Partial Dehn twists of free groups relative to local Dehn twists - a dichotomy

A criterion for quadratic or higher growth of group automorphisms is established which are represented by graph-of-groups automorphisms with certain well specified properties. As a consequence, it is derived (using results of a previous paper of the author) that every partial Dehn twist automorphism of \FN relative to local Dehn twist automorphisms is either an honest Dehn twist automorphism, or else has quadratic growth

When is a polynomially growing automorphism of FnF_n geometric ?

The main result of this paper is an algorithmic answer to the question raised in the title, up to replacing the given $\hat{\phi} \in Out(F_n)$ by a positive power. In order to provide this algorithm, it is shown that every polynomially growing automorphism $\hat \phi$ can be represented by an iterated Dehn twist on some graph-of-groups $\cal{G}$ with $\pi_1{\cal{G}} = F_n$. One then uses results of two previous papers \cite{KY01, KY02} as well as some classical results such as the Whitehead algorithm to prove the claim

Communication-Efficient Decentralized Federated Learning via One-Bit Compressive Sensing

Decentralized federated learning (DFL) has gained popularity due to its practicality across various applications. Compared to the centralized version, training a shared model among a large number of nodes in DFL is more challenging, as there is no central server to coordinate the training process. Especially when distributed nodes suffer from limitations in communication or computational resources, DFL will experience extremely inefficient and unstable training. Motivated by these challenges, in this paper, we develop a novel algorithm based on the framework of the inexact alternating direction method (iADM). On one hand, our goal is to train a shared model with a sparsity constraint. This constraint enables us to leverage one-bit compressive sensing (1BCS), allowing transmission of one-bit information among neighbour nodes. On the other hand, communication between neighbour nodes occurs only at certain steps, reducing the number of communication rounds. Therefore, the algorithm exhibits notable communication efficiency. Additionally, as each node selects only a subset of neighbours to participate in the training, the algorithm is robust against stragglers. Additionally, complex items are computed only once for several consecutive steps and subproblems are solved inexactly using closed-form solutions, resulting in high computational efficiency. Finally, numerical experiments showcase the algorithm's effectiveness in both communication and computation

Real Time Scanning-Modeling System for Architecture Design and Construction

The disconnection between architectural form and materiality has become an important issue in recent years. Architectural form is mainly decided by the designer, while material data is often treated as an afterthought which doesn’t factor in decision-making directly. This study proposes a new, real-time scanning-modeling system for computational design and autonomous robotic construction. By using cameras to scan the raw materials, this system would get related data and build 3D models in real time. These data would be used by a computer to calculate rational outcomes and help a robot make decisions about its construction paths and methods. The result of an application pavilion shows that data of raw materials, architectural design, and robotic construction can be integrated into a digital chain. The method and gain of the material-oriented design approach are discussed and future research on using different source materials is laid out

Expected Sensitivity to Galactic/Solar Axions and Bosonic Super-WIMPs based on the Axio-electric Effect in Liquid Xenon Dark Matter Detectors

We present systematic case studies to investigate the sensitivity of axion searches by liquid xenon detectors, using the axio-electric effect (analogue of the photoelectric effect) on xenon atoms. Liquid xenon is widely considered to be one of the best target media for detection of WIMPs (Weakly Interacting Massive Particles which may form the galactic dark matter) using nuclear recoils. Since these detectors also provide an extremely low radioactivity environment for electron recoils, very weakly-interacting low-mass particles (< 100 keV/c^2), such as the hypothetical axion, could be detected as well - in this case using the axio-electric effect. Future ton-scale liquid Xe detectors will be limited in sensitivity only by irreducible neutrino background (pp-chain solar neutrino and the double beta decay of 136Xe) in the mass range between 1 and 100 keV/c^2. Assuming one ton-year of exposure, galactic axions (as non-relativistic dark matter) could be detected if the axio-electric coupling g_Ae is greater than 10^-14 at 1 keV/c^2 (or $10^-13 at 100 keV/c^2). Below a few keV/c^2, and independent of the mass, a solar axion search would be sensitive to a coupling g_Ae ~ 10^-12. This limit will set a stringent upper bound on axion mass for the DFSV and KSVZ models for the mass ranges m_A < 0.1 eV/c^2 and < 10 eV/c^2, respectively. Vector-boson dark matter could also be detected for a coupling constant alpha'/alpha > 10^-33 (for mass 1 keV/c^2) or > 10^-27 (for mass 100 keV/c^2).Comment: 17 pages, 10 figure