Variational principles for conformal geodesics

Conformal geodesics are solutions to a system of third-order equations, which makes a Lagrangian formulation problematic. We show how enlarging the class of allowed variations leads to a variational formulation for this system with a third-order conformally invariant Lagrangian. We also discuss the conformally invariant system of fourth-order ODEs arising from this Lagrangian and show that some of its integral curves are spirals.

The Histological Diagnosis of Breast Cancer by Employing scale invariant ResNet 18 With Spatial Supervised Technique

BackgroundBreast cancer is one of the most prevalent cause of morbidity and mortality in women all over the world. Histopathological diagnosis is a vital component in the management of breast cancer. The application of artificial intelligence is yielding promising results for the better patient care.AimThe main aim of the present research project is to explore the potential of spatial supervised technique to develop scale invariant system for the histological diagnosis of breast cancer.Materials and MethodsThe anonymized images of hematoxylin and eosin stained section of the dataset, which has been acquired from the website. The slides were taken at different zoom (magnification) levels. Spatial supervised learning has been employed to make a scale invariant system. We used 400x and 40x to generate the results. For the 400x, we trained our network on a dataset of 200x,100x, and 40x images. The datasets were split into training and validation sets. The training set contained 80% digital slides of the respected dataset, and the validation set contained 20% digital slides of the respected dataset. The final result was generated by splitting the dataset of 400x into the training and test dataset. The training set contained 50% digital slides, and the test set also contained 50% digital slides. This unusual split is done to show how good spatial supervised learning works. Similarly, for 40x, we trained our networks on a dataset of 400x,200x, and 100x. The same steps were followed to obtain the 40x results.ResultsThe result analysis revealed that the ResNet 18 with spatial supervised learning on dataset of 40x yielded the F-1 score of 1.0, while ResNet 18 with supervised learning only, on dataset of 40x yielded F-1 score of 0.9823. ResNet 18 with spatial supervised learning on dataset of 400x revealed F-1 score of 0.9957, and ResNet 18 with supervised learning only, on dataset of 400x showed the F-1 score of 0.9591. For supervised learning dataset is spited into training (80%) and testing (20% of dataset).ConclusionThe analysis of digitized pathology images with the application of convolutional neural network Resnet -18 architecture with spatial supervised learning revealed excellent results, which is demonstrated by a very high F-1 score of 1.0.The development of scale invariant system with application of spatial supervised technique solved the problem of images with variable magnifications. The finding would further pave the pathway for application of deep learning for the histological diagnosis of pathological lesions.

New Factors of Organizational Design in a Digital Society

In this paper, we propose an invariant system of factors for the organizational structure of activities in all spheres of society's life in order to systematize new organizational factors that arise during the implementation of the national program "Digital Economy of the Russian Federation" and other national development programs of Russia until 2024, integrated with it. The proposed invariant system of organizational factors in society is based on the results of the analysis of organizational concepts in the system of social sciences. The article examines the nature and mechanisms of its development. In the invariant system of organizational factors in society, four groups of antinomian factors are defined, each of which can enter into antinomy relations with any other group of antinomian factors. These groups of antinomian factors are formed, firstly, in equipment and nature, secondly, in culture and art, thirdly, in economics and politics, fourthly, in science and religion. Equipment and nature give rise to give rise to a group of conditioning factors, since these factors determine the means of activity. Culture and art generate determinants factors, as these factors determine the way one operates. Economics and politics give rise to executing factors, since these factors determine the technology of activity. Finally, science and religion give rise to setting factors, as they determine the methodology of activity. For organizational construction and implementation of activities in society, it is required to establish a continuous simultaneous antinomian correspondence between each pair of groups of antinomy organizational factors and ensure their same continuous and simultaneous synthesis. This synthesis is carried out in people or through people who form society, turning them into a living social organization of the continuous implementation of society's activities, which forms its structure. In accordance with this representation of an invariant system of organizational factors in society, we consider and systematize new factors of organizational design of modern enterprises, institutions and organizations, which are formed in the course of the comprehensive implementation of thirteen national programs. It turns out that the comprehensive implementation of all federal projects of these national programs forms a fundamentally new content of the structure of the invariant system of organizational factors in society, which is characterized by the appearance of imbalances in the structure. This creates for all enterprises, institutions and organizations a constantly accelerating actualization of the problem of their organizational designing. The problem of design organizational research is substantiated as a task of operational organizational modeling for the purpose of operational construction of relevant organizational models, which in turn provide the same operational organizational design of the current activities of enterprises, institutions and organizations. It is concluded that it is necessary to formulate new methodological principles for applying the methodology of a systematic approach to solving these research problems.

Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases

We propose and prove a family of generalized Lieb-Schultz-Mattis~(LSM) theorems for symmetry protected topological~(SPT) phases on boson/spin models in any dimensions. The ``conventional'' LSM theorem, applicable to e.g. any translation invariant system with an odd number of spin-1/2 particles per unit cell, forbids a symmetric short-range-entangled ground state in such a system. Here we focus on systems with no LSM anomaly, where global/crystalline symmetries and fractional spins within the unit cell ensure that any symmetric SRE ground state must be a non-trivial SPT phase with anomalous boundary excitations. Depending on models, they can be either strong or ``higher-order'' crystalline SPT phases, characterized by non-trivial surface/hinge/corner states. Furthermore, given the symmetry group and the spatial assignment of fractional spins, we are able to determine all possible SPT phases for a symmetric ground state, using the real space construction for SPT phases based on the spectral sequence of cohomology theory. We provide examples in one, two and three spatial dimensions, and discuss possible physical realization of these SPT phases based on condensation of topological excitations in fractionalized phases.

Lyapunov Perron Transformation for Quasi-Periodic Systems and its Applications

This paper depicts the application of symbolically computed Lyapunov Perron (L-P) Transformation to solve linear and nonlinear quasi-periodic systems. The L-P transformation converts a linear quasi-periodic system into a time-invariant one. State augmentation and the method of Normal Forms are used to compute the L-P transformation analytically. The state augmentation approach converts a linear quasi-periodic system into a nonlinear time invariant system as the quasi-periodic parametric excitation terms are replaced by ‘fictitious’ states. This nonlinear system can be reduced to a linear system via Normal Forms in the absence of resonances. In this process, one obtains near identity transformation that contains fictitious states. Once the quasi-periodic terms replace the fictitious states they represent, the near identity transformation is converted to the L-P transformation. The L-P transformation can be used to solve linear quasi-periodic systems with external excitation and nonlinear quasi-periodic systems. Two examples are included in this work, a commutative quasi-periodic system and a non-commutative Mathieu-Hill type quasi-periodic system. The results obtained via the L-P transformation approach match very well with the numerical integration and analytical results.

Invariant method for measuring wet gas flow rate

The article deals with one of the important tasks of modern flow measurement, which is related to the measurement of the flow rate and the amount of wet gas. This task becomes especially important when it becomes necessary to obtain information about the separate amount of the dry part of the gas that is contained in the form of a mixture in the wet gas stream. The paper presents the principle of operation and structure of the invariant system for measuring the flow rate of wet gas, which is based on the combined use of differential pressure flowmeters and Coriolis flowmeters. The operation of the invariant wet gas flow rate measurement system is based on the simultaneous application of the multichannel principle and the partial flow measurement method. Coriolis flowmeters and the differential pressure flowmeter are used as the main elements of the system. The proposed measurement system does not offer applications for gases with abundant drip humidity. The article provides information about the test results of the proposed invariant system. The estimation of the metrological characteristics of the invariant system when measuring the flow rate of wet gas is given. The obtained test results of the invariant wet gas flow rate measurement system are relevant for natural gas production, transportation, and storage facilities.