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Chasing Nested Convex Bodies Nearly Optimally [article]

Sébastien Bubeck, Bo'az Klartag, Yin Tat Lee, Yuanzhi Li, Mark Sellke
2021 arXiv   pre-print
In convex body chasing, for each timestep t∈ℕ, a convex body K_t⊆ℝ^d is given as a request, and the player picks a point x_t∈ K_t.  ...  The convex body chasing problem, introduced by Friedman and Linial, is a competitive analysis problem on any normed vector space.  ...  Optimal Memoryless Chasing In the chasing nested convex bodies problem, the optimal strategy potentially depends on the new request K t and the initial/current points x 0 and x t−1 .  ... 
arXiv:1811.00999v4 fatcat:3horsjgknrfeljkjfpbemgtaxa

A Nearly-Linear Bound for Chasing Nested Convex Bodies [article]

C.J. Argue and Sébastien Bubeck and Michael B. Cohen and Anupam Gupta and Yin Tat Lee
2018 arXiv   pre-print
In convex body chasing, at each time step t ∈N, the online algorithm receives a request in the form of a convex body K_t ⊆R^d and must output a point x_t ∈ K_t.  ...  We propose a different strategy which is O(d d)-competitive algorithm for this nested convex body chasing problem, improving substantially over previous work. Our algorithm works for any norm.  ...  In this paper we restrict to nested instances of convex body chasing, where the bodies are contained within each other, i.e., K 1 ⊇ K 2 ⊇ K 3 ⊇ . . . .  ... 
arXiv:1806.08865v2 fatcat:twphgb7xsnaddmcq6upnflybv4

Chasing Convex Bodies Optimally [article]

Mark Sellke
2021 arXiv   pre-print
The approach extends our prior work for nested convex bodies, which is based on the classical Steiner point of a convex body.  ...  In the chasing convex bodies problem, an online player receives a request sequence of N convex sets K_1,..., K_N contained in a normed space ℝ^d.  ...  Acknowledgement I thank Sébastien Bubeck, Bo'az Klartag, Yin Tat Lee, and Yuanzhi Li for the introduction to convex body chasing and the Steiner point, and many stimulating discussions.  ... 
arXiv:1905.11968v3 fatcat:fs55kpbd2fdedg4z3zv4djp7bq

Nested Convex Bodies are Chaseable [chapter]

Nikhil Bansa, Martin Böhm, Marek Eliáš, Grigorios Koumoutsos, Seeun William Umboh
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
In this work, we give a f (d)competitive algorithm for chasing nested convex bodies in R d .  ...  We consider the setting in which the convex bodies are nested: F 1 ⊃ . . . ⊃ F n .  ...  nearly-optimal competitive ratios for many MSS and is a natural candidate to be f (d)-competitive for convex body chasing.  ... 
doi:10.1137/1.9781611975031.81 dblp:conf/soda/BansalB0KU18 fatcat:qqg563nc55dshb5lvyz5rbdnum

Online Robust Control of Nonlinear Systems with Large Uncertainty [article]

Dimitar Ho, Hoang M. Le, John C. Doyle, Yisong Yue
2021 arXiv   pre-print
Our approach is based on decomposing the problem into two sub-problems, "robust control design" (which assumes small model uncertainty) and "chasing consistent models", which can be solved using existing  ...  Chasing nested convex bodies nearly optimally. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1496-1508. SIAM, 2020.  ...  We show in Section 4 that if the consistent map P returns always convex sets, we can design γ-competitive CMC-algorithms through a reduction to the nested convex body chasing problem.  ... 
arXiv:2103.11055v2 fatcat:ofakkysmtrdydg44nwqfm6g4ya

Experimental evidence for female choice and energetic costs of male tail elongation in red-collared widowbirds

2005 Biological Journal of the Linnean Society  
In contrast, however, although the longer-tailed control males spent less time in flight and courtship displays, they attracted significantly more prospecting and nearly three times as many nesting females  ...  Despite the higher activities of short-tailed males, control-tailed males showed a steeper decline in condition (relative body mass) during the breeding season.  ...  nearly three times as many nesting females as the short-tailed males (P < 0.001; Table 3 and Fig. 1) .  ... 
doi:10.1111/j.1095-8312.2005.00522.x fatcat:su5lixuxsjcyffw7ntbwydbmoq

Smoothed Online Optimization for Regression and Control [article]

Gautam Goel, Adam Wierman
2019 arXiv   pre-print
We consider Online Convex Optimization (OCO) in the setting where the costs are m-strongly convex and the online learner pays a switching cost for changing decisions between rounds.  ...  Additionally, we show that when the sequence of cost functions is ϵ-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy.  ...  The connection between Convex Body Chasing and SOCO was observed in [ABN + 16].  ... 
arXiv:1810.10132v2 fatcat:wmglvcrpsff2beqx4cl662hyra

Spatial organization of the fat dormouse (Glis glis) in an oak-hornbeam forest during the mating and post-mating season

M. Ściński, Z. Borowski
2008 Mammalian Biology  
Average HR size measured by 100% minimum convex polygons varied from 3.6 to 7.0 ha in males and from 0.55 to 0.76 ha in females.  ...  During the mating season, males were found to share nest sites with other males or with a single female.  ...  HR size was calculated as a minimum convex polygon linking all the outer position fixes (MCP100%).  ... 
doi:10.1016/j.mambio.2007.01.002 fatcat:su2wkzdbhvclhmym4fqgkggbdq

Wood Thrush Postfledging Movements and Habitat Use in Northern Virginia

J. H. Rappole, W. J. McShea, C. A. Haas
1998 The Condor  
We conclude that successful conservation of migratory species requires protection of habitats used during the postfledging period as well as those used during the nesting portion of the life cycle.  ...  Foraging optimization. According to this hypothesis, the main purpose of postfledging movements by juveniles is location of optimal foraging habitat.  ...  On 20 occasions that involved 10 of our radio-tagged juveniles, we observed birds chasing each other.  ... 
doi:10.2307/1369898 fatcat:xl7m6obbvzgurcixfr33u44d4i

Polygamy in the Marsh Harrier, Circus Aeruginosus: Individual Variation in Hunting Performance and Number of Mates

Wibe Altenburg, Jaap Starkenburg, Serge Daan, Menno Zijlstra
1982 Behaviour  
Non Joraging: Territorial behaviour: chasing intruders of both sexes, sometimes also crows, magpies, buzzards and kestrels.  ...  In the Lauwersmeer nests of marsh harriers were found nearly exclusively in the dense vegetation of reeds and willow herbs along the banks of the lake and creeks (Fig. 1 ).  ... 
doi:10.1163/156853982x00300 fatcat:gyundipihvdble5h5s7ujqjoky

Behavioral Monogamy and Fruit Aavailability in the Large Treeshrew (Tupaia tana) in Sabah, Malaysia

Jason Munshi-South, Louise H. Emmons, Henry Bernard
2007 Journal of Mammalogy  
Both males and females exhibited better body condition in selectively logged versus primary forests, but ranging patterns were not significantly different between these habitats.  ...  Comparison between masting and nonmasting forests indicated that females exhibited better body condition during masting, whereas males exhibited larger home-range areas and longer daily movements.  ...  In contrast to adults, large treeshrew young in the nest are nearly odorless and motionless (Emmons 2000) .  ... 
doi:10.1644/06-mamm-a-295r1.1 fatcat:ldxrzfvvercctpwwcvkhws2s2q

Influence of Reproductive Status: Home Range Size in Water Voles (Arvicola amphibius)

Karl Frafjord, Aaron W. Reed
2016 PLoS ONE  
Home range (m 2 ) as a function of body mass (g) in female (circles) and male (triangles) water voles.  ...  Body mass or year did not influence home range size. Overlap of home ranges varied, but could be extensive in both adult males and females.  ...  Reproduction took place from April to July, with nearly all litters born in May and June.  ... 
doi:10.1371/journal.pone.0154338 pmid:27115881 pmcid:PMC4846030 fatcat:d4u3kkpf7jdaphekn2bjxvyfee

Minimax estimation via wavelet shrinkage

David L. Donoho, Iain M. Johnstone
1998 The Annals of Statistics  
The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebel-and Besov-type smoothness constraints, and asymptotically minimax over Besov bodies with p q.  ...  Variants of our method based on simple threshold nonlinearities are nearly minimax.  ...  [BB1] For q < 1 , J s p;q () = k k q b s p;q is a convex functional of the moment sequence = ( p^q I ). For q = 1, the functional J s p;1 () = k k b s p;1 has nested convex level sets.  ... 
doi:10.1214/aos/1024691081 fatcat:3kcqbwl4iva5xijlaslpqhtldq

Phylogenetic Relationships of the Decumbentes Group of Paspalum, Thrasya, and Thrasyopsis (Poaceae: Panicoideae: Paniceae)

Silvia Denham, Fernando Zuloaga
2007 Aliso  
Beauv. nested within. MATERIALS AND METHODS Sampling Ingroup.  ...  Compression: plano-convex (0), biconvex (1), concavo-convex (2), biplanar (3). 25. Thickened base: absent (0), present (1). Thrasya axillaris, T. crucensis (ϭ P. crucense (Killeen) S.  ... 
doi:10.5642/aliso.20072301.41 fatcat:iqtmvkj2nnhhrcl6fbxwztlv64

Path Length Bounds for Gradient Descent and Flow [article]

Chirag Gupta, Sivaraman Balakrishnan, Aaditya Ramdas
2021 arXiv   pre-print
We derive bounds on the path length ζ of gradient descent (GD) and gradient flow (GF) curves for various classes of smooth convex and nonconvex functions.  ...  condition, ζ is at most 𝒪(√(κ)), where κ is the condition number, and at least Ω(√(d)∧κ^1/4); (c) for quadratics, ζ is Θ(min{√(d),√(logκ)}) and in some cases can be independent of κ; (d) assuming just convexity  ...  We thank Sébastien Bubeck for pointing us to some references on self-contracted curves, and Anupam Gupta for informing us about the nested convex body chasing problem that sparked our interest in path  ... 
arXiv:1908.01089v4 fatcat:spytuguoxrbabhcvk34dftmbb4
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