Balancing vectors and Gaussian measures ofn-dimensional convex bodies

Banaszczyk, Wojciech

doi:10.1002/(sici)1098-2418(199807)12:4<351::aid-rsa3>3.0.co;2-s

Random Struct. Alg.

1998

DOI: 10.1002/(sici)1098-2418(199807)12:4<351::aid-rsa3>3.0.co;2-s

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Balancing vectors and Gaussian measures ofn-dimensional convex bodies

Wojciech Banaszczyk

¹

Abstract: Let и be the Euclidean norm on R and ␥ the standard Gaussian measure n n Ž . ynr2 y5x5 2 r2

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Cited by 148 publications

(216 citation statements)

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“…This result essentially recovers the best known bound on the Komlós conjecture due to Banaszczyk [4] in an online algorithmic fashion, with the slight defect of requiring a +2-signing option. Furthermore due to the online nature of the algorithm, the algorithm will run in essentially input-sparsity time which is substantially faster than the Gram-Schmidt walk [7] which gives an algorithmic proof of the result of [4] (without the defect of requiring a +2-signing option).…”

Section: Corollary 12 For Any Vectorssupporting

confidence: 80%

A Gaussian fixed point random walk

Liu¹,

Sah²,

Sawhney³

2021

Preprint

3

0

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…This result essentially recovers the best known bound on the Komlós conjecture due to Banaszczyk [4] in an online algorithmic fashion, with the slight defect of requiring a +2-signing option. Furthermore due to the online nature of the algorithm, the algorithm will run in essentially input-sparsity time which is substantially faster than the Gram-Schmidt walk [7] which gives an algorithmic proof of the result of [4] (without the defect of requiring a +2-signing option).…”

Section: Corollary 12 For Any Vectorssupporting

confidence: 80%

A Gaussian fixed point random walk

Liu¹,

Sah²,

Sawhney³

2021

Preprint

3

0

Get access via publisher Add to collection Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…A bound in terms of the maximum degree. If F has maximum degree t, i.e., no point is in more than t sets, then we get disc F = O( √ t log m) by (A) and (B), which recovers the current best bound for this problem, due to Banaszczyk [Ban98]. However, this example is not quite fair, since inequality (2) used in (A) relies on a more general form of Banaszczyk's estimate.…”

Section: Simple Proofs Of Known Discrepancy Boundssupporting

confidence: 61%

Factorization Norms and Hereditary Discrepancy

Matoušek

¹

,

Nikolov

²

,

Talwar

³

2018

International Mathematics Research Notices

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…Suppose that B \ {0} is nonempty, and select an element t from it. By the same argument we had earlier, we have | f (1)…”

Section: The Continuity Argument and A Simple Lower Boundsupporting

confidence: 59%

On the Littlewood Problem Modulo a Prime

Green

¹

,

Konyagin

²

2009

Get access via publisher Add to collection Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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