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Quasi-convexity and optimal binary fusion for distributed detection with identical sensors in generalized Gaussian noise

2001
*
IEEE Transactions on Information Theory
*

For generalized Gaussian noises and some non-Gaussian noise

doi:10.1109/18.904560
fatcat:6hflqvoqbfg4xh3idjwopj2sxa
*distributions*, we show that for any admissible fusion rule, the probability of error is a quasi-*convex*function of*threshold*. ... Assuming equal a priori probability, we give a sufficient condition of the non-Gaussian noise*distribution*( ) for the probability of error to be quasi-*convex*. ... [14] generalize these results by showing quasi-*convexity*in the likelihood ratio function for any*distribution*on the i.i.d. observations x i . is*convex*. ...##
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Statistical optimization of dynamic importance sampling parameters for efficient simulation of communication networks

1993
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IEEE/ACM Transactions on Networking
*

For generalized Gaussian noises and some non-Gaussian noise

doi:10.1109/90.234852
fatcat:t7d7ouqwkret3bnj76cf7wgfhi
*distributions*, we show that for any admissible fusion rule, the probability of error is a quasi-*convex*function of*threshold*. ... Assuming equal a priori probability, we give a sufficient condition of the non-Gaussian noise*distribution*( ) for the probability of error to be quasi-*convex*. ... [14] generalize these results by showing quasi-*convexity*in the likelihood ratio function for any*distribution*on the i.i.d. observations x i . is*convex*. ...##
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Characterizing detection thresholds using extreme value theory in compressive noise radar imaging

2013
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Compressive Sensing II
*

However, when

doi:10.1117/12.2016899
fatcat:du4imygryndb7dl5qv22cnwhqa
*convex*optimization algorithms are used for compressive radar imaging, the recovered signal may have unknown and arbitrary probability*distributions*. ... In such cases, we resort to Monte Carlo simulations to construct empirical*distributions*. Computationally, this approach is impractical for computing*thresholds*for low probabilities of false alarm. ... We treat the*convex*optimization solver as an instance of an event whose reconstruction error has an unknown*distribution*. We wish to estimate accurate*thresholds*for low P F A . ...##
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Shape Sensitive Geometric Monitoring

2012
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IEEE Transactions on Knowledge and Data Engineering
*

An important problem in

doi:10.1109/tkde.2011.102
fatcat:4pffoqvctnbxzhqimcjy6xz3ge
*distributed*, dynamic databases is to continuously monitor the value of a function defined on the nodes, and check that it satisfies some*threshold*constraint. ... It is guaranteed that as long as none of these constraints is violated, the value of the function did not cross the*threshold*. ... As long as this*convex*hull remains monochromatic, the function's value did not cross the*threshold*and no communication is required. ...##
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Shape sensitive geometric monitoring

2008
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Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '08
*

An important problem in

doi:10.1145/1376916.1376958
dblp:conf/pods/SharfmanSK08
fatcat:jirdg57dnng2rpy5vuxadh66bm
*distributed*, dynamic databases is to continuously monitor the value of a function defined on the nodes, and check that it satisfies some*threshold*constraint. ... It is guaranteed that as long as none of these constraints is violated, the value of the function did not cross the*threshold*. ... As long as this*convex*hull remains monochromatic, the function's value did not cross the*threshold*and no communication is required. ...##
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Certifiable Risk-Based Engineering Design Optimization
[article]

2021
*
arXiv
*
pre-print

A reformulation of the short column structural design problem leading to a

arXiv:2101.05129v2
fatcat:5nbnsa7sgjef5bqypcvyfjabwi
*convex*CRiBDO problem is presented. ... problem to assign the appropriate conservativeness, exhibit superior optimization convergence by preserving properties of underlying functions, and alleviate the adverse effects of choosing hard failure*thresholds*... For this simple*distribution*, one can derive the PoF and bPoF analytically for any given*threshold*t. ...##
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Convexity properties in binary detection problems

1996
*
IEEE Transactions on Information Theory
*

It is shown that the error probability of the maximumlikelihood receiver is a

doi:10.1109/18.508867
fatcat:syezlvaqzjd2tk5j64zlif7bvq
*convex*function of the signal power when the noise has a unimodal*distribution*. ... This correspondence investigates*convexity*properties of error probability in the detection of binary-valued scalar signals corrupted by additive noise. ... Corollary 1 : 1 The error probability of a*threshold*detector is*convex*for any noise*distribution*in Du if its*threshold*tis) satisfies l d 2 t / d S 2 / I Sp3I2/4. ...##
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Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality

2009
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The B.E. Journal of Theoretical Economics
*

We show that if the

doi:10.2202/1935-1704.1518
fatcat:nbmxsl2vejhppief65ctiqpo4a
*threshold*is small relative to consumption levels, preferences will tend to be*convex*; whereas the opposite holds if the*threshold*is large. ...*threshold*level of this quality. ... In this section, we have established that in the case of uniformly*distributed*quality in the presence of a*threshold*payoff, preferences will be strictly*convex*if the*threshold*is "small enough" relative ...##
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Income distribution and macroeconomics: the persistence of inequality in a convex technology framework

2002
*
Economics Letters
*

I show that non-

doi:10.1016/s0165-1765(01)00625-5
fatcat:rpunv6ipoba3dorkxpydprouya
*convexities*in technology, assumed in the capital market imperfection literature on the relationship between income*distribution*and economic development, can be replaced by an assumption ... that the bequest function is*convex*with respect to income. ... It demonstrates that the non-*convexity*of the technology can be replaced by an assumption that saving, which is bequeathed to the next generation, is a*convex*function of income. ...##
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Cloud field segmentation via multiscale convexity analysis

2008
*
Journal of Geophysical Research
*

Segmenting such cloud fields through a simple

doi:10.1029/2007jd009369
fatcat:anhpc2d5vjgzxjywxj7ibdczdq
*thresholding*technique may not provide any structurally significant information about each segmented category. ... hulls, and (3) the estimation of*convexity*measures at corresponding resolutions by employing the areas of cloud fields and areas of corresponding*convex*hulls. ...*Convex*Hull Construction via Half-Plane Closing [20]*Convex*hull of a grayscale cloud field is defined as*threshold*superposed smallest*convex*sets of all possible*threshold*sets or level sets [e.g., ...##
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Structural protein interactions: From months to minutes
[chapter]

2004
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Advances in Parallel Computing
*

In this paper we review how to reduce the computation of PSIMAP from months to minutes, first by designing a new effective algorithm and second by

doi:10.1016/s0927-5452(04)80084-4
fatcat:2jprrk3z2jgcvf7rdyakzsnecu
*distributing*the computation over a Linux PC farm using ... This is done by shifting each polygon of the*convex*hull perpendicularly away from the*convex*hull by the distance*threshold*v . ... A*convex*hull for each of the two domains is computed. 2. Both*convex*hulls are swelled by the required contact distance*threshold*. 3. ...##
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Threshold Choice Methods: the Missing Link
[article]

2012
*
arXiv
*
pre-print

performance metrics have been introduced for the evaluation of classification performance, with different origins and niches of application: accuracy, macro-accuracy, area under the ROC curve, the ROC

arXiv:1112.2640v2
fatcat:4qryeaa4qzbgrd7xx56fgf7dta
*convex*... One dimension for the analysis has been precisely the*distribution*we take for this range of operating conditions, leading to some important connections in the area of proper scoring rules. ... A definition of*convex*hull for continuous*distributions*is given as follows: Definition 14 (Convexification). Let m be any model with score*distributions*f 0 (T ) and f 1 (T ). ...##
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Income Distribution and Macroeconomics: Convex Technology and the Role of Intergenerational Transfers

2000
*
Social Science Research Network
*

I show that non-

doi:10.2139/ssrn.254448
fatcat:lqcpjz7yonhenbsxtdsg4s6n3u
*convexities*in technology, assumed in the capital market imperfection literature on the relationship between income*distribution*and economic growth, can be replaced by an assumption that ... the bequest function is*convex*with respect to income. ... In poor economies, however, where average income is below the*threshold*level, inequality may have a positive effect on economic growth. 4 Interestingly, the mechanism of*convex*savings that generates ...##
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Using convex hulls to extract interaction interfaces from known structures

2004
*
Bioinformatics
*

The combination of pruning and

doi:10.1093/bioinformatics/bth106
pmid:15231539
fatcat:znhiorxbavbr3apzy4eg4mfspu
*distribution*makes the new algorithm scalable and sustainable even with the superlinear growth in PDB. ... Additionally, the algorithms allow a*distributed*computation, which we carry out on a farm of 80 Linux PCs. Overall, the new algorithms reduce the computation at atomic level from months to 20 min. ... In step 2, the swelling of the*convex*hull by the distance*threshold*, d, we perpendicularly shift each triangle by the distance*threshold*away from the*convex*hull: i.e. for each triangle t, we compute ...##
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A note on volume thresholds for random polytopes
[article]

2020
*
arXiv
*
pre-print

We study the expected volume of random polytopes generated by taking the

arXiv:2004.01119v2
fatcat:52zkcpjfdvejjofqtwmtqexzci
*convex*hull of independent identically*distributed*points from a given*distribution*. ... We show that for log-concave*distributions*supported on*convex*bodies, we need at least exponentially many (in dimension) samples for the expected volume to be significant and that super-exponentially ... In this work, we shall establish an exponential bound on N 0 for the family of log-concave*distributions*on*convex*sets and extend (5) to the family of the so-called κ-concave*distributions*. ...
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