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This paper presents a pseudocode algorithm for translating Entity-Relationship data models into (Elementary) Mathematical Data Model schemes. We prove that this algorithm is linear, sound, complete, and optimal. As an example, we apply this algorithm to an Entity-Relationship data model for a teaching sub-universe. We also provide the main additional features added to the implementation of this algorithm in MatBase, our intelligent knowledge and database management system prototype based on both the Entity-Relationship, (Elementary) Mathematical, and Relational Data Models.
In recent years, the landscape of federated learning has witnessed significant advancements, particularly in decentralized methodologies. This research paper presents a comprehensive comparison of Centralized Hierarchical Federated Learning (HFL) with Decentralized Aggregated Federated Learning (AFL) and Decentralized Continual Federated Learning (CFL) architectures. While HFL, in its centralized approach, faces challenges such as communication bottlenecks and privacy concerns due to centralized data aggregation, AFL and CFL provide promising alternatives by distributing computation and aggregation processes across devices. Through evaluation of Fashion MNIST and MNIST datasets, this study demonstrates the advantages of decentralized methodologies, showcasing how AFL and CFL outperform HFL in precision, recall, F1 score, and balanced accuracy. The analysis highlights the importance of decentralized aggregation mechanisms in AFL and CFL, which effectively enables collaborative model training across distributed devices. This comparative study contributes valuable insights into the evolving landscape of federated learning, guiding researchers and practitioners towards decentralized me
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual mapping can be its own inverse or it can preserve relative order (but not both). Generalisation to higher dimensions is also discussed. An elementary and very intuitive treatment of relationship between arrangements in $d+1$ dimensions and searching for $k$-nearest neighbour in $d$-dimensions is also given.
NASA’s Curiosity rover has entered a Martian valley covered by an astonishing “sea” of tiny polygon-shaped fractures。 The honeycomb patterns, each only a few inches wide, stretch across the landscape and even wrap around a nearby 20-foot-tall butte
China’s Tianwen-1 orbiter captured a faint but remarkable view of 3I/ATLAS as the interstellar comet raced past Mars。 The images reveal its tail and glowing coma, offering scientists a glimpse of material born beyond our solar system
Sony doesn't think the move will hurt it financially
Researchers discovered a proton-assisted mechanism that greatly improves how triplet energy moves between quantum dots and nearby molecules。 The proton briefly shifts position, helps coordinate electron movement, and then returns to where it started。 This quantum-driven shuttle could offer a powerful new way to tune solar cells, lasers, and catalyt
Astronomers may have been listening for alien civilizations in only a small slice of the radio spectrum while overlooking a largely unexplored range of higher frequencies。 Using archived data from the ALMA telescope in Chile, researchers conducted the observatory’s first SETI survey, searching for narrow signals that could indicate advanced technol
Rice University chemists have found a new way to make neodymium, a rare-earth metal, interact with oxygen。 Using a specially designed molecular structure described as a “basket,” the team positioned the atoms so they could form a bond once thought unlikely。 The breakthrough produced highly reactive compounds that could eventually give chemists alte
Primordial black holes may occasionally pass through white dwarf stars and trigger enormous Type Ia supernova explosions。 Researchers found that these events could explain chemical patterns seen in supernova remnants, nearby explosions, and stars across the Milky Way
Wavelength and intensity in the infrared are translated into colors in the visible
Dark matter particles may exert a hidden force on one another, but its effects are stranger than expected。 An extra attraction helps the particles cluster, yet it also makes dark matter effectively lighter as the Universe expands。 That weakens its gravitational impact and usually slows the growth of cosmic structure rather than accelerating it
A new analysis suggests the Sun holds far more silver than earlier estimates indicated。 More advanced models of the solar atmosphere raised the calculated amount by 55 percent, bringing it into much closer agreement with ancient meteorites。 The technique may also help scientists track the cosmic origins of silver and other heavy elements
Dying Sun-like stars may not fade away quietly。 As blobs of gas erupt unevenly from their swollen surfaces, each burst gives the star a tiny push in the opposite direction。 Thousands of these random kicks could eventually break apart distant stellar pairs or, in rare cases, drive two stars into a violent collision
Europa’s hidden ocean has made the icy moon one of the solar system’s most promising places to search for habitable conditions。 Scientists have hoped that water from this deep ocean might rise through cracks and form shallow reservoirs that future spacecraft could more easily study。 New simulations suggest that journey is unlikely because turbulent
A new theoretical study offers a possible explanation for how the Universe can grow more complex without violating the second law of thermodynamics。 Using a quantum gravity framework called Gravity from Entropy, mathematician Ginestra Bianconi found that the Universe’s total entropy may rise as space expands, even while entropy within each unit of
A new chemical process can transform three of the most common plastics into high-purity hydrogen without sorting them first。 The technique operates at much lower temperatures than traditional gasification and captures most of the plastic’s carbon in solid or liquid forms instead of releasing it as carbon dioxide