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129
Cognitive Radio: An InformationTheoretic Perspective
, 2009
"... We consider a communication scenario in which the primary and the cognitive radios wish to communicate to different receivers, subject to mutual interference. In the model that we use, the cognitive radio has noncausal knowledge of the primary radio’s codeword. We characterize the largest rate at w ..."
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Cited by 176 (1 self)
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We consider a communication scenario in which the primary and the cognitive radios wish to communicate to different receivers, subject to mutual interference. In the model that we use, the cognitive radio has noncausal knowledge of the primary radio’s codeword. We characterize the largest rate at which the cognitive radio can reliably communicate under the constraint that (i) no rate degradation is created for the primary user, and (ii) the primary receiver uses a singleuser decoder just as it would in the absence of the cognitive radio. The result holds in a “low interference ” regime in which the cognitive radio is closer to its receiver than to the primary receiver. In this regime, our results are subsumed by the results derived in a concurrent and independent work [24]. We also demonstrate that, in a “high interference ” regime, multiuser decoding at the primary receiver is optimal from the standpoint of maximal jointly achievable rates for the primary and cognitive users.
Algorithms in Discrete Convex Analysis
 Math. Programming
, 2000
"... this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects. ..."
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Cited by 156 (34 self)
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this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects.
Legendre Functions and the Method of Random Bregman Projections
, 1997
"... this paper, Bregman's method is studied within the powerful framework of Convex Analysis. New insights are obtained and the rich class of "Bregman/Legendre functions" is introduced. Bregman's method still works, if the underlying function is Bregman/Legendre or more generally if ..."
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Cited by 67 (15 self)
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this paper, Bregman's method is studied within the powerful framework of Convex Analysis. New insights are obtained and the rich class of "Bregman/Legendre functions" is introduced. Bregman's method still works, if the underlying function is Bregman/Legendre or more generally if it is Legendre but some constraint qualification holds additionally. The key advantage is the broad applicability and
From real affine geometry to complex geometry
, 2007
"... We construct from a real affine manifold with singularities (a tropical manifold) a degeneration of CalabiYau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking feature of our approach is that it yields an explicit and canonical orderbyorder description of ..."
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Cited by 57 (6 self)
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We construct from a real affine manifold with singularities (a tropical manifold) a degeneration of CalabiYau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking feature of our approach is that it yields an explicit and canonical orderbyorder description of the degeneration via families of tropical trees. This gives complete control of the Bmodel side of mirror symmetry in terms of tropical geometry. For example, we expect our deformation parameter is a canonical coordinate, and expect period calculations to be expressible in terms of tropical curves. We anticipate this will lead to a proof of mirror symmetry via tropical methods. This
Polyhedral Divisors and Algebraic Torus Actions
 Math. Ann
, 2006
"... Abstract. We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case, ..."
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Cited by 49 (9 self)
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Abstract. We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case, and it comprises the theory of affine toric varieties.
The Convex Analysis of Unitarily Invariant Matrix Functions
, 1995
"... this paper is to give a simple, selfcontained approach to this problem, giving back the subdifferential formula for (1.2) in [13] for example. Our idea will be to generalize von Neumann's result somewhat by asking which convex functions (rather than simply norms) are unitarily invariant: appro ..."
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Cited by 48 (3 self)
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this paper is to give a simple, selfcontained approach to this problem, giving back the subdifferential formula for (1.2) in [13] for example. Our idea will be to generalize von Neumann's result somewhat by asking which convex functions (rather than simply norms) are unitarily invariant: appropriately, the key idea will be a Fenchel conjugacy formula analogous to von Neumann's polarity formula (1.1): (f ffi oe)
Outer Bounds to the Capacity Region of Wireless Networks
 IEEE Trans. Inform. Theory
, 2006
"... [9] J. N. Laneman and G. W. Wornell, “Distributed spacetime coded protocols for exploiting cooperative diversity in wireless networks, ” IEEE ..."
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Cited by 36 (0 self)
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[9] J. N. Laneman and G. W. Wornell, “Distributed spacetime coded protocols for exploiting cooperative diversity in wireless networks, ” IEEE
The Lasso Problem and Uniqueness
, 2012
"... The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p> n, the lasso criterion is not strictly convex, and hence it may not have a unique minimum. An important question is: when is the l ..."
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Cited by 27 (4 self)
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The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p> n, the lasso criterion is not strictly convex, and hence it may not have a unique minimum. An important question is: when is the lasso solution welldefined (unique)? We review results from the literature, which show that if the predictor variables are drawn from a continuous probability distribution, then there is a unique lasso solution with probability one, regardless of the sizes of n and p. We also show that this result extends easily to ℓ1 penalized minimization problems over a wide range of loss functions. A second important question is: how can we manage the case of nonuniqueness in lasso solutions? In light of the aforementioned result, this case really only arises when some of the predictor variables are discrete, or when some postprocessing has been performed on continuous predictor measurements. Though we certainly cannot claim to provide a complete answer to such a broad question, we do present progress towards understanding some aspects of nonuniqueness. First, we extend the LARS algorithm for computing the lasso solution path to cover the nonunique case, so that this path algorithm works for any predictor matrix. Next, we derive a simple method for computing the componentwise uncertainty in lasso solutions of any given problem instance, based on linear programming. Finally, we review results from the literature on some of the unifying properties of lasso solutions, and also point out particular forms of solutions that have distinctive properties. 1
Multiplier Methods: A Survey
, 1976
"... The purpose of this paper is to provide a survey of convergence and rate of convergence aspects of a cltass of recently proposed methods for constrained nfinimizationthe, socalled, multiplier methods. The results discussed highlight the operational aspects of multiplier methods and demonstrate th ..."
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Cited by 26 (1 self)
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The purpose of this paper is to provide a survey of convergence and rate of convergence aspects of a cltass of recently proposed methods for constrained nfinimizationthe, socalled, multiplier methods. The results discussed highlight the operational aspects of multiplier methods and demonstrate their significant advantages over ordinary penalty methods.
2005) “Strategic Liquidity Supply and Security Design
 Review of Economic Studies
"... We study how securities and trading mechanisms can be designed to mitigate the adverse impact of market imperfections on liquidity. Following DeMarzo and Duffie (1999), we consider asset owners who seek to obtain liquidity by selling their claims on future cashflows, on which they have private info ..."
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Cited by 25 (3 self)
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We study how securities and trading mechanisms can be designed to mitigate the adverse impact of market imperfections on liquidity. Following DeMarzo and Duffie (1999), we consider asset owners who seek to obtain liquidity by selling their claims on future cashflows, on which they have private information. We allow for strategic liquidity supply and take a mechanism design approach to characterize both the optimal security and the optimal trading mechanism. For a given arbitrary security, issuers with cashflows below a threshold entirely sell their holdings of the securities, while issuers with larger cashflows are excluded from trading. The optimal security design entirely avoids this partial market breakdown phenomenon. We find that the optimal security is debt. Because of its low informational sensitivity, debt mitigates the adverse selection problem. Furthermore, by pooling all issuers with high cashflows, it reduces the ability of strategic liquidity suppliers to exclude them from trade to better extract rents from agents with lower cashflows. We also show that competition in nonexclusive schedules between finitely many oligopolistic liquidity suppliers implements the competitive trading mechanism.