A functional for the momentum equations of incompressible viscous flow

Vectorial mechanics and analytical mechanics are two time-honored forms of classical mechanics. Vectorial mechanics is mainly based on Newton’s l aws i n a c lear a nd simple mathematical form. It has achieved a high degree of sophistication and success in solid mechanics. Analytical mechanics is based on the principle of virtual work and D'Alembert’s principle, which is highly universal. Often, the term vectorial mechanics is applied to the form based on Newton's work, to contrast it with analytical mechanics which uses two scalar properties of motion, the kinetic and potential energies, instead of vector forces, to analyze the motions. Analytical mechanics was primarily developed to extend the scope of classical mechanics in a systematic, generalized and efficient way to solve problems using the concept of constraints on systems and path integrals. In this paper, we give a functional of fluid in Lagrangian form. Then we demonstrate that the momentum equations of incompressible viscous flow can be achieved after several mathematical operations. At last, we show the Eulerian approximation of the energy functional under some assumptions. Our work lays a good foundation for our numerical methods

A hazard analysis via an improved timed colored petri net with time–space coupling safety constraint

AbstractPetri nets are graphical and mathematical tools that are applicable to many systems for modeling, simulation, and analysis. With the emergence of the concept of partitioning in time and space domains proposed in avionics application standard software interface (ARINC 653), it has become difficult to analyze time–space coupling hazards resulting from resource partitioning using classical or advanced Petri nets. In this paper, we propose a time–space coupling safety constraint and an improved timed colored Petri net with imposed time–space coupling safety constraints (TCCP-NET) to fill this requirement gap. Time–space coupling hazard analysis is conducted in three steps: specification modeling, simulation execution, and results analysis. A TCCP-NET is employed to model and analyze integrated modular avionics (IMA), a real-time, safety-critical system. The analysis results are used to verify whether there exist time–space coupling hazards at runtime. The method we propose demonstrates superior modeling of safety-critical real-time systems as it can specify resource allocations in both time and space domains. TCCP-NETs can effectively detect underlying time–space coupling hazards

Experimental quantum key distribution with source flaws

Decoy-state quantum key distribution (QKD) is a standard technique in current quantum cryptographic implementations. Unfortunately, existing experiments have two important drawbacks: the state preparation is assumed to be perfect without errors and the employed security proofs do not fully consider the finite-key effects for general attacks. These two drawbacks mean that existing experiments are not guaranteed to be secure in practice. Here, we perform an experiment that for the first time shows secure QKD with imperfect state preparations over long distances and achieves rigorous finite-key security bounds for decoy-state QKD against coherent attacks in the universally composable framework. We quantify the source flaws experimentally and demonstrate a QKD implementation that is tolerant to channel loss despite the source flaws. Our implementation considers more real-world problems than most previous experiments and our theory can be applied to general QKD systems. These features constitute a step towards secure QKD with imperfect devices.Comment: 12 pages, 4 figures, updated experiment and theor

Liquiritin alleviates spinal cord injury through suppression of inflammation, oxidative stress, and cell apoptosis in a rat model

Purpose: Liquiritin is an extract from Glycyrrhiza Radix, one of the oldest traditional Chinese herbal medicines, which is commonly used to treat various injuries and swellings. This study is aimed to determine whether liquiritin can protect spinal cord injuries (SCIs) from secondary injuries. Methods: A rat SCI model was established. After liquiritin treatment, the neural-function of Rats was determined by Basso, Beattie and Bresnahan (BBB) scores, paw withdrawal threshold (PWT), and thermal withdrawal latency (PWL). The effects of anti-inflammation, anti-oxidation, and anti-apoptosis of liquiritin were also examined in the rats with SCI. Moreover, the activities of several signaling elements, such as, inflammation-associated nuclear factor kappa-light-chain-enhancer of activated B cells (NFκB), toll-like receptor 4 (TLR4), proliferative-related p38 mitogen-activated protein kinases (MAPK) and myeloid differentiation primary response 88 (MyD88) which was involved in the TLR4 signaling, were used for further investigation of the underlying molecular mechanisms. Results: Liquiritin improved locomotor function recovery, alleviated allodynia and hyperalgesia, and decreased water content of spinal cord in SCI rats. Also, liquiritin reduced SCI–induced inflammatory responses by decreasing the levels of tumor necrosis factor alpha (TNF-α), interleukin 1 beta (IL-1β), and IL-6. Liquiritin inhibited SCI–induced oxidative stress by decreasing malondialdehyde (MDA) level and increasing the levels of uperoxide dismutase (SOD) (p < 0.05), glutathione (GSH) (p < 0.01), and GSH-PX (p < 0.001). In addition, liquiritin alleviated spinal cord injury (SCI) –induced apoptosis of neural cells by decreasing the expression of cleaved caspase-9, -3 and cleaved poly ADP-ribose polymerase (PARP). Finally, liquiritin decreased spinal cord injury (SCI) -induced up-regulation of TLR4/MyD88/NF-κB and p38 MAPK signaling cascades. Conclusion: Liquiritin exerts protective role in SCI by reducing excessive inflammation, suppressing oxidative stress, and inhibiting neural cell apoptosis in a rat model of SCI. Thus, the agent can potentially be used for the management of SC

Effects of the Variation in Brain Tissue Mechanical Properties on the Intracranial Response of a 6-Year-Old Child

Brain tissue mechanical properties are of importance to investigate child head injury using finite element (FE) method. However, these properties used in child head FE model normally vary in a large range in published literatures because of the insufficient child cadaver experiments. In this work, a head FE model with detailed anatomical structures is developed from the computed tomography (CT) data of a 6-year-old healthy child head. The effects of brain tissue mechanical properties on traumatic brain response are also analyzed by reconstruction of a head impact on engine hood according to Euro-NCAP testing regulation using FE method. The result showed that the variations of brain tissue mechanical parameters in linear viscoelastic constitutive model had different influences on the intracranial response. Furthermore, the opposite trend was obtained in the predicted shear stress and shear strain of brain tissues caused by the variations of mentioned parameters

DiskANN++: Efficient Page-based Search over Isomorphic Mapped Graph Index using Query-sensitivity Entry Vertex

Given a vector dataset $\mathcal{X}$ and a query vector $\vec{x}_q$, graph-based Approximate Nearest Neighbor Search (ANNS) aims to build a graph index $G$ and approximately return vectors with minimum distances to $\vec{x}_q$ by searching over $G$. The main drawback of graph-based ANNS is that a graph index would be too large to fit into the memory especially for a large-scale $\mathcal{X}$. To solve this, a Product Quantization (PQ)-based hybrid method called DiskANN is proposed to store a low-dimensional PQ index in memory and retain a graph index in SSD, thus reducing memory overhead while ensuring a high search accuracy. However, it suffers from two I/O issues that significantly affect the overall efficiency: (1) long routing path from an entry vertex to the query's neighborhood that results in large number of I/O requests and (2) redundant I/O requests during the routing process. We propose an optimized DiskANN++ to overcome above issues. Specifically, for the first issue, we present a query-sensitive entry vertex selection strategy to replace DiskANN's static graph-central entry vertex by a dynamically determined entry vertex that is close to the query. For the second I/O issue, we present an isomorphic mapping on DiskANN's graph index to optimize the SSD layout and propose an asynchronously optimized Pagesearch based on the optimized SSD layout as an alternative to DiskANN's beamsearch. Comprehensive experimental studies on eight real-world datasets demonstrate our DiskANN++'s superiority on efficiency. We achieve a notable 1.5 X to 2.2 X improvement on QPS compared to DiskANN, given the same accuracy constraint.Comment: 15 pages including reference

Cytotoxicity Study of Cyclopentapeptide Analogues of Marine Natural Product Galaxamide towards Human Breast Cancer Cells

Herein, we report the cytotoxicity of cyclopentapeptide analogues of marine natural product galaxamide towards breast carcinoma cells and the underlying mechanisms. We examined the effect of the novel galaxamide analogues on cancer cell proliferation by MTT assay and also further examined the most active compound for morphological changes using Hoechst33342 staining technique, induction of apoptosis, cell cycle phases, mitochondrial membrane potential (MMP), and reactive oxygen species (ROS) generation using flow cytometry in human breast cancer MCF-7 cells in vitro. Galaxamide and its analogues effectively induced toxicity in human hepatocellular carcinoma HepG2, human breast carcinoma MCF-7, human epitheloid cervix carcinoma HeLa, and human breast carcinoma MB-MDA-231 cell lines. Amongst them, compound 3 exhibited excellent toxicity towards MCF-7 cells. This galaxamide analogue significantly induced apoptosis in a dose-dependent manner in MCF-7 cells involves cell cycle arrest in the G1 phase, a reduction of MMP, and a marked increase in generation of ROS. Particularly, compound 3 of galaxamide analogues might be a potential candidate for the treatment of breast cancer