On the Sensitivity Complexity of k-Uniform Hypergraph Properties

In this paper we investigate the sensitivity complexity of hypergraph properties. We present a k-uniform hypergraph property with sensitivity complexity O(n^{ceil(k/3)}) for any k >= 3, where n is the number of vertices. Moreover, we can do better when k = 1 (mod 3) by presenting a k-uniform hypergraph property with sensitivity O(n^{ceil(k/3)-1/2}). This result disproves a conjecture of Babai, which conjectures that the sensitivity complexity of k-uniform hypergraph properties is at least Omega(n^{k/2}). We also investigate the sensitivity complexity of other weakly symmetric functions and show that for many classes of transitive-invariant Boolean functions the minimum achievable sensitivity complexity can be O(N^{1/3}), where N is the number of variables. Finally, we give a lower bound for sensitivity of k-uniform hypergraph properties, which implies the sensitivity conjecture of k-uniform hypergraph properties for any constant k

On the Optimality of Tape Merge of Two Lists with Similar Size

The problem of merging sorted lists in the least number of pairwise comparisons has been solved completely only for a few special cases. Graham and Karp \cite{taocp} independently discovered that the tape merge algorithm is optimal in the worst case when the two lists have the same size. In the seminal papers, Stockmeyer and Yao\cite{yao}, Murphy and Paull\cite{3k3}, and Christen\cite{christen1978optimality} independently showed when the lists to be merged are of size $m$ and $n$ satisfying $m\leq n\leq\lfloor\frac{3}{2}m\rfloor+1$, the tape merge algorithm is optimal in the worst case. This paper extends this result by showing that the tape merge algorithm is optimal in the worst case whenever the size of one list is no larger than 1.52 times the size of the other. The main tool we used to prove lower bounds is Knuth's adversary methods \cite{taocp}. In addition, we show that the lower bound cannot be improved to 1.8 via Knuth's adversary methods. We also develop a new inequality about Knuth's adversary methods, which might be interesting in its own right. Moreover, we design a simple procedure to achieve constant improvement of the upper bounds for $2m-2\leq n\leq 3m$

Longitudinal Optogenetic Motor Mapping Revealed Structural and Functional Impairments and Enhanced Corticorubral Projection after Contusive Spinal Cord Injury in Mice

Current evaluation of impairment and repair after spinal cord injury (SCI) is largely dependent on behavioral assessment and histological analysis of injured tissue and pathways. Here, we evaluated whether transcranial optogenetic mapping of motor cortex could reflect longitudinal structural and functional damage and recovery after SCI. In Thy1-Channelrhodopsin2 transgenic mice, repeated motor mappings were made by recording optogenetically evoked electromyograms (EMGs) of a hindlimb at baseline and 1 day and 2, 4, and 6 weeks after mild, moderate, and severe spinal cord contusion. Injuries caused initial decreases in EMG amplitude, losses of motor map, and subsequent partial recoveries, all of which corresponded to injury severity. Reductions in map size were positively correlated with motor performance, as measured by Basso Mouse Scale, rota-rod, and grid walk tests, at different time points, as well as with lesion area at spinal cord epicenter at 6 weeks post-SCI. Retrograde tracing with Fluoro-Gold showed decreased numbers of cortico- and rubrospinal neurons, with the latter being negatively correlated with motor map size. Combined retro- and anterograde tracing and immunostaining revealed more neurons activated in red nucleus by cortical stimulation and enhanced corticorubral axons and synapses in red nucleus after SCI. Electrophysiological recordings showed lower threshold and higher amplitude of corticorubral synaptic response after SCI. We conclude that transcranial optogenetic motor mapping is sensitive and efficient for longitudinal evaluation of impairment and plasticity of SCI, and that spinal cord contusion induces stronger anatomical and functional corticorubral connection that may contribute to spontaneous recovery of motor function

A hybrid algorithm for quadratically constrained quadratic optimization problems

Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables on the amplitude of a quantum state, the requirement of the qubit number scales logarithmically with the dimension of the variables, which makes our algorithm suitable for current quantum devices. Using the primal-dual interior-point method in classical optimization, we can deal with general quadratic constraints. Our numerical experiments on typical QCQP problems, including Max-Cut and optimal power flow problems, demonstrate a better performance of our hybrid algorithm over the classical counterparts.Comment: 8 pages, 3 figure

Improved Real-time Post-Processing for quantum Random Number Generators

Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum-proof randomness extractors characterizing the input raw data as min-entropy sources, we find that the input raw data generated by a large class of trusted-device quantum random number generators can be characterized as the so-called reverse block source. This fact enables us to design improved extractors. Specifically, we propose two novel quantum-proof randomness extractors for reverse block sources that realize real-time block-wise extraction. In comparison with the general min-entropy randomness extractors, our designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make our design an adequate choice for the real-time post-processing of practical quantum random number generators. Applying our extractors to the raw data of the fastest known quantum random number generator, we achieve a simulated extraction speed as high as 374 Gbps.Comment: 11 pages, 3 figure

Discussion on Quality Control Mode of Internet + Greening Maintenance

With the rapid increase of the construction volume of our country's landscape industry, the scale of the stock gardens is getting larger and larger. Later gardening maintenance technology needs to be constantly updated, and management modes and methods should be constantly innovated to meet the development needs of the maintenance market. The quality of maintenance and management in the later stage of green space construction is intuitively presented to the viewers through the quality of landscape. Therefore, improving the quality control ability of green space is the most important thing for the rapid development of garden enterprises. This paper combines the Internet with traditional maintenance quality management through Internet thinking, and achieves several important points in quality control, such as planning, traces, inspection, reporting and customer service evaluation, on the Internet management and control platform. Among them, the work plan combined with the maintenance calendar, the climate and soil and other environmental data from all parts of the country can better guide the field work; Maintenance trace record can provide data feedback through pictures, videos, etc.; Patrol function discovers green space problems in time, records data of basic problems of green space and feedback processing; And reporting function can provide customers with more convenient maintenance services. The addition of customer evaluation forms an important closed-loop for staff management and site quality from the perspective of customers. To some extent, this study solved the problems of insufficient quality standards and low efficiency under the traditional maintenance management mode, which accords with people’s service demand for greening maintenance at the present stage, and helps to enhance people’s recognition of greening personnel. With the help of Internet management and control thinking, we can better solve the pain points existing in the development of maintenance enterprises, provide new tools for the better development of maintenance industry, and lay a foundation for the growth of maintenance industry

Bi-level optimal dispatching of distribution network considering friendly interaction with electric vehicle aggregators

The widespread application of electric vehicles (EVs) is a positive force driving green development. However, their widespread penetration also poses significant challenges and threats to the security and stable operation of the power grid. To address this urgent issue, this article constructs a bi-level optimal dispatching model fostering collaboration between electric vehicle aggregators and the distribution network. The upper-level optimization targets the minimization of peak-valley differences in the distribution network via considerably arranging power outputs of gas turbines, while the lower-level one focuses on reducing the charging expense of EV aggregators via efficient charging transfer. Note that the charging expense is not only composed of electric cost but also a dynamic carbon emission factor-based cost, which contributes to the electricity economy and carbon reduction concurrently. A geometric mean optimizer (GMO) is introduced to solve the mode. Its efficiency is evaluated against three typical algorithms, i.e., genetic algorithm, great-wall construction algorithm, and optimization algorithm based on an extended IEEE 33-bus system with different charging behaviors of EVs on both a typical weekday and weekend. Simulation results demonstrate that the GMO outperforms other competitive algorithms in accuracy and stability. The peak-valley difference between the distribution network and the total cost of EV aggregators can be decreased by over 98% and 76%, respectively

Effect of post-homogenisation cooling rate and Mn addition on Mg2Si precipitation and hot workability of AA6060 alloys

The microstructure evolution for different post-homogenisation cooling rates and the flow stress behaviour in direct chill cast AA6060 alloys were studied. Results revealed that decreasing cooling rates reduced the flow stress owing to the precipitation of Mg2Si and reduction of the solid solution level. Micro-alloying of Mn generated a distribution of α-Al(FeMn)Si dispersoids during the homogenisation, with the size and number density decreasing at higher homogenisation temperatures. TEM studies confirmed that the dispersoids acted as favourable nucleation sites for Mg2Si and significantly promoted the precipitation of Mg2Si during subsequent cooling. The high-temperature flow stress was controlled by the solid solution levels of Mg, Si, and Mn resulting from the interaction between dispersoids and Mg2Si. The combination of the Mn addition, a low cooling rate, and a low homogenisation temperature provided the lowest flow stress, which improved the hot workability of the alloy and promoted ready dissolution of Mg2Si during extrusion. On a étudié l’évolution de la microstructure pour différentes vitesses de refroidissement post-homogénéisation et le comportement de la contrainte d’écoulement des alliages AA6060 coulés à froid. Les résultats ont révélé que la diminution des vitesses de refroidissement réduisait la contrainte d’écoulement en raison de la précipitation du Mg2Si et de la réduction du niveau de solution solide. Le microalliage de Mn a engendré une distribution de dispersoïdes Al(FeMn)Si-α pendant l’homogénéisation, la taille et la densité numérique diminuant aux températures plus élevées d’homogénéisation. Les études de MET ont confirmé que les dispersoïdes agissaient comme des sites favorables à la nucléation du Mg2Si et favorisaient de manière significative la précipitation du Mg2Si lors du refroidissement subséquent. La contrainte d’écoulement à haute température était contrôlée par les niveaux de solution solide de Mg, Si et Mn résultant de l’interaction entre les dispersoïdes et le Mg2Si. La combinaison de l’addition de Mn, d’une faible vitesse de refroidissement et d’une basse température d’homogénéisation fournissait la contrainte d’écoulement la plus faible, ce qui améliorait la malléabilité à chaud de l’alliage et favorisait la dissolution rapide du Mg2Si pendant l’extrusion