Invariant Rules Research Articles

A novel causal feature learning-based domain generalization framework for bearing fault diagnosis with a mixture of data from multiple working conditions and machines

Data distribution shift usually deteriorates the performance of traditional supervised learning-based fault diagnosis models. Such issue can be well addressed by domain generalization fault diagnosis methods even if the test data are unavailable in training stage. However, most of these methods are designed and validated only for a single device, and also require the domain labels being provided, which hampers their further application. Therefore, this paper focuses a more realistic scenario, where the source training set is a mixture of data from multiple operation conditions and devices with domain information unavailable. First, a causal analysis is made for the task of domain generalization fault diagnosis, and a structural causal model (SCM) that describes the data generation process is constructed based on the relationships among different variables. A new learning rule for domain generalization, named object-conditional domain invariant (Obj-DI) rule, is also elicited. Then, to achieve domain generalization fault diagnosis, a three-stage based method named LOODG is proposed. Potential domains are mined and samples are given domain labels in latent domain discovery stage. Samples belonging to same object but different domains are explored in object discovery stage. In Obj-DI based causal feature learning stage, generalizable causal features are learned to finally obtain a generalized model. Experiments are conducted on tasks designed from three datasets, and the results demonstrate the superiority of the proposed method.

Historia sztuki w polu metodologii. Aktualne problemy i wyzwania

At the end of the 20th century, the theory of art history shifted from the area of methodology understood as a normative field of the philosophy of science to the area of the social practice of constructing knowledge. The term “art historical methodology” itself became trivialized when its meaning was detached from the horizon of epistemology and became extremely inclusive, encompassing all methods practised in the discipline, with a method being considered to be the use of any theory as a tool of interpretation. As a consequence, the basic problem of scientific methodology, which is the critical assessment of explanatory and interpretive theories due to the value of their justification, is not addressed in the self-reflection of contemporary art history. The retreat from the rigors of methodology was related to the reception of structuralism, initiated by Ernst Gombrich in the book Art and Illusion. Popper’s model of situational logic as a method of historical explanation of works of art was transformed into a structuralist model, referring to constant rules of pictorial representation, symbolization and communication. Michael Fried and Norman Bryson formulated their own theories of invariant rules defining the necessary initial conditions for the formation and reception of pictures, so that individual works could be interpreted in terms of these rules and, as a result, confirm the general theory, which created a vicious circle. Structuralist theories did not function as hypotheses requiring critical testing, but as interpretive codes that served to read each work of art within their own conceptual system. The next step in the process of the reception of structuralism was the development of theories defining general rules that would govern the discursive practice of art history, and the detection of which at the basis of this practice would discredit or invalidate its epistemological dimension. Hayden White’s narrativism was the theory that historical discourse is subject to narrative conventions, not to the laws of logic and the rigors of methodology that serve to limit the pool of alternative explanations or interpretations. This theory was intended to justify the pluralism of equal versions of history as a politically correct idea, appropriate for a “democratic” model of knowledge. Theorists developing White’s theses in the field of art history claimed that the discursive practice of this discipline was not governed by methodological rules but by political motivations (Keith Moxey) or aesthetic principles of artwriting (David Carrier). After the phase of open denial of the dependence of the art history discourse on methodology, the theory of the discipline turned into an analysis of techniques for building this discourse, which no longer included methodological issues, as in James Elkins’ book Our Beautiful, Dry, and Distant Texts. A critical review of theories separating art history from methodology leads to the conclusion that they are untenable. It is impossible to maintain the scientific status of our discipline without respecting the principles of methodology founded in the contemporary philosophy of science.

The Conceptual Flaws of Decentralized Automated Market Making

Decentralized exchanges (DEXs) are an essential component of the nascent decentralized finance (DeFi) ecosystem. The most common DEXs are so-called automated market makers (AMMs): smart contracts that pool liquidity and process trades as atomic swaps of tokens. AMMs price transactions with a deterministic liquidity invariance rule that only uses the AMM’s token deposits as inputs and that has no precedent in traditional finance. Yet, in the context of transparent and open blockchain operations, any liquidity invariance pricing function allows so-called sandwich attacks (akin to front running) that increase the cost of trading and threaten the long-term viability of the DeFi ecosystem. Invariance pricing is also not regret free. Linear pricing rules have similar problems except for uniform pricing, which has regret-free prices and limits sandwich attack profits but which invites excessive order splitting. Comparing trading costs using a model of liquidity provision, constant product pricing is often cheaper except when the variance of the underlying asset is small or when the order is large. This paper was accepted by Will Cong, Special Section of Management Science: Blockchains and Crypto Economics. Funding: A. Park received financial support from the Global Risk Institute and the Social Sciences and Humanities Research Council of Canada [Grant 435-2017-0647]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2021.02802 .

A strongly universal cellular automaton on the heptagrid with five states, but with not rotation invariance of the rules

ABSTRACT In this paper, we prove that there is a strongly universal cellular automaton on the heptagrid with five states under the relaxation of the assumption of rotation invariance for the rules. The result is different from that of a previous paper of the author with six states but with rotationally invariant rules. Here, the structures is more constrained than in the quoted paper with six states and rotation invariance of the rules.

Potential artifacts in conservation laws and invariants inferred from sequential state estimation

Abstract. In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as source or sink terms in conservation equations for heat, salt, mass, and momentum. These artificial terms obscure the inference of the system's variability or secular changes. Furthermore, for the purposes of calculating changes in important functions of state variables such as total mass and energy or volumetric current transports, results of both filter and smoother-based estimates are sensitive to misrepresentation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here, toy models of a coupled mass–spring oscillator system and of a barotropic Rossby wave system are used to demonstrate many of the issues that arise from such misrepresentations. Results from Kalman filter estimates and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in “reanalysis-like” estimates require a full understanding of models, observations, and underlying error structures. Application of smoother-type methods that are designed for optimal reconstruction purposes alleviate some of the issues.

EAPOTc: An integrated empirical interatomic potential optimization platform for compound solids

The extension of interatomic potentials from elemental solids to compound ones causes a bottleneck in atomistic simulations of multi-component solids such as intermetallic compounds and solid solutions. In contrast to several extensive tools released to construct elemental potentials, such as MEAMfit and ATOMICREX, very little software has been specifically designed for multi-component solids. Herein, we extend our recently proposed software EAPOTs (Empirical interAtomic POTentials for single elemental solids) to interatomic potentials of compound solids. This new software-termed as EAPOTc or the integrated Empirical interAtomic POTential optimization platform for compound solids-provides robust multi-level objective optimization strategies with various cross potential functions and extensive combinations of multiple targets such as energy, stress, force, and elasticity. Compatibility with published elemental potentials was also implemented in EAPOTc to ensure seamless combinations of different sources of elemental potentials by using the transformation invariance rules without reliability loss for the original elemental potentials. Similar to our EAPOTs code, a high-throughput (HT) scheme was designed based on automatic communication using first-principles code (e.g., VASP) to retrieve the derived properties based on energy, stress, force, and elasticity; in addition, multiple objective optimization procedures were included. The efficiency and flexibility of EAPOTc were critically validated and tested for various metallic and covalent compound systems, including HT implementation and applicability testing for extreme scenarios. Our software demonstrated several advantages, such as a concise and user-friendly graphical user interface, extensive compatibility between elemental potentials, robust optimization schemes, and a high degree of functional integration.

Ograniczenia jawności postępowania w sprawach cywilnych w dobie pandemii ? potrzeba chwili czy trwałe rozwiązanie?

Pandemia koronawirusa, wprowadzanie tzw. lockdownu i daleko idących ograniczeń społecznych dały asumpt do podjęcia działań ustawowych z jednej strony ułatwiających i propagujących przeprowadzanie rozpraw online, z drugiej jednak dezawuujących rolę i rangę zasady jawności na rzecz realizacji postulatu szybkości i sprawności postępowania. Zasada jawności postępowania formalnie zagwarantowana w art. 45 Konstytucji RP oraz potwierdzona w przepisach ustrojowych staje się, na skutek coraz liczniejszych odstępstw wprowadzanych do przepisów procesowych, zasadą pozorną. Kontestowanie wprowadzanych rozwiązań jest jednak trudne w świetle argumentu, że mechanizmy te mają mieć charakter tymczasowy, a ustawodawca kieruje się potrzebą ochrony konstytucyjnych wartości w postaci bezpieczeństwa, porządku i zdrowia publicznego. Dążenie do usprawniania przebiegu postępowań sądowych i zapewnienia operatywności instytucji procesowych wielokrotnie wiąże się z potrzebą oraz koniecznością ważenia wartości i pryncypiów. Od legislatora nie należy żądać utrzymywania sztywnych i niezmiennych zasad w ich czystej formie, lecz powinno się oczekiwać dbałości o to, żeby wprowadzane instytucje nie zaprzeczały fundamentalnym regułom obowiązującym w danej dziedzinie prawa.

Turn-Taking in the Surfing Lineup

This article addresses the specific issue of rules and turn-taking in surfing from an ethnomethodological approach. The naturally occurring coordination of turn-taking of surfers riding ocean waves permits us to examine the nature of organizing local orderlinesses. Operating without officials or external supervision, surfers find ways to enhance safety and keep conflict to a minimum, while avoiding a burdensome structure of rule governance. The microsocial structures that envelop them expose unexpected properties of rules, including a fundamental “occasioned” character that is respectful of the complexity of their affairs. Further, moralities are dependent upon local contingencies that are less than stable and too numerous and shifting to be accounted for by a comprehensive and invariant rule set.

PRESCHOOLERS’ REGULATORY FUNCTIONS IN THE CONTEXT OF A NORMATIVE SITUATION

Methodology. The development of a child’s self-regulation at preschool age is conditioned by the peculiarities of a cultural situation, which is represented by a set of invariant normative rules. Mastering the invariant cultural rules is understood as shaping the child’s cultural congruence and reflects the child’s development as an agent of his/her culture. To investigate the cognitive aspect of self-regulation, A. Miyake’s model of the “regulatory functions” was used. Within this model three interrelated and simultaneously independent factors were determined: working memory, the ability to shift attention and constraint control. The study purpose was to find out how the assimilation of the cultural rules of a “normative situation” (N. E. Veraksa) influenced the regulatory functions of preschool age children of different genders. Methods and research scheme. 113 children of 5–6 years old (58 boys and 55 girls) who attended the senior groups of the nursery schools of Sloviansk, Donetsk region and Pereiaslav,  Kyiv region and 113 mothers (from 24 to 44 years old) participated in the study. Cultural congruence was assessed using the questionnaire for parents that contained the invariant rules for children of 5–6 years old and allowed assessing the extent to which their children could comply with these rules. The regulatory functions was examined using the set of techniques which included the subscales of the testing battery NEPSY-II (Korkman et al., 2007) and the technique DCCS (Zelazo, 2006). Results. The verbal memory of the boys with higher cultural congruence was developed better, and the boys with the low congruency were able to shift their attention better from one task to another and better retain visual images. As for the girls, the development of their regulatory functions did not depend on their cultural congruence. Conclusions. The data obtained indicate the gender specificity of the influence of cultural congruence on the children’s regulatory functions, which makes it possible to refine and compare the results with other studies. &nbsp

Registration of Terrestrial Laser Scanning Surveys Using Terrain-Invariant Regions for Measuring Exploitative Volumes over Open-Pit Mines

Terrestrial laser scanning (TLS) techniques have been widely used in open-pit mine applications. It is a crucial task to measure the exploitative volume of open-pit mines, within a specific time interval. One major challenge is posed, however, when conducting accurate registrations for temporal TLS surveys in continuously changing areas, created by excavation activities. In this paper, we propose a coarse-to-fine registration method, based on terrain-invariant regions (TIR), for temporal TLS surveys. More specifically, an approximate four-point congruent set (4PCS) of temporal TLS surveys is first identified, based on affine invariant rules. Second, a set of correspondences among temporal TLS surveys were collected by matching multi-scale sparse features of the 3D neighbors, centered at the approximate 4PCS. Third, the correspondences were used to estimate a rigid motion between the overlapping TLS surveys for the coarse registration, according to which the initial TIR from temporal TLS surveys were identified. Finally, the rigid motion between temporal TLS was iteratively optimized, based on the point clouds, only from the TIR. Based on the fine-level registered TLS surveys, Digital Elevation Models (DEMs) can be generated to calculate the exploitative volume, through a DEM differential. We applied the proposed method to two open-pit mines in China, and also compared our method with five state-of-the-art methods for registering temporal TLS surveys. Experimental results indicated that the proposed method achieved a higher registration accuracy than the state-of-the-art methods. Based on the registered result, our method achieved a 98.03% overall accuracy for measuring the exploitative volume, compared to in-situ measurement.

Kim Daerak’s Perception of Reality and Responses to It

한말까지 지식인들에게 성리학적 가치체계는 국가와 사회를 지도하는 이념이었다. 유교로 자신의 삶을 성찰하고 세계를 바라보았던 지식인들에게 성리학은 절대 불변의 법칙처럼 여겨졌다. 그러나 19세기 후반 서구 세력의 등장으로 이 가치관은 큰 혼선을 맞게 되었다. 유학자 들은 서구 문명에 놀라움을 금치 못하였다. 당시 사회지도자 층이었던 유학자들은 서구와 통 상을 해서는 안된다는 집단과 제한적으로 수용하자는 부류 그리고 빨리 받아들여야한다 사람들로 나뉘었다. 그런데 한 사람이 이런 세 가지 유형을 자발적으로 경험한 사람은 매우 희소하다. 백하 김대락은 이런 유형의 독립운동가이다. 그는 초기에는 완강한 위정척사계열의 보수주의자로 의병전쟁을 지원하였다. 1907년 무렵에는 매부인 이상룡의 설득으로 「대한협회보」와 같은 잡지를 읽고 협동학교 교사(校舍)로 자신의 집을 내놓을 정도로 계몽운동가로 변화하였다. 나라가 일제에 의해 강제로 병합되자 그는 울분을 참지 못하고 가족과 친척들을 데리고 만주 서간도로 망명길에 나섰는데 이 때 그의 나이 66세였다. 김대락은 만주 서간도 유하현 삼원포로 망명한 이후 교민사회의 좌장으로서 교민들의 단합 을 도모하고, 독립투쟁에 대한 용기를 불어 넣는데 힘썼다. 교민들은 경학사라는 독립운동 단체를 조직하고, 신흥학교라는 교육기관을 세워 청소년들의 교육에 힘썼다. 김대락은 권유문이 라는 글을 지어 학생들에게 학업에 정진해달라는 당부를 하였다. 교민 사회의 결속을 다지기 위해 자치조직인 공리회를 조직하여 구성원들의 단결을 도모하였다. 그는 만주에서의 힘든 생활을 고스란히 일기에 기록하여 후세에 전했다. 특히 그는 분통가 라는 국한문 혼용체의 가사를 지었는데 그 내용은 독립정신을 고취시키는 것이었다. 이 가사는 독립의식을 고취시키고, 나아가서 미래에 독립된 조국은 입헌정치와 공화정이 시행되는 자유로운 국가가 되어야 한다고 역설하였다.The value system of Neo-Confucianism was the ideology that intellectuals led the country and society until the latter era of the Joseon Dynasty. The intellectuals who had reflected on their lives and looked at the world with Confucianism considered Neo-Confucianism as the invariable rule. However, the appearance of the Western powers in the late 19th century caused much confusion in this value. Confucian scholars were very surprised at Western civilization. The Confucian scholars who were the leadership of society at that time were classified into the group who said not to engage in commerce with the West, the class who adopt the Western culture restrictively, and the people who insisted to accept it quickly. However, there were few persons who experienced these three types voluntarily. Baekha Kim, Daerak was this kind of an independent activist. He joined the army raised in the cause of justice as a stubborn conservative of Wijeong Cheoksa at the initiatory stage. In 1907, he read magazines like 「 Daehanhyeophoibo」 as Lee, Sangryong, his sister’s husband persuaded him to do and changed to be an enlightenment activist who allowed Hyeopdong School to use his house as a school building. As Japan was forced to occupy Korea, he could not control his anger and he sought refuge in West Yanji, Manchuria, China with his family and relatives when he was 66 years old. After seeking refuge in Sanyuanpu, Liuhe Xian, West Yanji, Manchuria, China, he promoted unity of overseas Koreans as the top of the table of the society of overseas Koreans and strived to inspire bravery of struggles for independence. The overseas Koreans organized an independence movement group called Gyeonghaksa and worked for juvenile education by founding a school called Shinheung School. Kim, Daerak requested students to devote themselves to study by writing a composition called Recommendations. And he promoted unity of the members by organizing Gongrihoi, the independent organization to strengthen the solidarity of the society of overseas Koreans. He recorded his tough life in Manchuria with nothing missed in his diary and transmitted to posterity. Especially, he wrote the words of a song of a mixed style of writing Korean with Chinese characters in it called 「Buntongga」 . This words of the song instilled independent consciousness and furthermore, emphasized that the independent country of the future must be the free country which conducts a constitutional government and secular republic.

Acousto-elastic theory for the coupling parameters in terms of nonlinear elastic, piezoelectric, electrostrictive, and dielectric constants in trigonal and hexagonal crystalline systems: applied in the crystal and solid-state physics

The aim of the acousto-elastic theory was to measure ultrasonic velocity changes which characterize the mechanical nonlinearity of a prestressed material. In this context, our purpose is to tabulate the invariant third-order elastic coefficients including the piezoelectric, electrostrictive, and dielectric corrections. The investigation is limited to trigonal and hexagonal crystalline structures, which represent the most often encountered symmetry classes for the piezoelectric materials. In fact, the enumeration includes the high-order tensors involved in the analysis of nonlinear behaviors associated with various electromechanical coupling forms. The obtained results are extensions to previous calculations in this area which bring some corrections to certain published combinations related to the invariance rules. The numerical procedure built using the software MATLAB is based on coordinate system transformations performed on the eigenbasis of their corresponding symmetry axes three- and sixfold. In this purpose, we found some contradictions between our results and a former paper published in Journal of Applied Physics. To the authors’ knowledge, rechecking of the relationships between the invariant third-order constants and comparison with this last reference has not been discussed yet. The relationships between the invariant third-order coefficients presented in this work provide a number of attractive properties for use in mechanical and physical applications.

Circumferential Binary Feature Extraction and Matching Search Algorithms

Binary features allow for the effective comparison, fast calculation, and compact storage in image matching and localization. Binary feature extraction algorithms, however, tend to have poor mirror invariance, and search algorithms that match binary features have a lower inlier ratio. To address these issues, we employ a scale space pyramid to simulate human eye imaging and then detect FAST (FAST feature detector) points at each level in the pyramid and calculate the FAST point feature's orientation with an image intensity centroid. We propose circumferential binary string mirror invariance rules and a circumferential binary feature (CBF) extraction algorithm to enhance the mirror invariance of binary features, and a fast calculate bitmap (FCBM) algorithm and bitmap local sensitive hash (BMLSH) to improve the inlier ratio of matching binary features. Experiments show that the CBF performs well in mirror invariance and has stronger adaptability and that BMLSH searches inliers more efficiently.

Hysteresis behaviors of compressor rotating stall with cusp catastrophic model

Rotating stall is a complex nonlinear dynamic phenomenon which is always characterized by catastrophe and hysteresis in high aerodynamic-loading compressor. Exploring the key contributing factors and characteristic rules of hysteresis is very important for compressor design and flow instability control. In this paper, a novel model method is proposed to analyze the hysteresis behaviors to extend the understanding of compressor rotating stall. The equilibrium states of compressor system under different conditions are first described based on Moore-Greitzer model. Then, through assessing the stability of the equilibrium points by Liapunov's theorem, the ratio of shutoff head to compressor characteristic semi-height is found to affect the stall hysteresis: the size of hysteresis loop will gradually decrease, even disappear with the increase of the ratio. Combing the effects of both the ratio and throttle coefficient, the hysteresis behaviors of compressor stall under multi-parameters can be found to be consistent with the topological properties of cusp catastrophic model by Thom’s catastrophe theory. Finally, according to topological invariant rules, from the perspective of potential function, the equilibrium surface equation of compressor system is developed by standard cusp catastrophic model to describe the various hysteresis behaviors of compressor rotating stall along different control routes.

Catastrophe-Theory-Based Modeling of Airfoil-Stall Boundary at Low Reynolds Numbers

Airfoil stall at low Reynolds numbers is a complex nonlinear dynamic phenomenon, which is characterized by catastrophe and hysteresis. It is difficult but important to mathematically describe the stall points under different Reynolds numbers. In this paper, taking the clockwise hysteresis as an example, a modeling method is proposed to describe the boundary of static airfoil stall according to the topological properties and physical characteristics of airfoil stall. Through numerical simulations, the lift characteristics of an airfoil at different Reynolds numbers are computed, and it is found that Reynolds number can affect not only the catastrophe and hysteresis of airfoil stall, but also the size of the hysteresis loop. Next, the static stall at low Reynolds numbers and the dynamic behavior described by the cusp-catastrophic model are proved to have a similarity in spatial topology and physical properties. According to the topological invariant rules, the topological-mapping relationship between the catastrophe-point set of the cusp-catastrophic model and the stall points of the airfoil stall is established through the development of an accurate topological-transformation function. Consequently, the catastrophe lines described by the cusp-catastrophic model can be used to represent the static-stall boundary of the airfoil at different Reynolds numbers. The effect of model description is verified by comparing the model-predicted values with the simulated values, and the error is found to be less than 1%.

Resale Price Maintenance: Consignment Agreements, Copyrighted or Patented Products and the First Sale Doctrine

The rule of reason adopted for resale price maintenance in the Supreme Court’s Leegin decision, which upset the century old Dr. Miles rule of per se illegality, requires some reconsideration of a number of issues about antitrust treatment of RPM. Under the old per se rule, bona fide “consignment” agreements were not covered by Section 1 of the Sherman Act at all because there was said to be no qualifying “agreement” between the supplier and the dealer. Rather the dealer was simply said to be acting as an agent of the seller. However, insofar as RPM produces competitive dangers, such as those occasioned by powerful dealers, these harms do not seem to depend on whether the transfer from the supplier to the dealer was a sale or a consignment. Secondly, while Leegin took RPM in one direction, applying a rule of reason to conduct that had previously been unlawful per se, the Supreme Court’s Quanta Computer decision went in the other direction, restoring an invariant rule prohibiting resale price maintenance requirements from being enforced by means of patent infringement suits.

Cumulative Dynamics of Independent Information Spreading Behaviour: A Physical Perspective

The popularization of information spreading in online social networks facilitates daily communication among people. Although much work has been done to study the effect of interactions among people on spreading, there is less work that considers the pattern of spreading behaviour when people independently make their decisions. By comparing microblogging, an important medium for information spreading, with the disordered spin glass system, we find that there exist interesting corresponding relationships between them. And the effect of aging can be observed in both systems. Based on the analogy with the Trap Model of spin glasses, we derive a model with a unified power-function form for the growth of independent spreading activities. Our model takes several key factors into consideration, including memory effect, the dynamics of human interest, and the fact that older messages are more difficult to discover. We validate our model by a real-world microblogging data set. Our work indicates that, other than various features, some invariable rules should be considered during spreading prediction. This work also contributes a useful methodology for studying human dynamics.

Ritual as reflected by censorship. The Control Bureau as the custodian of the cultural image of the authorities in the early days of the People’s Republic of Poland

The ritual as a series of actions specified by traditions or a given political system, defined in detail and repeatable, was also fulfilled in the communist system. There it was aimed at introducing and amalgamating the order imposed on Poland by the Soviets after WWII. It could only be achieved by strictly observing the rules of Socialist rites. And that did not only apply to, however important, the celebrations of holidays according to the communist calendar, but also to the master principles which the enforcers of the new order used towards society. The indicated research material, extracted from censorship archives, shows that regardless of the changing media policy in the first decade after WWII, from the very beginning there existed invariable rules which constituted a compass for specific choices: the ban on criticising or disturbing the good name of the authorities, starting with Generalissimo Stalin, through the leaders of the states subordinate to him, higher-ranking officials, police and the army, to udarniks. The Control Bureau for Press, Publications and Performances was one of the most active bodies in the field. In the privacy of their offices, without the publicity so common for the clamorous ceremonies and rallies, censors worked to maintain the Stalinist rituals.

A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.

Optical Scale Polarimetric Device for Nanotube Forest Measurement: An Opportunity to Anticipate Bistatic Polarimetric SAR Images of Tree Trunk Forests at P-Band

This paper investigates a new polarimetric device that produces reduced scale measurements for bistatic radar. The optical scale device is proposed to overcome the lack of real bistatic and full polarimetric radar acquisitions for forest of trunks. It is based on the scale invariant rule that is deduced from the Maxwell equations. From this principle, the electromagnetic (EM) response is kept at the reduced scale if the illumination wavelength is scaled and if the permittivity remains the same. This last condition needs the use of a carefully chosen material at optical scale. Nanoscale scenes are composed of carbon nanotubes (CNTs). They present several advantages: their arrangement is similar to the structure of a forest of trunks, their shape, and density can be controlled, it is possible to create very large scenes composed of thousands of elements, and finally their permittivity at optical wavelength is about the same order of magnitude than the permittivity of the tree trunks at radar wavelength. They are measured under the view of a microscope objective with a 633-nm wavelength laser playing the role of the EM source. The device images at once the forest polarimetric response, for a given transmitter location, and for the entire set of angular positions of reception. Two samples of forests with different densities are measured. They are analyzed using the Cloude and Pottier decomposition and the Lu and Chipman decomposition. The produced results are unprecedented on forest-like environment and it would be very helpful for the radar community.