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Dynamic consistency and rectangularity for the smooth ambiguity model

JOURNAL OF ECONOMIC THEORY 2025年 225卷

作者： Savochkin, Andrei Shklyaev, Alexander Galatenko, Alexey Bocconi Univ Bocconi Italy Moscow State Univ Moscow Russia

We study the Smooth Ambiguity decision criterion in the dynamic setting to understand when it can satisfy the Dynamic Consistency and Consequentialism properties. These properties allow one to rewrite the decision criterion recursively and solve for optimal decisions by Dynamic Programming. Our result characterizes the possibility of having these properties through a condition that resembles Epstein and Schneider's (2003) rectangularity condition for the maxmin model. At the same time, we show that Dynamic Consistency and Consequentialism can be achieved for Smooth Ambiguity preferences in a narrower set of scenarios than one would hope for.

关键词： Smooth ambiguity Dynamic consistency Consequentialism rectangularity

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rectangularity VERSUS PIECEWISE rectangularity OF PRODUCT-SPACES

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CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES 1987年第1期30卷 49-56页

作者： TSUDA, K EHIME UNIV DEPT MATHMATSUYAMAEHIME 790JAPAN

We shall discuss relations between rectangularity and piecewise rectangularity of product spaces. In particular, we show that for each positive integer n there exists an n-dimensional, collectionwise normal, non-piece... 详细信息

关键词： 54D20 54F45 Covering dimension normality piecewise rectangularity product space strongly 0-dimensionality rectangularity

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Measuring rectangularity

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MACHINE VISION AND APPLICATIONS 1999年第4期11卷 191-196页

作者： Rosin, PL Brunel Univ Dept Informat Syst & Comp Uxbridge UB8 3PH Middx England

Three new methods for measuring the rectangularity of regions are developed. They are tested together with the standard minimum bounding rectangle method on synthetic and real data. It is concluded that, while all the... 详细信息

关键词： shape descriptor rectangularity region

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A Novel Flow-Balanced Friction Stir Channeling Technology: High rectangularity Design and Channel Formation Mechanisms

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ADVANCED ENGINEERING MATERIALS 2024年第22期26卷

作者： Huang, Yongxian Shan, Cheng Hu, Shengnan Wang, Shenglong Xie, Yuming Ma, Xiaotian Wang, Naijie Meng, Xiangchen Harbin Inst Technol State Key Lab Precis Welding & Joining Mat & Struc Harbin 150001 Peoples R China Harbin Inst Technol Zhengzhou Res Inst Zhengzhou 450046 Peoples R China Beijing Hangxing Machinery Mfg Co Ltd Beijing 100013 Peoples R China

Friction stir channeling (FSC) presents a promising approach for achieving continuous channels in heat exchangers, which are considered as leading candidates for high-efficiency thermal dissipation. However, the irregular cross-sectional shape of prepared channels induces stress concentration and compromises the load-bearing capacity and structural integrity. Herein, flow-balanced FSC (FB-FSC) technology is proposed to fabricate channels with enhanced rectangularity. This technique allows for precise control over the shape, path, position, and arrangement of the channels. The channel formation in FB-FSC is affected by material overflow-reflux behaviors and stick-slip conditions. Material overflows onto the shoulder due to shearing and extraction then refluxes under axial pressure to close the channel. The material stuck to the probe rotates accordingly and is pulled out into the channel cavity to form a deposition layer. By regulating channel formation mechanisms, channel rectangularity of 90.8%, continuous formation of 14 m, minimum spacing of 2 mm, variable arc radius, and gradient distribution are directly achieved via FB-FSC. The FB-FSC technology enables the efficient formation of cooling channels with high quality, which is significant for the design of heat exchangers to realize desired performances. Flow-balanced friction stir channeling is proposed for the fabrication of channels with high rectangularity. Balanced material overflow-reflux behaviors are achieved to get regular channels. Stick-slip condition guides the easing of material deposition behavior. High channel rectangularity achieves 90.8% with excellent processing *** (c) 2024 WILEY-VCH GmbH

关键词： channel formation mechanisms flow-balanced friction stir channeling material overflow-reflux behaviors rectangularity stick-slip condition

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Robust Markov Decision Processes: Beyond rectangularity

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MATHEMATICS OF OPERATIONS RESEARCH 2023年第1期48卷 203-226页

作者： Goyal, Vineet Grand-Clement, Julien Columbia Univ Dept Ind Engn & Operat Res New York NY 10027 USA Ecole Hautes Etud Commerciales HEC Paris Dept Informat Syst & Operat Management F-78350 Jouy En Josas France

We consider a robust approach to address uncertainty in model parameters in Markov decision processes (MDPs), which are widely used to model dynamic optimization in many applications. Most prior works consider the case in which the uncertainty on transitions related to different states is uncoupled and the adversary is allowed to select the worst possible realization for each state unrelated to others, potentially leading to highly conservative solutions. On the other hand, the case of general uncertainty sets is known to be intractable. We consider a factor model for probability transitions in which the transition probability is a linear function of a factor matrix that is uncertain and belongs to a factor matrix uncertainty set. This is a fairly general model of uncertainty in probability transitions, allowing the decision maker to model dependence between probability transitions across different states, and it is significantly less conservative than prior approaches. We show that under an underlying rectangularity assumption, we can efficiently compute an optimal robust policy under the factor matrix uncertainty model. Furthermore, we show that there is an optimal robust policy that is deterministic, which is of interest from an interpretability standpoint. We also introduce the robust counterpart of important structural results of classical MDPs, including the maximum principle and Blackwell optimality, and we provide a computational study to demonstrate the effectiveness of our approach in mitigating the conservativeness of robust policies.

关键词： Markov decision processes robust optimization rectangularity

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A role of rectangularity in perceiving a 3D shape of an object

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VISION RESEARCH 2024年 221卷 108433页

作者： Dvoeglazova, Maria Sawada, Tadamasa HSE Univ Sch Psychol Moscow Russia Amer Univ Armenia Akian Coll Sci & Engn Yerevan Armenia Russian Armenian Slavon Univ Dept Psychol Yerevan Armenia European Univ Armenia Yerevan Armenia

rectangularity and perpendicularity of contours are important properties of 3D shape for the visual system and the visual system can use them as a priori constraints for perceiving shape veridically. The present article provides a comprehensive review of prior studies of the perception of rectangularity and perpendicularity and it discusses their effects on 3D shape perception from both theoretical and empirical approaches. It has been shown that the visual system is biased to perceive a rectangular 3D shape from a 2D image. We thought that this bias might be attributable to the likelihood of a rectangular interpretation but this hypothesis is not supported by the results of our psychophysical experiment. Note that the perception of a rectangular shape cannot be explained solely on the basis of geometry. A rectangular shape is perceived from an image that is inconsistent with a rectangular interpretation. To address this issue, we developed a computational model that can recover a rectangular shape from an image of a parallelopiped. The model allows the recovered shape to be slightly inconsistent so that the recovered shape satisfies the a priori constraints of maximum compactness and minimal surface area. This model captures some of the phenomena associated with the perception of the rectangular shape that were reported in prior studies. This finding suggests that rectangularity works for shape perception by incorporating it with some additional constraints.

关键词： rectangularity Perpendicularity 3D shape perception Manhattan world Carpenter world

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SHAPE rectangularity MEASURES

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INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2012年第6期26卷 1254002-1254002页

作者： Zunic, Dragisa Martinez-Ortiz, Carlos Zunic, Jovisa Ecole Polytech Fed Lausanne IC LARA BC CH-1015 Lausanne Switzerland Fac Econ & Engn Management Novi Sad Serbia Univ Exeter Exeter EX4 4QF Devon England

This paper introduces a family of rectangularity measures. The measures depend on two parameters which enable their exibility, i.e. the possibility to adapt with respect to a concrete application. Several rectangularity measures exist in the literature, and they are designed to evaluate numerically how much the shape considered differs from a perfect rectangle. None of these measures distinguishes rectangles whose edge ratios differ, i.e. they assume that all rectangles (including squares) have the same shape. Such property can be a disadvantage in applications. In this paper, we consider differently elongated rectangles to have different shapes, and propose a family of new rectangularity measures which assigns different values to rectangles whose edge ratios direr. The new rectangularity measures are invariant with respect to translation, rotation and scaling transformations. They range over the interval ]0, 1] and attain the value 1 only for perfect rectangles with a desired edge ratio.

关键词： Shape rectangularity measuring shape image retrieval image processing

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Variations in the morphometric characteristics of Fragilariopsis kerguelensis in the Southwest Pacific sector of the Southern Ocean over the past 40,000 years

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MARINE MICROPALEONTOLOGY 2025年 195卷

作者： Crosta, Xavier Sutre, Thibault Univ Bordeaux CNRS EPHE UMR 5805EPOC F-33405 Pessac France

High-throughput measurements demonstrated the presence of two morphotypes of Fragilariopsis kerguelensis in the Atlantic sector of the Southern Ocean, the proportions of which in downcore samples may be used to reconstruct past sea-surface temperatures quantitatively. We here measured the mean length, width, area, and rectangularity in core SO136-111 to assess variations in both morphotypes in the Polar Front Zone of the western Pacific sector of the Southern Ocean over the past 40,000 years. Mean length, width, and area increased rapidly at the end of the glacial period when the Polar Front migrated southward to reach the core site, ocean temperature increased, and sea ice was no longer present. In contrast, mean rectangularity decreased at the end of the glacial period, when the proportion of the cold-water, high-rectangularity morphotype declined as the ocean warmed at the core site. Downcore patterns and quantitative values of all morphometric characteristics in the southwest Pacific sector agree well with previous studies from the Atlantic sector, suggesting the presence of a similar population of F. kerguelensis in the open Southern Ocean. Nevertheless, rectangularity-based relationships can ultimately produce unrealistic estimates of sea-surface temperatures in core SO136-111 when the proportion of the high-rectangularity morphotype is too low, indicating that these approaches are now limited to temperatures below 3-4 degrees C.

关键词： Fragilariopsis kerguelensis Morphometrics rectangularity Biogeography Sea-surface temperature

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Increasing Biomass Production on Limited Land Area Through an Optimal Planting Arrangement

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BIOENERGY RESEARCH 2018年第1期11卷 13-21页

作者： Oswald, Scott W. Aubrey, Doug P. Univ Georgia Warnell Sch Forestry & Nat Resources Athens GA 30602 USA Univ Georgia Savannah River Ecol Lab Aiken SC 29802 USA

Planting density is a primary consideration in silviculture;however, planting arrangement is often ignored. Most, if not all, forest plantations are arranged in rectangular or square lattices (i.e., grids). Using a simple mathematical model, we investigate the potential influence of planting arrangement on planting density, biomass yield, and rotation period by assuming that efficiently arranging trees is similar to packing congruent circles on a plane. The hexagonal lattice achieves the densest circle packing on a plane;therefore, a hexagonal or triangular lattice arrangement of stems provides the highest planting density for a given spacing. Using packing density to quantify arrangement efficiency, tree crowns in a hexagonal lattice fill approximately 90.7% of available area at initial canopy contact, while tree crowns in a square lattice fill approximately 78.5% of available area at initial canopy contact. The hexagonal lattice permits about a 15% higher density than the square lattice, which allows canopy closure to occur earlier without any change in individual tree growth. Short rotation woody crop (SRWC) systems are excellent candidates under the model's assumptions of level stand with even-age monoculture. If belowground resources are non-limiting, a hexagonal lattice arrangement shortens rotation period and thus optimizes the biomass yield per land area over time. Higher productivity over time is central to sustainable and efficient use of limited area for bioenergy and biomass products.

关键词： Forest productivity Planting density Tree spacing Bioenergy production Hexagonal lattice Triangular lattice Biomass yield rectangularity Short rotation woody crops

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Rectangular Sets of Probability Measures

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OPERATIONS RESEARCH 2016年第2期64卷 528-541页

作者： Shapiro, Alexander Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

In this paper we consider the notion of rectangularity of a set of probability measures from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent risk measures. Consequently, we discuss robust formulations of multistage stochastic optimization problems in frameworks of stochastic programming, stochastic optimal control, and Markov decision processes.

关键词： multistage stochastic optimization rectangularity risk-averse optimization robust optimal control and Markov decision processes dynamic programming coherent risk measures time consistency

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