Concept Of Invariance Research Articles

Galileo's ship and the relativity principle

AbstractIt is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It is also commonly believed that this principle holds the key to answering why, for example, we do not notice the orbital velocity of the Earth as we go about our day. And yet, I argue in this paper that the precise content of this principle is ambiguous: standard presentations, in both physics and philosophy, fail to distinguish between two principles that are ultimately inequivalent, the “External Galilean Relativity Principle” (EGRP) and the “Internal Galilean Relativity Principle” (IGRP). I demonstrate that EGRP and IGRP play distinct roles in physics practice (e.g., EGRP is connected to the concept of Galilean invariance, but IGRP is not) and that many classical systems that satisfy IGRP fail to satisfy EGRP. I further show that the Relativity Principle famously discussed by Einstein in 1905—which is not restricted to classical systems—also leads to two inequivalent principles, an external one analogous to EGRP, and an internal one analogous to IGRP. I conclude by highlighting that the phenomenon originally captured by Galileo's famous ship passage is much more general than contemporary discussions in the philosophy of symmetries suggest.

Проверка измерительной инвариантности для тестов когнитивных и языковых способностей

<p style="text-align: justify;">This paper discusses the measurement invariance of assessment instruments. The purpose of measurement invariance testing is to assess the extent to which a measured construct has comparable meaning across different groups or measurement points, to ensure that comparisons of these groups or measures to each other are appropriate. The paper provides an overview of recent and classic papers discussing conceptual and methodological aspects of invariance testing. Specific focus is placed on the available data on invariance testing for the assessments of cognitive and language abilities, and on the significance of invariance for the accurate assessment of individual and between-group differences. Finally, current approaches to invariance testing within structural equation modelling and item response theory are discussed. This paper may serve as an introduction to the concept of measurement invariance. It will be useful to readers interested in improving the quality of measurement instruments and making more reliable inferences about psychological phenomena.</p>

Permutation-invariant linear classifiers

Invariant concept classes form the backbone of classification algorithms immune to specific data transformations, ensuring consistent predictions regardless of these alterations. However, this robustness can come at the cost of limited access to the original sample information, potentially impacting generalization performance. This study introduces an addition to these classes—the permutation-invariant linear classifiers. Distinguished by their structural characteristics, permutation-invariant linear classifiers are unaffected by permutations on feature vectors, a property not guaranteed by other non-constant linear classifiers. The study characterizes this new concept class, highlighting its constant capacity, independent of input dimensionality. In practical assessments using linear support vector machines, the permutation-invariant classifiers exhibit superior performance in permutation experiments on artificial datasets and real mutation profiles. Interestingly, they outperform general linear classifiers not only in permutation experiments but also in permutation-free settings, surpassing unconstrained counterparts. Additionally, findings from real mutation profiles support the significance of tumor mutational burden as a biomarker.

Detecting differential item functioning in presence of multilevel data: do methods accounting for multilevel data structure make a DIFference?

Assessment practices are, among other things, concerned with issues of fairness and appropriate score interpretation, in particular when making claims about subgroup differences in performance are of interest. In order to make such claims, a psychometric concept of measurement invariance or differential item functioning (DIF) ought to be considered and met. Over the last decades, researchers have proposed and developed a plethora of methods aimed at detecting DIF. However, DIF detection methods that allow multilevel data structures to be modeled are limited and understudied. In the current study, we evaluated the performance of four methods, including the model-based multilevel Wald and the score-based multilevel Mantel–Haenszel (MH), and two well-established single-level methods, the model-based single-level Lord and the score-based single-level MH. We conducted a simulation study that mimics real-world scenarios. Our results suggested that when data were generated as multilevel, mixed results regarding performances were observed, and not one method consistently outperformed the others. Single-level Lord and multilevel Wald yielded best control of the Type I error rates, in particular in conditions when latent means were generated as equal for the two groups. Power rates were low across all four methods in conditions with small number of between- and within-level units and when small DIF was modeled. However, in those conditions, single-level MH and multilevel MH yielded higher power rates than either single-level Lord or multilevel Wald. This suggests that current practices in detecting DIF should strongly consider adopting one of the more recent methods only in certain contexts as the tradeoff between power and complexity of the method may not warrant a blanket recommendation in favor of a single method. Limitations and future research directions are also discussed.

ПРИДУШЕННЯ ПАРАЗИТНИХ КОМПОНЕНТІВ ДИНАМІКИ. МАГНІТОЛЕВІТУЮЧОГО ПОЇЗДА

Part of a maglev train’s partial motiones are parasitic - not useful, or malicious to the successful solution of it’s motor task. Under the conditions of unpredictable system’s disturbances, the requirement to preserve it’s purposefulness makes it rational the passive suppression of such motiones by the methods of the invariance theory. These methods are used to find conditions, the observance of which guarantees the independence of a suppressed coordinates from certain perturbations. Suppression can be done by achieving the invariance of coordinates that represent unwanted motiones with respect to ignored disturbances, as well as by isolating such coordinates from influences that destroy the desired invariance. Suppression of a parasitic motion components is carried out automatically. To do it, the structure and parameters of the system must be rationally selected, physically realizable and ensure its high dynamic qualities. It is convenient to choose the structure and parameters using the concepts of structural and parametric invariance. Their implementation is possible only if the two-channel principle is observed.

Chemo and immunotherapy effects on stability regions of tumor models

This paper deals with the problem of estimating the regions of attraction (or Safe regions) of two well-known nonlinear tumor growth models by redefining each model as a set of independent artificial systems and utilizing the novel concept of individual invariance. The first model describes leukemia growth in the presence of chemotherapy where the stable tumor-free equilibrium point vanishes once the treatment is stopped, therefore, we define a safe region around the tumor-free equilibrium point. Then, we compute its region of attraction corresponding one treatment protocol. The second model, known as the Stepanova model, describes immune tumor interactions with chemo- and immunotherapy. First, an initial estimate of an invariant set around its tumor-free equilibrium without therapeutic effects is provided. The estimate is used in a second step to validate the invariant set for a higher-order model with chemo- and immunotherapy. Moreover, a parametric sensitivity analysis is carried out to study the effect of model parameter uncertainties on the size of the region of attraction (RoA) for both models. The proposed model restructuring and the associated analysis method prove to be accurate, scalable, and efficient. It allows for sensitivity analysis and an analytical description of the safe regions in tumor growth models giving an insightful look at the tumor dynamics in association with the treatment protocols.

TopoGCL: Topological Graph Contrastive Learning

Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant unlabeled information. However, existing GCL approaches largely tend to overlook the important latent information on higher-order graph substructures. We address this limitation by introducing the concepts of topological invariance and extended persistence on graphs to GCL. In particular, we propose a new contrastive mode which targets topological representations of the two augmented views from the same graph, yielded by extracting latent shape properties of the graph at multiple resolutions. Along with the extended topological layer, we introduce a new extended persistence summary, namely, extended persistence landscapes (EPL) and derive its theoretical stability guarantees. Our extensive numerical results on biological, chemical, and social interaction graphs show that the new Topological Graph Contrastive Learning (TopoGCL) model delivers significant performance gains in unsupervised graph classification for 8 out of 12 considered datasets and also exhibits robustness under noisy scenarios.

Self-Supervised Representation Learning with Meta Comprehensive Regularization

Self-Supervised Learning (SSL) methods harness the concept of semantic invariance by utilizing data augmentation strategies to produce similar representations for different deformations of the same input. Essentially, the model captures the shared information among multiple augmented views of samples, while disregarding the non-shared information that may be beneficial for downstream tasks. To address this issue, we introduce a module called CompMod with Meta Comprehensive Regularization (MCR), embedded into existing self-supervised frameworks, to make the learned representations more comprehensive. Specifically, we update our proposed model through a bi-level optimization mechanism, enabling it to capture comprehensive features. Additionally, guided by the constrained extraction of features using maximum entropy coding, the self-supervised learning model learns more comprehensive features on top of learning consistent features. In addition, we provide theoretical support for our proposed method from information theory and causal counterfactual perspective. Experimental results show that our method achieves significant improvement in classification, object detection and semantic segmentation tasks on multiple benchmark datasets.

Similarities of Jonsson spectra’s classes

The study of syntactic and semantic properties of a first-order language, generally speaking, for incomplete theories, is one of the urgent problems of mathematical logic. In this article we study Jonsson theories, which are satisfied by most classical examples from algebra and which, generally speaking, are not complete. A new and relevant method for studying Jonson theories is to study these theories using the concepts of syntactic and semantic similarities. The most invariant concept is the concept of syntactic similarity of theories, because it preserves all the properties of the theories under consideration. The main result of this article is the fact that any perfect Jonson theory which are complete for existential sentences, is syntactically similar to some polygon theory (S-polygon, where S is a monoid). This result extends to the corresponding classes of Jonsson theories from the Jonsson spectrum of an arbitrary model of an arbitrary signature.

Analytical advances alleviate model misspecification in non-Brownian multivariate comparative methods.

Adams and Collyer argue that contemporary multivariate (Gaussian) phylogenetic comparative methods are prone to favouring more complex models of evolution and sometimes rotation invariance can be an issue. Here we dissect the concept of rotation invariance and point out that, depending on the understanding, this can be an issue with any method that relies on numerical instead of analytical estimation approaches. We relate this to the ongoing discussion concerning phylogenetic principal component analysis. Contrary to what Adams and Collyer found, we do not observe a bias against the simpler Brownian motion process in simulations when we use the new, improved, likelihood evaluation algorithm employed by mvSLOUCH, which allows for studying much larger phylogenies and more complex model setups.

Forgery Detection by Weighted Complementarity between Significant Invariance and Detail Enhancement

Generative adversarial networks have shown impressive results in the modeling of movies and games, but what if such powerful image generation capability is used to harm the Multimedia? The face replacement methods represented by Deepfakes are becoming a threat to everyone, so the development of image authenticity detection methods has become a top priority. For achieving accurate detection resistant to compression effects, we propose a weighted complementary dual-stream detection method. Firstly, to alleviate the influence of image compression on manipulation detection, we propose the concept of pixel-wise saliency invariance. We map fake images onto saliency maps via Quaternary Fourier Transform, which discovers the invariant properties of image phase spectra on different compressions. Meanwhile, to capture boundary traces more easily, we propose the concept of pixel-wise detail enhancement. We apply Bilateral Filtering to preserve the texture edges of fake images and amplify the fake boundaries. Finally, to take full advantage of the two proposed concepts, a weighted complementary dual-stream network (WCD Network) is designed as a classifier to fuse features and identify real and fake. On different benchmarks like FaceForensics++(FF++), Celeb-DF and DFDC, the experimental results show that the proposed method has the average best detection accuracy compared to existing methods.

Computation of Input Disturbance Sets for Constrained Output Reachability

Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data through set-membership identification. However, the problem of computing a suitable input disturbance set in case the set of possible output values is assigned a priori has received relatively little attention. This problem arises in many contexts, such as in supervisory control, actuator design, decentralized control, and others. In this paper, we propose a method to compute input disturbance sets (and the corresponding set of states) such that the resulting set of outputs matches as closely as possible a given set of outputs, while additionally satisfying strict (inner or outer) inclusion constraints. We formulate the problem as an optimization problem by relying on the concept of robust invariance. The effectiveness of the approach is demonstrated in numerical examples that illustrate how to solve safe reference set and input-constraint set computation problems.

Market Crashes and Time-Translation Invariance

The general framework for quantitative technical analysis of market prices is revisited and extended. The concept of a global time-translation invariance and its spontaneous violation and restoration is introduced and discussed. We find that different temporal patterns leading to some famous crashes (e.g., bubbles, hockey sticks, etc.) exhibit analogous probabilistic distributions found only in the time series for the stock market indices. A number of examples of crashes are presented. We stress that our goal here is to study the crash as a particular phenomenon created by spontaneous time-translation symmetry breaking/restoration. We ask only “how to calculate and interpret the probabilistic pattern which we encounter in the day preceding crash, and how to calculate the typical market reactions to shock?”.

Local scale invariance and robustness of proper scoring rules

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most popular proper scoring rules, such as the continuous ranked probability score (CRPS), give more importance to observations with large uncertainty, which can lead to unintuitive rankings. To describe this issue, we define the concept of local scale invariance for scoring rules. A new class of generalized proper kernel scoring rules is derived and as a member of this class we propose the scaled CRPS (SCRPS). This new proper scoring rule is locally scale invariant and, therefore, works in the case of varying uncertainty. Like the CRPS, it is computationally available for output from ensemble forecasts, and does not require the ability to evaluate densities of forecasts. We further define robustness of scoring rules, show why this also can be an important concept for average scores unless one is specifically interested in extremes, and derive new proper scoring rules that are robust against outliers. The theoretical findings are illustrated in three different applications from spatial statistics, stochastic volatility models and regression for count data.

The metaphysical underdetermination of time-reversal invariance

In this paper I argue that the concept of time-reversal invariance in physics suffers from metaphysical underdetermination, that is, that the concept may be understood differently depending on one’s metaphysics about time, laws, and a theory’s basic properties. This metaphysical under-determinacy also affects subsidiary debates in philosophy of physics that rely on the concept of time-reversal invariance, paradigmatically the problem of the arrow of time. I bring up three cases that, I believe, fairly illustrate my point. I conclude, on the one hand, that any formal representation of time reversal should be explicit about the metaphysical assumptions of the concept that it intends to represent; on the other, that philosophical arguments that rely on time reversal to argue against a direction of time require additional premises.

Fuzzy Esscher changes of measure and copula invariance in Lévy markets

In the context of a multidimensional exponential Lévy market, we focus on the Esscher change of measure and suggest a more flexible tool allowing for a fuzzy version of the standard Esscher transform. Motivated both by the empirical incompatibility of market data and the analytical form of the standard Esscher transform (see [8]) and by the desire to introduce a pricing technique under incompleteness conditions, we detect the impact of fuzziness in terms of measure change function and in contingent claims' pricing. In a multidimensional setting the fuzzy Esscher transform is a copula whose invariance, under margins' transformations induced by a change of measure, is investigated and connected to the notion of the absence of arbitrage opportunities. We highlight how Esscher transform, primarily used in pricing techniques, preserves the invariance of the aggregation operator and it can be generalized to the fuzzy version assuming that the measurable functions defining the Choquet marginal integrals are increasing. Furthermore, the empirical evidence seems to suggest that a weaker concept of invariance may be more suitable, i.e. the ε-measure invariance, coherent with the Esscher fuzzy copula tool. An empirical experiment for our model will make clear how this blurring technique fits the market data.

Pitch and tone: Primacy of production criteria in auditory perception

The brain performs diverse and complex operations effortlessly. Its sensitivity to minute stimulus changes, and precision in scaling sensory magnitudes, are yet to be understood by humans. Nevertheless, its limitless vault is accessible only if scientists can discipline themselves to abide by the laws of their science. There exist well-established psychophysical principles for dealing with sensory, mental, and all intangible phenomena. However, in hearing research, the generation of law-abiding scientists are long gone; the current generation of computer-oriented scientists hope to resolve all problems through random and effortless computations of endless varieties of meaningless variables without the concept of invariance. The case in point is hearing research; we are still searching for pitch (or tone) after 2,500 years of intensive inquiry. The failure augurs the existence of fundamental errors in the science. This paper describes a search for the origin of pitch which plays lexical and intonational roles in Yoruba, a tone language. The approach is based on the ecological conception of sound, with experimental evidence from speech surrogates (drums) and strings, guided by the concept of invariance. The investigations attain the conclusion that the brain does not perform any computations at all in pitch and tone perception, neither in music nor in speech. Rather, the data show that the brain measures a unique mechanical parameter of the sound source to which all physical and mechanical transformations lead. In every pitch/tone perception context, therefore, the brain discards all other factors which convey other attributes of sound outside pitch and tone. This finding accounts for constancy in auditory code perception despite overwhelming variability at the production and acoustic levels. Implications for all aspects of auditory perception research and neurophysiological investigations into brain mechanisms are discussed.

Invariant Policy Learning: A Causal Perspective.

Contextual bandit and reinforcement learning algorithms have been successfully used in various interactive learning systems such as online advertising, recommender systems, and dynamic pricing. However, they have yet to be widely adopted in high-stakes application domains, such as healthcare. One reason may be that existing approaches assume that the underlying mechanisms are static in the sense that they do not change over different environments. In many real-world systems, however, the mechanisms are subject to shifts across environments which may invalidate the static environment assumption. In this paper, we take a step toward tackling the problem of environmental shifts considering the framework of offline contextual bandits. We view the environmental shift problem through the lens of causality and propose multi-environment contextual bandits that allow for changes in the underlying mechanisms. We adopt the concept of invariance from the causality literature and introduce the notion of policy invariance. We argue that policy invariance is only relevant if unobserved variables are present and show that, in that case, an optimal invariant policy is guaranteed to generalize across environments under suitable assumptions.

Shift invariant deep convolution neural learning for resource efficient healthcare data transmission in WSN

Wireless Sensor Network (WSN) comprises many small sensors nodes incorporated by IoT which plays vital role in several applications. IoT incorporates physical devices into a network structure that includes software, sensors to collect data from the surrounding environment, and sinks for data transmission. To increase network lifespan during data transmission, a resource-efficient routing system is needed. Different academics have been working on improving routing techniques recently to increase effectiveness and route discovery. The key issue affecting the performance of WSNs is an efficient resource usage of routing. In order to overcome this problem, a new technique called Hierarchical Point wise Mutual Informative Clustering-based Shift Invariant Deep Convolutive Neural Learning (HPMIC-SIDCNL) technique is introduced in WSN. The HPMIC-SIDCNL technique uses the Shift Invariant Convolutive Deep neural learning concept to learn the given input with help of several layers such as input, three hidden layers, and output layer. Initially, the IoT devices are used in sensor nodes for sensing and collecting patient data. In the input layer, sensor nodes are considered as input. Then input is transmitted into first hidden layer where resource of the sensor nodes such as energy and bandwidth are measured. Then estimated resources are transmitted into second hidden layer where the clustering process is carried out using the Hierarchical IBM Point wise Mutual Informative Clustering technique. The Hierarchical IBM clustering uses the Point wise Mutual Information for collection of sensor nodes depend on energy and bandwidth. In the third hidden layer, the cluster is selected on higher residual energy and minimum bandwidth for improving the data transmission and reduces the delay. The cluster head receives the patient data after it has been sent by the source node in that particular cluster. In order to perform data transmission from source to sink node at output layer, cluster then locates the closest cluster head. In this manner, cluster heads are used to execute resource-efficient healthcare data transmission from source to sink node, minimizing the latency. The obtained findings show that the suggested HPMIC-SIDCNL technique outperforms in terms of high delivery ratio with little packet loss and delay. The advantage of the proposed HPMIC-SIDCNL technique, it is simple to understand because it represents a solution to a given problem step by step and is not dependent on any programming language. Since everyone can understand it, even those without programming experience, it is simple.

Multilabel causal variable discovery in multisource

AbstractMultilabel causal feature selection, as a well‐known and effective approach in dealing with high‐dimensional multilabel data, is a popular topic. Amount of causal feature selection algorithms have achieved a great deal of success in classification and prediction tasks. However, the descriptive information of data is collected from different data sources in many practical applications. While few researches focus on the causal variable discovery in multisource environments due to the complex causal relationships. To address these problems, we propose a causal feature selection framework in multisource environments to solve the above problems. Firstly, we mine the causal mechanism with respect to the class attribute under the assumption that only a single data source is included. Secondly, by utilizing the concept of causal invariance in causal inference, we formulate the problem of causal feature selection with multiple data sources as a search problem for an invariant set across data sources. In addition, we give the upper and lower bounds of the causal invariant set. Finally, we design a novel multisource multilabel causal feature selection (MMCFS) algorithm. To verify the effectiveness of the proposed algorithm, we compare it with 12 feature selection methods on synthetic datasets. Experiment results show that the classification performance of MMCFS achieves highly competitive performance against other comparing algorithms.