In this paper, we first find a type of viscosity solution of $G$-heat equation under degenerate case, and then obtain the related $G$-capacity $c({B_{T}in A})$ for any Borel set $A$. Furthermore, we prove that $I_{A}(B_{T})$ is not quasi-continuous when it is not a constant function.
The effect of linear chirp frequency on the process of electron-positron pairs production from vacuum in the combined potential wells is investigated by computational quantum field theory. Numerical results of electron number and energy spectrum unde
r different frequency modulation parameters are obtained. By comparing with the fixed frequency, it is found that frequency modulation has a significant enhancement effect on the number of electrons. Especially when the frequency is small, appropriate frequency modulation enhances multiphoton processes in pair creation, thus promoting the pair creation. However, the number of electrons created by high frequency oscillating combined potential wells decreases after frequency modulation due to the phenomenon of high frequency suppression. The contours of the number of electrons varying with frequency and frequency modulation parameters are given, which may provide theoretical reference for possible experiments.
Peptide bonds, as the molecular bridges that connect amino acids, are crucial to the formation of proteins. Searches and studies of molecules with embedded peptide-like bonds are thus important for the understanding of protein formation in space. Her
e we report the first tentative detection of propionamide (C2H5CONH2), the largest peptide-like molecule detected in space toward Sagittarius B2(N1) at a position called N1E that is slightly offset from the continuum peak. A new laboratory measurements of the propionamide spectrum were carried out in the 9-461 GHz, which provide good opportunity to check directly for the transition frequencies of detected interstellar lines of propionamide. Our observing result indicates that propionamide emission comes from the warm, compact cores in Sagittarius B2, in which massive protostellars are forming. The column density of propionamide toward Sgr B2(N1E) was derived to be 1.5times 10^{16} cm^-2, which is three fifths of that of acetamide, and one nineteenth of that of formamide. This detection suggests that large peptide-like molecules can form and survive during star-forming process and may form more complex molecules in the interstellar medium. The detection of propionamide bodes well for the presence of polypeptides, as well as other complex prebiotic molecules in the interstellar medium.
In this paper we consider a class of {it conditional McKean-Vlasov SDEs} (CMVSDE for short). Such an SDE can be considered as an extended version of McKean-Vlasov SDEs with common noises, as well as the general version of the so-called {it conditiona
l mean-field SDEs} (CMFSDE) studied previously by the authors [1, 14], but with some fundamental differences. In particular, due to the lack of compactness of the iterated conditional laws, the existing arguments of Schauders fixed point theorem do not seem to apply in this situation, and the heavy nonlinearity on the conditional laws caused by change of probability measure adds more technical subtleties. Under some structure assumptions on the coefficients of the observation equation, we prove the well-posedness of solution in the weak sense along a more direct approach. Our result is the first that deals with McKean-Vlasov type SDEs involving state-dependent conditional laws.
This short note provides a new and simple proof of the convergence rate for Pengs law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
Approximate joint diagonalization of a set of matrices provides a powerful framework for numerous statistical signal processing applications. For non-unitary joint diagonalization (NUJD) based on the least-squares (LS) criterion, outliers, also refer
red to as anomaly or discordant observations, have a negative influence on the performance, since squaring the residuals magnifies the effects of them. To solve this problem, we propose a novel cost function that incorporates the soft decision-directed scheme into the least-squares algorithm and develops an efficient algorithm. The influence of the outliers is mitigated by applying decision-directed weights which are associated with the residual error at each iterative step. Specifically, the mixing matrix is estimated by a modified stationary point method, in which the updating direction is determined based on the linear approximation to the gradient function. Simulation results demonstrate that the proposed algorithm outperforms conventional non-unitary diagonalization algorithms in terms of both convergence performance and robustness to outliers.
Recently, deep learning methods have been proposed for quantitative susceptibility mapping (QSM) data processing: background field removal, field-to-source inversion, and single-step QSM reconstruction. However, the conventional padding mechanism use
d in convolutional neural networks (CNNs) can introduce spatial artifacts, especially in QSM background field removal and single-step QSM which requires inference from total fields with extreme large values at the edge boundaries of volume of interest. To address this issue, we propose an improved padding technique which utilizes the neighboring valid voxels to estimate the invalid voxels of feature maps at volume boundaries in the neural networks. Studies using simulated and in-vivo data show that the proposed padding greatly improves estimation accuracy and reduces artifacts in the results in the tasks of background field removal, field-to-source inversion, and single-step QSM reconstruction.
In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under $tilde{G}$-expectation. Under standard assumptions, we establi
sh the comparison theorem for this kind of BSDE and give a novel and simple method to obtain the dynamic programming principle. Finally, we prove that the value function is the unique viscosity solution of a type of fully nonlinear HJB equation.
In open-domain conversational systems, it is important but challenging to leverage background knowledge. We can use the incorporation of knowledge to make the generation of dialogue controllable, and can generate more diverse sentences that contain r
eal knowledge. In this paper, we combine the knowledge bases and pre-training model to propose a knowledge-driven conversation system. The system includes modules such as dialogue topic prediction, knowledge matching and dialogue generation. Based on this system, we study the performance factors that maybe affect the generation of knowledge-driven dialogue: topic coarse recall algorithm, number of knowledge choices, generation model choices, etc., and finally made the system reach state-of-the-art. These experimental results will provide some guiding significance for the future research of this task. As far as we know, this is the first work to study and analyze the effects of the related factors.
Inspired by our serendipitous discovery of six AGNs with varying broad-Halpha fluxes over years out of our searching for intermediate-mass black holes (IMBHs), we conduct a systematic investigation of changing-look (CL) and large-variability AGNs. We
collect all the CL AGNs at z<0.15 and the reverberation mapped AGNs with strongly variable broad Halpha, and perform careful decomposition fittings to both their images and spectra. We find two observational facts: (1) The host galaxies of local CL and large-variability AGNs, mainly being Seyferts, are in the red (gas-poor) tail of the general Seyfert galaxy population. (2) In contrast, there is a significant trend that their more luminous counterparts namely CL and extremely variable quasars (CLQs and EVQs) are different: CLQs are generally in blue galaxies; in terms of the diagram of SFR and M* local CL Seyfert galaxies are located in the green valley, whereas CLQ hosts are in the star-forming main sequence. We propose explanations for those strongly variable Seyferts and quasars, respectively, under the thought that accretion disks broadly depend on nuclear fueling modes. Local large-variability and CL Seyferts are in nuclear famine mode, where cold-gas clumps can be formed stochastically in the fueling flow, and their episodic infall produces sharp peaks in the accretion-rate curve. CLQs and EVQs are in feast fueling mode, which may account for both their preference to blue galaxies and their variability pattern (high-amplitude tail of the continuous distribution). Lastly, we propose a new thinking: to search for IMBHs by optical variability in red galaxies.
