SOLVING SYSTEMS OF PHASELESS EQUATIONS VIA RIEMANNIAN OPTIMIZATION WITH OPTIMAL SAMPLING COMPLEXITY

A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations|Ax|^(2)=y.The algorithms are developed by exploiting the inherent low rank structure of the problem based on the embedded manifold of rank-1 positive semidefinite matrices.Theoretical recovery guarantee has been established for the truncated variant,showing that the algorithm is able to achieve successful recovery when the number of equations is proportional to the number of unknowns.Two key ingredients in the analysis are the restricted well conditioned property and the restricted weak correlation property of the associated truncated linear operator.Empirical evaluations show that our algorithms are competitive with other state-of-the-art first order nonconvex approaches with provable guarantees.

Logistic Regression Modelling for Complex Survey Data with an Application for Bed Net Use in Mozambique

Logistic Regression Models have been widely used in many areas of research, namely in health sciences, to study risk factors associated to diseases. Many population based surveys, such as Demographic and Health Survey (DHS), are constructed assuming complex sampling, i.e., probabilistic, stratified and multistage sampling, with unequal weights in the observations;this complex design must be taken into account in order to have reliable results. However, this very relevant issue usually is not well analyzed in the literature. The aim of the study is to specify the logistic regression model with complex sample design, and to demonstrate how to estimate it using the R software survey package. More specifically, we used Mozambique Demographic Health and Survey data 2011 (MDHS 2011) to illustrate how to correct for the effect of sample design in the particular case of estimating the risk factors associated to the probability of using mosquito bed nets. Our results show that in the presence of complex sampling, appropriate methods must be used both in descriptive and inferential statistics.

QSRR Study on the Components of Styrax Japonicus Sieb Flowers Using Improved Molecular Electronegativity-distance Vector (I-MEDV)

Atoms in most organic molecules are often carbon,oxygen,nitrogen,sulfur,halogens,etc. Based on the three-dimensional structure of a molecule,a molecular structural characterization（MSC） method called improved molecular electronegativity-distance vector（I-MEDV） was developed. It was used to describe the structures of 37 compounds of styrax japonicus sieb flowers. Through multiple linear regression（MLR）,a QSRR model was built up. The correlation coefficient（R1） of the model was 0.980. Then,4 vectors were selected to build another model through the method of stepwise multiple regression（SMR） ,and the correlation coefficient（R2） of the model was 0.975. Moreover,all the two models were evaluated by performing the crossvalidation with the leave-one-out（LOO） procedure and the correlation coefficients（Rcv） were 0.948 and 0.968,respectively. The results show that the I-MEDV could successfully describe the structures of organic compounds. The stability and predictability of the models were good.

Multi-scale morphology analysis of acoustic emission signal and quantitative diagnosis for bearing fault

Monitoring of potential bearing faults in operation is of critical importance to safe operation of high speed trains.One of the major challenges is how to differentiate relevant signals to operational conditions of bearings from noises emitted from the surrounding environment.In this work,we report a procedure for analyzing acoustic emission signals collected from rolling bearings for diagnosis of bearing health conditions by examining their morphological pattern spectrum（MPS） through a multi-scale morphology analysis procedure.The results show that acoustic emission signals resulted from a given type of bearing faults share rather similar MPS curves.Further examinations in terms of sample entropy and Lempel-Ziv complexity of MPS curves suggest that these two parameters can be utilized to determine damage modes.

Rapid fabrication of zwitterionic sulfobetaine vinylimidazole-based monoliths via photoinitiated copolymerization for hydrophilic interaction chromatography

Zwitterionic sulfobetaine-based monolithic stationary phases have attracted increasing attention for their use in hydrophilic interaction chromatography.In this study,a novel hydrophilic polymeric monolith was fabricated through photo-initiated copolymerization of 3-(3-vinyl-1-imidazolio)-1-propanesulfonate(SBVI)with pentaerythritol triacrylate using methanol and tetrahydrofuran as the porogenic system.Notably,the duration for the preparation of this novel monolith was as little as 5 min,which was significantly shorter than that required for previously reported sulfobetaine-based monoliths prepared via conventional thermally initiated copolymerization.Moreover,these monoliths showed good morphology,permeability,porosity(62.4%),mechanical strength(over 15 MPa),column efficiency(51,230 plates/m),and reproducibility(relative standard deviations for all analytes were lower than 4.6%).Mechanistic studies indicated that strong hydrophilic and negative electrostatic interactions might be responsible for the retention of polar analytes on the zwitterionic SBVI-based monolith.In particular,the resulting monolith exhibited good anti-protein adhesion ability and low nonspecific protein adsorption.These excellent features seem to favor its application in bioanalysis.Therefore,the novel zwitterionic sulfobetaine-based monolith was successfully employed for the highly selective separation of small bioactive compounds and the efficient enrichment of N-glycopeptides from complex samples.In this study,we prepared a novel zwitterionic sulfobetaine-based monolith with good performance and developed a simpler and faster method for preparation of zwitterionic monoliths.

Learning the Mapping x→Σi=1^d xi^(2):the Cost of Finding the Needle in a Haystack

The task of using the machine learning to approximate the mapping x→Σi=1^d xi^(2)with Xi∈[-1,1]seems to be a trivial one.Given the knowledge of the separable structure of the function,one can design a sparse network to represent the function very accurately,or even exactly.When such structural information is not available,and we may only use a dense neural network,the optimization procedure to find the sparse network embedded in the dense network is similar to finding the needle in a haystack,using a given number of samples of the function.We demonstrate that the cost(measured by sample complexity)of finding the needle is directly related to the Barron norm of the function.While only a small number of samples are needed to train a sparse network,the dense network trained with the same number of samples exhibits large test loss and a large generalization gap.To control the size of the generalization gap,we find that the use of the explicit regularization becomes increasingly more important as d increases.The numerically observed sample complexity with explicit regularization scales as G(d^(2.5)),which is in fact better than the theoretically predicted sample complexity that scales as 0(d^(4)).Without the explicit regularization(also called the implicit regularization),the numerically observed sample complexity is significantly higher and is close to 0(d^(4.5)).

Dynamical intricacy and average sample complexity of amenable group actions

In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain network and probability theory.If one wants to take into account underlying system geometry in applications,more general group actions may need to be taken into consideration.In this paper,we consider this notion in the case of amenable group actions.We show that many basic properties in the Z-action case remain true.We also show that their suprema over covers or partitions are equal to the amenable topological entropy and the measure entropy,using the quasitiling technique in the theory of the amenable group.

ACCELERATED DISCOVERY AND PROFILING OF PHYSIOLOGICALLY ACTIVE COMPONENTS IN COMPLEX SAMPLES BY HPTLC-EDA-HRMS

On the one hand,the separation of thousands of compounds in a complex extract is thrilling,but may be still be separated unsatisfactorily.Hence,the question arises where to stop in high-sophisticated separation science?Which technical effort is economically justifiable in routine?On the other hand,the separation itself does not imply an effect-directed answer to questions such

A policy gradient algorithm integrating long and short-term rewards for soft continuum arm control

The soft continuum arm has extensive application in industrial production and human life due to its superior safety and flexibility. Reinforcement learning is a powerful technique for solving soft arm continuous control problems, which can learn an effective control policy with an unknown system model. However, it is often affected by the high sample complexity and requires huge amounts of data to train, which limits its effectiveness in soft arm control. An improved policy gradient method, policy gradient integrating long and short-term rewards denoted as PGLS, is proposed in this paper to overcome this issue. The shortterm rewards provide more dynamic-aware exploration directions for policy learning and improve the exploration efficiency of the algorithm. PGLS can be integrated into current policy gradient algorithms, such as deep deterministic policy gradient(DDPG). The overall control framework is realized and demonstrated in a dynamics simulation environment. Simulation results show that this approach can effectively control the soft arm to reach and track the targets. Compared with DDPG and other model-free reinforcement learning algorithms, the proposed PGLS algorithm has a great improvement in convergence speed and performance. In addition, a fluid-driven soft manipulator is designed and fabricated in this paper, which can verify the proposed PGLS algorithm in real experiments in the future.