L 2 C: Combining Lossy and Lossless Compression on Memory and I/O

In this article, we introduce L 2 C, a hybrid lossy/lossless compression scheme applicable both to the memory subsystem and I/O traffic of a processor chip. L 2 C employs general-purpose lossless compression and combines it with state-of-the-art lossy compression to achieve compression ratios up to 16:1 and to improve the utilization of chip’s bandwidth resources. Compressing memory traffic yields lower memory access time, improving system performance, and energy efficiency. Compressing I/O traffic offers several benefits for resource-constrained systems, including more efficient storage and networking. We evaluate L 2 C as a memory compressor in simulation with a set of approximation-tolerant applications. L 2 C improves baseline execution time by an average of 50% and total system energy consumption by 16%. Compared to the lossy and lossless current state-of-the-art memory compression approaches, L 2 C improves execution time by 9% and 26%, respectively, and reduces system energy costs by 3% and 5%, respectively. I/O compression efficacy is evaluated using a set of real-life datasets. L 2 C achieves compression ratios of up to 10.4:1 for a single dataset and on average about 4:1, while introducing no more than 0.4% error.

Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation

This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.

Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe

We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian, canonical isomorphism between different gauge-fixing surfaces and spacetime reconstruction. We relate this approach to the gauge-fixing procedure for non-perturbative canonical relativity. We discuss the issue of propagating a basis for the scalar-vector-tensor decomposition as, in an anisotropic universe, the wavefronts of plane waves undergo a non-trivial evolution. We show that the definition of a gravitational wave as a traceless-transverse mode of the metric perturbation needs to be revised. Moreover there exist coordinate systems in which a polarization mode of the gravitational wave is given entirely in terms of a scalar metric perturbation. We first develop the formalism for the universe with a single minimally coupled scalar field and then extend it to the multi-field case. The obtained fully canonical formalism will serve as a starting point for a complete quantization of the cosmological perturbations and the cosmological background.

From Classical to Quantum Mechanics

In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.