GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc

Efficient protection of the pipeline core for safety-critical processor-based systems

The increasing number of safety-critical commercial applications has generated a need for components with high levels of reliability. As CMOS process sizes continue to shrink, the reliability of ICs is negatively affected since they become more sensitive to transient faults. New circuit designs must take this fact into consideration, and incorporate adequate protection against the effects of transient faults. This paper presents a novel method for protecting the pipelined execution unit of an embedded processor. It is based on a self-configured architecture with hybrid redundancy that can mask single and multiple errors, which can occur on storage elements due to transient or permanent faults. This concept can be easily applied to any processing architecture of this nature with a high safety integrity level. Results from error-injection experiments are also reported that show that this design can maintain a non-interrupted and failure-free operation under single and double errors with a probability that exceeds 99.4%

Study of the effects of SEU-induced faults on a pipeline protected microprocessor

This paper presents a detailed analysis of the behavior of a novel fault-tolerant 32-bit embedded CPU as compared to a default (non-fault-tolerant) implementation of the same processor during a fault injection campaign of single and double faults. The fault-tolerant processor tested is characterized by per-cycle voting of microarchitectural and the flop-based architectural states, redundancy at the pipeline level, and a distributed voting scheme. Its fault-tolerant behavior is characterized for three different workloads from the automotive application domain. The study proposes statistical methods for both the single and dual fault injection campaigns and demonstrates the fault-tolerant capability of both processors in terms of fault latencies, the probability of fault manifestation, and the behavior of latent faults

Toric anti-self-dual Einstein metrics via complex geometry

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen (math.DG/0105263), who describe where the Einstein metrics appear amongst the Joyce spaces, leading to a different classification. Taking the twistor transform of our result gives a new proof of their theorem.Comment: v2. Published version. Additional references. 14 page

Application of Pulsed Field Gel Electrophoresis to Determine γ-ray-induced Double-strand Breaks in Yeast Chromosomal Molecules

The frequency of DNA double-strand breaks (dsb) was determined in yeast cells exposed to γ-rays under anoxic conditions. Genomic DNA of treated cells was separated by pulsed field gel electrophoresis, and two different approaches for the evaluation of the gels were employed: (1) The DNA mass distribution profile obtained by electrophoresis was compared to computed profiles, and the number of DSB per unit length was then derived in terms of a fitting procedure; (2) hybridization of selected chromosomes was performed, and a comparison of the hybridization signals in treated and untreated samples was then used to derive the frequency of dsb

Estimating energy consumption of residential buildings at scale with drive-by image capture

Data-driven approaches to addressing climate change are increasingly becoming a necessary solution to deal with the scope and scale of interventions required to reach net zero. In the UK, housing contributes to over 30% of the national energy consumption, and a massive rollout of retrofit is needed to meet government targets for net zero by 2050. This paper introduces a modular framework for quantifying building features using drive-by image capture and utilising them to estimate energy consumption. The framework is demonstrated on a case study of houses in a UK neighbourhood, showing that it can perform comparatively with gold standard datasets. The paper reflects on the modularity of the proposed framework, potential extensions and applications, and highlights the need for robust data collection in the pursuit of efficient, large-scale interventions

Component-level residential building material stock characterization using computer vision techniques

Residential building material stock constitutes a significant part of the built environment, providing crucial shelter and habitat services. The hypothesis concerning stock mass and composition has garnered considerable attention over the past decade. While previous research has mainly focused on the spatial analysis of building masses, it often neglected the component-level stock analysis or where heavy labor cost for onsite survey is required. This paper presents a novel approach for efficient component-level residential building stock accounting in the United Kingdom, utilizing drive-by street view images and building footprint data. We assessed four major construction materials: brick, stone, mortar, and glass. Compared to traditional approaches that utilize surveyed material intensity data, the developed method employs automatically extracted physical dimensions of building components incorporating predicted material types to calculate material mass. This not only improves efficiency but also enhances accuracy in managing the heterogeneity of building structures. The results revealed error rates of 5 and 22% for mortar and glass mass estimations and 8 and 7% for brick and stone mass estimations, with known wall types. These findings represent significant advancements in building material stock characterization and suggest that our approach has considerable potential for further research and practical applications. Especially, our method establishes a basis for evaluating the potential of component-level material reuse, serving the objectives of a circular economy

Noncommutative Electromagnetism As A Large N Gauge Theory

We map noncommutative (NC) U(1) gauge theory on R^d_C X R^{2n}_{NC} to U(N -> \infty) Yang-Mills theory on R^d_C, where R^d_C is a d-dimensional commutative spacetime while R^{2n}_{NC} is a 2n-dimensional NC space. The resulting U(N) Yang-Mills theory on R^d_C is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R^d_C. We show that the gauge-Higgs system (A_\mu,\Phi^a) in the U(N -> \infty) Yang-Mills theory on R^d_C leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A_\mu,\Phi^a) in half-BPS configurations describes self-dual Einstein gravity.Comment: 25 pages; More clarifications, to appear in Eur. Phys. J.