4,553 research outputs found

    Scheduling Sensors for Guaranteed Sparse Coverage

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    Sensor networks are particularly applicable to the tracking of objects in motion. For such applications, it may not necessary that the whole region be covered by sensors as long as the uncovered region is not too large. This notion has been formalized by Balasubramanian et.al. as the problem of κ\kappa-weak coverage. This model of coverage provides guarantees about the regions in which the objects may move undetected. In this paper, we analyse the theoretical aspects of the problem and provide guarantees about the lifetime achievable. We introduce a number of practical algorithms and analyse their significance. The main contribution is a novel linear programming based algorithm which provides near-optimal lifetime. Through extensive experimentation, we analyse the performance of these algorithms based on several parameters defined

    Chaos in an Exact Relativistic 3-body Self-Gravitating System

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    We consider the problem of three body motion for a relativistic one-dimensional self-gravitating system. After describing the canonical decomposition of the action, we find an exact expression for the 3-body Hamiltonian, implicitly determined in terms of the four coordinate and momentum degrees of freedom in the system. Non-relativistically these degrees of freedom can be rewritten in terms of a single particle moving in a two-dimensional hexagonal well. We find the exact relativistic generalization of this potential, along with its post-Newtonian approximation. We then specialize to the equal mass case and numerically solve the equations of motion that follow from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining orbits in both the hexagonal and 3-body representations of the system, and plot the Poincare sections as a function of the relativistic energy parameter η\eta . We find two broad categories of periodic and quasi-periodic motions that we refer to as the annulus and pretzel patterns, as well as a set of chaotic motions that appear in the region of phase-space between these two types. Despite the high degree of non-linearity in the relativistic system, we find that the the global structure of its phase space remains qualitatively the same as its non-relativisitic counterpart for all values of η\eta that we could study. However the relativistic system has a weaker symmetry and so its Poincare section develops an asymmetric distortion that increases with increasing η\eta . For the post-Newtonian system we find that it experiences a KAM breakdown for η0.26\eta \simeq 0.26: above which the near integrable regions degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon reques

    Decomposition theorem on matchable distributive lattices

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    A distributive lattice structure M(G){\mathbf M}(G) has been established on the set of perfect matchings of a plane bipartite graph GG. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a distributive lattice. It is natural to ask which lattices are MDLs. We show that if a plane bipartite graph GG is elementary, then M(G){\mathbf M}(G) is irreducible. Based on this result, a decomposition theorem on MDLs is obtained: a finite distributive lattice L\mathbf{L} is an MDL if and only if each factor in any cartesian product decomposition of L\mathbf{L} is an MDL. Two types of MDLs are presented: J(m×n)J(\mathbf{m}\times \mathbf{n}) and J(T)J(\mathbf{T}), where m×n\mathbf{m}\times \mathbf{n} denotes the cartesian product between mm-element chain and nn-element chain, and T\mathbf{T} is a poset implied by any orientation of a tree.Comment: 19 pages, 7 figure

    Local spin density in two-dimensional electron gas with hexagonal boundary

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    The intrinsic spin-Hall effect in hexagon-shaped samples is investigated. To take into account the spin-orbit couplings and to fit the hexagon edges, we derive the triangular version of the tight-binding model for the linear Rashba [Sov. Phys. Solid State 2, 1109 (1960)] and Dresselhaus [Phys. Rev. 100, 580 (1955)] [001] Hamiltonians, which allow direct application of the Landauer-Keldysh non-equilibrium Green function formalism to calculating the local spin density within the hexagonal sample. Focusing on the out-of-plane component of spin, we obtain the geometry-dependent spin-Hall accumulation patterns, which are sensitive to not only the sample size, the spin-orbit coupling strength, the bias strength, but also the lead configurations. Contrary to the rectangular samples, the accumulation pattern can be very different in our hexagonal samples. Our present work provides a fundamental description of the geometry effect on the intrinsic spin-Hall effect, taking the hexagon as the specific case. Moreover, broken spin-Hall symmetry due to the coexistence of the Rashba and Dresselhaus couplings is also discussed. Upon exchanging the two coupling strengths, the accumulation pattern is reversed, confirming the earlier predicted sign change in spin-Hall conductivity.Comment: 7 pages, 4 figure

    Design and performance of a compact and stationary microSPECT system

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    Purpose: Over the last ten years, there has been an extensive growth in the development of microSPECT imagers. Most of the systems are based on the combination of conventional, relatively large gamma cameras with poor intrinsic spatial resolution and multipinhole collimators working in large magnification mode. Spatial resolutions range from 0.58 to 0.76 mm while peak sensitivities vary from 0.06% to 0.4%. While pushing the limits of performance is of major importance, the authors believe that there is a need for smaller and less complex systems that bring along a reduced cost. While low footprint and low-cost systems can make microSPECT available to more researchers, the ease of operation and calibration and low maintenance cost are additional factors that can facilitate the use of microSPECT in molecular imaging. In this paper, the authors simulate the performance of a microSPECT imager that combines high space-bandwidth detectors and pinholes with truncated projection, resulting in a small and stationary system. Methods: A system optimization algorithm is used to determine the optimal SPECT systems, given our high resolutions detectors and a fixed field-of-view. These optimal system geometries are then used to simulate a Defrise disk phantom and a hot rod phantom. Finally, a MOBY mouse phantom, with realistic concentrations of Tc99m-tetrofosmin is simulated. Results: Results show that the authors can successfully reconstruct a Defrise disk phantom of 24 mm in diameter without any rotating system components or translation of the object. Reconstructed spatial resolution is approximately 800 mu m while the peak sensitivity is 0.23%. Finally, the simulation of the MOBY mouse phantom shows that the authors can accurately reconstruct mouse images. Conclusions: These results show that pinholes with truncated projections can be used in small magnification or minification mode to obtain a compact and stationary microSPECT system. The authors showed that they can reach state-of-the-art system performance and can successfully reconstruct images with realistic noise levels in a preclinical context. Such a system can be useful for dynamic SPECT imaging. 2013 American Association of Physicists in Medicine
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