Rainfall forecasting by technological machine learning models

Accurate forecasting of rainfall has been one of the most important issues in hydrological research. Due to rainfall forecasting involves a rather complex nonlinear data pattern; there are lots of novel forecasting approaches to improve the forecasting accuracy. Recurrent artificial neural networks (RNNS) have played a crucial role in forecasting rainfall data. Meanwhile, support vector machines (SVMs) have been successfully employed to solve nonlinear regression and time series problems. This investigation elucidates the feasibility of hybrid model of RNNs and SVMs, namely RSVR, to forecast rainfall depth values. Moreover, chaotic particle swarm optimization algorithm (CPSO) is employed to choose the parameters of a SVR model. Subsequently, example of rainfall values during typhoon periods from Northern Taiwan is used to illustrate the proposed RSVRCPSO model. The empirical results reveal that the proposed model yields well forecasting performance, RSVRCPSO model provides a promising alternative for forecasting rainfall values.     

A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra with applications to the Metro-bus public transport system in Mexico city

In this paper, an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to the Metro-bus public transport system in Mexico city. A timed event Petri net model is constructed from the data table that characterizes the transport system. A max-plus recurrence equation, with a reducible and regular matrix, is associated with the transport system timed event Petri net. Next, given the reducible and regular matrix, the problem consists of giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The generalized eigenmode obtained sets a timetable for the transport system.     

Efficacy of cidofovir injection for the treatment of recurrent respiratory papillomatosis

To evaluate the efficacy of intralesional cidofovir injection for the treatment of recurrent respiratory papillomatosis (RRP). It is a prospective, open-label study design. This prospective study included 16 RRP patients, ages 9 to 68 years, who were treated with intralesional injections of cidofovir combined with surgical excision of RRP. The disease states of the patients pretreatment and posttreatment were assessed by assigning RRP severity scores, examining the need for any surgical excision of RRP, and evaluating the presence of RRP upon long-term follow-up. Sixteen patients were treated with cidofovir; however, three were lost to follow-up. Thirteen patients are the subjects of this report. This study group included three pediatric patients. Ten of thirteen patients (76.9%) responded to the treatment and are presently in remission. One patient did not respond, and two patients relapsed after initial success or had a partial response. The responders consisted of eight adults and two children. The mean number of injections the responders received was 3.5, and the average follow-up period of the responders was 25.4 months. No immediate complication of cidofovir treatment was evident. However, three patients were found to have significant vocal fold scarring after long-term follow-up. Cidofovir has been found to be efficacious in treating RRP. Further study regarding long-term follow-up and the assessment of possible side effects after cidofovir intralesional injection for RRP is required.     

Random time change and recurrent boundary

The purpose of this paper is to study some properties of random time changes in recurrent potential theory. In particular we show that the Martin recurrent boundary is not invariant under a random time change. We then obtain a characterization of random time change destroying a boundary point. We also give some complement about the recurrent boundary connected with “special additive functionals”. We have for example a representation at the boundary of solutions of the Poisson's equation $\text{?(I-U}{}_1\text{)=-U}{}_1\text{(x,·)}$ by using local time at x.     

Recurrent traveling waves in a two-dimensional saw-toothed cylinder and their average speed

We study a curvature-dependent motion of plane curves in a two-dimensional infinite cylinder with spatially undulating boundary. The law of motion is given by V=κ+A$V=\kappa +A$, where V is the normal velocity of the curve, κ is the curvature, and A is a positive constant. The boundary undulation is assumed to be almost periodic, or, more generally, recurrent in a certain sense. We first introduce the definition of recurrent traveling waves and establish a necessary and sufficient condition for the existence of such traveling waves. We then show that the traveling wave is asymptotically stable if it exists. Next we show that a regular traveling wave has a well-defined average speed if the boundary shape is strictly ergodic. Finally we study what we call “virtual pinning”, which means that the traveling wave propagates over the entire cylinder with zero average speed. Such a peculiar situation can occur only in non-periodic environments and never occurs if the boundary undulation is periodic.     

A Convergence Analysis of Newton-Like Method for Singular Equations Using Recurrent Functions

We provide new semilocal convergence results for Newton-like method involving outer or generalized inverses in a Banach space setting. Using our new idea of recurrent functions and the same or weaker conditions than before [5-19 A. Ben-Israel and N.E. Greville ( 1974 ). Generalized Inverses: Theory and Applications, Pure and Applied Mathematics . Wiley-Interscience , New York . X. Chen and T. Yamamoto ( 1989 ). Convergence domains of certain iterative methods for solving nonlinear equations . Numer. Funct. Anal. Optimiz. 10 : 37 – 48 . J.E. Dennis , Jr. ( 1968 ). On Newton-like methods . Numer. Math. 11 : 324 – 330 . P. Deuflhard and C. Heindl ( 1979 ). Convergence theorems for Newton's method and extensions to related methods . SIAM J. Numer. Anal. 16 : 1 – 10 . J.M. Gutiérrez ( 1997 ). A new semilocal convergence theorem for Newton's method . J. Comp. Appl. Math. 79 : 131 – 145 . J.M. Gutiérrez , M.A. Hernández , and M.A. Salanova ( 1995 ). Accessibility of solutions by Newton's method . Internat. J. Comput. Math. 57 : 239 – 247 . W.M. Häubler ( 1986 ). A Kantorovich-type convergence analysis for the Gauss–Newton methods . Numer. Math. 48 : 119 – 125 . L.V. Kantorovich and G.P. Akilov ( 1964 ). Functional Analysis . Pergamon Press , Oxford . M.Z. Nashed and X. Chen ( 1993 ). Convergence of Newton-like methods for singular operator equations using outer inverses . Numer. Math. 66 : 235 – 257 . F.A. Potra and V. Ptàk ( 1980 ). Sharp error bounds for Newton's process . Numer. Math. 34 : 67 – 72 . W.C. Rheinboldt ( 1968 ). A unified convergence theory for a class of iterative processes . SIAM J. Numer. Anal. 5 : 42 – 63 . W.C. Rheinboldt ( 1977 ). An adaptive continuation process for solving systems of nonlinear equations . Polish Academy of Sciences, Banach Ctr. Publ. 3 : 129 – 142 . T. Yamamoto ( 1987 ). A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions . Numer. Math. 49 : 203 – 230 . T. Yamamoto ( 1987 ). A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. 51 : 545 – 557 . T. Yamamoto ( 1989 ). Uniqueness of the solution in a Kantorovich-type theorem of Haubler for the Gauss–Newton method . Japan J. Appl. Math. 6 : 77 – 81 . ], we provide more precise information on the location of the solution and finer bounds on the distances involved. Moreover, since our Newton–Kantorovich-type hypothesis is weaker than before, we can now cover cases not previously possible.

Applications and numerical examples involving a nonlinear integral equation of Chandrasekhar-type and a differential equation with Green's function are also provided in this study.     

Statistical Computations on Biological Rhythms I: Dissecting Variable Cycles and Computing Signature Phases in Activity-Event Time Series

We propose a computational methodology to compute and extract circadian rhythmic patterns from an individual animal’s activity-event time series. This lengthy dataset, composed of a sequential event history, contains an unknown number of latent rhythmic cycles of varying duration and missing waveform information. Our computations aim at identifying the onset signature phase which individually indicates a sharp event intensity surge, where a subject-night ends and a brand new cycle’s subject-day begins, and collectively induces a linearity manifesting the individual circadian rhythmicity and information about the average period. Based on the induced linearity, the least squares criterion is employed to choose an optimal sequence of computed onset signature phases among a finite collection derived from the hierarchical factor segmentation (HFS) algorithm. The multiple levels of coding schemes in the HFS algorithm are designed to extract contrasting patterns of aggregation against sparsity of activity events along the entire temporal axis. This optimal sequence dissects the whole time series into a sequence of rhythmic cycles without model assumptions or ad hoc behavioral definitions regarding the missing waveform information. The performance of our methodology is favorably compared with two popular approaches based on the periodogram in a simulation study and in real data analyses. The computer code and data used in this article are available on the JCGS webpage.     

基于双向循环神经网络的汉语语音识别*

当前基于深度神经网络模型中,虽然其隐含层可设置多层,对复杂问题适应能力强,但每层之间的节点连接是相互独立的,这种结构特性导致了在语音序列中无法利用上下文相关信息来提高识别效果,而传统的循环神经网络虽然做出了改进,但是只能对上文信息进行利用。针对以上问题,该文采用可以同时利用语音序列中上下文相关信息的双向循环神经网络模型与深度神经网络模型相结合,并应用于语音识别。构建具有5层隐含层的模型,其中第3层为双向循环神经网络结构,其他层采用深度神经网络结构。实验结果表明:加入了双向循环神经网络结构的模型与其他模型相比,较好地提高了识别正确率;噪声对双向循环神经网络汉语识别有重要影响,尤其是训练集和测试集附加噪声类型不同时,单一的含噪声语音的训练模型无法适应不同噪声类型的语音识别;调整神经网络模型中隐含层神经元数量后,识别正确率并不是一直随着隐含层中神经元数量的增加而增加,神经元数量数目增加到一定程度后正确率出现了降低的趋势。     

Complex dynamics in the Leslie–Gower type of the food chain system with multiple delays

In this paper, we present a Leslie–Gower type of food chain system composed of three species, which are resource, consumer, and predator, respectively. The digestion time delays corresponding to consumer-eat-resource and predator-eat-consumer are introduced for more realistic consideration. It is called the resource digestion delay (RDD) and consumer digestion delay (CDD) for simplicity. Analyzing the corresponding characteristic equation, the stabilities of the boundary and interior equilibrium points are studied. The food chain system exhibits the species coexistence for the small values of digestion delays. Large RDD/CDD may destabilize the species coexistence and induce the system dynamic into recurrent bloom or system collapse. Further, the present of multiple delays can control species population into the stable coexistence. To investigate the effect of time delays on the recurrent bloom of species population, the Hopf bifurcation and periodic solution are investigated in detail in terms of the central manifold reduction and normal form method. Finally, numerical simulations are performed to display some complex dynamics, which include multiple periodic solution and chaos motion for the different values of system parameters. The system dynamic behavior evolves into the chaos motion by employing the period-doubling bifurcation.     

复发性阿弗他溃疡与相关的营养因素研究进展

以国内外研究复发性阿弗他溃疡营养因素的相关论文为依据,综述了近十年有关对复发性阿弗他溃疡（RAU）营养因素的研究进展。包括：RAU与微量元素锌、铁、硒、铜,维生素A、C、E、B2、B12,蛋白质,膳食纤维和谷类的关系。RAU的发生与体内微量元素锌、铁、硒、铜的减少,维生素A、C、E、B2、B12,蛋白质和膳食纤维的摄取不足密切相关,全谷类食品（功能稻米）对缓解RAU有帮助。