关于双向加细方程的L^1-解的一点注记

研究了双向加细方程f(x)=sum(c(n,1)f(αx-β_n))from n=0 to N+sum(c(n,-1)f(-αx-β_n))from n=0 to N的L1-解,其中α∈R且α>1,β0<…<βN∈R.利用傅里叶方法和迭代函数系将证明双向加细方程的所有L1-解所做成的解空间至少是1维的,并且给出了双向加细方程非平凡L1-解存在的充分条件与必要条件,同时给出非平凡L1-解不存在的条件,所得结果容易验证.

L1 norm optimal solution match processing in the wavelet domain

Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic data, matching seismic data with different ages and sources, 4-D seismic monitoring, and so on. The traditional match filtering method is subject to many restrictions and is usually difficult to overcome the impact of noise. Based on the traditional match filter, we propose the wavelet domain L1 norm optimal matching filter. In this paper, two different types of seismic data are decomposed to the wavelet domain, different detailed effective information is extracted for Ll-norm optimal matching, and ideal results are achieved. Based on the model test, we find that the L1 norm optimal matching filter attenuates the noise and the waveform, amplitude, and phase coherence of result signals are better than the conventional method. The field data test shows that, with our method, the seismic events in the filter results have better continuity which achieves the high precision seismic match requirements.

Seizure detection using earth movers' distance and SVM in intracranial EEG

Seizure detection is extremely essential for long-term monitoring of epileptic patients. This paper investigates the detection of epileptic seizures in multi-channel long-term intracranial electroencephalogram （iEEG）. The algorithm conducts wavelet decomposition of iEEGs with five scales, and transforms the sum of the three frequency bands into histogram for computing the distance. The proposed method combines a novel feature called EMD-L1, which is an efficient algorithm of earth movers＇ distance （EMD）, with support vector machine （SVM） for binary classification between seizures and non-sei- zures. The EMD-LI used in this method is characterized by low time complexity and high processing speed by exploiting the L~ metric structure. The smoothing and collar technique are applied on the raw outputs of SVM classifier to obtain more ac- curate results. Several evaluation criteria are recommended to compare our algorithm with other conventional methods using the same dataset from the Freiburg EEG database. Experiment results show that the proposed method achieves a high sensi- tivity, specificity and low false detection rate, which are 95.73 %, 98.45 % and 0.33/h, respectively. This algorithm is char- acterized by its robustness and high accuracy with the possibility of performing real-time analysis of EEG data, and may serve as a seizure detection tool for monitoring long-term EEG.

Bis(acetylacetonato)-oxidovanadium(Ⅳ) inhibits isoproterenol-induced lipolysis in insulin-resistant 3T3-L1 adipocytes by reducing phosphorylation of perilipin and hormone-sensitive lipase

Insulin resistance is characterized as one of crucial pathological changes in type 2 diabetes mellitus（T2DM）, and dyslipidaemia is frequently detected in T2DM. A variety of vanadium compounds have been studied as drug candidates for diabetes based on their insulin-like action. However, few studies focus on their antilipolytic effect. In the present study, we established an insulin-resistant model in 3T3-L1 adipocytes to mimic pathological conditions of T2DM according to a well-established method by the treatment of high concentrations of glucose and insulin, which was validated by oil red O staining and the decreased levels of phosphorylated Akt, AS160 and GSK3 after insulin treatment. The results demonstrated that bis（acetylacetonato）-oxidovanadium（Ⅳ）（VO（acac）_2） could inhibit isoproterenol-stimulated lipolysis through the reduction of the phosphorylated HSL and perilipin levels in both insulin-sensitive and insulin-resistant 3T3-L1 adipocytes. Moreover, although the levels of phosphorylated Akt induced by VO（acac）_2 were decreased, the rates of lipolytic inhibition were not significantly altered compared with those under insulin-sensitive condition, indicating that the anti-lipolytic effect of VO（acac）_2 might also function in an Akt-independent way in insulin-resistant adipocytes. Our work here help elucidate the anti-diabetic effects of vanadium compounds. It may not only shed light on the utility of vanadium-based compounds as potential anti-diabetic drugs but also serve as a useful screening model for new anti-diabetic drugs.