Dilation theorem via Schr\"odingerisation, with applications to the quantum simulation of differential equations

Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. When used in quantum computing, its practical implementation primarily relies on block-encoding techniques, based on finite-dimensional scenarios. In this study, we delve into the recently devised Schr\"odingerisation approach and demonstrate its viability as an alternative dilation technique. This approach is applicable to operators in the form of $V(t)=\exp(-At)$, which arises in wide-ranging applications, particularly in solving linear ordinary and partial differential equations. Importantly, the Schr\"odingerisation approach is adaptable to both finite and infinite-dimensional cases, in both countable and uncountable domains. For quantum systems lying in infinite dimensional Hilbert space, the dilation involves adding a single infinite dimensional mode, and this is the continuous-variable version of the Schr\"odingerisation procedure which makes it suitable for analog quantum computing. Furthermore, by discretising continuous variables, the Schr\"odingerisation method can also be effectively employed in finite-dimensional scenarios suitable for qubit-based quantum computing

Visual Analytics of Neuron Vulnerability to Adversarial Attacks on Convolutional Neural Networks

Adversarial attacks on a convolutional neural network (CNN) -- injecting human-imperceptible perturbations into an input image -- could fool a high-performance CNN into making incorrect predictions. The success of adversarial attacks raises serious concerns about the robustness of CNNs, and prevents them from being used in safety-critical applications, such as medical diagnosis and autonomous driving. Our work introduces a visual analytics approach to understanding adversarial attacks by answering two questions: (1) which neurons are more vulnerable to attacks and (2) which image features do these vulnerable neurons capture during the prediction? For the first question, we introduce multiple perturbation-based measures to break down the attacking magnitude into individual CNN neurons and rank the neurons by their vulnerability levels. For the second, we identify image features (e.g., cat ears) that highly stimulate a user-selected neuron to augment and validate the neuron's responsibility. Furthermore, we support an interactive exploration of a large number of neurons by aiding with hierarchical clustering based on the neurons' roles in the prediction. To this end, a visual analytics system is designed to incorporate visual reasoning for interpreting adversarial attacks. We validate the effectiveness of our system through multiple case studies as well as feedback from domain experts.Comment: Accepted by the Special Issue on Human-Centered Explainable AI, ACM Transactions on Interactive Intelligent System

Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit

The exact elementary excitations in a typical U(1) symmetry broken quantum integrable system, that is the twisted J1-J2 spin chain with nearest-neighbor, next nearest neighbor and chiral three spin interactions, are studied. The main technique is that we quantify the energy spectrum of the system by the zero roots of transfer matrix instead of the traditional Bethe roots. From the numerical calculation and singularity analysis, we obtain the patterns of zero roots. Based on them, we analytically obtain the ground state energy and the elementary excitations in the thermodynamic limit. We find that the system also exhibits the nearly degenerate states in the regime of $\eta\in \mathbb{R}$, where the nearest-neighbor couplings among the z-direction are ferromagnetic. More careful study shows that the competing of interactions can induce the gapless low-lying excitations and quantum phase transition in the antiferromagnetic regime with $\eta\in \mathbb{R}+i\pi$.Comment: 29 pages, 20 figure

Study on the Reasonable Smoke Exhaust Rate of the Crossrange Exhaust Duct in Double-layer Shield Tunnel

AbstractThe research on the concentrated smoke extraction system of crossrange exhaust duct in double-layer shield tunnel is still very lack in the world. This paper is on the smoke extraction system of double-layer shield tunnel. It will provide the supports and references for the smoke control of tunnel fire and the determination of related technical parameters in the design of tunnel fire ventilation and smoke extraction, so it has important scientific value, practical significance and application prospects. This paper bases on the tunnel project of Slender West Lake in Yangzhou. By using the method of combining theory and numerical simulation, a conclusion can be drawn that the reasonable smoke exhaust rate of the upper tunnel is 140 m3/s

An Accurate Bilinear Cavern Model for Compressed Air Energy Storage

Compressed air energy storage is suitable for large-scale electrical energy storage, which is important for integrating renewable energy sources into electric power systems. A typical compressed air energy storage plant consists of compressors, expanders, caverns, and a motor/generator set. Current cavern models used for compressed air energy storage are either accurate but highly nonlinear or linear but inaccurate. The application of highly nonlinear cavern models in power system optimization problems renders them computationally challenging to solve. In this regard, an accurate bilinear cavern model for compressed air energy storage is proposed in this paper. The charging and discharging processes in a cavern are divided into several real/virtual states. The first law of thermodynamics and ideal gas law are then utilized to derive a cavern model, i.e., a model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bilinear model. The accuracy of the bilinear cavern model is verified via comparison with both an accurate nonlinear model and two sets of field-measured data. The bilinear cavern model can be easily linearized and is then suitable for integration into optimization problems considering compressed air energy storage. This is verified via comparatively solving a self-scheduling problem of compressed air energy storage using different cavern models.Comment: 18 pages, 15 figures, accepted by Applied Energy on March 201

Energy saving strategy for the development of icephobic coatings and surfaces

Aircraft are frequently exposed to cold environments and ice accumulation on aircraft surface may lead to catastrophic accidents. An effective solution of ice protection is a critical requirement in the aerospace industry. For the research and development of icephobic coatings, the current coating design target mainly focuses on lowering the ice adhesion strength between the ice and the surface. However, as a passive ice protection approach, the use of icephobic coating often has to be combined with an active ice protection solution (e.g. electro-thermal heating, hot air bleeding, and vibration, etc.), especially for the in-flight application where the reliability of ice protection must be ensured. Therefore, ice adhesion strength is no longer the sole criterion to evaluate the icephobic performance of a coating or a surface. It is a need to establish a more practical strategy for the design of icephobic coatings and surface. In this work, an energy saving strategy is proposed to assess the de-icing performance of the icephobic coating and surface when active heating is involved. The energy consumed for the de-icing operation assisted by the ice gravity is used as the key criterion for the overall performance of icephobic coating and surface. Successful validation has been achieved for evaluating the de-icing performance of selected coatings and surfaces, which demonstrates an alternative strategy for the design and practical application of icephobic coatings and surfaces in ice protection

Gillespie’s questions and Grothendieck duality

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings $R$ do we have $\mathrm{K}(\mathrm{AC})=\mathrm{K}(R\text{-}\mathrm{Inj})$?”. We give an answer to such a question. As applications, we obtain a new homological approach that unifies some well-known conditions of rings such that Krause’s recollement holds, and give an example to show that there exists a Gorenstein injective module which is not Gorenstein AC-injective. We also improve Neeman’s angle of view to the Grothendieck duality for derived categories of modules from the case of left Noether and right coherent rings such that all flat left modules have finite projective dimension to the case of left and right coherent rings