Deterministic and stochastic methods for computing volumetric moduli of convex cones

Gourion, Daniel; Seeger, Alberto

doi:10.1590/s1807-03022010000200007

Cited by 17 publications

(19 citation statements)

References 26 publications

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“…where B S is the closed unit ball in dimension S ( Gourion and Seeger, 2010;Saavedra et al, 2016a ). Note that the least upper bound of ( A ) is 0.5, as the largest cone that can be generated by (3) ).…”

Section: Probabilistic Interpretation Of Feasibilitymentioning

confidence: 99%

A guideline to study the feasibility domain of multi-trophic and changing ecological communities

Song

Rohr

Saavedra

2018

Journal of Theoretical Biology

155

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The feasibility domain of an ecological community can be described by the set of environmental abiotic and biotic conditions under which all co-occurring and interacting species in a given site and time can have positive abundances. Mathematically, the feasibility domain corresponds to the parameter space compatible with positive (feasible) solutions at equilibrium for all the state variables in a system under a given model of population dynamics. Under specific dynamics, the existence of a feasible equilibrium is a necessary condition for species persistence regardless of whether the feasible equilibrium is dynamically stable or not. Thus, the size of the feasibility domain can also be used as an indicator of the tolerance of a community to random environmental variations. This has motivated a rich research agenda to estimate the feasibility domain of ecological communities. However, these methodologies typically assume that species interactions are static, or that input and output energy flows on each trophic level are unconstrained. Yet, this is different to how communities behave in nature. Here, we present a step-by-step quantitative guideline providing illustrative examples, computational code, and mathematical proofs to study systematically the feasibility domain of ecological communities under changes of interspecific interactions and subject to different constraints on the trophic energy flows. This guideline covers multitrophic communities that can be formed by any type of interspecific interactions. Importantly, we show that the relative size of the feasibility domain can significantly change as a function of the biological information taken into consideration. We believe that the availability of these methods can allow us to increase our understanding about the limits at which ecological communities may no longer tolerate further environmental perturbations, and can facilitate a stronger integration of theoretical and empirical research.

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Section: Probabilistic Interpretation Of Feasibilitymentioning

confidence: 99%

A guideline to study the feasibility domain of multi-trophic and changing ecological communities

Song

Rohr

Saavedra

2018

Journal of Theoretical Biology

155

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“…Firstly, we are the first to study the k-hit query, which has a wide range of applications since all applications for topk queries and skyline queries can naturally be used in our k-hit query. Secondly, since there are a lot of existing studies [36,5,7,20,3,6,27,12,17,35] considering that the utility functions are in the linear form, we study our k-hit query when the functions are in this form and present its relevance to a geometry concept called "solid angle" [13,26] and some existing database queries, namely top-k queries [27,12,17,35,10,24], skyline queries [3,12,17,6,18,19,29], k-regret queries [20,22] and k-representative skyline queries [29]. Besides, if the distribution Θ on (linear) utility functions is uniform, we find an interesting geometry property based on "solid angle" and develop a novel algorithm called k-Hit_Alg based on this property.…”

Section: Contributions and Organizationmentioning

confidence: 99%

k-Hit Query

Peng

Wong

2015

Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data

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Multi-criteria decision making problem has been well studied for many years. One popular query for multi-criteria decision making is top-k queries which require each user to specify an exact utility function. In many cases, the utility function of a user is probabilistic and finding the distribution on the utility functions has been widely explored in the machine learning areas, such as user's recommender systems, Bayesian learning models and user's preference elicitation, for improving user's experience. Motivated by this, we propose a new type of queries called k-hit queries, which has not been studied before. Given a set D of tuples in the database, the distribution Θ on utility functions and a positive integer k, we would like to select a set of k tuples from D in order to maximize the probability that at least one of tuples in the selection set is the favorite of a user. All applications for top-k queries can naturally be used in k-hit queries. In this paper, we present various interesting properties of k-hit queries. Besides, based on these properties, we propose a novel algorithm called k-hit_Alg for k-hit queries. Finally, we conducted comprehensive experiments to show that the performance of our proposed method, k-hit_Alg, is superior compared with other existing algorithms which were originally used to answer other existing queries.

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“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php appears over and over again in diverse situations (cf. [46,47]). By writing down the optimality conditions for (1.1), one arrives at a complementarity system of the form…”

Section: Spectral Properties Of Copositive Matricesmentioning

confidence: 99%

“…This can be better explained by using the concept of normalized volume studied in [47]. The fact that C n fills only a small portion of S n should not be very surprising.…”

Section: Probabilistic Considerations Concerning Copositivitymentioning

confidence: 99%