Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders

We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectiveness of the method

Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders

We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectiveness of the method

Metagenomic Evidence for a Methylocystis Species Capable of Bioremediation of Diverse Heavy Metals

Heavy metal pollution has become an increasingly serious problem worldwide. Co-contamination with toxic mercury (Hg) and arsenic (As) presents a particularly difficult bioremediation trouble. By oxidizing the greenhouse gas methane, methanotrophs have been demonstrated to have high denitrification activity in eutrophic waters, indicating their possible potential for use in bioremediation of Hg(II) and As(V) in polluted water. Using metagenomics, a novel Methylocystis species (HL18), which was one of the most prevalent bacteria (9.9% of the relative abundance) in a CH4-based bio-reactor, is described here. The metagenomic-assembled genome (MAG) HL18 had gene products whose average amino acid identity against other known Methylocystis species varied from 69 to 85%, higher than the genus threshold but lower than the species boundary. Genomic analysis indicated that HL18 possessed all the genes necessary for the reduction of Hg(II) and As(V). Phylogenetic investigation of mercuric reductase (MerA) found that the HL18 protein was most closely affiliated with proteins from two Hg(II)-reducing bacteria, Bradyrhizobium sp. strain CCH5-F6 and Paracoccus halophilus. The genomic organization and phylogeny of the genes in the As(V)-reducing operon (arsRCCB) had significant identity with those from a As(V)-reducing bacterium belonging to the Rhodopseudomonas genus, indicating their reduction capability of As(V). Further analysis found that at least eight genera of methanotrophs possess both Hg(II) and As(V) reductases, illustrating the generally overlooked metabolic potential of methanotrophs. These results suggest that methanotrophs have greater bioremediation potential in heavy metal contaminated water than has been appreciated and could play an important role in the mitigation of heavy metal toxicity of contaminated wastewater

A UTP semantics for communicating processes with shared variables and its formal encoding in PVS

CSP# (communicating sequential programs) is a modelling language designed for specifying concurrent systems by integrating CSP-like compositional operators with sequential programs updating shared variables. In this work, we define an observation-oriented denotational semantics in an open environment for the CSP# language based on the UTP framework. To deal with shared variables, we lift traditional event-based traces into mixed traces which consist of state-event pairs for recording process behaviours. To capture all possible concurrency behaviours between action/channel-based communications and global shared variables, we construct a comprehensive set of rules on merging traces from processes which run in parallel/interleaving. We also define refinement to check process equivalence and present a set of algebraic laws which are established based on our denotational semantics. We further encode our proposed denotational semantics into the PVS theorem prover. The encoding not only ensures the semantic consistency, but also builds up a theoretic foundation for machine-assisted verification of CSP# specifications.Full Tex

Cross Entropy versus Label Smoothing: A Neural Collapse Perspective

Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC), a powerful empirical and theoretical framework which characterizes model behavior during the terminal phase of training. We first show empirically that models trained with label smoothing converge faster to neural collapse solutions and attain a stronger level of neural collapse. Additionally, we show that at the same level of NC1, models under label smoothing loss exhibit intensified NC2. These findings provide valuable insights into the performance benefits and enhanced model calibration under label smoothing loss. We then leverage the unconstrained feature model to derive closed-form solutions for the global minimizers for both loss functions and further demonstrate that models under label smoothing have a lower conditioning number and, therefore, theoretically converge faster. Our study, combining empirical evidence and theoretical results, not only provides nuanced insights into the differences between label smoothing and cross-entropy losses, but also serves as an example of how the powerful neural collapse framework can be used to improve our understanding of DNNs