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I discuss various formulations of stochastic Einstein locality(SEL), which is a version of the idea of relativistic causality,that is, the idea that influences propagate at most as fastas light. SEL is similar to Reichenbach's Principle of the CommonCause (PCC), and Bell's Local Causality. My main aim is to discuss formulations of SEL for a fixed backgroundspacetime. I previously argued that SEL is violated by the outcomedependence shown by Bell correlations, both in quantum mechanicsand in quantum field theory. Here I reassess those verdictsin the light of some recent literature which argues that outcomedependence does not violate the PCC. I argue that the verdictsabout SEL still stand. Finally, I briefly discuss how to formulate relativistic causalityif there is no fixed background spacetime.

1 Introduction

2Formulating Stochastic Einstein Locality

2.1 Events and regions

2.2 The idea of SEL

2.3 Three formulations of SEL

2.3.1The formulations

2.3.2Comparisons

2.4 Implications betweenthe formulations

2.4.1 Conditions forthe equivalence of SELD1and SELD2

2.4.2 Conditions for theequivalence of SELS andSELD2

3 Relativistic Causality in the Bell Experiment

3.1 The background

3.1.1 The Bell experiment reviewed

3.1.2My previous position

3.2 A common common cause? The Budapestschool

3.2.1 Resuscitatingthe PCC

3.2.2 Known proofs of aBell inequality need a strongPCC

3.2.3 Two distinctions

3.2.4Szabó's model

3.2.5A common common cause is plausible

3.2.6 Bell inequalitiesfrom a weak PCC: the Bern school

3.3 SEL in the Bell experiment

3.3.1 PCC and SEL are connectedby PPSI

3.3.2 The need forother judgments

3.3.3 Weak vs.strong SELD

4 SEL in Algebraic Quantum Field Theory

4.1 The story so far

4.2 Questions

4.2.1 Our formulations

4.2.2 The BudapestandBern schools

5 SEL in DynamicalSpacetimes

5.1 SEL for metric structure?

5.2 SEL for causalsets?

5.2.1 The causal set approach

5.2.2Labelled causalsets; general covariance

5.2.3 Deducing thedynamics

5.2.4The fate of SEL

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6.

The reflection of hydrogen atoms from lithium fluoride

Thomas H. Johnson 《Journal of The Franklin Institute》1930,210(2):135-152

The paper describes the phenomena associated with the reflection of a sharply defined beam of hydrogen atoms from a crystal of LiF. Of primary interest is the fact that the atoms show interference effects in agreement with the wave mechanics theory and plane grating diffraction patterns are photographed. Evidence of the thermal agitation of the surface ions is obtained from the diffuse reflection with surrounds the specular beam.The Schrödinger wave equation for the motion of a free particle of mass m is

▽^{2} ψ ? 4πmi h ?ψ ?t = 0 (I)

. The solution of this equation corresponding to the kinetic energy

mv^{2} 2

is

ψ = Ae^{2πi(vt?σ_{x}x?σ_{y}y?σ_{x}z)}, (2)

where

v  mv^{2} 2 and σ mv h

. The motion of such a particle should have the characteristics of a plane wave of frequency ν and wave-length

λ = 1 σ

. The experiments of various investigators¹ have shown the validity of the wave theory of the motion of the free electron and have given values of the wave-length in agreement with the theory.The free motion of atoms, ions and molecules should likewise have wave characteristics. In the case of the hydrogen atom, as the simplest example, the complete wave equation may be written in the form

I m ▽^{2} x,y,zψ + I μ ▽^{2} η,μζψ ? 8π^{2} μ?ψ mh^{2} η^{2} + μ^{2} + ζ^{2}

? 4πi h ?ψ ?t = 0, (3)

where x, y, z, are the coördinates of the center of mass of the atom and ξ, η, ζ the coördinates of the electron with respect to the center of mass. If m_? and m₊ are the masses of electron and proton, m and μ have the significance

m = m_{?} + m_{+} and I μ = I m_{?} + I m_{+}

. Equation (3) is solved by

ψ = U_{1} (x,y,z) U_{2} (η, ν ζ) ?^{2πiEth}

, where E may have a continuous set of values and represents the total energy. U₁ and U₂ must satisfy the equations

▽_{1}^{2} U_{1} + 8π^{2} mβU_{1} h^{2} = 0, (4)

and

▽_{2}^{2} U_{2} + 8π^{2} μ h^{2} (α ? μ? m η^{2} + ν^{2} + ζ^{2}) U_{2} = 0 (5)

, where

α + β + E

. 相似文献

7.

Bayes not Bust! Why Simplicity is no Problem for Bayesians

Dowe David L.; Gardner Steve; Oppy Graham 《The British journal for the philosophy of science》2007,58(4):709-754

The advent of formal definitions of the simplicity of a theoryhas important implications for model selection. But what isthe best way to define simplicity? Forster and Sober ([1994])advocate the use of Akaike's Information Criterion (AIC), anon-Bayesian formalisation of the notion of simplicity. Thisforms an important part of their wider attack on Bayesianismin the philosophy of science. We defend a Bayesian alternative:the simplicity of a theory is to be characterised in terms ofWallace's Minimum Message Length (MML). We show that AIC isinadequate for many statistical problems where MML performswell. Whereas MML is always defined, AIC can be undefined. WhereasMML is not known ever to be statistically inconsistent, AICcan be. Even when defined and consistent, AIC performs worsethan MML on small sample sizes. MML is statistically invariantunder 1-to-1 re-parametrisation, thus avoiding a common criticismof Bayesian approaches. We also show that MML provides answersto many of Forster's objections to Bayesianism. Hence an importantpart of the attack on Bayesianism fails.

Introduction
TheCurve Fitting Problem
2.1 Curves and families of curves
2.2 Noise
2.3 Themethod of Maximum Likelihood
2.4 ML and over-fitting
Akaike's Information Criterion(AIC)
The Predictive Accuracy Framework
The Minimum MessageLength (MML) Principle
5.1 The Strict MML estimator
5.2 Anexample: Thebinomial distribution
5.3 Properties ofthe SMML estimator
5.3.1  Bayesianism
5.3.2  Languageinvariance
5.3.3Generality
5.3.4  Consistencyand efficiency

5.4 Similarity to false oracles
5.5 Approximationsto SMML
Criticisms of AIC
6.1 Problems with ML
6.1.1  Smallsample biasin a Gaussian distribution
6.1.2  Thevon Misescircular and von Mises—Fisherspherical distributions
6.1.3  The Neyman–Scottproblem
6.1.4  Neyman–Scott,predictive accuracyandminimum expected KL distance

6.2 Otherproblems with AIC
6.2.1  Univariate polynomial regression
6.2.2  Autoregressiveeconometric time series
6.2.3  Multivariatesecond-orderpolynomial modelselection
6.2.4  Gapor no gap:a clustering-like problem forAIC

6.3 Conclusionsfrom the comparison of MML and AIC
Meeting Forster's objectionsto Bayesianism
7.1 The sub-family problem
7.2 Theproblem of approximation,or, which framework forstatistics?
Conclusion

Details of the derivation of the Strict MMLestimator
MML, AIC and the Gap vs. No Gap Problem
B.1 Expectedsize of the largest gap
B.2 Performanceof AIC on thegap vs. no gap problem
B.3 Performanceof MML in thegap vs. no gap problem

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8.

Linear time-variant systems: Lyapunov functions and invariant sets defined by Hölder norms

Octavian Pastravanu Mihaela-Hanako Matcovschi 《Journal of The Franklin Institute》2010,347(3):627-640

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9.

Hybrid L1×l1-gain analysis of T-S fuzzy positive impulsive systems

《Journal of The Franklin Institute》2022,359(15):8218-8242

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10.

Quad-rotor adaptive sliding mode control using only position and yaw sensors: Generalized relative degree approach

《Journal of The Franklin Institute》2022,359(1):492-519

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11.

Cooperative convex optimization with subgradient delays using push-sum distributed dual averaging

《Journal of The Franklin Institute》2021,358(14):7254-7269

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12.

中国金腰属的研究(续)

潘锦堂《中国科学院研究生院学报》1986,24(3):203-214

This paper deals with the taxonomy and geographic distribution of the ge- nus Chrysosplenium L. in China. Based on the characters and evolution of the seed, capsule, disk, ovary and leaf, the species of this genus can be grouped into 2 subgenera, 5 sections and 16 series. There are 2 subgenera, 5 sections and 11 series in China. They are as follows: I. Subgen. Gamosplenium Maxim. emend. J. T. Pan Leaves alternate. Lectotype: Chrysosplenium carnosum Hook. f. et Thoms. 1. Sect. Alternifolia Franch. emend. J. T. Pan Seeds smooth and glabrous. Type: Chrysosplenium alternifolium L. (1) Ser. Nudicaulia Maxim. emend. J. T. Pan Disk obscure or absent; ovary nearly half-inferior, sometimes mostly inferior; cap- sule generally subtruncate and emarginate at top and bilobed with equal and horizontal- ly divaricate or suberect lobes; seeds smooth and glabrous. Type: Chrysosplenium nudicaule Maxim. (2) Ser. Alternifolia Maxim. emend. J. T. Pan Disk 8-lobed; ovary nearly half-inferior; capsule generally subtruncate and emar- ginate at top, and bilobed with equal and horizontally divaricate lobes; seeds smooth and glabrous. Type: Chrysosplenium alternifolia L. 2. Sect. Nephrophylloides Turcz. Seeds minutely papillose or pilose. Type: Chrysosplenium sedakowii Turcz. (1) Ser. Macrophylla Franch. emend. J. T. Pan Disk obscure or absent; ovary nearly half-inferior; capsule nearly truncate and em- arginate at top, and bilobed with equal lobes; seeds minutely papillose. Type: Chrysosplenium macrophyllum Oliv. (2) Ser. Ovalifolia Maxim. emend. J. T. Pan Disk generally 8-, rarely 4-, lobed, papillae absent around disk; ovary mostly infe- rior; capsule subtruncate and emarginate at top; seeds minutely papillose or pilose. Type: Chrysosplenium ovalifolium M. Bieb. ex Bunge (3) Ser. Lanuginosa Hara, emend. J. T. Pan Papillae numerous, brown around reduced disk; ovary mostly inferior; capsule ne- arly truncate and emarginate at top; seeds minutely papillose. Type: Chrysosplenium lanuginosum Hook. f. et Thoms. II. Subgen. Chrysosplenium Leaves opposite. Type: Chrysosplenium oppositifolium L. 1. Sect. Trichosperma J. T. Pan, sect. nov. Capsule not truncate at top, and bilobed with subequal, suberect or divergent lobes. Type: Chrysosplenium trichospermum Edgew. ex Hook. f. et Thoms. This section is divided into 4 series in the world, with only 1 in China. (1) Ser. Nepalensia Maxim. emend. J. T. Pan Disk obscure or absent; ovary generally mostly inferior; cassule not truncate at top, and bilobed with subequal and suberect or divergent lobes; seeds smooth and gla- brous. Type: Chrysosplenium nepalense D. Don 2. Sect. Grayana J. T. Pan, sect. nov. Capsule bilobed with distinctly unequal and ascending lobes. Type: Chrysosplenium grayanum Maxim. This section consists of 4 series in the world, with 3 series in China. (1) Ser. Sinica Maxim. emend. J. T. Pan Disk obscure or absent; ovary nearly half-superior; capsule bilobed with distinctly unequal and ascending lobes; seeds minutely papillose. Type: Chrysosplenium sinicum Maxim. (2) Ser. Esulcata Franch. emend. J. T. Pan Disk (4)-8-lobed; ovary generally half-inferior; capsule bilobed with unequal and ascending lobes; seeds minutely papillose or pilose. Lectotype: Chrysosplenium dubium J. Gayex DC. (3) Ser. pilosa maxim. emend. J. T. Pan Disk obscure or absent; ovary nearly half-inferior; capsule bilobed with distinctly unequal and ascending lobes; seeds distinctly longitudinally ll-18-costate and minu- tely papillose or tuberculate on the ridge. Type: Chrysosplenium pilosum Maxim. 3. Sect. Chrysosplenium Capsule nearly truncate and emarginate at top, and bilobed with equal and horizon- tally divaricate lobes. Type: Chrysosplenium oppositifolium L. (1) Ser. Romosa J. T. Pan, ser. nov. Disk distinctly 8-lobed, papillae sparse, brown around disk; ovary mostly inferior; ca- psule nearly truncate and emarginate at top, and bilobed with equal and horizontally divaricate lobes; seeds smooth and glabrous. Type: Chrysosplenium ramosum Maxim. This series is monospecific one, also occurring in China, namely C. ramosum Maxim. (2) Ser. Delavayi Hara Disk distinctly 8-lobed, Papillae sparse, brown around the disk; ovary mostly infe- rior; capsule nearly truncate and emarginate at top, and bilobed with equal and hori- zontally divaricate lobes; seeds distinctly longitudinally 10-16-costate and transverse- ly striate on the ridge. Type: Chrysosplenium delavayi Franch. This series can be considered as the most advanced one in the Chrysaspleninm L. So far, the Chrysosplenium L. comprises 64 species in the world, among which 1 spe- cies is found in North Africa, 2 in South America, 4 in Europe, 5 in North America, 56 in Asia, of which 3 occur in Sikkim, 5 Bhutan, 5 Mongolia, 6 north Burma, 6 Korea, 7 north India, 8 Nepal, 12 Japan, 17 U.S.S.R. (of which 3 also in Europe), 34 China (in- cluding 22 endemic species and 3 new species). In China, Fujian and Guangdong Provinces and Zhuang Autonomous Region of Gu- angxi each has only 1 species, Taiwan, Zhejiang, Shanxi and Hebei Provinces and Uy- gur Autonomous Region of Xinjiang each has 2, Anhui, Jiangxi and Hunan Provinces each has 3, Qinghai Province 4, Heilongjiang, Liaoning and Guizhou Provinces each has 5, Jilin and Hubei Provinces each has 6, Gausu Province 8, Shaanxi Province and Xi- zang (Tibet) Autonomous Region each has 10, Yunnan Province has 11, Sichuan Provi- nce has 14. Thus the distribution centre of this genus should be in the north temperate zone of Asia, and the region covering Shaanxi Gansu, Sichuan, Yunnan and Xizang may be regarded as an important part of this centre. The 7 species of Ser. Nudicaula Maxim. emend. J. T. Pan can be considered as the most primitive ones in this genus. They are mostly distributed in Shaanxi (Qin Ling), south Gansu, southeast Qinghai, southwest Sichuan and nothwest Yunnan of China. This region may be considered as the centre of the origin (or at least differentiation) of this genus. The new species and the new varieties described in this paper are as follows: C. hy- drocotylifolium Levl. et Vant. var. emeiense J. T. Pan, C. taibaishanense J. T. Pan, C. lixianense Jien ex J. T. Pan, C. qinlingense Jien ex J. T. Pan. 相似文献

13.

Adaptive neural-network-based distributed fault estimation for heterogeneous multi-agent systems

《Journal of The Franklin Institute》2022,359(16):9334-9356

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14.

竹亚科酸竹属的研究

赵奇僧朱政德《中国科学院研究生院学报》1991,29(6):517-524

在对竹亚科散生竹全面研究基础上，本文对酸竹属进行了系统的整理和研究，讨论了本属与相近属之间亲缘和区别。本文确认有6种，其中有1新组合和5个新异名。相似文献

15.

Control of homoclinic bifurcation in two-dimensional dynamical systems by a feedback law based on Lp spaces

《Journal of The Franklin Institute》2022,359(10):5097-5124

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