of salmon fly patterns are tied on a "cactus hook" which was cut from a fish hook barrel cactus… a "cactus fly" that his father, Bob, tied about thirty years ago with barbs cut from the fish hook barrel cactus. The cactus is most commonly found in Arizona and northern Mexico.
Here's another shot, with fisherman.
You can also bookmark this on del.icio.us or check the cosmos
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One Response
Cactus Says:
February 4th, 2010 at 4:49 pm
It appears I got the story wrong. The gentleman in question is in Colorado. Serves me right for not reading the article, but only looking at the pictures.


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METROPOLIS — While I was in the city on business, I had a rather interesting interaction with a gent named Clark Kent at the hotel bar. The watering hole was just down the street from mega newspaper The Daily Planet — where Kent had just quit.
"I just couldn't in good conscience do it anymore," I overheard him say to a former co-worker. "There's no soul in today's media landscape. I just couldn't do real reporting anymore. I'm just a cog in the wheel!"
As a former newspaperman myself, I couldn't help but sidle over as the harrumphing died down and Kent's tipsy pals slapped him on the back and wandered toward the exit.
"Hold up there, Kent," I said. "I used to work in the newspaper biz — and let me tell you, there is a ton of great reporting going on out there. Journalism is far from dead — it's just the profits that have disappeared. The real reason people leave is because the pay sucks and the business is dying. So level with me: Is it really your morality talking here, or your bank account?"
Clark Kent opened his mouth to say something, then shut it and collapsed onto a bar stool.
"OK, OK, you got me." He took his glasses off and wiped his face with a sleeve, then quickly replaced the frames on his nose. "Outwardly I'm all sanctimonious about new media and making a difference … but the real reason is that I just can't sit around waiting for the ax to fall. You heard what happened to Peter Parker a few years back, right?"
"So you plan to get out voluntarily before the music stops, is that it?"
"You got that right. Stock of The New York Times Co. (NYSE:NYT) is off over 50% in the past five years — and even though it has recovered lately, NYT just sold off 20% on bad earnings. USA Today publisher Gannett (NYSE:GCI) is off almost 60% in five years. And despite a big dividend hike, the payouts at GCI are still half what they were in 2007."
"Yikes. If your company is in the same boat, hope you didn't participate in the Daily Planet employee stock purchase plan." I sipped my beer. "But come on, Warren Buffett believes in newspapers. Berkshire Hathaway (NYSE:BRK.A, BRK.B) just bought a stake in a boatload of them."
"That's just the altruism of a rich billionaire." Kent waved his hand dismissively. "I admire it, don't get me wrong … but it's not a good investment."
"OK, print is unprofitable. So where are you going, digital media? You can probably make your way on a site like The Huffington Post."
"What are you, crazy? AOL (NYSE:AOL) is even more of a mess than The Daily Planet! At least print media has flopped and knows its days are numbered. Sites like AOL and Yahoo! (NASDAQ:YHOO) have no self-awareness. Just as the Internet disrupted print, mobile is disrupting the previous generation of digital media sites reliant on display advertising."
"There's video," I said. "Didn't you do a stint as a TV reporter in the 1970s for Galaxy Broadcasting?"
"Lordy, don't remind me…"
He pounds his drink. We both stare at each other in silence.
"So what's the plan then, Kent? Where can you go in this new age of digital media to find a secure company with well-paid employees?"
"Google (NASDAQ:GOOG) or Amazon (NASDAQ:AMZN), I guess. Those are just about the only places that have figured out how to make money off content in 2012 and have upside from here."
"Unless you're planning on working there as a janitor, good luck. Even Superman would have a hard time getting a job at an elite company like that."
Startled, Clark Kent jumped to his feet and eyed me suspiciously… it was like he was looking right through me. Then he relaxed and slumped back onto his bar stool.
"Yeah, you're right." He slid his glass across the bar and called for another beer. "If you're in the content game, I guess it's like this everywhere — mediocre pay, the risk of layoffs, and the need to crank out lowbrow celebrity news and 'infotainment' just to meet the demands of the unwashed masses."
"It's a dirty business, Kent. But take solace in the fact that every once in a while, after you feed the beast, you get to write an article that matters." I finished my drink and plunked the empty glass down on the bar. "Or at least write something fun like a fake interview with a superhero or something."
"True enough." We shook hands, his tight grip squeezing my fingers so much they hurt. "Well, I guess I should march back over there and beg for my job back or I'll regret it. After all, I've left the paper three times before and come crawling back … why stop now?"
Jeff Reeves is the editor of InvestorPlace.com and the author of "The Frugal Investor's Guide to Finding Great Stocks." Write him at email@example.com or follow him on Twitter via @JeffReevesIP. As of this writing, he did not own a position in any of the stocks named here.


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2BR,1BA DUPLEX, heat pump, central air,water & sewer included. $600./mth + $600./sec. dep. Call 540-330-9219
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2BR,1BA DUPLEX, heat pump, central air,water & sewer included. $600./mth + $600./sec. dep. Call 540-330-9219
FOR RENT. 2 Bdrm, 1.5 bath Townhouse. End unit. New windows, wood floor, newer HP. Just outside town limits. $625/mth. Call 540-871-0858 Owner/Agent.
Peaks View Apartments available for rent. Located on Centerville Road. One level w/private entrances. Central heat & air. Water/sewer & trash removal included with rent. Please call Brownstone Properties, Inc @ 434-385-1025 for details and showings.
OFFICE SPACE FOR RENT- PRIME LOCATION!! Convenient Main Street, ground level, great parking. Utilities and Wi-Fi included. 410 square foot. Calltomake appointment to see. 540-586-8519 $ 325/mth.
2 Bdrm Country Cottage near hospital. $650. month + utilities. Security deposit req'd. 540-586-8735 for application
LOG HOME ON 20 ac. 4 BRs 2-1/2 BAs, $1,600 mon, pets welcome. 757-603-0273.
MOBILE HOME LOT for rent, 1.5 acre, close to town, lays well, some views. Call 586-3724, leave message.
MOBILE HOME LOTS for rent at Meadow Ridge Mobile Home Park. Call 540-871-6724
SML Very Nice Furnished 2 Bdrm Cabin, No wake cove, Bedford Co. side near dam, Private dock, 2006 Pontoon boat w/70hp, 4 stroke motor. $80,000. Possible owner financing. Call 540-586-4188 or 312-8124 (cell)


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>Brookings Oregon News, Sports, & Weather | The Curry Coastal Pilot
Ernie Ladd, 78, Brookings, died April 15, 2001.
He was born Dec. 29, 1923.
A celebration of life will be held April 20 at 1 p.m. at the Performing Arts Center in Harbor.
Friends are invited to share their memories of Mr. Ladd at this informal gathering. Following the celebration, light snacks and desserts will be served.


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Jenn's residence [email protected] of Seoul
Size36.36 m²
Floor No.(with elevator)
- Family/child friendly
- Internet/WiFi
- Kitchen
- Air conditioning
- Washer/dryer
- Breakfast
- Elevator in building
|익선동 비즈웰 오피스텔, 110340 서울, South Korea
|Property type
|Property ID
The apartment is neat, comfortable and cozy with the amenities necessary for a great stay in Seoul.
It is furnished with new modern furniture. The kitchen is a fully equipped with cookware for your American style simple breakfast. You can be provided with bread for toast, jam, butter, cereals, egg and milk.
You will also get clean and fresh linens and towels.
Bedrooms are furnished with double Size bed, closet, comfort sofa bed, table,and etc
Air conditioner, heater and wi-fi are all provided.
There are 24 hour security guards in the lobby.
Absolutely amazing location!
Wherever you want to visit in the area north of the Han river, you can get there in 15 taxi or bus ride away. (The subway covers the distance less than 15minutes)
There are many nice and famous restaurants
Great places to visit nearby
Changdeokgung (palace)
Jongmyo Shrine
The national folk museum of Korea
Samchong-dong : gallery, artshop and nice restaurant
Lotte departments store
It's near the subway transfer station and bus stop.
Jongno 3(sam)-ga Station (line no 1,3,5) : Only a 5 –minute walk away
You can eaily access to Kangnam ( the south area of Seoul) by Line No 3
Airport limousine 6002 bus
The bus for Nami island, very famous setting of the popular Korean TV drama Winter Sonata departs from near near the Tapgol Park every morning
If you need specific bus information, pls feel free contact to me!
Start your Seoul experience in this clean and comfortable home-away-from-home.
It will greatly enhance your Seoul experience
If you need some information for nice restaurant or shopping place in Seoul, You may feel free to contact me with any questions
- Non-smoker (well not in the apartment anyway!)
- Clean, responsible and courteous
- Not looking to party in the apartment – why would you anyway with so many awesome bars close by !
|Weekly rate for up to 3 guests
|380 €
|Monthly rate for up to 3 guests
|1756 €
|Price for > 3 guests
|5 € per guest/night extra
|Check-in after
|Check-in before
|On arrangement
|Check-out before
|Cancellation Policy
There were 3 of us and we stayed at Jenn's residence Y for 7 nights.
The walk from the apartment to the subway entrance 5 is 5 mins and another 5 mins to the platform of line 1. To get to the platforms of line 3 and 5, it's another 10 mins walk from entrance 5 of the subway station.
The airport limo shuttle bus stop is about 15 mins walk from the apartment.
We took the AREX from the airport to Gongdeok station and then changed to line 5. It was very tedious to lug our luggage up and down the stairs between stations and platforms and walk another 15 mins to the apartment.
We were provided with 2 bath towels, 1 odd size bath towel and 10 hand towels.
The eggs, milk and bread provided were only good for 2 days.
There is no dryer or TV in the apartment even though they are mentioned under "Amenities".
3 sachets (size of a sugar stick each) of laundry detergent were provided.
There is no hand soap.
The bathroom is small and no space for our toiletries.
The room is too bright to sleep in. There is no curtain and the sunshade does not shade off lights from the opposite buildings.
The host Jenn has been very friendly and helpful during our stay. She upgraded us to a bigger apartment so we could have more space for our little boy. The location couldn't have been better. Near Insadong street (nice tourist street with many shops and restaurants) and walking distance to many interesting places and areas. But still quite quiet at night. Also close to subway station. The apartment was clean and furniture new. There's a mini shop in the same building where we could buy coffee in the morning and a few groceries.
What we were not as satisfied with was the fact that we couldn't change the bed linen for four weeks that we stayed there. There was a washing machine, but no tumble dryer which made the change impossible. no extra sheets at all. The kitchen appliances could have been bigger. The small frying pan only had room for one egg. There was very little space in bathroom to take a shower. I would say no space at all. Every time we took a shower, the hall bathroom was wet.
Over all worth the money. Mainly for the location and nice host!
Jen residence X was great! very comfortable, cozy and clean.
Close to restaurants and the subway (jongno 3)
would recommend!
Apartment was lovely and clean, and close to Subway. 5 minute walk away from the lovely Insadong shopping area. Loved the place. Lots of food close by. Jenn was really helpful when we needed direction. We couldn't get the washing machine to work properly and Jenn's husband came to our aid the same morning and was a great help and got it going. We had a great conversation with him. A very nice man.
Both speak excellent english. Would stay there again. Thank you Jenn for a lovely stay.
The apartment was small but cosy. It had everything that we needed with kitchen, towels, fridge, washing machine, etc. The location was great, central and walking distance to Insadong. The train station was also very near so it was very convenient.
As this was my first trip, the host was very helpful in explaining to us how to go around and what are the nice places to eat and shop. It was a great trip.
- Quality assured accommodation
- Every host is verified by telephone
- Secure payment via SSL encryption


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Skydiving.com now has a network skydiving location serving Minonk and Woodford County in Illinois. Call Skydiving.com at 1-800-617-7948 for details, free information and specials on skydiving in Minonk, IL today!
Popular Tags for Skydiving Minonk:
Skydiving Minonk, Skydiving in Minonk, Sky Diving Minonk, Skydive Minonk IL, Skydiving 61760, Minonk Skydiving, Skydiving Minonk Illinois, Skydiving near Minonk, Skydiving in Minonk Illinois, Minonk Sky Diving, Skydive 61760, Skydiving Minonk IL, Skydive Minonk, Skydiving Woodford County, Skydive in 61760, Skydiving IL, Sky Diving Minonk IL, Minonk, Illinois
Sign up for our newsletter and receive updatesand specials on skydiving across America!


text:
Skydiving.com now has a network skydiving location serving Vida and Lane County in Oregon. Call Skydiving.com at 1-800-617-7948 for details, free information and specials on skydiving in Vida, OR today!
Popular Tags for Skydiving Vida:
Skydiving Vida, Skydiving in Vida, Sky Diving Vida, Skydive Vida OR, Skydiving 97488, Vida Skydiving, Skydiving Vida Oregon, Skydiving near Vida, Skydiving in Vida Oregon, Vida Sky Diving, Skydive 97488, Skydiving Vida OR, Skydive Vida, Skydiving Lane County, Skydive in 97488, Skydiving OR, Sky Diving Vida OR, Vida, Oregon
Sign up for our newsletter and receive updatesand specials on skydiving across America!


text:
A rich Ham Casserole that uses Wise® Potato Chips.
It will leave your family and friends asking for more.
1 can condensed Cheddar cheese soup
3/4 cup sour cream
1 cup cubed cooked ham
1 (10 oz) package frozen cauliflower, thawed, drained and
1 cup crushed Wise Potato Chips
Preheat oven to 350°. In a medium bowl, combine soup and sour
cream; blend well. Stir in ham, cauliflower and
3/4 cup chips. Spoon into lightly greased
1-qt casserole; sprinkle with remaining chips. Bake 40 to 45
minutes or until hot.
Download our 1959 recipe book
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Memorials Available
We have a range of memorials available which offer families a choice of ways to remember loved ones but will also help the appearance of the Woodland Area.
These items may be ordered at the cemetery office or you can print an order form using the attachments at the bottom of this page and post to the cemetery office.
Payment can be made either by cheque (made payable to Birmingham City Council) or by credit / debit card over the telephone once your order has been received.


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That's a question I sometimes like to ask when visiting a law firm or speaking to an audience of lawyers: "Who is your biggest competitor?" I usually let the respondent decide what "biggest" means — sometimes they interpret it to mean the competitor who poses the greatest threat to their book of business, or who… Read more »
Posts Categorized: Competition
The incidental lawyer
The South Carolina Supreme Court ruled this week that LegalZoom's services do not constitute the unauthorized practice of law. As reported by Greg Lambert at 3 Geeks, LegalZoom's press release celebrates the news, while also taking pains to note that the company's documents have been reviewed by the state Supreme Court and that it frequently refers its customers… Read more »
ABS in Canada? Closer than you might think
This post was originally published as two articles in the October 25 and November 1, 2013 issues of Canada's The Lawyers Weekly newspaper. Reproduced here with thanks. Unless you've been making a special effort not to notice them, you're probably aware of Alternative Business Structures (ABS), the most radical of several developments introduced in England… Read more »
Losing the confidence game
Here are six observations about the legal marketplace for you to consider, each supported by a news report filed just in the last few days. 1. Fewer people want to be lawyers. Number of law school applicants continues to slide: "[US law school] applications submitted are down 13.6%…. That translates to about 66,696 applicants and… Read more »
The year of living dangerously
So there goes 2011, and from a legal marketplace perspective, you could probably call it the year of hanging on. Large law firms hung on in the face of flat-lined or diminishing revenues, in no small part through the wonders of de-equitization. Small law firms hung on despite an expanding sea of legal service providers… Read more »
Law schools and the law of supply and demand
If law schools were publicly traded companies and you held some in your portfolio, I would be strongly advising you to sell. Fast. Here's a quick review of some recent news concerning the US legal education industry and the legal profession it is purportedly preparing its graduates to enter. As reported by the Wall Street… Read more »
Not wanted on the voyage
From the incumbent's point of view, the only thing worse than a revolution that topples you is one that renders you irrelevant. You can mount a comeback from exile; you can't mount a comeback from Nobody Cares. Law firms, pay close attention. We're now less than six months away from the implementation of the Alternative… Read more »
Lawyers and the red balloon
Like many parents of small children, I've gotten to know Thomas The Tank Engine, and the peculiar universe he inhabits, far too well. As an example, I've now read the story James and the Red Balloon so often that I've begun to draw lessons for the legal profession from it. To summarize: among the trains… Read more »
The new battlefield: convenience
Whatever happened to Napster? Depending on your age, you might remember it either as a piracy-enabling nuisance, a groundbreaking music-swapping service, or the dusty antecedent of iTunes. Time magazine caught up with Napster's founder, Shawn Fanning, and three other pioneering hackers in a recent article that describes them as "The Men Who Changed The World."… Read more »
The law firm of the future: Thomson Reuters
Earlier this month, I wrote a blog post called "Destroying your own business" that explained why law firms, in order to adapt to the emerging marketplace, needed to blow up their own business models and essentially start over. I also lamented the fact that hardly any law firm was willing or able to do this…. Read more »


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The Groundhogs Day Blizzard, record cold and lake effect snow top the list of Michigan weather events on this day in history. From the National Weather Service archives here are the events that happened on February 2.
1936- For Detroit, this marked the last day of a streak of 11 days (Jan 23-Feb 2, 1936) with daily temperatures colder than 19 degrees!
1868 - It is a chilly Groundhog Day as Lansing sets their all-time record low with a reading of -37°.
1967 - Flint measured 9.3" of snow from a snowstorm that occurred February 1st-2nd. The groundhog probably had trouble getting out of his burrow that morning, let alone see his shadow.
1996 - A record low of -26° occurred at the Weather Forecast Office in Marquette with a record low high temperature of -13°. A low temperature of -33° with a high of -9° at Bergland Dam, low of -37° and a high of -14° in Ironwood, low of -30° and a high of -7° in Champion occurred. Some of the extreme low temperatures included Kenton -44°, Iron River -41°, Ironwood -37°, Amasa -37°, Stephenson -36°, Bergland -32°, Ontonagon -30°, Iron Mountain -30°, and Alberta -29°.
2001 - A low pressure center and its attendant cold front moving across the northern Great Lakes brought significant snow to the lake effect snowbelt of northwest Upper Michigan. Nine inches of snow accumulated in Wakefield overnight, Ontonagon and Calumet reported 8 inches, and in the highlands of the Keweenaw Peninsula, Laurium had 10 inches and Phoenix received 10.5 inches of snowfall from late in the afternoon on the 1st, to early in the morning on the 2nd.
2009 - East to northeast winds in the wake of a cold front brought heavy lake effect snow to portions of Upper Michigan on the 2nd and 3rd. Spotters in Carney estimated snowfall of 13 to 16 inches during the afternoon and evening of the 2nd. Spotters in Powers and Cedar River also measured seven inches of snow on the 2nd.
2011 - The Groundhogs Day Blizzard affected a large area of the country from Oklahoma to the New England States, including Michigan. The blizzard struck Michigan with wind gusts over 40 mph, more than a foot of snow, whiteout conditions and snowdrifts of 3 to 5 feet. The storm began on the evening of February 1st and ended during the morning of the 2nd. Thunder accompanied the snow in some areas with snowfall rates exceeding two inches per hour. For southeast Michigan the snow started during the evening hours of the 1st and continued into the 2nd. Snowfall accumulations generally ranging from 6 to 12 inches. Isolated higher amounts were recorded across the Thumb and Tri-Cities Region. Northeast winds gusting between 25 to 35 mph caused some blowing and drifting of snow. Frequent wind gusts to 35 mph came off Lake Huron and Saginaw Bay, leading to blizzard conditions north of the I-69 corridor. Some of the higher snowfall reports across the area included: Pigeon 14 inches; Port Huron 14 inches; Lapeer 13.6 inches; Lexington 13.5 inches; Bridgeport 13 inches; Mayville 13 inches; Pinconning 12 inches; Flushing 11 inches; Lake Orion 10 inches; and Romulus 9 inches. Read more about this storm at these links:
Snowfall records fall
February 2011 blizzard summary
Southeast Michigan total snowfall


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West Palm Beach & Miami --
Law & Politics magazine, a consumer's guide to the best attorneys, has released its annual Florida Super Lawyers' edition recognizing the top five percent of attorneys in Florida. Richman Greer, P.A. West Palm Beach attorneys and shareholders Gary S. Betensky, Gerald F. Richman and John 'Jay" White III, and Miami attorneys and shareholders John M. Brumbaugh, Bruce A. Christensen, Manuel A. Garcia-Linares, Alan G. Greer and Charles H. Johnson, have been named among the best lawyers in Florida. Super Lawyers recognizes the top attorneys in 47 states.
Gary S. Betensky, a resident of Boca Raton, maintains a civil trial, business litigation and appellate practice concentrating in complex commercial litigation and business disputes. Betensky currently serves on the Professional Ethics Committee of the Florida Bar, and is a member of the Board of Directors for the Palm Beach County Chapter of the American Jewish Committee and the Board of Governors of Nova Southeastern University's Shepard Broad Law Center.
Gerald F. Richman, President of the firm and Board Certified in Civil Trial Law and Business Litigation, is one of South Florida's leading complex commercial litigation law practitioners. A resident of Palm Beach Gardens, Richman is a former President of the Florida Bar and currently serves as the President of the Palm Beach County Chapter of the American Board of Trial Advocates (ABOTA), member of the Board of Directors of the Economic Council of Palm Beach County and member of the Criminal Justice Commission of Palm Beach County.
John 'Jay" White III, a resident of West Palm Beach, practices primarily in the areas of commercial and complex business litigation, personal injury, wrongful death, professional malpractice litigation, class actions, and officer and director representation. White is the President-Elect Designate of the Florida Bar for 2007 and currently serves on the organization's Board of Governors.
John M. Brumbaugh, who is Board Certified in Civil Trial Law, concentrates his practice in commercial litigation. A resident of South Miami, Brumbaugh is currently the President of Two Hundred Club of Greater Miami, where he also serves on the board and executive committee.
Coral Gables resident Bruce A. Christensen concentrates his practice in family law, divorce and domestic relations. A Board Certified attorney in Marital and Family Law, Christensen serves on the Board of Managers of the Florida Chapter of the American Academy of Matrimonial Lawyers and is a member of the Coral Gables Chamber of Commerce.
Manuel A. Garcia-Linares, Managing Shareholder of the firm and a resident of Coral Gables, practices primarily in the areas of commercial and class action litigation as well as corporate and transactional matters. Garcia-Linares currently serves as a Vice President of the Cuban American Bar Association and is a Trustee of the Coral Gables Chamber of Commerce. He is also a member of the City of Coral Gables Retirement Board and the City of Coral Gables Partnership Committee.
Board Certified in Civil Trial Law and Business Litigation, attorney Alan G. Greer concentrates his practice in the areas of civil commercial litigation. A Coral Gables resident, Greer is the Vice President of the Florida Supreme Court Historical Society, Chairman Emeritus of the Board of Directors of Friends of WLRN Public Radio and Television, Board Member of Probono.net and a Fellow of the American College of Trial Lawyers, the International Society of Barristers and the American Bar Foundation.
Charles H. Johnson, a Board Certified attorney in the area of Wills, Trusts and Estates, practices primarily in the areas of estate planning, probate, guardianship and probate/guardianship litigation. A resident of Coral Gables, Johnson currently serves on the Orange Bowl Committee and the Cable Television Board for the City of Coral Gables and is a Trustee Member of the Greater Miami Chamber of Commerce.
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Tonight at Hiro Ballroom, we will be bringing you the latest sensation from across the pond, V V Brown, along with special guest DJ GE-OLOGY. V V will be performing the latest from her debut album Travelling Like The Light. If you haven't yet, you need to remember to RSVP, before we close the list.
V.V. Brown and DJ GE-OLOGY at Hiro Ballroom – Feburary 17
England's latest and hottest export V.V. Brown will be performing live at Hiro Ballroom on Wednesday, February 17 with special guest DJ GE-OLOGY. If you haven't picked it up yet, the sultry singer/songwriter's debut album Travelling Like The Light has been making waves all the way from across the ocean. The single "Shark In The Water" was last week's featured single of the week on iTunes. As always entrance is strictly RSVP only.


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Aurora Borealis Showtimes and Tickets
Read Movie Reviews about Aurora Borealis Write a Movie Review for Aurora Borealis
Release Date: 2006-09-15 (NY)
Genre: Drama,
Rating: R
Duration: 1hr 50min
Duncan Shorter. Bright. Charming. Never met a job from which he couldn't be fired. His buddies are growing up and beginning lives of responsibility, but Duncan is still looking for that spark. It arrives from a most unexpected corner. Visiting his grandmother Ruth's new senior residence, Duncan jumps at the chance to become the building's handyman. It will keep him close to his grandfather Ronald, whose faculties are failing as quickly as the light of this Minnesota winter. When Ronald goes, Duncan realizes, he'll take with him the last shadow of Duncan's father, whose unresolved death years earlier still haunts him. And, then there's Ronald's feisty home nurse, Kate, a restless spirit as free as Duncan is trapped. They soon find themselves drawn together in a relationship neither one wants but both of them need. Kate's freedom is seductive, but what is it hiding? With the burning light of Kate on one side and Ronald's dying flame on the other, Duncan confronts his own darkness and takes his first fledgling steps into a brighter tomorrow.
Cast and Crew
- Starring
Donald Sutherland, Juliette Lewis, Joshua Jackson, Zack Ward, Steven Pasquale, Louise Fletcher, Steve Vai, Niamh Wilson
- Directed by James CE Burke
- Produced by Rick Bieber, Scott Disharoon
- Written by Brent Boyd
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Margie's Chili RecipeRead Reviews Be the first to add a review
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I simply spice up canned tomato soup to create a flavorful chili.—Margaret Ganzel, Mankato, Minnesota
- 1 pound ground beef
- 2 small onions, chopped
- 1 can (10-3/4 ounces) condensed tomato soup, undiluted
- 1 can (15-1/2 ounces) kidney beans, rinsed and drained
- 3/4 cup chili sauce
- 2 teaspoons chili powder or prepared horseradish
- 1/4 teaspoon salt
- 1/4 teaspoon pepper
- In a large saucepan, brown beef and onions; drain. Add remaining ingredients; bring to a boil. Reduce heat; simmer, uncovered, for 5-10 minutes or until thickened. Yield: 4 servings.
Originally published as Margie's Chili in Country Woman January/February 1996, p35
Reviews for Margie's Chili
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Reviewed Mar. 5, 2015
"While this was quick and easy to make, it was not a good chili recipe. It was too sweet and tasted more like baked beans. I will not make this one again."
Reviewed Mar. 18, 2014
"I added a can of tomatoes to the recipe, thought the addition of the chili sauce gave it a nice slightly sweet taste."
Reviewed Nov. 24, 2013
"The chili was good, a little too sweet for me though. I also added a can of diced tomatoes with jalepenos in it and some chopped garlic, green pepper and celery. I will see how it tastes the next day."
Reviewed Oct. 29, 2012
"I gave this recipe four stars because I added canned diced tomato and bell peppers.This chili was very good and would make again."
Reviewed Jan. 7, 2011
"This is a sweet and spicy chili, and my family of 7 enjoyed it. I served it with angel hair pasta, and will definitely make it again. :-)"


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This double feature includes 2 stories based on the novels by Sir Arthur Conan Doyle. In The Adventures of Sherlock Holmes, Professor Moriarty (George Zucco) has at long last been brought to trial for murder. But the Napoleon of Crime is acquitted after the court finds a lack of sufficient evidence. Moments after the judge releases the defendant, Sherlock Holmes dashes into the courtroom with proof that will destroy Moriarty's alibi and send the professor to the gallows...or will it? In The Scarlet Claw, Sherlock Holmes and Dr. Watson journey to Canada to attend a meeting of the Royal Canadian Occult Society in Quebec. Before long, they find themselves investigating a series of gruesome murders that the locals attribute to the legendary phantom marsh monster of La Morte Rouge. But Holmes suspects a master of disguise is the real killer, who might be anyone in the village. He contrives a clever trap and courageously sets himself up to be the killer's next victim.Product Features:
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A CAMPAIGN has been launched to close a bail house because unruly and lewd behaviour is causing misery for residents.
The three-bed house in Mapplewell is operated by BASS and offers accommodation for those on bail awaiting trial or are on a home detention curfew.
Neighbouring residents on Pye Avenue are calling for it to be shut, branding it a blight on their street.
They claim some of those placed there have made threats to kill; been running across flat roofs at the back of neighbouring properties; peering in bedroom windows; playing loud music late in to the night and making lewd comments to women.
Residents have launched a petition to get it shut, which has been backed by Coun Roy Miller.
Jolan Gergely, head of BASS, said: "We don't tolerate antisocial behaviour from any of our service users and we'll always take action to tackle it.
"We've successfully run our service from the same property since June 2010.
"We'd be happy to talk with any neighbours who have concerns."


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T-Mobile, still lone ticket to iPhone in Germany
While more countries are purportedly going to get the iPhone than ever before, and slowly the exclusivity deals are coming to an end, here we have word from T-Mobile Germany which tells us the only one selling the iPhone to Germans will be them. And it will remain to be them, even after the much-awaited launch of the 3G iPhone.
The comment came from T-Mobile Chief Executive Hamid Akhavan, who on Tuesday spoke about T-Mobile's relationship with Apple and a bit about what lies ahead for both companies as far as the world's most loved smartphone is concerned.
Akhavan spoke to Reuters Technology at Media and Telecoms Summit in Paris, and said this:
"We have a very good relationship with Apple…at least in Germany it is exclusive, and we expect it to remain as such."
He further comments that, "If and when there is a 3G iPhone we expect to have it exclusively in Germany as well." Certainly goes to show how much they value and want to protect the exclusive hold they have on such a best-selling handset. But then again, their move is understandable, given all the profit they will be able to make out of this, since June 9 is getting very very near.
In any case, this means bad news for any and all other carriers who were hoping to get in on some iPhone lovin'. Perhaps, T-Mobile may still change its mind. You never know.


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While most cruise lines are adding cabins to existing ships and building newer and bigger ships (think Oasis of the Seas or NCL's F3 ships), Crystal Cruises is actually decreasing the passenger capacity of Crystal Serenity. During a November dry dock, the luxury line will convert 12 deluxe staterooms into 8 penthouses. Fleetmate Crystal Symphony will not be getting the new cabins.
The penthouses are some of the most highly sought after cabins on Crystal Serenity. They're 403 square ft. with a large balcony and living area, and feature butler service, a bar stocked with wine and liquor, Jacuzzi tub and walk-in closet. Penthouse guests can order room service from Serenity's specialty restaurants (24-hours) and receive complimentary pressing.
Following the dry dock, Crystal Serenity will have a total of 72 penthouses and 32 penthouse suites. Four of the new Penthouses will be able to connect with penthouse suites for groups traveling together.
There will also still be 70 category AA deluxe staterooms. A representative from the luxury cruise line assures us that with so many deluxe staterooms available, no pre-booked passengers will need to be switched to another departure or room type because their original cabin has been converted into a penthouse.
--by Erica Silverstein, Associate Editor
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Crystal Adds Penthouses to Serenity
Crystal Adds Penthouses to Serenity
June 20, 2008


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WASHINGTON - The FBI on Friday ordered a formal review of some aspects of the 1995 Oklahoma City bombing investigation, reopening the question of whether Timothy McVeigh may have had more accomplices in the worst domestic terrorist attack in U.S. history, The Associated Press has learned.
Reacting to an AP story this week, the FBI ordered agents to determine why some documents did not properly reach the bureau's Oklahoma City task force during the original investigation or get turned over to McVeigh's lawyers before he was executed in 2001, officials said.
The review of evidence and documents will also try to determine whether FBI agents in a separate investigation of white supremacist bank robbers may have failed to alert the Oklahoma City investigation of a possible link between the robbers and McVeigh, and allowed some of that evidence to be destroyed.
Review uncovers poor record-keeping by NASA
CAPE CANAVERAL, Fla. - NASA is doing a poor job keeping track of breakdowns and other problems aboard the international space station, an internal audit released Friday found.
The post-Columbia safety review also found that the space agency has failed to maintain a complete set of blueprints of space station equipment, and that many documents, agreements and instructions are outdated and filled with inconsistencies.
Soon after Columbia was destroyed in February 2003, NASA's space station program began examining its own operations to identify safety risks. This is the second such report issued on the space station.
The 172-page report offered no examples of any breakdowns or other problems that are not being adequately tracked. But it said that NASA analysis of trends is seriously lacking, with inadequately trained personnel.
Grocery workers set to vote on contract offer
LOS ANGELES - Lily Salazar kept her three children fed and managed to avoid eviction during the supermarket strike by working a part-time job, collecting pay for picketing and skipping Christmas presents.
Along the way, the 32-year-old single mother racked up thousands of dollars in unpaid bills and credit card debt, a burden the Ralphs cashier says she will not be able to handle even after she gets back to work.
"I'm probably going to file bankruptcy," Salazar said Friday. "I've lost maybe $7,000, maybe more. I'm never going to be able to catch up."
Salazar and thousands of other grocery workers on strike or locked out since Oct. 11 will learn the details of a proposed agreement between the United Food and Commercial Workers and supermarket operators and begin voting today. If they ratify the deal, some could be back at work by midweek.
Chicago schools make dropouts sign consentP>
CHICAGO - The Chicago school system has a new requirement for would-be dropouts and their parents - they must sign a consent form warning of the possible pitfalls of quitting school, including jail and unemployment.
Arne Duncan, chief executive of the nation's third-largest school district, said the form is a way of being "brutally honest" about the consequences of dropping out.
"This is also a way to teach decision-making skills," Duncan said Friday. "In order for them to make good decisions throughout life, you have to give them the facts. We want our students, our parents, to understand the devastating impact that this decision will have on students' lives."
Duncan said he knew of no other U.S. school districts taking Chicago's approach.
Schwarzenegger pins hopes on bond measure
SACRAMENTO, Calif. - Gov. Arnold Schwarzenegger's plan to borrow $15 billion faces a tough fight in Tuesday's election, worrying voters and Wall Street alike and presenting the former action star with the biggest challenge of his young political career.
Proposition 57 authorizes the state to borrow up to $15 billion to pay off short-term loans that come due in June and to help close next year's budget gap, expected to be about $17 billion.
Most experts agree that without the bonds, California's already bleak economic outlook would turn decidedly worse. The measure also could have an effect on other areas of the nation's economy, with Wall Street investors closely watching the vote.
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Monday at the Brazilian World Cup we saw two very entertaining games—France vs. Nigeria and Germany vs. Algeria—the matches underscored the great strides the sport has made in all corners of the world.
The Nigerians previously played Argentina, and today played France, even, for large stretches of games that were ultimately decided against the Africans, not because they lacked skill or athleticism or heart but simply because they lacked tactical acumen and longer-term experience at higher levels of competition.
Algeria, one of the cup's technically superior teams, deserved to be in the Round of 16 and almost pulled off an upset. Imagine if Mesut Ozil's insurance goal had not been scored. We would be in another penalty shootout with Rais M'Bolhi the hot goalkeeper.
The German sports daily Kicker had a front page article with a headline: "With Luck! A wild ride into the quarterfinals." The headline in the Algerian El Watan was straightforward: "Algerians eliminated by Germans in World Cup." The first sentence of the article stated "The Algerians did not bend in their match with the Germans and scored a goal of honor at the end."
Today we also saw perhaps the competition's best referee, Mark Geiger, who, with the exception of handing out a yellow card that could have been red, did an excellent job in the day's first match.
Unfortunately, we also saw Sandra Meira Ricci's poor performance in the second game, not so much for making poor calls that in and of themselves determined the game, such as we have witnessed often enough in this cup, but by making calls that allowed the favored Germans multiple, subtle, unfair advantages.
We also saw a number of stateside media outlets reconsidering several of the controversial plays of the past few weeks. We learned via several major television network news coverages that Luis Suarez apologized to Giorgio Chiellini via Twitter and that the Italian in turn responded that it was "no biggie" and he reiterated his previous comment directly to Suarez that he thought the FIFA ban was excessive.
Univision and ESPN Deportes dedicated entire football commentary shows to dissecting the Mexico- Netherlands match and the way Miguel Herrera coached ("He made too many mistakes in substitutions and tactics," was the verdict). Others discussed whether Arjen Robben should have been given two yellows at least for his multiple dives ("He should not have been in the game by the time the final penalty was called," was the consensus). ESPN, via commentator Alexi Lalas, said that it was Rafa Marquez's fault the penalty was called as he was "aware of Robben's reputation and intent" and thus the defender should have "laid back from the Dutch striker once he entered the Mexican area."
Uruguayan and Chilean pundits and politicians were less cordial calling the proceedings that resulted in their eliminations a farce or worse. Italy' Gazzetto dello Sport has moved on from criticizing the Italian team's performance to doing a survey of the best ever World Cup goal with Maradona's 1986 masterpiece garnering 46% and the closest rivals coming in at 18.6% for James Rodriguez goal against Uruguay, and at 17% Baggio's 1990 goal against Czechoslovakia.
Tomorrow we have another great doubleheader: Argentina plays Switzerland in Sao Paulo and the USA plays Belgium in Salvador.


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Update: CoroCoro has clarified that the broadcast will discuss and show all previously revealed characters and stages.
Nintendo will release Super Smash Bros. 4 for Wii U and Nintendo 3DS later this year, and now a probable release date for each version has been leaked by multiple retailers. According to a report by KDramaStars from Aug. 6, the release date for Super Smash Bros. 4 for 3DS and Wii U will differ by a little more than a month in North America with supplementary retailer rumors suggesting that the Wii U version will come with a free Amiibo figure. Additionally, it has been confirmed that the full character roster and all the stages will be revealed in a couple of weeks.
Masahiro Sakurai along with Nintendo previously confirmed that Super Smash Bros. 4 would see release in 2014 for Wii U and Nintendo 3DS. Currently, the Wii U version is slated as a Holiday 2014 release, with the 3DS version locked in for a release on Oct. 3 in North America. However, several retailers have started to advertise a potential release date for Super Smash Bros. 4 for Wii U and it would position the game's release date just before Black Friday in North America.
The two speculated release dates for Super Smash Bros. 4 are currently Tuesday, Nov. 25 or Friday, Nov. 21. To coincide with these release dates, a report by Gamer Headlines from earlier this month suggests that Super Smash Bros. 4 will release on Nov. 21 and those that purchase a physical copy of the game will receive a free Amiibo figure. A Nov. release date would make sense for Nintendo as the company commonly uses the month to launch its biggest holiday software – Super Mario 3D World was released in Nov. for Wii U.
It has been confirmed that Nintendo will reveal the official character roster and all the stages of Super Smash Bros. 4 later this month. According to a listing on CoroCoro.tv, a special Super Smash Bros. 4 broadcast will air on Aug. 12 and all the characters and stages of the title will be revealed. Thus far, 36 characters have been announced for the official character roster of Super Smash Bros. 4 for Wii U and 3DS.
We'll have our hands-on impressions for both the Wii U and 3DS version of Super Smash Bros. 4 early next week. Stay tuned.


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Published: September 24, 2011
Senate Majority Leader Harry Reid of Nev., left, accompanied by House Minority Leader Nancy Pelosi of Calif., take part in a news conference on Capitol Hill in Washington, Friday, Sept. 23 2011, to talk about their conflict with Republican lawmakers over whether funding for victims of natural disasters should be paid for by cuts to other government programs. (AP Photo/J. Scott Applewhite)
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