An application of kissing number in sum-product estimates
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-018-0831-x
Abstract: AbstractThe boundedness of the kissing numbers of convex bodies has been known to Hadwiger [9] for long. We present an application of it to the sum-product estimate $$\max(\mid{\mathcal{A}+\mathcal{A}}\mid,\mid{\mathcal{A}\mathcal{A}}\mid)\gg \frac {\mid{\mathcal{A}\mid}^{4/3}}{\lceil\log\mid{\mathcal{A}\mid} \rceil^{1/3}}$$max(∣A+A∣,∣AA∣)≫∣A∣4/3⌈log∣A∣⌉1/3for finite sets $${\mathcal{A}}$$A of… read more here.
Keywords: application kissing; sum product; mathcal mid; mid mathcal ... See more keywords
Visualizing and understanding Sum-Product Networks
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DOI: 10.1007/s10994-018-5760-y
Abstract: Sum-Product Networks (SPNs) are deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. They have been largely used as black box density estimators, assessed… read more here.
Keywords: understanding sum; sum product; product networks; visualizing understanding ... See more keywords
Coupled hybrid fixed point theory involving the sum and product of three coupled operators in a partially ordered Banach algebra with applications
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Fixed Point Theory and Applications"
DOI: 10.1007/s11784-017-0471-8
Abstract: In this paper we prove a couple of coupled hybrid fixed point theorems involving the sum and the product of three coupled operators in a partially ordered Banach algebra and derive two applicable fixed point… read more here.
Keywords: hybrid fixed; sum product; point; involving sum ... See more keywords
GCD sums and sum-product estimates
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DOI: 10.1007/s11856-019-1932-0
Abstract: In this note we prove a new estimate on so-called GCD sums (also called Gál sums), which, for certain coefficients, improves significantly over the general bound due to de la Bretèche and Tenenbaum. We use… read more here.
Keywords: product estimates; sums sum; sum product; gcd sums ... See more keywords
Tomographic reconstruction from a small number of projections by an efficient sum-product reasoning method
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DOI: 10.1007/s40314-016-0313-0
Abstract: Tomographic reconstruction from a small number of projections is still a challenging problem. In the paper, we formulate this problem as a statistical graphical model by the smooth assumption that the image has a structure… read more here.
Keywords: tomographic reconstruction; sum product; small number; reconstruction small ... See more keywords
Zeta Functions of Discrete Self-similar Sets and Applications to Point Configuration and Sum–Product-Type Problems
Sign Up to like & getrecommendations! Published in 2019 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rny019
Abstract: In this paper we first prove analytical properties of zeta functions for discrete subsets of R that exhibit “self-similarity” with respect to an arbitrary finite set of (affine) similarities. We then show how such properties… read more here.
Keywords: type problems; point configuration; functions discrete; sum product ... See more keywords
On the Discretized Sum-Product Problem
Sign Up to like & getrecommendations! Published in 2020 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnz360
Abstract: We give a new proof of the discretized ring theorem for sets of real numbers. As a special case, we show that if $A\subset \mathbb {R}$ is a $(\delta ,1/2)_1$-set in the sense of Katz… read more here.
Keywords: sum product; product problem; discretized sum;
Generating synthetic mixed discrete-continuous health records with mixed sum-product networks
Sign Up to like & getrecommendations! Published in 2022 at "Journal of the American Medical Informatics Association : JAMIA"
DOI: 10.1093/jamia/ocac184
Abstract: OBJECTIVE Privacy is a concern whenever individual patient health data is exchanged for scientific research. We propose using mixed sum-product networks (MSPNs) as private representations of data and take samples from the network to generate… read more here.
Keywords: health; synthetic data; mixed discrete; sum product ... See more keywords
Boost Sum-Product Performance for Multiuser Detection in mMTC at Millimeter Wave
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Mobile Computing"
DOI: 10.1109/tmc.2021.3089359
Abstract: We consider the multiuser detection (MUD) problem, i.e., how to separate and decode colliding data streams, in the uplink of massive Machine Type Communications (mMTC) at millimeter wave (mmWave). Operating on factor-graphs by passing messages,… read more here.
Keywords: sum product; multiuser detection; millimeter wave; product ... See more keywords
On the Latent Variable Interpretation in Sum-Product Networks
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DOI: 10.1109/tpami.2016.2618381
Abstract: One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM… read more here.
Keywords: sum product; interpretation sum; interpretation; product networks ... See more keywords