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Equation 5.4, incorporating density dependence, is known as the discrete logistic equation and represents a strategic model for the population dynamics of annual species. K is the carrying capacity, de ned as the maximum number of individuals a habitat can support. Equation 5.4 is sometimes written as Nt+1 = Nt(1 Nt); that is, replacing 1/K by . Berryman (1992) and Elliott (1994) review the use of the discrete logistic and similar equations whereas May et al. (1974) and May (1981) discuss the density-dependent terms. Modelling of intraspeci c competition has lead to a variety of equations incorporating density dependence. The model of Hassell (1975), described by the equation Nt+1 = Nt(1 + aNt) b, provides parameters a and b which can describe change from contest to scramble competition. a gives the threshold

Cryptography has a very broad objective: to design schemes that (whatever their intended functionalities) are robust against malicious attempts to make the schemes deviate from those functionalities (Goldreich 1999) Encryption and digital signatures are well-known examples of cryptosystems they help make the con dentiality and authenticity of wireless communications robust against malicious attacks, such as eavesdropping and spoo ng but they are just speci c examples of cryptosystems within the broad objective, designed to protect a few speci c functionalities It is really no exaggeration to say that purview of cryptography is every bit as broad as the universe of systems that it seeks to protect and the universe of malicious attacks against these systems that an adversary may devise Given cryptography s broad objective, the challenge of securing XG is that it will offer a rich variety of functionalities (applications, network services, personalized aspects, etc.

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) over increasingly heterogeneous devices and contexts As the offered functionalities become more complex, so does the cryptographic problem of making these functionalities robust against attacks Unfortunately, to solve this problem (ef ciently, anyway), it is often not enough to simply kludge together simple atomic cryptosystems in the right way; instead, cryptosystems often need to be tailored for individual services and applications Consider a simple example One of the hallmarks of XG will be heterogeneity devices of differing capabilities (eg, laptops, PDAs, cell phones, wrist watches, and kitchen appliances), differing connection characteristics (wired and wireless, lossless and lossy, cable modem and wireless LAN, etc), and changes in context (such as network handoff due to user mobility).

To handle this heterogeneity and enhance performance in other ways, one might consider placing value-added proxies near user devices to transcode data before transmitting it to users, so that the data is customized for a user s speci c device and connection characteristics, or to facilitate the user s changes in context For example, one might enable a network proxy to adapt a content provider s multimedia stream to the particular display capabilities of a user s cell phone in real time However, neither the content provider nor the user is likely to trust such a proxy completely; both would like some assurance that the proxy has not modi ed the stream too much In other words, we need a cryptosystem that allows limited transcoding but still provides robustness against malicious attempts (by the proxy or anyone else) to modify the data beyond what is permitted by the content provider.

Instead, Doris has a lifetime pattern of solitary activities such as sewing her own clothes and spending her evenings alone Her own life experiences include giving up a 2-month-old child for adoption because of the consequential infringement on her personal time Doris has no interest in sexual activities and denies any emotional relationship with the baby s father In fact, she shows no need to have close relationships at all and not much use for others How does the schizoid personality develop from an interpersonal perspective No one is really sure, but clinical intuition suggests that schizoids probably possess interpersonal deficits from the very beginning of life Whereas most infants develop one of several styles of attachment to caretakers, future schizoids are only weakly attached, if at all.

Traditional digital signature schemes, in accordance with the principle of end-to-end security, do not allow any modi cation of the message after the content provider has signed it; if a single bit of data is modi ed, the signature veri cation check will fail Making this limited transcoding functionality robust against attacks, while preserving the ability of the proxy to operate in real time, requires a cryptosystem speci cally tailored for the application As a slightly more complex example, consider one of the most commonly used applications on the Internet: a search engine What robust functionalities might we want a search engine to have First, we may want to ensure that the user s queries and the search engine s responses are authentic, unmodi ed, and con dential with respect to third parties (These functionalities can essentially be secured using conventional encryption and signature schemes.

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