Locally recurrent head and neck squamous cell carcinoma(HNSCC)is often unresectable,and a repeat course of radiotherapy is associated with incremental toxicities.Boron neutron capture therapy(BNCT)is a novel targeted ...Locally recurrent head and neck squamous cell carcinoma(HNSCC)is often unresectable,and a repeat course of radiotherapy is associated with incremental toxicities.Boron neutron capture therapy(BNCT)is a novel targeted radiotherapy modality that can achieve a high dose gradient between cancerous and adjacent normal tissues.However,the relationships among the dose resulting from BNCT,tumor response to BNCT,and survival are not completely understood.Recently,a study published in Radiotherapy and Oncology investigated the efficacy of BNCT in the treatment of patients with locally recurrent HNSCC and the factors associated with favorable treatment response and survival.In this article,the findings,strengths and limitations of this study are discussed in depth,and the significance of the study and motivations for future research are highlighted.展开更多
In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation functi...In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.展开更多
We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is c...We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.展开更多
Let G be a locally compact group, and let 1≤p〈∞. We characterize topolog- ically multiply recurrent weighted translation operators on LP（G） in terms of the Haax mea- sure and the weight function. We also show tha...Let G be a locally compact group, and let 1≤p〈∞. We characterize topolog- ically multiply recurrent weighted translation operators on LP（G） in terms of the Haax mea- sure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L^∞ （G）.展开更多
文摘Locally recurrent head and neck squamous cell carcinoma(HNSCC)is often unresectable,and a repeat course of radiotherapy is associated with incremental toxicities.Boron neutron capture therapy(BNCT)is a novel targeted radiotherapy modality that can achieve a high dose gradient between cancerous and adjacent normal tissues.However,the relationships among the dose resulting from BNCT,tumor response to BNCT,and survival are not completely understood.Recently,a study published in Radiotherapy and Oncology investigated the efficacy of BNCT in the treatment of patients with locally recurrent HNSCC and the factors associated with favorable treatment response and survival.In this article,the findings,strengths and limitations of this study are discussed in depth,and the significance of the study and motivations for future research are highlighted.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY18F030023,LY17F030016,and LY18F020028)the National Natural Science Foundation of China(Grant Nos.61503338,61502422,and 61773348)
文摘In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.
基金supported by the Ministry of Science and Technology of Taiwan,China(Grant Nos.NSC-99-2112-M-032-002-MY3 and NSC 102-2112-M-032-003-MY3)the National Center for Theoretical Sciences(North)(NCTS-n)of China
文摘We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.
基金supported by MOST of Taiwan(MOST104-2115-M-142-002-)
文摘Let G be a locally compact group, and let 1≤p〈∞. We characterize topolog- ically multiply recurrent weighted translation operators on LP（G） in terms of the Haax mea- sure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L^∞ （G）.
