Co-Training for Visual Object Recognition Based on Self-Supervised Models Using a Cross-Entropy Regularization

Automatic recognition of visual objects using a deep learning approach has been successfully applied to multiple areas. However, deep learning techniques require a large amount of labeled data, which is usually expensive to obtain. An alternative is to use semi-supervised models, such as co-training, where multiple complementary views are combined using a small amount of labeled data. A simple way to associate views to visual objects is through the application of a degree of rotation or a type of filter. In this work, we propose a co-training model for visual object recognition using deep neural networks by adding layers of self-supervised neural networks as intermediate inputs to the views, where the views are diversified through the cross-entropy regularization of their outputs. Since the model merges the concepts of co-training and self-supervised learning by considering the differentiation of outputs, we called it Differential Self-Supervised Co-Training (DSSCo-Training). This paper presents some experiments using the DSSCo-Training model to well-known image datasets such as MNIST, CIFAR-100, and SVHN. The results indicate that the proposed model is competitive with the state-of-art models and shows an average relative improvement of 5% in accuracy for several datasets, despite its greater simplicity with respect to more recent approaches.     

自适应光学系统变形镜控制电压预测

在校正大气湍流畸变波前相差的自适应光学系统中,利用基于Levenberg-Marquardt学习算法的非线性反向传播神经网络技术（LMBP）对变形镜控制电压进行预测。以对受横向风影响的大气湍流畸变波前斜率数据为研究对象,通过数值仿真方法,研究了基于LMBP算法的自适应光学系统变形镜电压非线性预测控制算法。通过实验发现,预测电压和变形镜实际控制电压拟合效果良好。讨论了回溯帧数对预测效果的影响,并与基于递推最小二乘（RLS）算法的线性预测算法进行比较。对比结果表明,基于LMBP算法的非线性电压预测方法比基于递推最小二乘法的线性电压预测方法能更有效地降低系统由伺服延迟引起的误差。

     

Student enrichment in mathematics: a case study with first year university students

ABSTRACT

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an enrichment programme. Following the intervention, students completed a questionnaire and a few were interviewed to establish their experiences of the enrichment programme. We discuss the successes and pitfalls of the intervention and report on the impact it had on the participants.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

Chaos in social learning with multiple true states

Most existing social learning models assume that there is only one underlying true state. In this work, we consider a social learning model with multiple true states, in which agents in different groups receive different signal sequences generated by their corresponding underlying true states. Each agent updates his belief by combining his rational self-adjustment based on the external signals he received and the influence of his neighbors according to their communication. We observe chaotic oscillation in the belief evolution, which implies that neither true state could be learnt correctly by calculating the largest Lyapunov exponents and Hurst exponents.     

Quantum chemical electron impact mass spectrum prediction for de novo structure elucidation: Assessment against experimental reference data and comparison to competitive fragmentation modeling

We investigate the success of the quantum chemical electron impact mass spectrum (QCEIMS) method in predicting the electron impact mass spectra of a diverse test set of 61 small molecules selected to be representative of common fragmentations and reactions in electron impact mass spectra. Comparison with experimental spectra is performed using the standard matching algorithms, and the relative ranking position of the actual molecule matching the spectra within the NIST‐11 library is examined. We find that the correct spectrum is ranked in the top two matches from structural isomers in more than 50% of the cases. QCEIMS, thus, reproduces the distribution of peaks sufficiently well to identify the compounds, with the RMSD and mean absolute difference between appropriately normalized predicted and experimental spectra being at most 9% and 3% respectively, even though the most intense peaks are often qualitatively poorly reproduced. We also compare the QCEIMS method to competitive fragmentation modeling for electron ionization, a training‐based mass spectrum prediction method, and remarkably we find the QCEIMS performs equivalently or better. We conclude that QCEIMS will be very useful for those who wish to identify new compounds which are not well represented in the mass spectral databases.     

Distance versus Capillary Flow Dynamics-Based Detection Methods on a Microfluidic Paper-Based Analytical Device (μPAD)

In recent years, there has been high interest in paper-based microfluidic sensors or microfluidic paper-based analytical devices (μPADs) towards low-cost, portable, and easy-to-use sensing for chemical and biological targets. μPAD allows spontaneous liquid flow without any external or internal pumping, as well as an innate filtration capability. Although both optical (colorimetric and fluorescent) and electrochemical detection have been demonstrated on μPADs, several limitations still remain, such as the need for additional equipment, vulnerability to ambient lighting perturbation, and inferior sensitivity. Herein, alternative detection methods on μPADs are reviewed to resolve these issues, including relatively well studied distance-based measurements and the newer capillary flow dynamics-based method. Detection principles, assay performance, strengths, and weaknesses are explained for these methods, along with their potential future applications towards point-of-care medical diagnostics and other field-based applications.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

FFLUX: Transferability of polarizable machine‐learned electrostatics in peptide chains

The fully polarizable, multipolar, and atomistic force field protein FFLUX is being built from machine learning (i.e., kriging) models, each of which predicts an atomic property. Each atom of a given protein geometry needs to be assigned such a kriging model. Such a knowledgeable atom needs to be informed about a sufficiently large environment around it. The resulting complexity can be tackled by collecting the 20 natural amino acids into a few groups. Using substituted deca‐alanines, we present the proof‐of‐concept that a given atom's charge can be modeled by a few kriging models only. © 2017 Wiley Periodicals, Inc.     

Complex dynamics in equilibrium asset pricing models with boundedly rational,heterogeneous agents

We study a simple model based upon the Lucas framework where heterogeneous agents behave rationally in a fully intertemporal setting but do not know other investors' personal preferences, wealth or investment portfolios. As a consequence, agents initially do not know the equilibrium asset pricing function and must make guesses, which they update via adaptive learning with constant gain. We demonstrate that even in this simple environment the economy can, depending on parameters, exhibit either stable convergence to equilibrium, or chaotic dynamical behavior of asset prices and trading volume without converging to the rational expectations equilibrium of the Lucas model. This contradicts the assertion that the Lucas model is stable in the face of modest deviations from the strong assumptions required to compute the equilibrium. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–55, 2014