Miracle-dz/UniFAR-FTUs huggingface dataset:
Deformation limit and bimeromorphic embedding of Moishezon manifolds

Let $\pi: \mathcal{X}\rightarrow \Delta$ be a holomorphic family of compact complex manifolds over an open disk in $\mathbb{C}$. If the fiber $\pi^{-1}(t)$ for each nonzero $t$ in an uncountable subset $B$ of $\Delta$ is Moishezon and the reference fiber $X_0$ satisfies the local deformation invariance for Hodge number of type $(0,1)$ or admits a strongly Gauduchon metric introduced by D. Popovici, then $X_0$ is still Moishezon. We also obtain a bimeromorphic embedding $\mathcal{X}\dashrightarrow\mathbb{P}^N\times\Delta$. Our proof can be regarded as a new, algebraic proof of several results in this direction proposed and proved by Popovici in 2009, 2010 and 2013. However, our assumption with $0$ not necessarily being a limit point of $B$ and the bimeromorphic embedding are new. Our strategy of proof lies in constructing a global holomorphic line bundle over the total space of the holomorphic family and studying the bimeromorphic geometry of $\pi:\mathcal{X}\rightarrow \Delta$. S. -T. Yau's solutions to certain degenerate Monge--Amp\`ere equations are used.
Rare event process and entry times distribution for arbitrary null sets on compact manifolds

We establish the general equivalence between rare event process for arbitrary continuous functions whose maximal values are achieved on non-trivial sets, and the entry times distribution for arbitrary measure zero sets. We then use it to show that the for differentiable maps on a compact Riemannian manifold that can be modeled by Young's towers, the rare event process and the limiting entry times distribution both converge to compound Poisson distributions. A similar result is also obtained on Gibbs-Markov systems, for both cylinders and open sets. We also give explicit expressions for the parameters of the limiting distribution, and a simple criterion for the limiting distribution to be Poisson. This can be applied to a large family of continuous observables that achieve their maximum on a non-trivial set with zero measure.
Testing graphs against an unknown distribution

The area of graph property testing seeks to understand the relation between the global properties of a graph and its local statistics. In the classical model, the local statistics of a graph is defined relative to a uniform distribution over the graph’s vertex set. A graph property P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document} is said to be testable if the local statistics of a graph can allow one to distinguish between graphs satisfying P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}$$\end{document} and those that are far from satisfying it. Goldreich recently introduced a generalization of this model in which one endows the vertex set of the input graph with an arbitrary and unknown distribution, and asked which of the properties that can be tested in the classical model can also be tested in this more general setting. We completely resolve this problem by giving a (surprisingly “clean ”) characterization of these properties. To this end, we prove a removal lemma for vertex weighted graphs which is of independent interest.
Spatio-Temporal Wind Modeling for UAV Simulations.

Wind affects the stability and maneuverability of UAVs, which can be particularly dangerous when operating near obstacles or each other. In order to test the effectiveness of formation control laws and the impact of windy environments on the vehicles, spatio-temporal wind fields must be modeled. Each vehicle within the formation experiences unique wind conditions, but these conditions are correlated to the conditions experienced by the other vehicles. This report develops a spatio-temporal model for over-land and over-water environments that produces a representative wind field capable of running on a personal computer that also includes turbulence and gusting.
Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates

Recent works have shown that stochastic gradient descent (SGD) achieves the fast convergence rates of full-batch gradient descent for over-parameterized models satisfying certain interpolation conditions. However, the step-size used in these works depends on unknown quantities and SGD's practical performance heavily relies on the choice of this step-size. We propose to use line-search techniques to automatically set the step-size when training models that can interpolate the data. In the interpolation setting, we prove that SGD with a stochastic variant of the classic Armijo line-search attains the deterministic convergence rates for both convex and strongly-convex functions. Under additional assumptions, SGD with Armijo line-search is shown to achieve fast convergence for non-convex functions. Furthermore, we show that stochastic extra-gradient with a Lipschitz line-search attains linear convergence for an important class of non-convex functions and saddle-point problems satisfying interpolation. To improve the proposed methods' practical performance, we give heuristics to use larger step-sizes and acceleration. We compare the proposed algorithms against numerous optimization methods on standard classification tasks using both kernel methods and deep networks. The proposed methods result in competitive performance across all models and datasets, while being robust to the precise choices of hyper-parameters. For multi-class classification using deep networks, SGD with Armijo line-search results in both faster convergence and better generalization.
Kinematics of multiple stellar populations in Globular Clusters with Gaia

Abstract The internal dynamics of multiple stellar populations in Globular Clusters (GCs) provides unique constraints on the physical processes responsible for their formation. Specifically, the present-day kinematics of cluster stars, such as rotation and velocity dispersion, seems to be related to the initial configuration of the system. In recent work (Milone et al. 2018), we analyzed for the first time the kinematics of the different stellar populations in NGC 0104 (47 Tucanae) over a large field of view, exploiting the Gaia Data Release 2 proper motions combined with multi-band ground-based photometry. In this paper, based on the work by Cordoni et al. (2019), we extend this analysis to six GCs, namely NGC 0288, NGC 5904 (M 5), NGC 6121 (M 4), NGC 6752, NGC 6838 (M 71) and further explore NGC 0104. Among the analyzed clusters only NGC 0104 and NGC 5904 show significant rotation on the plane of the sky. Interestingly, multiple stellar populations in NGC 5904 exhibit different rotation curves.
Refined Generalization Analysis of Gradient Descent for Over-parameterized Two-layer Neural Networks with Smooth Activations on Classification Problems

Recently, several studies have proven the global convergence and generalization abilities of the gradient descent method for two-layer ReLU networks by making a positivity assumption of the Gram-matrix of the neural tangent kernel. However, the performance of gradient descent on classification problems has not been well studied, and further investigation of the problem structure is possible. In this work, we present a partially stronger but reasonable assumption for binary classification problems compared to the positivity assumption of the Gram-matrix, where a data distribution can be perfectly classifiable by a tangent model, and we provide a refined generalization analysis of the gradient descent method for two-layer networks with smooth activations. A remarkable point of this study is that our generalization bound has much better dependence on the network width compared to existing results. As a result, our theory significantly enlarges a class of over-parameterized networks having provable generalization ability, with respect to network width, while most studies require much higher over-parameterization.
Federated Forest

Most real-world data are scattered across different companies or government organizations, and cannot be easily integrated under data privacy and related regulations such as the European Union’s General Data Protection Regulation (GDPR) and China’ Cyber Security Law. Such data islands situation and data privacy & security are two major challenges for applications of artificial intelligence. In this article, we tackle these challenges and propose a privacy-preserving machine learning model, called Federated Forest, which is a lossless learning model of the traditional random forest method, i.e., achieving the same level of accuracy as the non-privacy-preserving approach. Based on it, we developed a secure cross-regional machine learning system that allows a learning process to be jointly trained over different regions’ clients with the same user samples but different attribute sets, processing the data stored in each of them without exchanging their raw data. A novel prediction algorithm was also proposed which could largely reduce the communication overhead. Experiments on both real-world and UCI data sets demonstrate the performance of the Federated Forest is as accurate as of the non-federated version. The efficiency and robustness of our proposed system had been verified. Overall, our model is practical, scalable and extensible for real-life tasks.
Evolutionary dynamics with game transitions

Significance Evolving populations are constantly subjected to changing environmental conditions. The environment can determine how the expression of traits affects the individuals possessing them. Just as important, however, is the fact that the expression of traits can also alter the environment. We model this phenomenon by introducing game transitions into classical models of evolutionary dynamics. Interacting individuals receive payoffs from the games that they play, and these games can change based on past actions. We find that game transitions can significantly reduce the critical benefit-to-cost threshold for cooperation to evolve in social dilemmas. This result improves our understanding of when cooperators can thrive in nature, even when classical results predict a high critical threshold. The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds k−k′, where k is the average number of neighbors of an individual and k′ captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.
Clinical Evaluation of Blood Pressure Lowering, Endothelial Function Improving, Hypolipidemic and Anti‐Inflammatory Effects of Pomegranate Juice in Hypertensive Subjects

Pomegranate (Punica granatum L.) juice (PJ) contains different types of antioxidants and bioactive polyphenols and has been reported to promote cardiovascular health through several mechanisms. The present study aimed to examine the effects of 2‐week intake of fresh PJ on blood pressure, flow‐mediated dilatation (FMD), serum lipid profile and concentrations of inflammatory and endothelial function biomarkers. Twenty‐one hypertensive patients (aged 30–67 years) were recruited into the trial and assigned to receive either PJ (150 ml/day in a single occasion between lunch and dinner; n = 11) or the same amount of water (n = 10) for a period of 2 weeks. Systolic (SBP) and diastolic (DBP) pressures together with FMD and serum concentrations of lipid profile parameters, apolipoproteins A and B, intracellular adhesion molecule‐1 (ICAM‐1), vascular endothelial adhesion molecule 1 (VCAM‐1), E‐selectin, high‐sensitivity C‐reactive protein (hs‐CRP) and interleukin‐6 (IL‐6) were measured at baseline and at the end of trial. PJ consumption was associated with significant reductions in SBP (p = 0.002) and DBP (p = 0.038) but not FMD (p > 0.05). Serum levels of VCAM‐1 (p = 0.008) were significantly reduced by PJ while those of E‐selectin were elevated (p = 0.039). However, no significant effect was observed from PJ on serum levels of ICAM‐1, hs‐CRP, lipid profile parameters, apolipoproteins and IL‐6 in any of the study groups (p > 0.05). Consumption of PJ for 2 weeks has effective hypotensive effects, and may improve endothelial function by decreasing serum concentrations of VCAM‐1. These findings suggest PJ as a beneficial cardioprotective supplement for hypertensive subjects. Copyright © 2013 John Wiley & Sons, Ltd.
Autoregressive Planet Search: Application to the Kepler Mission

The 4 yr light curves of 156,717 stars observed with NASA’s Kepler mission are analyzed using the autoregressive planet search (ARPS) methodology described by Caceres et al. The three stages of processing are maximum-likelihood ARIMA modeling of the light curves to reduce stellar brightness variations, constructing the transit comb filter periodogram to identify transit-like periodic dips in the ARIMA residuals, and Random Forest classification trained on Kepler team confirmed planets using several dozen features from the analysis. Orbital periods between 0.2 and 100 days are examined. The result is a recovery of 76% of confirmed planets, 97% when period and transit depth constraints are added. The classifier is then applied to the full Kepler data set; 1004 previously noticed and 97 new stars have light-curve criteria consistent with the confirmed planets, after subjective vetting removes clear false alarms and false positive cases. The 97 Kepler ARPS candidate transits mostly have periods of P < 10 days; many are ultrashort period hot planets with radii <1% of the host star. Extensive tabular and graphical output from the ARPS time series analysis is provided to assist in other research relating to the Kepler sample.
Large deviations for sticky Brownian motions

We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has positive Lebesgue measure with positive probability. These diffusions can also be seen as n random motions in a random environment whose distribution is given by so-called stochastic flows of kernels. For a specific type of sticky interaction, we prove exact formulas characterizing the stochastic flow and show that in the large deviations regime, the random fluctuations of these stochastic flows are Tracy-Widom GUE distributed. An equivalent formulation of this result states that the extremal particle among n sticky Brownian motions has Tracy-Widom distributed fluctuations in the large n and large time limit. These results are proved by viewing sticky Brownian motions as a (previously known) limit of the exactly solvable beta random walk in random environment.
Butterfly: A Panacea for All Difficulties in Wildly Unsupervised Domain Adaptation

In unsupervised domain adaptation (UDA), classifiers for the target domain (TD) are trained with clean labeled data from the source domain (SD) and unlabeled data from TD. However, in the wild, it is hard to acquire a large amount of perfectly clean labeled data in SD given limited budget. Hence, we consider a new, more realistic and more challenging problem setting, where classifiers have to be trained with noisy labeled data from SD and unlabeled data from TD---we name it wildly UDA (WUDA). We show that WUDA provably ruins all UDA methods if taking no care of label noise in SD, and to this end, we propose a Butterfly framework, a panacea for all difficulties in WUDA. Butterfly maintains four models (e.g., deep networks) simultaneously, where two take care of all adaptations (i.e., noisy-to-clean, labeled-to-unlabeled, and SD-to-TD-distributional) and then the other two can focus on classification in TD. As a consequence, Butterfly possesses all the necessary components for all the challenges in WUDA. Experiments demonstrate that under WUDA, Butterfly significantly outperforms existing baseline methods.
Occurrence of 3-monochloropropanediol esters and glycidyl esters in commercial infant formulas in the United States

ABSTRACT This work presents occurrence data for fatty acid esters of 3-chloro-1,2-propanediol (3-MCPD) and glycidol in 98 infant formula samples purchased in the United States. These contaminants are considered potentially carcinogenic and/or genotoxic, making their presence in refined oils and foods a potential health risk. Recently, attention has focused on methodology to quantify MCPD and glycidyl esters in infant formula for risk-assessment purposes. Occurrence data for 3-MCPD and glycidyl esters were produced using a procedure for extracting fat from infant formula and an LC-MS/MS method for analysing fat extracts for intact esters. Infant formulas were produced by seven manufacturers, five of which use palm oil and/or palm olein in their formulations. In formulas containing palm/palm olein, concentrations for bound 3-MCPD and glycidol ranged from 0.021 to 0.92 mg kg–1 (ppm) and from < LOQ to 0.40 mg kg–1 (ppm), respectively. Formulas not containing palm/palm olein, bound 3-MCPD and glycidol concentrations ranged from 0.072 to 0.16 mg kg–1 (ppm) and from 0.005 to 0.15 mg kg–1 (ppm), respectively. Although formulas from manufacturers A and G did not contain palm/palm olein, formulas from manufacturer E (containing palm olein) had the lowest concentrations of bound 3-MCPD and glycidol, demonstrating the effectiveness of industrial mitigation strategies. Graphical Abstract
SCRAM: Spatially Coherent Randomized Attention Maps

Attention mechanisms and non-local mean operations in general are key ingredients in many state-of-the-art deep learning techniques. In particular, the Transformer model based on multi-head self-attention has recently achieved great success in natural language processing and computer vision. However, the vanilla algorithm computing the Transformer of an image with n pixels has O(n^2) complexity, which is often painfully slow and sometimes prohibitively expensive for large-scale image data. In this paper, we propose a fast randomized algorithm --- SCRAM --- that only requires O(n log(n)) time to produce an image attention map. Such a dramatic acceleration is attributed to our insight that attention maps on real-world images usually exhibit (1) spatial coherence and (2) sparse structure. The central idea of SCRAM is to employ PatchMatch, a randomized correspondence algorithm, to quickly pinpoint the most compatible key (argmax) for each query first, and then exploit that knowledge to design a sparse approximation to non-local mean operations. Using the argmax (mode) to dynamically construct the sparse approximation distinguishes our algorithm from all of the existing sparse approximate methods and makes it very efficient. Moreover, SCRAM is a broadly applicable approximation to any non-local mean layer in contrast to some other sparse approximations that can only approximate self-attention. Our preliminary experimental results suggest that SCRAM is indeed promising for speeding up or scaling up the computation of attention maps in the Transformer.
Motor Imagery to Enhance Recovery After Subcortical Stroke: Who Might Benefit, Daily Dose, and Potential Effects

Background. Motor imagery may enhance motor recovery after stroke. Objectives. To estimate the proportion of patients able to perform motor imagery, the feasibility of delivery of motor imagery training (MIT), and the effects of MIT on motor recovery in an exploratory study. Methods. An immediate pretreatment and posttreatment single-group design was used to study 10 patients after subcortical stroke with neuromuscular weakness in the upper limb. MIT that included upper limb activities reflecting everyday tasks was provided for 10 consecutive working days. Measures included assessment of chaotic motor imagery, patient report of tolerability of MIT, Motricity Index (MI), Nine Hole Peg Test (9HPT), and quality of movement (MAL-QOM). MIT dose was changed in response to patient feedback. Graphed motor function scores were inspected visually for clinically important changes. Results. Four of the 10 patients were unable to perform motor imagery. Patient opinion was positive about the content and shaped daily dose of MIT given in two 20-minute periods separated by a 10-minute rest. Clinically important changes in motor scores were found. Four patients increased MI score (range 8-16), 3 patients increased 9HPT score (range 0.02-0.04 pegs/second), and 4 patients increased MAL-QOM score (range 0.63-1.29). Conclusions. MIT was received positively by patients, but 40% were unable to perform imagery and interindividual variations were found on motor function.
Secrecy Rate Maximization for Intelligent Reflecting Surface Assisted Multi-Antenna Communications

We investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective. The design goal is to maximize the system secrecy rate subject to the source transmit power constraint and the unit modulus constraints imposed on phase shifts at the IRS. To solve this complicated non-convex problem, we develop an efficient alternating algorithm where the solutions to the transmit covariance of the source and the phase shift matrix of the IRS are achieved in closed form and semi-closed form, respectively. The convergence of the proposed algorithm is guaranteed theoretically. Simulation results validate the performance advantage of the proposed optimized design.
Optimal nonparametric change point detection and localization.

We study change point detection and localization for univariate data in fully nonparametric settings in which, at each time point, we acquire an i.i. d. sample from an unknown distribution. We quantify the magnitude of the distributional changes at the change points using the Kolmogorov--Smirnov distance. We allow all the relevant parameters -- the minimal spacing between two consecutive change points, the minimal magnitude of the changes in the Kolmogorov--Smirnov distance, and the number of sample points collected at each time point -- to change with the length of time series. We generalize the renowned binary segmentation (e.g. Scott and Knott, 1974) algorithm and its variant, the wild binary segmentation of Fryzlewicz (2014), both originally designed for univariate mean change point detection problems, to our nonparametric settings and exhibit rates of consistency for both of them. In particular, we prove that the procedure based on wild binary segmentation is nearly minimax rate-optimal. We further demonstrate a phase transition in the space of model parameters that separates parameter combinations for which consistent localization is possible from the ones for which this task is statistical unfeasible. Finally, we provide extensive numerical experiments to support our theory. R code is available at this https URL.