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Topic: Subadditive

	Subadditive function - Wikipedia, the free encyclopedia
		In mathematics, a subadditive function is a function f : A → B, having a domain A and a codomain B that are both closed under addition, with the following property:
		The major reason for use of subadditive sequences is the following lemma due to M.
		This article incorporates material from subadditivity on PlanetMath, which is licensed under the GFDL.
	en.wikipedia.org /wiki/Subadditive_function (302 words)

	PlanetMath: subadditivity
		The major reason for use of subadditive sequences is the following lemma due to Fekete.
		There are also results that allow one to deduce the rate of convergence to the limit whose existence is stated in Fekete lemma if some kind of both super- and subadditivity is present.
		This is version 6 of subadditivity, born on 2003-08-19, modified 2003-09-08.
	planetmath.org /encyclopedia/Subadditivity.html (158 words)

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		An ergodic theorem is proved which extends the subadditive ergodic theorem of Kingman and the Banach valued ergodic theorem of Mouner The theorem is applied to several problems, in particular to a problem on empirical distribution functions.
		The subadditive ergodic theorem of Kingman [2, 5, 6, 16, 17,
		The usefulness of subadditive ergodic theory is substantially extended by a reformulation in terms of stationary pro6esses.
	www-stat.wharton.upenn.edu /~steele/Papers/HTML/Vvspaa.html (3727 words)

	Subadditive Function (Site not responding. Last check: 2007-10-23)
		In mathematics, a subadditive function is a function f : A → B, having a domain A and a codomain B that are both closed under addition, with...
		the main definitions: the maximal growth rate of a subadditive function and the growth rate of a subbadditive function with respect to an...
		For a nonnegative subadditive function $h$ on $\mathbb{Z}^d$, with limiting approximation $g(x) = \lim_n h(nx)/n$, it is of interest to obtain...
	www.subadditivefunction.info (398 words)

	VaR and Subadditivity (Site not responding. Last check: 2007-10-23)
		Subadditivity means that aggregating risks does not increase overall risk and is a fundamental requirement of any “good” risk measure.
		The reason for this action would be that the sum of the capital requirements of the smaller units would be less than the capital requirement of the firm as a whole.
		The failure of VaR to be subadditive is a fundamental problem because it means, in essence, that VaR has no claim to be regarded as a “proper” risk measure at all.
	www.fenews.com /fen40/risk-reward/risk-reward.htm (1311 words)

	Citations: Ergodic theorems for subadditive superstationary families of convex compact random sets - urger ... (Site not responding. Last check: 2007-10-23)
		....Utrecht, the Netherlands Abstract Pointwise and mean ergodic theorems under different assumptions for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented.
		Subadditive superstationary families (F s;t) of multivalued functions with values being weakly (respectively strongly) compact convex....
		proved pointwise and mean ergodic theorems for subadditive superstationary families of convex compact random sets in R d.
	citeseer.ist.psu.edu /context/608122/0 (402 words)

	Ergodic Theorems for Subadditive Superstationary Families of Random Sets with Values in Banach Spaces - Krupa ...
		Abstract: Pointwise and mean ergodic theorems under different assumptions for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented.
		Krupa, G. (1996) Ergodic theorems for subadditive superstationary families of random sets in Banach spaces.
		2 Ergodic theorems for subadditive superstationary families of..
	citeseer.ist.psu.edu /krupa96ergodic.html (473 words)

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		The final section similarly estimates the "time constant" of the subadditive process associated to the class of lower layers and consequently obtains as corollaries results due to, Blum [1] and DeHardt [5, 6].
		The existence of the limits on the left side of equations (4.9), (4.10), and (4.11) is an immediate consequence of Kingman's subadditive ergodic theorem and Theorem 2.
		The Theorem 6.1 is then an instance of computing the "time constant" of a subadditive process, and the calculation of such constants was pointed out by Kingman [131 to be a basic problem in the theory of subadditive processes.
	www-stat.wharton.upenn.edu /~steele/Papers/HTML/Edasp.html (3255 words)

	Citebase - Linear repetitivity, I. Uniform subadditive ergodic theorems and applications (Site not responding. Last check: 2007-10-23)
		We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings.
		This theorem unifies and extends various known (sub)additive ergodic theorems on tilings.
		The results of this paper can be applied in the study of both random operators and lattice gas models on tilings.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0005062 (133 words)

	Igitur-archive (Site not responding. Last check: 2007-10-23)
		Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces
		show / hidePointwise and mean ergodic theorems under dierent assumptions for subadditive super- stationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented.
		The results generalize the results of [14], where random sets in Rd are considered.
	igitur-archive.library.uu.nl /math/2001-0703-131158/UUindex.html (62 words)

	Fuglede: The quasi topology associated with a countably subadditive set function (Site not responding. Last check: 2007-10-23)
		The quasi topology associated with a countably subadditive set function.
		This is a general study of an increasing, countably subadditive set function, called a capacity, and defined on the subsets of a topological space
		The principal aim is the study of the ``quasi-topological'' properties of subsets of
	www.numdam.org /numdam-bin/item?id=AIF_1971__21_1_123_0 (288 words)

	Summation of Forces From Multiple Motor Units in the Cat Soleus Muscle -- Perreault et al. 89 (2): 738 -- Journal of ...
		summation undergoes a transition from superadditive to subadditive
		superadditive, instances of subadditive summation also were observed.
		the observed transition from superadditive to subadditive summation.
	jn.physiology.org /cgi/content/full/89/2/738 (4728 words)

	BrainBlog
		Recently, behavioral economists have reported that impatience/impulsivity in intertemporal choice is increased if a delay period is presented as a sum of divided time-blocks, which is referred to as subadditive discounting (i.e., "total patience" over the delay period is larger than the "sum of patience" over divided delay periods).
		This finding implies that abstinent drug addicts may more readily relapse into addiction if an abstinence period is presented as a series of shorter abstinent periods, rather than a single block of a long abstinence period.
		Therefore, understanding of neuropsychological processing underlying subadditive discounting is important for establishing medical treatments of drug addiction, although to date, no study has addressed this question.
	www.neuropsychological.blogspot.com (4105 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Energy Citations Database (ECD) Document #20428759 - Subadditive interaction of radiation and taxol in vitro
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		Subadditive interaction of radiation and taxol in vitro
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20428759 (427 words)

	Memorandum 1779, Abstract (Site not responding. Last check: 2007-10-23)
		In this article we focus on approximation algorithms for facility location problems with subadditive costs.
		,1)- reduction of the facility location problem with subadditive costs to a soft capacitated facility location problem, which implies the existence of a 2(1+
		For a special subclass of subadditive functions, we obtain a 2-approximation algorithm by reduction to the linear cost facility location problem.
	www.math.utwente.nl /publications/2005/1779abs.html (103 words)

	A subadditive thermodynamic formalism for mixing repellers
		The thermodynamical description of fractals that has recently attracted much interest both experimentally and theoretically in the study of dynamical systems is, in some ways, limited, being essentially an additive theory.
		The author presents a subadditive thermodynamic formalism for which he derives a variational principle and shows how it may be used to study the dynamics of non-conformal transformations.
		In particular the author discusses an analogue of Bowen's formula for the dimension of a mixing repeller.
	stacks.iop.org /0305-4470/21/L737 (208 words)

	subadditive ergodic theorem (Site not responding. Last check: 2007-10-23)
		Definition: If a stationary and ergodic process satisfies the subadditive inequality, it grows almost surely linearly in time.
		Note: From Algorithms and Theory of Computation Handbook, page 14-35, Copyright © 1999 by CRC Press LLC.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "subadditive ergodic theorem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/subadditive.html (117 words)

	CreditMetrics. Is Value-at-Risk subadditive ? (Site not responding. Last check: 2007-10-23)
		It means it is possible to reduce the risk on a portfolio simply by splitting the portfolio up on several accounts.
		Does anybody know more about value-at-risk and subadditivity ?
		If value-at-risk does not satisfy the condition is it of any use ?
	www.contingencyanalysis.com /archive/archive98-3/000000fd.htm (80 words)

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