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AN ALTERNATIVE PROOF OF ELEZOVIĆGIORDANOPEČARIĆ’S THEOREM
, 903
"... Abstract. In the present note, an alternative proof is supplied for Theorem 1 ..."
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Abstract. In the present note, an alternative proof is supplied for Theorem 1
Some monotonicity properties of gamma and qgamma functions, Available onlie at http://arxiv.org/abs/0709.1126v2
"... Abstract. We prove some properties of completely monotonic functions and apply them to obtain results on gamma and qgamma functions. 1. ..."
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Cited by 3 (0 self)
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Abstract. We prove some properties of completely monotonic functions and apply them to obtain results on gamma and qgamma functions. 1.
OrderPreserving Encryption Revisited: Improved Security Analysis and Alternative Solutions
"... We further the study of orderpreserving symmetric encryption (OPE), a primitive for allowing efficient range queries on encrypted data, recently initiated (from a cryptographic perspective) by Boldyreva et al. (Eurocrypt ’09). First, we address the open problem of characterizing what encryption via ..."
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We further the study of orderpreserving symmetric encryption (OPE), a primitive for allowing efficient range queries on encrypted data, recently initiated (from a cryptographic perspective) by Boldyreva et al. (Eurocrypt ’09). First, we address the open problem of characterizing what encryption via a random orderpreserving function (ROPF) leaks about underlying data (ROPF being the “ideal object ” in the security definition, POPF, satisfied by their scheme.) In particular, we show that, for a database of randomly distributed plaintexts and appropriate choice of parameters, ROPF encryption leaks neither the precise value of any plaintext nor the precise distance between any two of them. The analysis here introduces useful new techniques. On the other hand, we show that ROPF encryption leaks approximate value of any plaintext as well as approximate distance between any two plaintexts, each to an accuracy of about square root of the domain size. We then study schemes that are not orderpreserving, but which nevertheless allow efficient range queries and achieve security notions stronger than POPF. In a setting where the entire database is known in advance of keygeneration (considered in several prior works), we show that recent constructions of “monotone minimal perfect hash functions ” allow to efficiently achieve (an adaptation of) the notion
1 Spectrum Sharing Between Cellular and Mobile Ad Hoc Networks: TransmissionCapacity TradeOff
, 808
"... Spectrum sharing between wireless networks improves the efficiency of spectrum usage, and thereby alleviates spectrum scarcity due to growing demands for wireless broadband access. To improve the usual underutilization of the cellular uplink spectrum, this paper studies spectrum sharing between a ce ..."
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Spectrum sharing between wireless networks improves the efficiency of spectrum usage, and thereby alleviates spectrum scarcity due to growing demands for wireless broadband access. To improve the usual underutilization of the cellular uplink spectrum, this paper studies spectrum sharing between a cellular uplink and a mobile ad hoc networks. These networks access either all frequency subchannels or their disjoint subsets, called spectrum underlay and spectrum overlay, respectively. Given these spectrum sharing methods, the capacity tradeoff between the coexisting networks is analyzed based on the transmission capacity of a network with Poisson distributed transmitters. This metric is defined as the maximum density of transmitters subject to an outage constraint for a given signaltointerference ratio (SIR). Using tools from stochastic geometry, the transmissioncapacity tradeoff between the coexisting networks is analyzed, where both spectrum overlay and underlay as well as successive interference cancelation (SIC) are considered. In particular, for small target outage probability, the transmission capacities of the coexisting networks are proved to satisfy a linear equation, whose coefficients depend on the spectrum sharing method and whether SIC is applied. This linear equation shows that spectrum overlay is more efficient than spectrum underlay. Furthermore, this result also provides insight into the effects of different network parameters on transmission capacities, including link diversity gains, transmission distances, and the base station density. In particular, SIC is shown to increase transmission capacities of both coexisting networks by a linear factor, which depends on the interferencepower threshold for qualifying canceled interferers.
Bayesian estimation in Kibble’s bivariate gamma distribution
"... The paper describes Bayesian estimation for the parameters of Kibble’s (1941) bivariate gamma distribution. The density of this distribution can be written as a mixture, allowing for a simple data augmentation scheme. An MCMC algorithm is constructed to facilitate Bayesian estimation. We show that t ..."
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The paper describes Bayesian estimation for the parameters of Kibble’s (1941) bivariate gamma distribution. The density of this distribution can be written as a mixture, allowing for a simple data augmentation scheme. An MCMC algorithm is constructed to facilitate Bayesian estimation. We show that the resulting chain is geometrically ergodic and thus a regenerative sampling procedure is applicable allowing for estimation of ergodic means ’ standard errors. Bayesian hypothesis testing procedures are developed to test both the dependence hypothesis of the two variables as well as the hypothesis that their means are equal. A reversible jump MCMC algorithm is proposed to carry out this model selection problem. Real and simulated datasets are used to illustrate the proposed methodology. Key words and phrases: Downton’s bivariate exponential distribution; Kibble’s bivariate gamma distribution; Markov chain Monte Carlo; regenerative simulation; reversible jump. 1
Authors ’ Note
"... Most of the errors in the original paper had to do with saying that certain functions related to the qgamma function were not completely monotonic. We discovered these errors through reading the paper Some completely monotonic functions involving the qgamma function, by Peng Gao, ..."
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Most of the errors in the original paper had to do with saying that certain functions related to the qgamma function were not completely monotonic. We discovered these errors through reading the paper Some completely monotonic functions involving the qgamma function, by Peng Gao,
INEQUALITIES FOR 3LOGCONVEX FUNCTIONS
, 2008
"... ABSTRACT. This note gives a simple method for obtaining inequalities for ratios involving 3logconvex functions. As an example, an inequality for Wallis’s ratio of GautchiKershaw type is obtained. Inequalities for generalized means are also considered. ..."
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ABSTRACT. This note gives a simple method for obtaining inequalities for ratios involving 3logconvex functions. As an example, an inequality for Wallis’s ratio of GautchiKershaw type is obtained. Inequalities for generalized means are also considered.
Full Screen
, 2007
"... Abstract: This note gives a simple method for obtaining inequalities for ratios involving 3logconvex functions. As an example, an inequality for Wallis’s ratio of GautchiKershaw type is obtained. Inequalities for generalized means are also considered. ..."
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Abstract: This note gives a simple method for obtaining inequalities for ratios involving 3logconvex functions. As an example, an inequality for Wallis’s ratio of GautchiKershaw type is obtained. Inequalities for generalized means are also considered.
Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels
, 2009
"... We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Ra ..."
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We examine the capacity of beamforming over a singleuser, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multiinput singleoutput (MISO) and multiinput multioutput (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2B i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (ratemaximizing) training and feedback overhead (T and B) as L and the number of transmit antennas Nt both become large. The optimal Nt is limited by the coherence time, and increases as L / logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1 / logNt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1 / log² Nt).