Approximate Analyzing of Labeled Transition Systems

As the most important formal semantic model, labeled transition systems are widely used, which can describe the general concurrent systems or control systems without disturbance. However, under normal circumstance, transition systems are complex and difficult to use due to large amount of calculation and the state space explosion problems. In order to overcome these problems, approximate equivalent labeled transition systems are proposed by means of incomplete low-up matrix decomposition factorization. This technique can reduce the complexity of computation and calculate under the allowing errors. As for continuous-time linear systems, we develop a modeling method of approximated transition system based on the approximate solution of matrix, which provides a facility for approximately formal semantic modeling for linear systems and to effectively analyze errors. An example of application in the context of linear systems without disturbances is studied

A Deductive Approach towards Reasoning about Algebraic Transition Systems

Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible

Research on Design Method of Long-life Asphalt Pavement

In recent years, the problem of early damage of asphalt pavement has been basically solved, and the service performance has been improved, but there are still some deficiencies in design life and service life. This paper investigates the long-life asphalt pavement structure, analyzes the design method of asphalt mixture, and summarizes the pavement design theory and related software. The long-life asphalt pavement with semi-rigid base, flexible base and combined base structure has been designed by four method, including typical load, Per-Road, D50-2006 and D50-2017. Four methods were compared by designing long-life pavements with semi-rigid base and flexible base. The results show that the proposed asphalt pavement structure can meet the requirements of Per-Road, typical load design and D50-2006. However, D50-2017 has higher requirements for the bending and tensile fatigue life of the base layer and requires a thicker base layer. When d50-2017 is used to design flexible base pavement, the fatigue life of asphalt layer should be the main control index, and the fatigue life of sub base course should be the main control index in other pavement de-sign. It remains to be seen whether the proposed highway structure can achieve the design goal of long-life asphalt pavement

Research on Design Method of Long-life Asphalt Pavement

In recent years, the problem of early damage of asphalt pavement has been basically solved, and the service performance has been improved, but there are still some deficiencies in design life and service life. This paper investigates the long-life asphalt pavement structure, analyzes the design method of asphalt mixture, and summarizes the pavement design theory and related software. The long-life asphalt pavement with semi-rigid base, flexible base and combined base structure has been designed by four method, including typical load, Per-Road, D50-2006 and D50-2017. Four methods were compared by designing long-life pavements with semi-rigid base and flexible base. The results show that the proposed asphalt pavement structure can meet the requirements of Per-Road, typical load design and D50-2006. However, D50-2017 has higher requirements for the bending and tensile fatigue life of the base layer and requires a thicker base layer. When d50-2017 is used to design flexible base pavement, the fatigue life of asphalt layer should be the main control index, and the fatigue life of sub base course should be the main control index in other pavement de-sign. It remains to be seen whether the proposed highway structure can achieve the design goal of long-life asphalt pavement

Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit

In the noisy-intermediate-scale-quantum era, Variational Quantum Eigensolver (VQE) is a promising method to study ground state properties in quantum chemistry, materials science, and condensed physics. However, general quantum eigensolvers are lack of systematical improvability, and achieve rigorous convergence is generally hard in practice, especially in solving strong-correlated systems. Here, we propose an Orbital Expansion VQE~(OE-VQE) framework to construct an efficient convergence path. The path starts from a highly correlated compact active space and rapidly expands and converges to the ground state, enabling simulating ground states with much shallower quantum circuits. We benchmark the OE-VQE on a series of typical molecules including H$_{6}$-chain, H$_{10}$-ring and N$_2$, and the simulation results show that proposed convergence paths dramatically enhance the performance of general quantum eigensolvers.Comment: Wu et al 2023 Quantum Sci. Techno

Contrasting response of coexisting plant's water-use patterns to experimental precipitation manipulation in an alpine grassland community of Qinghai Lake watershed, China

Understanding species-specific changes in water-use patterns under recent climate scenarios is necessary to predict accurately the responses of seasonally dry ecosystems to future climate. In this study, we conducted a precipitation manipulation experiment to investigate the changes in water-use patterns of two coexisting species (Achnatherum splendens and Allium tanguticum) to alterations in soil water content (SWC) resulting from increased and decreased rainfall treatments. The results showed that the leaf water potential (Psi) of A. splendens and A. tanguticum responded to changes in shallow and middle SWC at both the control and treatment plots. However, A. splendens proportionally extracted water from the shallow soil layer (0-10cm) when it was available but shifted to absorbing deep soil water (30-60 cm) during drought. By contrast, the A. tanguticum did not differ significantly in uptake depth between treatment and control plots but entirely depended on water from shallow soil layers. The flexible water-use patterns of A. splendens may be a key factor facilitating its dominance and it better acclimates the recent climate change in the alpine grassland community around Qinghai Lake

Approximate Equivalence of the Hybrid Automata with Taylor Theory

Hybrid automaton is a formal model for precisely describing a hybrid system in which the computational processes interact with the physical ones. The reachability analysis of the polynomial hybrid automaton is decidable, which makes the Taylor approximation of a hybrid automaton applicable and valuable. In this paper, we studied the simulation relation among the hybrid automaton and its Taylor approximation, as well as the approximate equivalence relation. We also proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid automata could be compared quantitatively, for example, the approximate equivalence we proposed in the paper