1,684 research outputs found
On two optimal control problems for magnetic fields
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)Two optimal control problems for instationary magnetization processes are considered in 3D spatial domains that include electrically conducting and non-conducting regions. The magnetic fields are generated by induction coils. In the first model, the induction coil is considered as part of the conducting region and the electrical current is taken as control. In the second, the coil is viewed as part of the non-conducting region and the electrical voltage is the control. Here, an integro-differential equation accounts for the magnetic induction law that couples the given electrical voltage with the induced electrical current in the induction coil. We derive first-order necessary optimality conditions for the optimal controls of both problems. Based on them, numerical methods of gradient type are applied. Moreover, we report on the application of model reduction by POD that lead to tremendous savings. Numerical tests are presented for academic 3D geometries but also for a real-world application
Fair assignment of indivisible objects under ordinal preferences
We consider the discrete assignment problem in which agents express ordinal
preferences over objects and these objects are allocated to the agents in a
fair manner. We use the stochastic dominance relation between fractional or
randomized allocations to systematically define varying notions of
proportionality and envy-freeness for discrete assignments. The computational
complexity of checking whether a fair assignment exists is studied for these
fairness notions. We also characterize the conditions under which a fair
assignment is guaranteed to exist. For a number of fairness concepts,
polynomial-time algorithms are presented to check whether a fair assignment
exists. Our algorithmic results also extend to the case of unequal entitlements
of agents. Our NP-hardness result, which holds for several variants of
envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang
(ECAI 2010). We also propose fairness concepts that always suggest a non-empty
set of assignments with meaningful fairness properties. Among these concepts,
optimal proportionality and optimal weak proportionality appear to be desirable
fairness concepts.Comment: extended version of a paper presented at AAMAS 201
Nonparametric Analysis of Hedge Funds Lifetimes
Most of hedge funds databases are now keeping history of dead funds in order to control biases in empirical analysis. It is then possible to use these data for the analysis of hedge funds lifetimes and survivorship. This paper proposes two nonparametric specifications of duration models. First, the single risk model is an alternative to parametric duration models used in the literature. Second, the competing risks model consider the two reasons why hedge funds stop reporting. We apply the two models to hedge funds data and compare our results to the literature. In particular, we show that a cohort effect must be considered. Moreover, the reason of the exit is a crucial information for the analysis of funds' survival as for a large part of disappearing funds, exit cannot be explained by low performance or low level of assets.
Computational Aspects of Multi-Winner Approval Voting
We study computational aspects of three prominent voting rules that use
approval ballots to elect multiple winners. These rules are satisfaction
approval voting, proportional approval voting, and reweighted approval voting.
We first show that computing the winner for proportional approval voting is
NP-hard, closing a long standing open problem. As none of the rules are
strategyproof, even for dichotomous preferences, we study various strategic
aspects of the rules. In particular, we examine the computational complexity of
computing a best response for both a single agent and a group of agents. In
many settings, we show that it is NP-hard for an agent or agents to compute how
best to vote given a fixed set of approval ballots from the other agents
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