Inversion Principle Research Articles

Applying SOLID principles for the refactoring of legacy code: An experience report

The presence of technical debt in legacy systems is an inevitable consequence of years of development. Metrics play a significant role in informing the prioritisation process of maintenance activities to reduce this debt. However, it is important to note that not all metrics are equally important or readily available in real industrial settings.This paper summarises an experience report of refactoring activities performed at a Dutch partnering company, aimed at identifying, prioritising and repaying parts of the architectural technical debt accumulated in two decades of development.Given the size of the refactoring task, a data-driven prioritisation was necessary, and based on the impact that the maintenance activity would have on the base system. However, the metrics available from the monitoring of the system formed a limited set, and were not always focused on architectural aspects. Even so, the impact analysis was performed and resulted in the selection of a subset of components that needed urgent maintenance.The refactoring of the identified components was centred around the well-known SOLID design principles, particularly the Dependency Inversion (DI) principle. Additionally, a set of recurring actions was established into ‘refactoring patterns’ and systematically applied to more than 5,000 source, header and custom domain language files.This work, albeit limited to the period where the activity was planned for, was well received by the industrial collaborator. The patterns have proven very valuable in the process of maintaining such a large project scope. The data-driven approach and the identified patterns have helped the team navigate this large space and consistently refactor similar architectural issues that fall under the same category.

Monic inversion principle and complete intersection

Let A be a regular ring of dimension d essentially of finite type over an infinite field k of characteristic ≠2. Let P be a projective A-module of rank n with 2n≥d+3. Let I be an ideal of A[T] of height n and ϕ:P[T]↠I/I2 be a surjection. If ϕ⊗A(T) has a surjective lift θ:P[T]⊗A(T)↠IA(T), then ϕ has a surjective lift Φ:P[T]↠I. The case P=An is due to Das-Tikader-Zinna [7].

Comparative Analysis of Starlight Occultation Data Processing

In order to improve the inversion accuracy of stellar occultation data and to provide a reference for the selection of inversion methods with higher accuracy in the future, this study compared and analyzed the inversion effects of two different methods on the same set of data, which are the effective cross-section method and the onion-peeling method, respectively. Firstly, the inversion principle of the effective cross-section method is introduced in detail. The regularisation parameters and screening conditions for the observation data in the inversion process were clarified based on the ozone observation characteristics. Second, the algorithm was applied to invert the GOMOS observational data from 1 December 2002. The atmospheric radiative transmittance obtained from the observations was filtered, and the inversion results were compared with those obtained using the onion-peeling method. Third, the errors in the height distribution obtained by both methods were calculated using the GOMOS secondary results from 1 December 2002 as the reference value. Finally, the inversion errors of other trace components were computed to further validate the accuracy of the two methods. The results demonstrate that the effective cross-sectional method is more accurate for the inversion of ozone, particularly in low-altitude regions affected by refraction. The method achieved a maximum error of 1.2%, with an apparent magnitude of 2, an effective temperature greater than 10,000 K, and a regularisation parameter of 1015. Furthermore, when applying the same method to the inversion of nitrogen trioxide and calculating the error, it was observed that the results of both methods were comparable at altitude of 30–60 km, with an error value ranging from 0 to 2%. However, at approximately 25 km, the inversion accuracy of the onion-peeling method surpassed that of the effective cross-sectional method. This research provides a theoretical foundation for further investigation of the stellar occultation inversion method and enhancing the accuracy of inversions.

Comprehensive Evaluation and Comparison of AIRS, VASS, and VIRR Water Vapor Products Over Antarctica

AbstractThe detection capability of the water vapor mixing ratio (q) and total precipitable water vapor (PWV) products of the Atmospheric Infrared Sounder (AIRS), the Atmospheric Vertical Sounder System (VASS), and Visible and Infrared Radiometer (VIRR) in Antarctica is unclear due to the harsh environment and the scarcity of ground‐based stations. This study compares these products with data from nine radiosonde stations and 10 Global Navigation Satellite Systems Stations and evaluates them using the CCHZ‐DISO method. In the low atmosphere, the average wet bias of about 22% of VASS q is significantly greater than that of AIRS q (<15%), and the dry bias of AIRS is gradually corrected with increasing cloudiness, but the trend of exacerbated wet bias at 700 hPa requires attention. Meanwhile, VASS should optimize the inversion principle in the presence of clouds and refine the utilization weights of the channels heavily influenced by clouds under different cloud fraction conditions. Furthermore, when the atmospheric pressure is less than 500 hPa, VASS q exhibits a significant wet bias, and these data should be used cautiously. Both AIRS and VIRR detect PWV well in coastal areas, but VIRR PWV is significantly overestimated in the dry ice sheet plateau region. The CCHZ‐DISO value intuitively reveals that AIRS outperforms VASS and VIRR in both q and PWV detection. The findings of this study contribute to a more comprehensive understanding of the detection capability of the above satellite water vapor products to promote the wider application of satellite data in the Antarctic region.

Finitary Type Theories With and Without Contexts

We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin–Löf type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We prove several general meta-theorems about finitary type theories: weakening, admissibility of substitution and instantiation of metavariables, derivability of presuppositions, uniqueness of typing, and inversion principles. We then give a second formulation of finitary type theories in which there are no explicit contexts. Instead, free variables are explicitly annotated with their types. We provide translations between finitary type theories with and without contexts, thereby showing that they have the same expressive power. The context-free type theory is implemented in the nucleus of the Andromeda 2 proof assistant.

Unbiased Estimates for Products of Moments and Cumulants for Finite Populations

Let FN be the distribution function of a finite real population of size N. Let Fn be the empirical distribution function of a sample of size n drawn from the population without replacement. Let TFN be any product of the moments or cumulants of FN, let TFn denote the sample version, and let Tn,NFN denote the expected value of TFn with respect to FN. We prove the following remarkable inversion principle that the expected value of TN,nFn is equal to TFN. We also obtain an explicit expression for Tn,NFN for all TFN of orders up to six.

Inversion Principle and Application of Ultrasonic Detecting Surface or Interface Integrity Parameters of Aviation Functional Coatings

Inversion Principle and Application of Ultrasonic Detecting Surface or Interface Integrity Parameters of Aviation Functional Coatings

Harmony in the Light of Computational Ludics

Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction. In the literature on proof-theoretic semantics, this principle is often coupled with another that is called the recovery principle. By adopting the Computational Ludics framework, we reformulate these principles into one and the same condition, which we call the harmony condition. We show that this reformulation allows us to reveal two intuitive ideas standing behind these principles: the idea of "containment" present in the inversion principle, and the idea that the recovery principle is the "converse" of the inversion principle. We also formulate two other conditions in the Computational Ludics framework, and we show that each of them is equivalent to the harmony condition.

Do children with mathematical learning disabilities use the inversion principle to solve three-term arithmetic problems?: The impact of presentation mode

Numerical inversion is the ability to understand that addition is the opposite of subtraction and vice versa. Three-term arithmetic problems can be solved without calculation using this conceptual shortcut. To verify that this principle is used, inverse problems (a + b − b) can be compared with standard problems (a + b − c). If this principle is used, performance on inverse problems will be higher than performance on standard problems because no calculation is required. To our knowledge, this principle has not been previously studied in children with mathematical learning disabilities (MLD). Our objectives were (a) to study whether 10-year-olds with MLD are able to use this conceptual principle in three-term arithmetic problems and (b) to evaluate the impact of the presentation mode. A total of 64 children with or without MLD solved three-term arithmetic problems (inverse and standard) in two presentation modes (symbolic and picture). The results showed that even though children with MLD have difficulties in performing arithmetic problems, they can do so when the inverse problem is presented with pictures. The picture presentation mode allowed children with MLD to efficiently identify and use the conceptual inversion shortcut and thus to achieve a similar performance to that of typically developing children. These results provide interesting perspectives for the care of children with MLD.

Proof‐theoretic semantics of natural deduction based on inversion

AbstractThe article presents a full proof‐theoretic semantics for natural deduction based on an extended inversion principle: the elimination rule for an operator q may invert the introduction rule for q, but also vice versa, the introduction rule for a connective q may invert the elimination rule for q. Such an inversion—extending Prawitz' concept of inversion—gives the following theorem: Inversion for two rules of operator q (intro rule, elim rule) exists iff a reduction of a maximum formula for q exists. The inversion theorem is specified to two logics, Lambek calculus (LC) and intuitionistic linear logic (ILL), with four propositional connectives: two multiplicatives (implication and conjunction) and two additives (conjunction and disjunction), with two quantifiers and two modals. LC is defined by using elimination rules by composition. ILL is defined by using usual general elimination rules. Elimination rules by composition are an exciting alternative to general elimination rules; in some cases, they do not need permutations.

Mathematical formalism on "Arabic Language DNA"

In this work we formalize new findings on formal Arabic language by constructing equivalence classes on letters depending on inversion principle. This equivalent relation furnishes a conjecture that Arabic language has a DNA-like inversion controller, called language DNA (LDNA) (Al-Rawajfeh, 2020, Ref [2]) and it can be even considered as a part of the full language DNA that can be discovered by more investigations similar to this work.

One-dimensional constrained inversion of electrical source transient electromagnetic method

The damped least squares inversion principle is applied to the transient electromagnetic one-dimensional inversion of electrical sources, and a new model is obtained by continuously iterating the initial model, thereby fitting the observed transient electromagnetic response, and performing one-dimensional inversion through induced electromotive force play. In the damped least squares inversion, constraints are added to the Jacobian matrix, and simultaneous constraint equations and conventional inversion equations are solved. By weighting the constraint parameters, the difference between adjacent resistivities and layer thicknesses is minimized. Finally, K-type and H-type theoretical models were used to verify the reliability of the algorithm, and compared with the conventional transient electromagnetic damping least squares inversion.

Application of electrical resistivity tomography method in archaeological excavation

Archaeology has always been an important application field of geophysical methods. In this paper, multi-electrode resistivity method is used to detect the sites of Yangshao periods in Xia county, Yuncheng city, Shanxi Province. The inversion principle of multi-electrode resistivity method is introduced, the data are also processed and interpreted in two and three - dimensional inversion. Through this exploration, the resistivity characteristics of the cultural layer of the site and the location and depth of its concentrated distribution are found out, which provides an important basis for further archaeological exploration and excavation.

Rebels in Biblical and Chinese Texts: A Comparative Study on the Interplay of Myth and History

This study offers a new approach for studying biblical myth in two directions: first, by expanding the scope of investigation beyond the clearly mythological elements to other areas of biblical literature, and second, by drawing comparisons to classical Chinese literature. This article thus reconsiders the relationship between myth and history in both biblical and Chinese literature, while seeking to broaden the endeavor of the comparative method in biblical studies. Two examples are offered: (1) the story of Moses’s call narrative and his relationship with Aaron in Exodus in light of the story of Xiang Liang and Xiang Ji in the Shiji; (2) the story of Saul and David in 1 Samuel compared with the story of Dong Zhuo and Lü Bu in the Romance of the Three Kingdoms. Both comparisons demonstrate the operation of Claude Lévi-Strauss’s inversion principle. Conclusions regarding each of these literatures are presented separately, followed by cross-cultural insights and shared aspects in the study of myth, historiography, and religion.

Development of a novel component-based open CNC software system

Component-based software development (CBSD) is widely utilized to develop open CNC applications. It aims to build an open CNC application by composing a set of components, each implementing specific CNC sub-domain logic. Components conform to a certain component model to keep conformant interactive behaviors. Due to there is no standard granularity to decompose CNC domain and no general component model, as well as seldom consider extra-functional properties, components are heterogeneous. Moreover, they have a direct dependency rather than depending on abstractions. In a nutshell, there are many open-source CNC applications built by heterogeneous and tightly coupled components. They can implement CNC functionality but are good at functional extension and reconfiguration. In this paper, we apply CBSD and dependency inversion principle to develop a novel open CNC application which allows customizing CNC functionality. Specifically, a new granularity to decompose CNC domain is proposed. A special sub-domain is designed to encapsulate the execution logic of other sub-domains at an abstract level and instantiate concrete implementation details at runtime according to configuration. The functional properties of sub-domains are exposed via abstractions. Therefore, as long as re-writing the execution logic and configuring corresponding implementation details, CNC functionality can be extended or reconfigured. A prototype and several components have been developed to test the performance of the application.

Potential Vorticity and Balanced and Unbalanced Moisture

Abstract Atmospheric flows are often decomposed into balanced (low frequency) and unbalanced (high frequency) components. For a dry atmosphere, it is known that a single mode, the potential vorticity (PV), is enough to describe the balanced flow and determine its evolution. For a moist atmosphere with phase changes, on the other hand, balanced–unbalanced decompositions involve additional complexity. In this paper, we illustrate that additional balanced modes, beyond PV, arise from the moisture. To support and motivate the discussion, we consider balanced–unbalanced decompositions arising from a simplified Boussinesq numerical simulation and a hemispheric-sized channel simulation using the Weather Research and Forecasting (WRF) Model. One important role of the balanced moist modes is in the inversion principle that is used to recover the moist balanced flow: rather than traditional PV inversion that involves only the PV variable, it is PV-and-M inversion that is needed, involving M variables that describe the moist balanced modes. In examples of PV-and-M inversion, we show that one can decompose all significant atmospheric variables, including total water or water vapor, into balanced (vortical mode) and unbalanced (inertio-gravity wave) components. The moist inversion, thus, extends the traditional dry PV inversion to allow for moisture and phase changes. In addition, we illustrate that the moist balanced modes are essentially conserved quantities of the flow, and they act qualitatively as additional PV-like modes of the system that track balanced moisture.

Incidence bicomodules, Möbius inversion and a Rota formula for infinity adjunctions

In the same way decomposition spaces, also known as unital 2-Segal spaces, have incidence (co)algebras, and certain relative decomposition spaces have incidence (co)modules, we identify the structures that have incidence bi(co)modules: they are certain augmented double Segal spaces subject to some exactness conditions. We establish a M\"obius inversion principle for (co)modules, and a Rota formula for certain more involved structures called M\"obius bicomodule configurations. The most important instance of the latter notion arises as mapping cylinders of infinity adjunctions, or more generally of adjunctions between M\"obius decomposition spaces, in the spirit of Rota's original formula.

Application of Seismic Waveform Inversion in Prediction of Tight Sandstone Conglomerate Reservoir in Surenuoer Oilfield

The reservoir of Tongluomiao Temple in Surenuoer Oilfield is dominated by glutenite. The sand body is dense, the buried depth is shallow, the heterogeneity is strong, and the oil-water relationship is complex. The favorable reservoir sand body prediction has always plagued the block exploration and development. Therefore, based on the seismic waveform indication inversion principle, process and key parameter settings, based on the petrophysical analysis in the study area, the reservoir inversion technique is studied, and the well interpolation model and the waveform indication inversion model are proposed. The method generates the inversion prediction model of the study area. On this basis, the threshold value of the layer is used to extract the thickness distribution of the sand body plane, and then the favorable target area is predicted. The actual drilling results show that the thickness of the sand body predicted by the method and the actual drilling The results are in good agreement and the oil and gas shows good, providing a reliable technical method for reservoir prediction.

Mesozoic–Cenozoic stress field magnitude in Sichuan Basin, China and its adjacent areas and the implication on shale gas reservoir: Determination by acoustic emission in rocks

ABSTRACT The Sichuan Basin is one of the vital basins in China, boasting abundant hydrocarbon reservoirs. To clarify the intensity of the tectonic stress field of different tectonic episodes since the Mesozoic and to identify the regional dynamic background of different tectonic movements in the Sichuan Basin and its adjacent areas, the characteristics of the acoustic emission in rocks in different strata of these areas were researched in this paper. Meanwhile, the tectonic stress magnitude in these areas since the Mesozoic was restored. The laws state that the tectonic stress varied with depth was revealed, followed by the discussion of the influence of structural stress intensity on structural patterns in different tectonic episodes. These were conducted based on the paleostress measurement by acoustic emission method and the inversion principle of the stress fields in ancient periods and the present, as well as previous research achievements. The results of this paper demonstrate that the third episode of Yanshanian Movement (Yanshanian III) had the maximum activity intensity and tremendously influenced the structural pattern in the study area. The maximum horizontal principal stress of Yanshanian III varied with depth as follows: 0.0168 x + 37.001 (MPa), R2 = 0.8891. The regional structural fractures were mainly formed in Yanshanian III in Xujiahe Formation, west Sichuan Basin, of which the maximum paleoprincipal stress ranging from 85.1 MPa to 120.1 MPa. In addition, the law stating the present maximum horizontal principal stress varies with depth was determined to be 0.0159 x+10.221 (MPa), R2=0.7868 in Wuling Mountain area. Meanwhile, it was determined to be 0.0221 x+9.4733 (MPa), R2=0.9121 in the western part of Xuefeng Mountain area and 0.0174 x+10.247 (MPa), R2=0.8064 in the whole study area. These research results will not only provide data for the simulation of stress field, the evaluation of deformation degree, and the prediction of structural fractures, but also offer absolute geological scientific bases for the elevation of favorable shale gas preservation.

Simple and efficient inverse hysteretic model and associated experimental procedure for precise piezoelectric actuator control and positioning

This paper exposes inversion techniques of a simple yet efficient system-level approach for modeling quasi-static hysteretic behavior of piezoelectric actuators, allowing the transducer voltage to be properly shaped to get the desired target strain response. The inversion principles lie in considering a coefficient relating the voltage derivative to the target strain derivative through a simple formulation using a function of the input strain, combined with equivalent strain cancellation and inversion when the desired target strain derivative crosses zero value. Conceptual and theoretical developments are validated through experimental measurements that show good control capabilities of the quasi-static strain. Hence, the proposed concept provides a lightweight yet efficient approach for embedded control systems.