Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

New Interfaces and Approaches to Machine Learning When Classifying Gestures within Music

Interactive music uses wearable sensors (i.e., gestural interfaces—GIs) and biometric datasets to reinvent traditional human–computer interaction and enhance music composition. In recent years, machine learning (ML) has been important for the artform. This is because ML helps process complex biometric datasets from GIs when predicting musical actions (termed performance gestures). ML allows musicians to create novel interactions with digital media. Wekinator is a popular ML software amongst artists, allowing users to train models through demonstration. It is built on the Waikato Environment for Knowledge Analysis (WEKA) framework, which is used to build supervised predictive models. Previous research has used biometric data from GIs to train specific ML models. However, previous research does not inform optimum ML model choice, within music, or compare model performance. Wekinator offers several ML models. Thus, we used Wekinator and the Myo armband GI and study three performance gestures for piano practice to solve this problem. Using these, we trained all models in Wekinator and investigated their accuracy, how gesture representation affects model accuracy and if optimisation can arise. Results show that neural networks are the strongest continuous classifiers, mapping behaviour differs amongst continuous models, optimisation can occur and gesture representation disparately affects model mapping behaviour; impacting music practice.     

基于工作电流分析的回转副摩擦状态识别实验研究

回转副摩擦状态的变化对机械设备的运行有着重要影响. 针对回转副摩擦状态的识别问题, 设计了以回转副工作电流为摩擦特征来源的实验方案. 通过采集摩擦过程的回转副驱动电机工作电流信号, 分析实验信号的频域和时频域特征, 建立工作电流的摩擦特征库, 用于训练多分类支持向量机分类器, 并在分类器上完成摩擦状态的识别. 实验结果表明, 经特征提取与降维处理后建立的多分类支持向量机分类器具有近90%的识别正确率, 所提出的实验方案有利于实现远距离信号的采集, 适用实际生产加工.     

Intertwining wavelets or multiresolution analysis on graphs through random forests

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate solutions of Markov intertwining relation to provide a subgraph structure and a filter bank leading to a wavelet basis of the set of functions. Our construction involves two parameters q and $q^{\prime }$. The first one controls the mean number of kept vertices in the downsampling, while the second one is a tuning parameter between space localization and frequency localization. We provide an explicit reconstruction formula, bounds on the reconstruction operator norm and on the error in the intertwining relation, and a Jackson-like inequality. These bounds lead to recommend a way to choose the parameters q and $q^{\prime }$. We illustrate the method by numerical experiments.     

Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids

In this article, we describe a non‐intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non‐intrusive reduced‐order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non‐intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hypersurfaces representing the reduced‐porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high‐fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude. Copyright © 2016 John Wiley & Sons, Ltd.     

Integral representation in the theory of continuous trading

This paper deals with predictable representation in continuous trading. First of all we give a positive answer to a conjecture of Harrison and Pliska [2]. Then we prove the completeness of a model of mixed type (see[2]). A slight modificationof this example shows that the continuous and purely discontinuous parts of a local martingale depend on the filtration.     

Nmr and Mass Spectroscopic Studies of the Competitive-Angiotensin II Antagonist “Sarmesin”

Fast atom bombardment mass spectrometry (FAB-MS) and high resolution (400 Mz) proton nuclear magnetic resonance (NMR spectroscopy) on the competitive angiotensin II antagonist, |Sar¹, Tyr(Me)⁴ (ANGII (Sarmesin) and its he-ptapeptide homolog, [Tyr(Me)³ |ANGIII, yield spectra which provide confirmation of structure and molecular weight. The characteristics of the spectra are discussed and compared with the spectra of natural ANG II, ANG III and |Sar¹|ANG II. The NMR data are suggestive of interactions in angiotensin between: 1) the phenolic hydroxyl group and the imidazole ring, and 2) the N-terminal amino group and the Tyrring. These interactions may be important for the formation of the proposed charge transfer system in angiotensin II involving the phenoxyl and α-carboxylate groups.     

Consciousness and the structuring property of typical data

The theoretical base for consciousness, in particular, an explanation of how consciousness is defined by the brain, has long been sought by science. We propose a partial theory of consciousness as relations defined by typical data. The theory is based on the idea that a brain state on its own is almost meaningless but in the context of the typical brain states, defined by the brain's structure, a particular brain state is highly structured by relations. The proposed theory can be applied and tested both theoretically and experimentally. Precisely how typical data determines relations is fully established using discrete mathematics. © 2012 Wiley Periodicals, Inc. Complexity, 2012