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

Wei Shi, T.W. Sun, R.D. Wesel
2001 IEEE Transactions on Information Theory  
For generalized Gaussian noises and some non-Gaussian noise 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.  ... 
doi:10.1109/18.904560 fatcat:6hflqvoqbfg4xh3idjwopj2sxa

Statistical optimization of dynamic importance sampling parameters for efficient simulation of communication networks

M. Devetsikiotis, J.K. Townsend
1993 IEEE/ACM Transactions on Networking  
For generalized Gaussian noises and some non-Gaussian noise 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.  ... 
doi:10.1109/90.234852 fatcat:t7d7ouqwkret3bnj76cf7wgfhi

Characterizing detection thresholds using extreme value theory in compressive noise radar imaging

Mahesh C. Shastry, Ram M. Narayanan, Muralidhar Rangaswamy, Fauzia Ahmad
2013 Compressive Sensing II  
However, when 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 .  ... 
doi:10.1117/12.2016899 fatcat:du4imygryndb7dl5qv22cnwhqa

Shape Sensitive Geometric Monitoring

Daniel Keren, Izchak Sharfman, Assaf Schuster, Avishay Livne
2012 IEEE Transactions on Knowledge and Data Engineering  
An important problem in 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.  ... 
doi:10.1109/tkde.2011.102 fatcat:4pffoqvctnbxzhqimcjy6xz3ge

Shape sensitive geometric monitoring

Izchak Sharfman, Assaf Schuster, Daniel Keren
2008 Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '08  
An important problem in 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.  ... 
doi:10.1145/1376916.1376958 dblp:conf/pods/SharfmanSK08 fatcat:jirdg57dnng2rpy5vuxadh66bm

Certifiable Risk-Based Engineering Design Optimization [article]

Anirban Chaudhuri, Boris Kramer, Matthew Norton, Johannes O. Royset, Karen Willcox
2021 arXiv   pre-print
A reformulation of the short column structural design problem leading to a 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.  ... 
arXiv:2101.05129v2 fatcat:5nbnsa7sgjef5bqypcvyfjabwi

Convexity properties in binary detection problems

M. Azizoglu
1996 IEEE Transactions on Information Theory  
It is shown that the error probability of the maximumlikelihood receiver is a 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.  ... 
doi:10.1109/18.508867 fatcat:syezlvaqzjd2tk5j64zlif7bvq

Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality

Trenton G. Smith, Attila Tasnádi
2009 The B.E. Journal of Theoretical Economics  
We show that if the 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  ... 
doi:10.2202/1935-1704.1518 fatcat:nbmxsl2vejhppief65ctiqpo4a

Income distribution and macroeconomics: the persistence of inequality in a convex technology framework

Omer Moav
2002 Economics Letters  
I show that non-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.  ... 
doi:10.1016/s0165-1765(01)00625-5 fatcat:rpunv6ipoba3dorkxpydprouya

Cloud field segmentation via multiscale convexity analysis

Sin Liang Lim, B. S. Daya Sagar
2008 Journal of Geophysical Research  
Segmenting such cloud fields through a simple 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.,  ... 
doi:10.1029/2007jd009369 fatcat:anhpc2d5vjgzxjywxj7ibdczdq

Structural protein interactions: From months to minutes [chapter]

P. Dafas, J. Gomoluch, A. Kozlenkov, M. Schroeder
2004 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 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.  ... 
doi:10.1016/s0927-5452(04)80084-4 fatcat:2jprrk3z2jgcvf7rdyakzsnecu

Threshold Choice Methods: the Missing Link [article]

José Hernández-Orallo, Peter Flach, Cèsar Ferri
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 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 ).  ... 
arXiv:1112.2640v2 fatcat:4qryeaa4qzbgrd7xx56fgf7dta

Income Distribution and Macroeconomics: Convex Technology and the Role of Intergenerational Transfers

Omer Moav
2000 Social Science Research Network  
I show that non-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  ... 
doi:10.2139/ssrn.254448 fatcat:lqcpjz7yonhenbsxtdsg4s6n3u

Using convex hulls to extract interaction interfaces from known structures

P. Dafas, D. Bolser, J. Gomoluch, J. Park, M. Schroeder
2004 Bioinformatics  
The combination of pruning and 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  ... 
doi:10.1093/bioinformatics/bth106 pmid:15231539 fatcat:znhiorxbavbr3apzy4eg4mfspu

A note on volume thresholds for random polytopes [article]

Debsoumya Chakraborti, Tomasz Tkocz, Beatrice-Helen Vritsiou
2020 arXiv   pre-print
We study the expected volume of random polytopes generated by taking the 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.  ... 
arXiv:2004.01119v2 fatcat:52zkcpjfdvejjofqtwmtqexzci
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