Sumset Fractal Properties

In this paper we introduce two notions of fractal sumset properties. A set $K\subset\mathbb{R}^d$ is said to have the Hausdorff sumset property (HSP) if for any $\ell\in\mathbb{N}_{\ge 2}$ there exist sets $K_1, K_2,\ldots, K_\ell$ such that $K_1+K_2+\cdots+K_\ell\subset K$ and $\dim_H K_i=\dim_H K$ for all $1\le i\le \ell$. Analogously, if we replace the Hausdorff dimension by the packing dimension in the definition of HSP, then the set $K\subset\mathbb{R}^d$ is said to have the packing sumset property (PSP). We show that the HSP and the PSP hold for a large class of sets in $\mathbb{R}^d$ with any given dimension $\alpha\in(0, d)$. On the other hand, the HSP fails for certain homogeneous self-similar sets satisfying the strong separation condition, while the PSP holds for all homogeneous self-similar sets in $\mathbb{R}^d$.Comment: 11 page

Analysis of Aseismic Reliability Considering the Uncertainties Both Structural Parameters and Earthquake Loadings for the Gravity Type Earth-Retaining Wall

A simple numerical deterministic approach for evaluating stochastic properties of structural systems with uncertain parameters under random seismic excitations (“double-random problem”) is presented. The method is based on the impulse response function method, the perturbation law and random central differential law. On the other hand, the equivalent linear model is used to account for the nonlinearity of soil. On the basis of the above random response analysis method, the aseismic reliability of earth-retaining wall is calculated and the analysis flow of dynamic reliability under the stationary random seismic action is also presented. From the above analysis, we can see that it is equally important both structural parameters and seismic excitations, the maximum value response including the displacement, moment and resultant force will increase with the heightening of reliability index and the aseismic design by linear model will result risk than non-linear model. The simulation analysis result verifies that the proposed method is applicable to the aseismic reliability analysis by contrast with the Richard-Elms displacement method and field actual measurements, which also provides a practical way for analyzing the aseismic reliability of other geotechnical engineering structures

Restricted phase space thermodynamics of charged AdS black holes in conformal gravity

The thermodynamics of charged spherically symmetric AdS black holes in conformal gravity is revisited using the recently proposed restricted phase space (RPS) formalism. This formalism avoids all the bizarreness that arose in the extended phase space formalism for this model. It is found that the charged AdS black holes in this model may belong to a new universality class which is different from all previously studied cases under the RPS formalism. Besides the distinguished isocharge $T-S$ and isothermal $\Phi-Q_e$ behaviors, the absence of Hawking-Page transition is another notable feature. On the other hand, in the high temperature limit, the thermodynamic behavior of the present model become exactly the same as that of the Einstein gravity and the black hole scan models, which add further evidence for the universality of the recently reported correspondence between high temperature AdS black holes and low temperature quantum phonon gases in nonmetallic crystals.Comment: 20 pages, 11 pdf figure

Topological black holes in Einstein-Maxwell and 4D conformal gravities revisited

The thermodynamics of charged topological black holes (TBHs) with different horizon geometries in $d$-dimensional Einstein-Maxwell and 4-dimensional conformal gravities is revisited using the restricted phase space formalism. The concept of subsystems for black holes is introduced, which enables a precise description for the thermodynamic behaviors of (non-compact) black holes with infinitely large horizon area. The concrete behaviors can be different for TBHs in the same underlying theory but with different horizon geometries, or for those with the same horizon geometry but from different underlying theories. In some concrete thermodynamic processes, the non-compact black holes in 4-dimensional conformal gravity can reach certain state with zero entropy but nonvanishing temperature, which is physically unsounded. This suggests a novel use of black hole thermodynamics as a tool for testing the viability of gravity models or constraining the model parameters or integration constants. The high and low temperature limits of the TBHs are also considered, and it is found that, at high temperature, all TBHs behave like low temperature phonon gases, while at low temperature, all charged as well as neutral hyperbolic TBHs in Einstein-Maxwell gravity behave like strongly degenerated electron gases. Finally, using the concept of subsystems, some conceptual issues in the description for thermal fluctuations in black hole systems are clarified, and the relative thermal fluctuations for finite subsystems are also analyzed in some detail.Comment: 52 pages, 11 pdf figures. Version matching published versio

PhotoRedshift-MML: a multimodal machine learning method for estimating photometric redshifts of quasars

We propose a Multimodal Machine Learning method for estimating the Photometric Redshifts of quasars (PhotoRedshift-MML for short), which has long been the subject of many investigations. Our method includes two main models, i.e. the feature transformation model by multimodal representation learning, and the photometric redshift estimation model by multimodal transfer learning. The prediction accuracy of the photometric redshift was significantly improved owing to the large amount of information offered by the generated spectral features learned from photometric data via the MML. A total of 415,930 quasars from Sloan Digital Sky Survey (SDSS) Data Release 17, with redshifts between 1 and 5, were screened for our experiments. We used |{\Delta}z| = |(z_phot-z_spec)/(1+z_spec)| to evaluate the redshift prediction and demonstrated a 4.04% increase in accuracy. With the help of the generated spectral features, the proportion of data with |{\Delta}z| < 0.1 can reach 84.45% of the total test samples, whereas it reaches 80.41% for single-modal photometric data. Moreover, the Root Mean Square (RMS) of |{\Delta}z| is shown to decreases from 0.1332 to 0.1235. Our method has the potential to be generalized to other astronomical data analyses such as galaxy classification and redshift prediction. The algorithm code can be found at https://github.com/HongShuxin/PhotoRedshift-MML .Comment: 10 pages, 8 figures, accepted for publication in MNRA

Unsupervised Video Domain Adaptation for Action Recognition: A Disentanglement Perspective

Unsupervised video domain adaptation is a practical yet challenging task. In this work, for the first time, we tackle it from a disentanglement view. Our key idea is to handle the spatial and temporal domain divergence separately through disentanglement. Specifically, we consider the generation of cross-domain videos from two sets of latent factors, one encoding the static information and another encoding the dynamic information. A Transfer Sequential VAE (TranSVAE) framework is then developed to model such generation. To better serve for adaptation, we propose several objectives to constrain the latent factors. With these constraints, the spatial divergence can be readily removed by disentangling the static domain-specific information out, and the temporal divergence is further reduced from both frame- and video-levels through adversarial learning. Extensive experiments on the UCF-HMDB, Jester, and Epic-Kitchens datasets verify the effectiveness and superiority of TranSVAE compared with several state-of-the-art methods. The code with reproducible results is publicly accessible.Comment: 18 pages, 9 figures, 7 tables. Code at https://github.com/ldkong1205/TranSVA

ANALYSIS AND STUDY ON 47 CASES OF ADVERSE REACTIONS OF CHINESE MEDICINE INJECTION

Background: Along with efficacy, Chinese medicine is increasingly being known to people, Chinese medicine and its preparations are increasingly widespread in clinical use. People generally believe that Chinese medicine has few side effects and is safe, especially Chinese medicine injections. Due to the direct injection in blood, rapid onset and good efficacy, they are welcomed by people. However, with increased use, adverse reactions are increasing, even causing serious consequences. The objective is to learn about the characteristics and laws of the adverse effects of Chinese medicine injections, provide references for the clinical safe drug use, and reduce the incidence of adverse reactions. Materials and Methods: The method was established to analyze the data of 47 cases of adverse reactions caused by Chinese medicine injections in our hospital from the year, 2009 to 2010. Results: The organs / systems involved in the 47 cases of adverse reactions are primarily skin and its accessories and secondly systemic damage, involving a total of eight varieties of drugs. Conclusion: The adverse reactions of Chinese medicine injections are mostly in Chinese patent drugs, which should be paid attention to, to find out the problems and laws, use the drugs rationally, and reduce the incidence of the adverse reactions

Modeling and Analysis of ETC Control System with Colored Petri Net and Dynamic Slicing

Nowadays, an Electronic Toll Collection (ETC) control system in highways has been widely adopted to smoothen traffic flow. However, as it is a complex business interaction system, there are inevitably flaws in its control logic process, such as the problem of vehicle fee evasion. Even we find that there are more than one way for vehicles to evade fees. This shows that it is difficult to ensure the completeness of its design. Therefore, it is necessary to adopt a novel formal method to model and analyze its design, detect flaws and modify it. In this paper, a Colored Petri net (CPN) is introduced to establish its model. To analyze and modify the system model more efficiently, a dynamic slicing method of CPN is proposed. First, a static slice is obtained from the static slicing criterion by backtracking. Second, considering all binding elements that can be enabled under the initial marking, a forward slice is obtained from the dynamic slicing criterion by traversing. Third, the dynamic slicing of CPN is obtained by taking the intersection of both slices. The proposed dynamic slicing method of CPN can be used to formalize and verify the behavior properties of an ETC control system, and the flaws can be detected effectively. As a case study, the flaw about a vehicle that has not completed the payment following the previous vehicle to pass the railing is detected by the proposed method

Plastic regulates its co-pyrolysis process with biomass: Influencing factors, model calculations, and mechanisms

Co-pyrolysis of plastics and biomass can effectively improve the quality of bio-oil and solve the problem of plastic pollution. However, synergistic effect of co-pyrolysis on kinetics and the role of biomass H/Ceff in co-pyrolysis are still not conclusive. In this work, the co-pyrolysis synergistic effects of three different hydrogen-to-carbon ratio (H/Ceff) of biomass-rice husk (RH), sugarcane bagasse (SUG), and poplar wood (PW) with hydrogen-rich polypropylene (PP) were studied using a thermogravimetric method. The total synergy degree (φ) and the difference between experimental and theoretical weight losses (ΔW) were defined, and the activation energies of various experimental materials were calculated by the isoconversional method. The results showed that the addition of PP reduced the dependence of product species on biomass H/Ceff during co-pyrolysis. The synergistic effect of biomass and PP was related to biomass types, pyrolysis temperature, and mass ratio of biomass to PP. The mixture of SUG and PP showed positive synergistic effect at all mass ratios. Simultaneously, at the low temperature of pyrolysis, the synergistic effect is inhibited in all mixtures, which might be due to the melting of PP. Kinetic analysis showed that the activation energy could be reduced by 11.14–31.78% by co-pyrolysis with biomass and PP. A multi-step mechanism was observed in both the pyrolysis of a single sample and the co-pyrolysis of a mixture, according to Criado’s schematic analysis