This paper develops a dynamic model of a financial market, using some properties of the formalism of quantum physics. The model aims to take into account several aspects of modern financial markets: Trades take place ...
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ISBN:
(纸本)9781728100333
This paper develops a dynamic model of a financial market, using some properties of the formalism of quantum physics. The model aims to take into account several aspects of modern financial markets: Trades take place sequentially and prices change very often in a never ending movement;The state of the market evolves incessantly, the stream of financial information is renewed permanently, and each agent influences the price when he sends an order that is aggregated in a central order book (reciprocally the state of the market influences the decisions of agents). We consider that information is fully and freely available. An essential feature of the model is that information is partitioned in two subsets: Information is effective when it can be processed by an algorithm;If it cannot be processed by an algorithm, it is non-effective. We study the conditions on the nature and the structure of information that make it possible for the market to be efficient or at least powerful. A market is efficient (precisely semi-strong efficient) when the non effective information is negligible compared to effective information. A market is a powerful tool when it integrates information better than any independent agent deciding separately;we call that power the computational strength of the market. We also show that even without semistrong efficiency, during a bubble, there is a period when the market can keep its computational strength.
Combinatorial filters are discrete structures for modeling and reasoning about robotic systems. Such filters are of interest not only because of the potential for reduction of the computational power needed to execute...
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ISBN:
(纸本)9781538630815
Combinatorial filters are discrete structures for modeling and reasoning about robotic systems. Such filters are of interest not only because of the potential for reduction of the computational power needed to execute the filter, but also for the insight they can sometimes provide into the information requirements of certain robotic tasks. It is known that the filter minimization problem -that is, for a given filter, to find a combinatorial filter with the minimal number of states among all filters with equivalent behavioris NP-hard. Intuition might suggest that the well-known notion of bisimulation might be of direct use for this minimization problem. Indeed, the bisimilarity relation -the union of all bisimulation relations over the state space of the original filteris an equivalence relation, and one might attempt to reduce a filter by merging states that are equivalent under this relation. This paper studies this relationship between bisimulation and combinatorial filter reduction. Specifically, we show that every filter minimization problem can be solved by computing a quotient of the input filter with some relation, but that for some filters, the bisimilarity relation is not the correct relation for this purpose. We also characterize the result of the bisimulation quotient operation as the solution to a different, stricter filter minimization problem, and identify several classes of filters for which a variant of bisimulation, called compatibility, can be used to minimize filters in polynomial time.
作者：
Shen, ShenTedrake, RussMIT
Comp Sci & Artificial Intelligence Lab 77 Massachusetts Ave Cambridge MA 02139 USA
We consider the computationally prohibitive problem of stability and invariance verification of large-scale dynamical systems. We exploit the natural interconnected structure often arising from such systems in practic...
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ISBN:
(纸本)9781538654286
We consider the computationally prohibitive problem of stability and invariance verification of large-scale dynamical systems. We exploit the natural interconnected structure often arising from such systems in practice (i.e., they are interconnections of low-dimensional subsystems), and propose a compositional method. We construct independently for each subsystem a Lyapunov-like function, and guarantee that their sum automatically certifies the original high-dimensional system is stable or invariant. For linear time invariant systems, our method produces block-diagonal Lyapunov matrices without structural assumptions commonly found in the literature. For polynomial system tasks, our formulation results in significantly smaller sum-of-squares programs. Demonstrated on numerical and practical examples, our algorithms can handle problems beyond the reach of direct optimizations, and are orders of magnitude faster than existing compositional methods.
We study two multi-robot assignment problems for multi-target tracking. We consider distributed approaches in order to deal with limited sensing and communication ranges. We seek to simultaneously assign trajectories ...
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ISBN:
(纸本)9781538630815
We study two multi-robot assignment problems for multi-target tracking. We consider distributed approaches in order to deal with limited sensing and communication ranges. We seek to simultaneously assign trajectories and targets to the robots. Our focus is on local algorithms that achieve performance close to the optimal algorithms with limited communication. We show how to use a local algorithm that guarantees a bounded approximate solution within O(h log 1/epsilon) communication rounds. We compare with a greedy approach that achieves a 2-approximation in as many rounds as the number of robots. Simulation results show that the local algorithm is an effective solution to the assignment problem.
We present a parallel approximation algorithm for the problem of scheduling jobs on parallel identical machines to minimize makespan which is designed and optimized for running efficiently on the GPU. The algorithm is...
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ISBN:
(纸本)9781538655559
We present a parallel approximation algorithm for the problem of scheduling jobs on parallel identical machines to minimize makespan which is designed and optimized for running efficiently on the GPU. The algorithm is a Polynomial Time Approximation Scheme (PTAS) based on a higher-dimensional dynamic programming approach, where dimensionality refers to the number of variables in the dynamic programming equation characterizing the problem. The main component of our design consists of a novel data-partitioning technique that is employed to accelerate the higher-dimensional dynamic programming component of the algorithm. We present performance results to demonstrate how our proposed design improves the GPU utilization and makes it possible to solve large higher-dimensional dynamic programming problems with the limited GPU memory. Experimental results show that the GPU implementation outperforms the optimized OpenMP implementation of the approximation algorithm.
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