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440,637
CONSTRUCTIONS WITH FRACTIONAL IDEALS
, 2012
"... In preparation for the proof of the Main Theorem of Complex Multiplication, for an Abelian variety A0 over K with CM type (Φ, L) we need to construct an isomorphism θ so that ξσ,P ..."
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In preparation for the proof of the Main Theorem of Complex Multiplication, for an Abelian variety A0 over K with CM type (Φ, L) we need to construct an isomorphism θ so that ξσ,P
Extensions of Radical Operations to Fractional Ideals
"... In this paper, A will denote a commutative ring with identity. The notion of radical operations is a natural generalization of the usual radical of ideals, it was introduced and studied by the author in [6] and [7]. In the first section of this paper, we study the ∗primes; i.e., the prime ideals of ..."
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In this paper, A will denote a commutative ring with identity. The notion of radical operations is a natural generalization of the usual radical of ideals, it was introduced and studied by the author in [6] and [7]. In the first section of this paper, we study the ∗primes; i.e., the prime ideals
A Fractional Ideal Approach to Stabilization Problems
 in « European Control Conference », CDRom
, 2003
"... The purpose of this paper is to show how the theory of fractional ideals is a powerful mathematical framework for the study of stabilization problems of linear SISO systems. In particular, in terms of fractional ideals, we give necessary and sufficient conditions for a plant to be internally/strongl ..."
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Cited by 1 (0 self)
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The purpose of this paper is to show how the theory of fractional ideals is a powerful mathematical framework for the study of stabilization problems of linear SISO systems. In particular, in terms of fractional ideals, we give necessary and sufficient conditions for a plant to be internally
The Sybil Attack
, 2002
"... Largescale peertopeer systems face security threats from faulty or hostile remote computing elements. To resist these threats, many such systems employ redundancy. However, if a single faulty entity can present multiple identities, it can control a substantial fraction of the system, thereby unde ..."
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Cited by 1518 (1 self)
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Largescale peertopeer systems face security threats from faulty or hostile remote computing elements. To resist these threats, many such systems employ redundancy. However, if a single faulty entity can present multiple identities, it can control a substantial fraction of the system, thereby
Directed Diffusion for Wireless Sensor Networking
 IEEE/ACM Transactions on Networking
, 2003
"... Advances in processor, memory and radio technology will enable small and cheap nodes capable of sensing, communication and computation. Networks of such nodes can coordinate to perform distributed sensing of environmental phenomena. In this paper, we explore the directed diffusion paradigm for such ..."
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Cited by 658 (9 self)
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aggregation). We explore and evaluate the use of directed diffusion for a simple remotesurveillance sensor network analytically and experimentally. Our evaluation indicates that directed diffusion can achieve significant energy savings and can outperform idealized traditional schemes (e.g., omniscient
Taming the Underlying Challenges of Reliable Multihop Routing in Sensor Networks
 In SenSys
, 2003
"... The dynamic and lossy nature of wireless communication poses major challenges to reliable, selforganizing multihop networks. These nonideal characteristics are more problematic with the primitive, lowpower radio transceivers found in sensor networks, and raise new issues that routing protocols mu ..."
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Cited by 775 (21 self)
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The dynamic and lossy nature of wireless communication poses major challenges to reliable, selforganizing multihop networks. These nonideal characteristics are more problematic with the primitive, lowpower radio transceivers found in sensor networks, and raise new issues that routing protocols
A Digital Fountain Approach to Reliable Distribution of Bulk Data
 IN PROC. OF ACM SIGCOMM ’98
, 1998
"... The proliferation of applications that must reliably distribute bulk data to a large number of autonomous clients motivates the design of new multicast and broadcast prot.ocols. We describe an ideal, fully scalable protocol for these applications that we call a digital fountain. A digital fountain a ..."
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Cited by 498 (20 self)
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The proliferation of applications that must reliably distribute bulk data to a large number of autonomous clients motivates the design of new multicast and broadcast prot.ocols. We describe an ideal, fully scalable protocol for these applications that we call a digital fountain. A digital fountain
A learning algorithm for Boltzmann machines
 Cognitive Science
, 1985
"... The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a probl ..."
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Cited by 586 (13 self)
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The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
GPSless Low Cost Outdoor Localization For Very Small Devices
, 2000
"... Instrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where a given no ..."
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Cited by 994 (29 self)
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Instrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where a given node is physically located in a network is a challenging one, and yet extremely crucial for many of these applications. Practical considerations such as the small size, form factor, cost and power constraints of nodes preclude the reliance on GPS (Global Positioning System) on all nodes in these networks. In this paper, we review localization techniques and evaluate the effectiveness of a very simple connectivitymetric method for localization in outdoor environments that makes use of the inherent radiofrequency (RF) communications capabilities of these devices. A fixed number of reference points in the network with overlapping regions of coverage transmit periodic beacon signals. Nodes use a...
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