Two problems related to the Smarandache function

The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n) and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures

RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II)

The research on Smarandache Problems plays a key role in the development of number theory. Therefore, many mathematicians show their interest in the Smarandache problems and they conduct much research on them. Under such circumstances, we published the book , Vol. I, in September, 2004. That book stimulated more Chinese mathematicians to pay attention to Smarandache conjectures, open and solved problems in number theory. The First Northwest Number Theory Conference was held in Shangluo Teacher's College, China, in March 2005. One of the sessions was dedicated to the Smarandache problems. In that session, several professors gave a talk on Smarandache problems and many participants lectured on Smarandache problems both extensively and intensively. This book includes 34 papers, most of which were written by participants of the above mentioned conference. All these papers are original and have been refereed. The themes of these papers range from the mean value or hybrid mean value of Smarandache type functions, the mean value of some famous number theoretic functions acting on the Smarandache sequences, to the convergence property of some infinite series involving the Smarandache type sequences

Machine-learned control-oriented flow estimation for multiactuator multi-sensor systems exemplified for the fluidic pinball

We propose the first machine-learned control-oriented flow estimation for multiple-input multiple-output plants. Starting point is constant actuation with open-loop actuation commands leading to a database with simultaneously recorded actuation commands, sensor signals and flow fields. A key enabler is an estimator input vector comprising sensor signals and actuation commands. The mapping from the sensor signals and actuation commands to the flow fields is realized in an analytically simple, data-centric and general nonlinear approach. The analytically simple estimator generalizes Linear Stochastic Estimation (LSE) for actuation commands. The data-centric approach yields flow fields from estimator inputs by interpolating from the database -- similar to Loiseau et al. (2018) for unforced flow. The interpolation is performed with k Nearest Neighbors (kNN). The general global nonlinear mapping from inputs to flow fields is obtained from a Deep Neural Network (DNN) via an iterative training approach. The estimator comparison is performed for the fluidic pinball plant, which is a multiple-input, multiple-output wake control benchmark (Deng et al. 2020) featuring rich dynamics under steady controls. We conclude that the machine learning methods clearly outperform the linear model. The performance of kNN and DNN estimators are comparable for periodic dynamics. Yet, DNN performs consistently better when the flow is chaotic. Moreover, a thorough comparison regarding to the complexity, computational cost, and prediction accuracy is presented to demonstrate the relative merits of each estimator. The proposed method can be generalized for closed-loop flow control plants.Comment: 34 pages, 27 figures, 4 table

Tri-Attention: Explicit Context-Aware Attention Mechanism for Natural Language Processing

In natural language processing (NLP), the context of a word or sentence plays an essential role. Contextual information such as the semantic representation of a passage or historical dialogue forms an essential part of a conversation and a precise understanding of the present phrase or sentence. However, the standard attention mechanisms typically generate weights using query and key but ignore context, forming a Bi-Attention framework, despite their great success in modeling sequence alignment. This Bi-Attention mechanism does not explicitly model the interactions between the contexts, queries and keys of target sequences, missing important contextual information and resulting in poor attention performance. Accordingly, a novel and general triple-attention (Tri-Attention) framework expands the standard Bi-Attention mechanism and explicitly interacts query, key, and context by incorporating context as the third dimension in calculating relevance scores. Four variants of Tri-Attention are generated by expanding the two-dimensional vector-based additive, dot-product, scaled dot-product, and bilinear operations in Bi-Attention to the tensor operations for Tri-Attention. Extensive experiments on three NLP tasks demonstrate that Tri-Attention outperforms about 30 state-of-the-art non-attention, standard Bi-Attention, contextual Bi-Attention approaches and pretrained neural language models1

Discovering and Explaining the Non-Causality of Deep Learning in SAR ATR

In recent years, deep learning has been widely used in SAR ATR and achieved excellent performance on the MSTAR dataset. However, due to constrained imaging conditions, MSTAR has data biases such as background correlation, i.e., background clutter properties have a spurious correlation with target classes. Deep learning can overfit clutter to reduce training errors. Therefore, the degree of overfitting for clutter reflects the non-causality of deep learning in SAR ATR. Existing methods only qualitatively analyze this phenomenon. In this paper, we quantify the contributions of different regions to target recognition based on the Shapley value. The Shapley value of clutter measures the degree of overfitting. Moreover, we explain how data bias and model bias contribute to non-causality. Concisely, data bias leads to comparable signal-to-clutter ratios and clutter textures in training and test sets. And various model structures have different degrees of overfitting for these biases. The experimental results of various models under standard operating conditions on the MSTAR dataset support our conclusions. Our code is available at https://github.com/waterdisappear/Data-Bias-in-MSTAR

Hierarchical Disentanglement-Alignment Network for Robust SAR Vehicle Recognition

Vehicle recognition is a fundamental problem in SAR image interpretation. However, robustly recognizing vehicle targets is a challenging task in SAR due to the large intraclass variations and small interclass variations. Additionally, the lack of large datasets further complicates the task. Inspired by the analysis of target signature variations and deep learning explainability, this paper proposes a novel domain alignment framework named the Hierarchical Disentanglement-Alignment Network (HDANet) to achieve robustness under various operating conditions. Concisely, HDANet integrates feature disentanglement and alignment into a unified framework with three modules: domain data generation, multitask-assisted mask disentanglement, and domain alignment of target features. The first module generates diverse data for alignment, and three simple but effective data augmentation methods are designed to simulate target signature variations. The second module disentangles the target features from background clutter using the multitask-assisted mask to prevent clutter from interfering with subsequent alignment. The third module employs a contrastive loss for domain alignment to extract robust target features from generated diverse data and disentangled features. Lastly, the proposed method demonstrates impressive robustness across nine operating conditions in the MSTAR dataset, and extensive qualitative and quantitative analyses validate the effectiveness of our framework

Resveratrol attenuates ischemic brain damage in the delayed phase after stroke and induces messenger RNA and protein express for angiogenic factors

BackgroundIt has been reported recently that resveratrol preconditioning can protect the brain from ischemia–reperfusion injury. However, it was unclear whether resveratrol administration after stroke was beneficial to the delayed phases after focal cerebral ischemia injury. This study investigated the effects and possible protective mechanism of resveratrol on the delayed phase after focal cerebral ischemia injury in mice.MethodsMice were randomly assigned to five groups according to the time of administration of resveratrol. Control group mice received a corresponding volume of saline solution (0.9% NaCl) containing 20% hydroxypropyl h-cyclodextrin by gavage and were exposed to middle cerebral artery (MCA) occlusion and reperfusion injury. The treatment groups received resveratrol (50 mg/kg/d, gavage) until day 7. Ischemia group mice received their first dose 5 minutes before MCA ischemia, reperfusion group mice received their first dose 5 minutes before MCA reperfusion, first-day, group mice received their first dose 24 hours after MCA reperfusion, and third-day group mice received their first dose at 72 hours after MCA reperfusion. Brain injury was evaluated by triphenyltetrazolium chloride staining and neurologic examination 7 days after reperfusion. The microvascular cell number was examined with immunohistochemistry staining. Effect of resveratrol on matrix metalloproteinase-2 (MMP-2) and vascular endothelial growth factor (VEGF) gene expression was investigated with reverse transcriptase-polymerase chain reaction and Western blot.ResultsThe mean neurologic scores and infarct volumes of the ischemia and reperfusion groups were lower than that of the control group at 7 days after MCA reperfusion (P < .05). Immunohistochemistry staining showed significantly less reduction in the number of microvessels in the cortical area of mice of the ischemia and reperfusion groups compared with controls. The ischemic hemispheres of the ischemia and reperfusion groups showed significantly (P < .05) elevated levels of protein of MMP-2 and VEGF.ConclusionsResveratrol administration by gavage provided an important neuroprotective effect on focal cerebral ischemic injury in the delayed phase. The elevated MMP-2 and VEGF levels might be important in the neuroprotective effect of resveratrol administration by inducing angiogenesis.Clinical RelevanceStrokes can induce infarction size or neurologic disability and cause brain injury in millions of people world wide each year. However, there is no approved therapy currently, and so it is necessary to develop new treatments in the field of primary and secondary stroke to improve the prognosis. This study identified the benefits of early administration of resveratrol by gavage in the delayed phases after focal cerebral ischemic injury and further supports the possible use of resveratrol as a therapeutic agent to ameliorate ischemic infarction. Resveratrol may thus be considered as a potential candidate in the armamentarium of drugs for the early treatment in patients who sustain a stroke

Automatic Animation of Hair Blowing in Still Portrait Photos

We propose a novel approach to animate human hair in a still portrait photo. Existing work has largely studied the animation of fluid elements such as water and fire. However, hair animation for a real image remains underexplored, which is a challenging problem, due to the high complexity of hair structure and dynamics. Considering the complexity of hair structure, we innovatively treat hair wisp extraction as an instance segmentation problem, where a hair wisp is referred to as an instance. With advanced instance segmentation networks, our method extracts meaningful and natural hair wisps. Furthermore, we propose a wisp-aware animation module that animates hair wisps with pleasing motions without noticeable artifacts. The extensive experiments show the superiority of our method. Our method provides the most pleasing and compelling viewing experience in the qualitative experiments and outperforms state-of-the-art still-image animation methods by a large margin in the quantitative evaluation. Project url: \url{https://nevergiveu.github.io/AutomaticHairBlowing/}Comment: Accepted to ICCV 202