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The Cambridge Photographic Star Atlas
Using the latest methods in digital photography and image processing, The Cambridge Photographic Star Atlas presents the whole sky through large-scale photographic images with corresponding charts. Each double-page spread shows a section of the night sky and is accompanied by an inverted chart highlighting and naming double stars, variable stars, open clusters, galactic and planetary nebulae, globular clusters and galaxies. The 82 large-scale charts, with a scale of 1° per cm, identify over 1500 deep-sky objects and 2500 stars. Providing a giant mosaic of the entire sky, this unique atlas is unparalleled in detail and completeness, making it indispensable for visual observers and astrophotographers.
eBook
Entanglement Phase Transitions in Measurement-Only Dynamics
Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This finding motivates us to introduce measurement-only models, in which the “scrambling” and “unscrambling” effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. These models represent a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is frustration, or mutual incompatibility, of the measurements. Surprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (≳3-body) operators. We identify a class of exceptions to this behavior (“bipartite ensembles”) which cannot sustain an entangling phase but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light cone, despite the nonlocality inherent to quantum measurements.
Journal Article
The Bounded and Precise Word Problems for Presentations of Groups
We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining
relations. For example, for every finitely presented group, the bounded word problem is in
eBook
Mapping the sky
\"Introduces maps and teaches essential mapping skills, including how to create, use, and interpret maps of the stars and planets\"--Provided by publisher.
Book
A UML Activity Flow Graph-Based Regression Testing Approach
Regression testing is a crucial process that ensures that changes made to a system do not affect existing functionalities. However, there is currently no adequate technique for selecting test cases that consider changes in Unified Modeling Language (UML) activity flow graphs. This paper proposes a novel approach to regression testing of UML diagrams, focusing on healthcare management systems. We provide a formal definition of sequence and activity diagrams and their relationship and construct corresponding activity flow graphs, which are used to develop a regression testing algorithm. The proposed algorithm categorizes test cases into reusable, retestable, obsolete, and newly generated categories by comparing old and new versions of UML activity flow graphs. The methodology is evaluated using a custom-designed hospital management system website as the test case, and the results demonstrate a significant reduction in time and resources required for regression testing. Our study provides valuable insights into the application of UML diagrams and activity flow graphs in regression testing, making it an important contribution to software testing research.
Journal Article
Visualizing set relationships: EVenn's comprehensive approach to Venn diagrams
Venn diagrams serve as invaluable tools for visualizing set relationships due to their ease of interpretation. Widely applied across diverse disciplines such as metabolomics, genomics, transcriptomics, and proteomics, their utility is undeniable. However, the operational complexity has been compounded by the absence of standardized data formats and the need to switch between various platforms for generating different Venn diagrams. To address these challenges, we introduce the EVenn platform, a versatile tool offering a unified interface for efficient data exploration and visualization of diverse Venn diagrams. EVenn (http://www.ehbio.com/test/venn) streamlines the data upload process with a standardized format, enhancing the capabilities for multimodule analysis. This comprehensive protocol outlines various applications of EVenn, featuring representative results of multiple Venn diagrams, data uploads in the centralized data center, and step‐by‐step case demonstrations. Through these functionalities, EVenn emerges as a valuable and user‐friendly tool for the in‐depth exploration of multiomics data. The use of Venn diagrams greatly aids in illustrating and visualizing set relationships within metabolomics, genomics, transcriptomics, and proteomics. Here, we introduce EVenn, an all‐encompassing platform that provides a unified interface for a wide range of Venn diagram functionalities. This protocol delineates the features of EVenn, encompassing interactive Venn diagrams, interactive Edwards diagrams, Euler diagrams, UpSet plots, flower plots, and Venn network diagrams, solidifying its role as an invaluable tool for the analysis of multiomics data. Highlights Comprehensive Venn functionality: EVenn introduces a unified platform with diverse Venn diagram tools, from interactive diagrams to network representations, catering to the intricate needs of multiomics data analysis across metabolomics, genomics, transcriptomics, and proteomics. Efficient data exploration: EVenn's data center streamlines exploration by supporting a standardized data format, allowing researchers to effortlessly upload and analyze data. The manuscript demonstrates its practical utility through representative results and detailed case demonstrations. User‐friendly interface: With a user‐friendly interface, EVenn simplifies the generation of various Venn diagrams, Euler diagrams, UpSet plots, and more. This protocol establishes EVenn as a valuable resource for researchers seeking a cohesive and accessible tool for multiomics data interpretation.
Journal Article