Miracle-dz/UniFAR-FTUs huggingface dataset:
Robust Real-time UAV Replanning Using Guided Gradient-based Optimization and Topological Paths

Gradient-based trajectory optimization (GTO) has gained wide popularity for quadrotor trajectory replanning. However, it suffers from local minima, which is not only fatal to safety but also unfavorable for smooth navigation. In this paper, we propose a replanning method based on GTO addressing this issue systematically. A path-guided optimization (PGO) approach is devised to tackle infeasible local minima, which improves the replanning success rate significantly. A topological path searching algorithm is developed to capture a collection of distinct useful paths in 3-D environments, each of which then guides an independent trajectory optimization. It activates a more comprehensive exploration of the solution space and output superior replanned trajectories. Benchmark evaluation shows that our method outplays state-of-the-art methods regarding replanning success rate and optimality. Challenging experiments of aggressive autonomous flight are presented to demonstrate the robustness of our method. We will release our implementation as an open-source package1.
Basic Study on the Relation between Heart Rate Variability and Respiration Period for Children toward the Development of a Respiration Leading Stuffed Toy

Three years have passed since the Great East Japan Earthquake, but patients with post traumatic stress disorder (PTSD) still remain. Not only adults, but many children also need mental care. Learning the respiration control method, which relaxes the body and mind, is said to be effective for preventing PTSD. Therefore, we intended to develop a respiration leading stuffed toy, which leads children"s respiration by the up-and-down movement of abdomen and help them relax. We executed a preliminary experiment to study the effects of respiration guidance by it. The participants were 48 children (26 boys and 22 girls) aged 4-12 years. The results show that age under 6 years and boys showed the tendency not to be leaded well. Their respiration patterns suggest that the final respiration leading period (8sec) was too long for them. By the way, heart rate variability (HRV) biofeedback training indicates that the most suitable respiration period for improving chronic diseases is between 9-13 sec for adults. But the suitable respiration period for children has not studied yet. Therefore, we intended to study the relation between HRV and respiration period. The participants were 6 children (2 boys and 4 girls) aged 5-11 years. The amplitude of HRV which is regarded as the index for HRV biofeedback training became highest at 10 or 11 sec for all children similar to adults. But some of the children could not breathe smoothly at those respiration periods. So the most suitable respiration period for smooth breathing is considered to be different from the respiration period which makes amplitude of HRV the highest in children. Further study is needed to clarify their relations.
A Game-Theoretic Algorithm for Link Prediction

Predicting edges in networks is a key problem in social network analysis and involves reasoning about the relationships between nodes based on the structural properties of a network. In particular, link prediction can be used to analyse how a network will develop or - given incomplete information about relationships - to discover "missing" links. Our approach to this problem is rooted in cooperative game theory, where we propose a new, quasi-local approach (i.e., one which considers nodes within some radius k) that combines generalised group closeness centrality and semivalue interaction indices. We develop fast algorithms for computing our measure and evaluate it on a number of real-world networks, where it outperforms a selection of other state-of-the-art methods from the literature. Importantly, choosing the optimal radius k for quasi-local methods is difficult, and there is no assurance that the choice is optimal. Additionally, when compared to other quasi-local methods, ours achieves very good results even when given a suboptimal radius k as a parameter.
Numerical Method for Parameter Inference of Nonlinear ODEs with Partial Observations.

Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ODEs with partial observations. Our method combines fast Gaussian process based gradient matching (FGPGM) and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate and efficient.
Electrostatic interaction between colloids with constant surface potentials at fluid interfaces.

In this thesis, the electrostatic interaction between two chemically identical colloids, both carrying constant surface potential is studied in the limit of short inter-particle separation at the interface of two immiscible fluids. Using an appropriate model system, the problem is solved analytically within the framework of linearized Poisson-Boltzmann theory and classical density functional theory. The governing equation of the electrostatic problem is derived by minimization of the corresponding density functional, which leads to the Debye-Huckel equation. Subsequently, the Debye-Huckel equation is solved by exact calculations as well as by applying the widely used superposition approximation, each providing expressions for the electrostatic potential distribution inside the system. Furthermore, the obtained results of the electrostatic problem are used to calculate surface and line interaction energy densities between the colloidal particles. In all cases, the superposition approximation fails to predict the interaction energies correctly for both small and large separations. Additionally, analytic expressions for the surface tensions, line tension, and interfacial tension, which are all independent of the inter-particle separation, are obtained. The results of this thesis are expected to enrich the description of electrostatic interaction between colloids at fluid interfaces.
The Sprague-Grundy Functions of Saturations of Misère Nim

We consider misère Nim as a normal-play game obtained from Nim by removing the terminal position. While explicit formulas are known for the Sprague-Grundy functions of Nim and Welter's game, no explicit formula is known for that of misère Nim. All three of these games can be considered as position restrictions of Nim. What are the differences between them? We point out that Nim and Welter's game are saturated, but misère Nim is not. Moreover, we present explicit formulas for the Sprague-Grundy functions of saturations of misère Nim, which are obtained from misère Nim by adjoining some moves.
Spatio-temporal variation of temperature for the recent 40 years in Lhasa

It was all known that Lhasa went through a high temperature of 30.8$^{\circ}$C in late June 2019, which hit record highs. To better understand the reasons, based on observations recorded at automatic weather stations in Lhasa, we studied the characteristics of temperature variation at multiple time scales using the linear trend method, Mann-Kendall mutation test, morlet wavelet analysis, R/S analysis and so on. The results showed that: (a) The annual mean temperature (AMT) is rising at a rate of 0.5$^{\circ}$C/10yr, and the average temperature for different seasons also increased significantly, especially in winter. (b) Although there was an intersection in 1995, we found that AMT, did not pass the reliability test of significance level ${\alpha}$ =0.05, this means there are no abrupt changes for AMT, the values are 7.97$^{\circ}$C and 9.15$^{\circ}$C respectively before and after the intersection point. (c) AMT has a periodic oscillation for 18~25yr and 25~32yr based on a mass of data and the wavelet variance diagrams in Lhasa. AMT has a main cycle of 28yr, cyclic Patterns of temperature changes in spring, summer and autumn is similar to AMT, but it is relatively complex in winter. (d) The Hurst index of AMT and different seasons demonstrates that the temperature are likely to continue to rise in the future in Lhasa.
Laminar drag behavior of a viscoelastic pipe flow

Drag reduction by polymer additives, although a well-documented phenomenon in turbulent flows, has not been observed in experiments of steady laminar flows. Here, we show analytically, using the FENE-P model, that polymer additives instead enhance the laminar drag compared to the original pure Newtonian solvent. However, the non-Newtonian fluid with the added polymers (i.e., the solution) exhibits a lesser drag than a corresponding Newtonian fluid with a viscosity identical to the total viscosity of the solution. We investigate the cause of this phenomenon and arrive at bounds for the velocity, friction factor and effective viscosity of this flow. The lesser drag of the solution when compared to a viscosity-matched Newtonian flow is tracked to an increased strain rate needed to enhance viscous dissipation so as to compensate for a reduction in the opposing elastic shear force occurring away from the pipe center. Lastly, we show that the variation of effective viscosity is similar to that of the transverse diagonal components of the conformation tensor, a phenomenon shared by the turbulent case, and that this is tied to the stretching in axial direction.
Model-free bootstrap for a general class of stationary time series

A model-free bootstrap procedure for a general class of stationary time series is introduced. The theoretical framework is established, showing asymptotic validity of bootstrap confidence intervals for many statistics of interest. In addition, asymptotic validity of one-step ahead bootstrap prediction intervals is also demonstrated. Finite-sample experiments are conducted to empirically confirm the performance of the new method, and to compare with popular methods such as the block bootstrap and the autoregressive (AR)-sieve bootstrap.
A general higher‐order shell theory for compressible isotropic hyperelastic materials using orthonormal moving frame

The primary objective of this study is threefold: (1) to present a general higher‐order shell theory to analyze large deformations of thin or thick shell structures made of general compressible hyperelastic materials; (2) to formulate an efficient shell theory using the orthonormal moving frame, and (3) to develop and apply the nonlinear weak‐form Galerkin finite element model for the proposed shell theory. The displacement field of the line normal to the shell reference surface is approximated by the Taylor series/Legendre polynomials in the thickness coordinate of the shell. The use of an orthonormal moving frame makes it possible to represent kinematic quantities (e.g., the determinant of the deformation gradient) in a far more efficient manner compared with the nonorthogonal covariant bases. Kinematic quantities for the shell deformation are obtained in a novel way in the surface coordinate described in the appendix of this study with the help of exterior calculus. Furthermore, the governing equation of the shell deformation has been derived in the general surface coordinates. To obtain the nonlinear solution in the quasi‐static cases, we develop the weak‐form finite element model in which the reference surface of the shell is modeled exactly. The general invariant based compressible hyperelastic material model is considered. The formulation presented herein can be specialized for various other nonlinear compressible hyperelastic constitutive models, for example, in biomechanics and other soft‐material problems (e.g., compressible neo‐Hookean material, compressible Mooney–Rivlin material, Saint Venant–Kirchhoff model, and others). A number of numerical examples are presented to verify and validate the formulation presented in this study. The scope of potential extensions are outlined in the final section of this study.
Influence of simvastatin on the expressions of cardiac tumor necrosis factor-alpha and high mobility group protein-1 in septic rats and its mechanism

Objective To explore the mechanism of simvastatin in preventing myocardial injury in septic rats.Methods Forty-five male SD rats were randomly divided into 3groups:control group,sepsis group,simvastatin+sepsis group(observation group),with 15 rats in each group.Control group and sepsis group received gavage with normal saline for two weeks,and observation group received gavage with 20mg/kg simvastatin once a day for two weeks.Sepsis group and observation group were performed cecal ligation and puncture and control group received no treatment.The myocardial tissues were obtained and the pathological changes were observed 48 hours after operation.ELISA method was used to detect the expression of tumor necrosis factor-alpha(TNF-α),Western blot was used to detect the expression of high mobility group protein-1(HMGB-1),and TUNEL method was used to detect myocardial apoptosis index(AI). Results HE staining showed myocardial fibers edema,osteoporosis,interstitial hyperemia/edema,increased collagen fibers,and partial endocardial endothelial edema in sepsis group.Observation group had less myocardial pathological changes than sepsis group.TNF-α,HMGB-1and AI were the highest in sepsis group((47.34±0.47)ng/L,(0.85±0.01)μg/L,(21.57±2.67)%),followed by those in observation group((28.16±1.40)ng/L,(0.42±0.02)μg/L,(7.82±1.04)%)and control group((21.54±0.83)ng/L,(0.20±0.03)μg/L,(2.58±0.82)%)in turns(P0.05). Conclusion Simvastatin can reduce the expressions of TNF-α,HMGB-1and AI of myocardial tissue of septic rats,and has a protective effect on myocardial inhibition.
Plasmonic Drag in a Flowing Fermi Liquid

Collective modes in two-dimensional electron fluids show an interesting response to a background carrier flow. Surface plasmons propagating on top of a flowing Fermi liquid acquire a non-reciprocal character manifest in a $\pm k$ asymmetry of mode dispersion. The nonreciprocity arises due to Fermi surface polarization by the flow. The flow-induced interactions between quasiparticles make collective modes of the system uniquely sensitive to subtle "motional" Fermi-liquid effects. The flow-induced Doppler-type frequency shift of plasmon resonances, arising due to electron interactions, can strongly deviate from the classical value. This opens a possibility to directly probe motional Fermi-liquid effects in plasmonic near-field imaging experiments.
Hierarchical Variational Imitation Learning of Control Programs

Autonomous agents can learn by imitating teacher demonstrations of the intended behavior. Hierarchical control policies are ubiquitously useful for such learning, having the potential to break down structured tasks into simpler sub-tasks, thereby improving data efficiency and generalization. In this paper, we propose a variational inference method for imitation learning of a control policy represented by parametrized hierarchical procedures (PHP), a program-like structure in which procedures can invoke sub-procedures to perform sub-tasks. Our method discovers the hierarchical structure in a dataset of observation-action traces of teacher demonstrations, by learning an approximate posterior distribution over the latent sequence of procedure calls and terminations. Samples from this learned distribution then guide the training of the hierarchical control policy. We identify and demonstrate a novel benefit of variational inference in the context of hierarchical imitation learning: in decomposing the policy into simpler procedures, inference can leverage acausal information that is unused by other methods. Training PHP with variational inference outperforms LSTM baselines in terms of data efficiency and generalization, requiring less than half as much data to achieve a 24% error rate in executing the bubble sort algorithm, and to achieve no error in executing Karel programs.
Basis Pursuit and Orthogonal Matching Pursuit for Subspace-preserving Recovery: Theoretical Analysis

Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether $c^*$ can be recovered as the unique sparsest solution to $b = A c$. It is now well-understood that such recovery is possible by practical algorithms when the dictionary $A$ is incoherent or restricted isometric. In this paper, we consider the more general case where $b$ lies in a subspace $\mathcal{S}_0$ spanned by a subset of linearly dependent columns of $A$, and the remaining columns are outside of the subspace. In this case, the sparsest representation may not be unique, and the dictionary may not be incoherent or restricted isometric. The goal is to have the representation $c$ correctly identify the subspace, i.e. the nonzero entries of $c$ should correspond to columns of $A$ that are in the subspace $\mathcal{S}_0$. Such a representation $c$ is called subspace-preserving, a key concept that has found important applications for learning low-dimensional structures in high-dimensional data. We present various geometric conditions that guarantee subspace-preserving recovery. Among them, the major results are characterized by the covering radius and the angular distance, which capture the distribution of points in the subspace and the similarity between points in the subspace and points outside the subspace, respectively. Importantly, these conditions do not require the dictionary to be incoherent or restricted isometric. By establishing that the subspace-preserving recovery problem and the classical sparse signal recovery problem are equivalent under common assumptions on the latter, we show that several of our proposed conditions are generalizations of some well-known conditions in the sparse signal recovery literature.
Radio Positioning With EM Processing of the Spherical Wavefront

Next 5G and beyond applications have attracted a tremendous interest towards systems using antenna arrays with an extremely large number of antennas where the technology conceived for communication might also be exploited for high-accuracy positioning applications. In this paper, we investigate the possibility to infer the position of a single antenna transmitter using a single asynchronous receiving node by retrieving information from the incident spherical wavefront. To this end, we consider the adoption of a suitable mix of processing at electromagnetic (EM) and signal levels, as a lower complexity alternative to classical massive array systems where the processing is done entirely at signal level. Thus, we first introduce a dedicated general model for different EM processing architectures, entailing the use or not of a lens that can have either a reconfigurable or a fixed phase profile, and successively we investigate their attainable positioning performance. The effect of the interference is also investigated to evaluate the robustness of the considered system to the presence of multiple simultaneous transmitting sources. Results, obtained for different apertures of the exploited lens/array, confirm the possibility to achieve interesting positioning performance using a single antenna array with a limited aperture.
Singular Yamabe and Obata Problems

A conformal geometry determines a distinguished, potentially singular, variant of the usual Yamabe problem, where the conformal factor can change sign. When a smooth solution does change sign, its zero locus is a smoothly embedded separating hypersurface that, in dimension three, is necessarily a Willmore energy minimiser or, in higher dimensions, satisfies a conformally invariant analog of the Willmore equation. In any case the zero locus is critical for a conformal functional that generalises the total Q-curvature by including extrinsic data. These observations lead to some interesting global problems that include natural singular variants of a classical problem solved by Obata.
Detecting Out-of-Distribution Examples with In-distribution Examples and Gram Matrices

When presented with Out-of-Distribution (OOD) examples, deep neural networks yield confident, incorrect predictions. Detecting OOD examples is challenging, and the potential risks are high. In this paper, we propose to detect OOD examples by identifying inconsistencies between activity patterns and class predicted. We find that characterizing activity patterns by Gram matrices and identifying anomalies in gram matrix values can yield high OOD detection rates. We identify anomalies in the gram matrices by simply comparing each value with its respective range observed over the training data. Unlike many approaches, this can be used with any pre-trained softmax classifier and does not require access to OOD data for fine-tuning hyperparameters, nor does it require OOD access for inferring parameters. The method is applicable across a variety of architectures and vision datasets and, for the important and surprisingly hard task of detecting far-from-distribution out-of-distribution examples, it generally performs better than or equal to state-of-the-art OOD detection methods (including those that do assume access to OOD examples).
A Björling representation for Jacobi fields on minimal surfaces and soap film instabilities

We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal surface. When the amplitude vanishes, the curve forms part of the boundary to a critically stable domain, while when the gradient vanishes the Jacobi field is maximal along the curve. In the latter case, we show that the Jacobi field is maximally localized if its amplitude is taken to be the lowest eigenfunction of a one-dimensional Schrödinger operator. We present examples for the helicoid, catenoid, circular helicoids and planar Enneper minimal surfaces, and emphasize that the geometric nature of the Björling representation allows direct connection with instabilities observed in soap films.
On a Family of Hypergeometric Polynomials.

We work on the SCE problems. We establish the expressions of three integrals' sequences, related to it, in terms of five families of polynomials. Relations between these integrals are demonstrated and we focus on one of the three problems : the determination of the family of polynomials noted $e_n (n \in \mathbb{N})$. We show taht these polynomials are hypergeometric. From this property, the NU method can be applied to this family. We have been able to determine the Rodrigues formula. These polynomials have properties that distinguish them from classical hypergeometric polynomials. We state and demonstrate the theorem adapted to the determination of the generating function of $e_n$. Finally, the sequence of polynomials studied is expressed in terms of associated Laguerre polynomials with negative upper indices.