Miracle-dz/UniFAR-FTUs huggingface dataset:
Modifications in SIFT-based 3D reconstruction from image sequence

In this paper, we aim to reconstruct 3D points of the scene from related images. Scale Invariant Feature Transform( SIFT) as a feature extraction and matching algorithm has been proposed and improved for years and has been widely used in image alignment and stitching, image recognition and 3D reconstruction. Because of the robustness and reliability of the SIFT’s feature extracting and matching algorithm, we use it to find correspondences between images. Hence, we describe a SIFT-based method to reconstruct 3D sparse points from ordered images. In the process of matching, we make a modification in the process of finding the correct correspondences, and obtain a satisfying matching result. By rejecting the “questioned” points before initial matching could make the final matching more reliable. Given SIFT’s attribute of being invariant to the image scale, rotation, and variable changes in environment, we propose a way to delete the multiple reconstructed points occurred in sequential reconstruction procedure, which improves the accuracy of the reconstruction. By removing the duplicated points, we avoid the possible collapsed situation caused by the inexactly initialization or the error accumulation. The limitation of some cases that all reprojected points are visible at all times also does not exist in our situation. “The small precision” could make a big change when the number of images increases. The paper shows the contrast between the modified algorithm and not. Moreover, we present an approach to evaluate the reconstruction by comparing the reconstructed angle and length ratio with actual value by using a calibration target in the scene. The proposed evaluation method is easy to be carried out and with a great applicable value. Even without the Internet image datasets, we could evaluate our own results. In this paper, the whole algorithm has been tested on several image sequences both on the internet and in our shots.
Probabilistic Real-Time Scheduling and its Possible Link to Mixed-Criticality Systems

—Proving hard real-time guarantees based on a classical analysis may significantly underutilize the processor in the average case. Therefore, instead of considering a very rare worst-case scenario, a probabilistic scheduling analysis determines the probability of a deadline miss. Such an analysis assumes that task execution times are given by a set of modes representing the range of possible execution scenarios. Considering tasks with multiple modes and different levels of assurances, in this case expressed as different probabilities to miss deadlines, for different tasks provides a natural link to mixed-criticality systems. This work summarizes recent results in probabilistic real-time scheduling and some potential problems that should be considered when linking these results to mixed-criticality systems. In addition, possible connections between mixed-criticality systems and probabilistic analysis are detailed. The goal of this work is to start a discussion to determine whether such probabilistic results may be interesting for mixed-criticality research.
SEQUENTIAL STAR FORMATION IN THE Sh 254–258 MOLECULAR CLOUD: HEINRICH HERTZ TELESCOPE MAPS OF CO J = 2–1 AND 3–2 EMISSION

The molecular cloud associated with the Sh 254–258 group of five small H ii regions appears to be forming a (late)-OB association. We have mapped the associated molecular cloud in the J = 2–1 line of the CO and 13CO molecules over 0. °75 × 1°, and the CO J = 3–2 line toward the two main peaks, with the University of Arizona Heinrich Hertz Submillimeter Telescope. The data are analyzed with a statistical equilibrium code to estimate physical properties of the molecular gas. We compare the molecular cloud morphology with images at optical, IR, and radio wavelengths. From this analysis, we propose a scenario for sequential formation of the stars exciting the H ii regions, triggered by the compression of the molecular gas as a consequence of the expansion of the adjacent H ii regions.
Thickness of skeletons of arithmetic hyperbolic orbifolds

We show that closed arithmetic hyperbolic n-dimensional orbifolds with larger and larger volumes give rise to triangulations of the underlying spaces whose 1-skeletons are harder and harder to embed nicely in Euclidean space. To show this we generalize an inequality of Gromov and Guth to hyperbolic n-orbifolds and find nearly optimal geodesic triangulations of arithmetic hyperbolic n-orbifolds.
Non universality of fluctuations of outlier
eigenvectors for block diagonal deformations
of Wigner matrices

In this paper, we investigate the fluctuations of a unit eigenvector associated to an outlier in the spectrum of a spiked $N\times N$ complex Deformed Wigner matrices $M_N$. $M_N$ is defined as follows: $M_N = W_N/\sqrt{N} + A_N$ where $W_N$ is an $N \times N$ Hermitian Wigner matrix whose entries have a symmetric law $\mu$ satisfying a Poincar\'e inequality and the matrix $A_N$ is a block diagonal Hermitian deterministic matrix $A_N=\text{diag}(\theta, A_{N-1})$, $\theta \in \mathbb{R}$ has multiplicity one and generates an outlier in the spectrum of $M_N$. In the diagonal case, we prove that the fluctuations of a unit eigenvector corresponding to this outlier of $M_N$ are not universal: the limiting distribution is the convolution of $\mu$ and a Gaussian distribution. In the block diagonal case, the limiting law is replaced by a sequence of approximations with a Gaussian distribution depending on the size $N$, whose variance may not converge.
A random graph model based on 3-interactions

We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future interactions. We prove the scale free property of the model by exploring the asymptotic behaviour of the weight distribution. We also find the asympotics of the weight of a fixed vertex.
Action-angle coherent states for quantum systems with cylindric phase space

Quantum versions of cylindric phase space, like for the motion of a particle on a circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The method is illustrated with Gaussian distributions and uniform distributions on intervals, and resulting quantizations are explored.
Motivic model categories and motivic derived algebraic geometry.

In this paper, we develop an enhancement of derived algebraic geometry to apply to $\mathbb{A}^1$-homotopy theory introduced by Morel and Voevodsky. We call the enhancement "motivic derived algebraic geometry". We shall actually formulate "motivic" versions of $\infty$-categories, $\infty$-topoi, spectral schemes and spectral Deligne--Mumford stacks established by Joyal, Lurie, Toen and Vezzosi. By using the language of motivic derived algebraic geometry, we construct the Grassmannian and the algebraic $K$-theory. Furthermore we formulate the Thom spaces for vector bundles on (motivic) stacks, and we obtain the algebraic cobordism for (motivic) stacks. As the main result, we prove that the algebraic cobordism corepresents the motivic $\infty$-category which has the universal property of oriented (motivic) $\infty$-categories.
An identity connecting theta series associated with binary quadratic forms of discriminant $\Delta$ and $\Delta($prime$)^2$

We state and prove an identity which connects theta series associated with binary quadratic forms of idoneal discriminants $\Delta$ and $\Delta p^2$, for $p$ a prime. Employing this identity, we extend the results of Toh by writing the theta series of forms of discriminant $\Delta p^2$ as a linear combination of Lambert series. We then use these Lambert series decompositions to give explicit representation formulas for the forms of discriminant $\Delta p^2$. Lastly, we give a generalization of our main identity, which employs a map of Buell to connect forms of discriminant $\Delta$ to $\Delta p^2$. Our generalized identity links theta series associated with a single form of discriminant $\Delta$ to a theta series associated with forms of discriminant $\Delta p^2$, where $\Delta$ and $\Delta p^2$ are no longer required to be idoneal.
The amplification method in the context of $GL(n)$ automorphic forms

In \cite{SiVe2} and \cite{BlMa1}, the authors proved the existence of a so-called higher rank amplifier and in \cite{HoRiRo2}, the authors described an explicit version of a $GL(3)$ amplifier. This article provides, for $n\geq 4$, a totally explicit $GL(n)$ amplifier and gives all the results required to use it effectively.
Spectral invariants of distance functions

Calculating the spectral invariant of Floer homology of the distance function, we can find some kind of superheavy subsets in symplectic manifolds. We show if convex open subsets in Euclidian space with the standard symplectic form are disjointly embedded in a spherically negative monotone closed symplectic manifold, their compliment is superheavy. In particular, the $S^1$ bouquet in a closed Riemann surface with genus $g\geq 1$ is superheavy. We also prove some analogous properties of a monotone closed symplectic manifold. These can be used to extend Seyfaddni's result about lower bounds of Poisson bracket invariant.
Strong renewal theorems with infinite mean beyond local large deviations

Let $F$ be a distribution function on the line in the domain of attraction of a stable law with exponent $\alpha\in(0,1/2]$. We establish the strong renewal theorem for a random walk $S_1,S_2,\ldots$ with step distribution $F$, by extending the large deviations approach in Doney [Probab. Theory Related Fileds 107 (1997) 451-465]. This is done by introducing conditions on $F$ that in general rule out local large deviations bounds of the type $\mathbb{P}\{S_n\in(x,x+h]\}=O(n)\overline{F}(x)/x$, hence are significantly weaker than the boundedness condition in Doney (1997). We also give applications of the results on ladder height processes and infinitely divisible distributions.
Ice crystal terminal velocities.

Abstract Terminal velocities of different ice crystal forms were calculated using the most recent ice crystal drag coefficients, aspect ratios and densities. The equations derived were primarily for use in calculating precipitation rates by sampling particles with an aircraft in cirrus clouds, and determining particle size in cirrus clouds by Doppler radar. However, the equations are sufficiently general for determining particle terminal velocity at any altitude, and most any crystal type. Two sets of equations were derived. The “general” equations provide a good estimate of terminal velocities at any altitude. The “specific” equations are a set of equations for ice crystal terminal velocities at 1000 mb. The calculations are in good agreement with terminal velocity measurements. The results from the present study were also compared to prior calculations by others and seem to give more reasonable results, particularly at higher altitudes.
Fast magnetic reconnection and sudden enhancement of current sheets due to inward boundary flows

Magnetic reconnection is widely believed to be involved in dynamical phenomena such as solar flares or magnetospheric substorms. The Sweet–Parker model of magnetic reconnection in a Y‐type geometry predicts a characteristic time scale proportional to S1/2 (where S is the Lundquist number), which is too slow to account for the observed time scales. The Petschek model, in contrast, predicts a time scale proportional to ln S in an X‐point geometry. Numerical magnetohydrodynamic (MHD) simulations in the high‐S regime generally validate the Sweet–Parker model, unless the resistivity is enhanced in the diffusion region to large values (such that typically S<103). It is demonstrated in this paper that nonlinear reconnection dynamics in a Harris sheet driven by inward boundary flows occurs on a nonlinear time scale that is proportional to S1/5 and thus has a weaker dependence on resistivity than the Sweet–Parker time scale. The current sheet amplitude at the separatrix (spanning Y points) grows algebraically in t.
On Tu-Toeplitzness of weighted composition operators on H2

In this paper, we show that is -Toeplitz if and only if , where is a nonconstant inner function. We also provide necessary and sufficient conditions for -Toeplitzness of . Indeed, is -Toeplitz if and only if is an inner function. Finally, we study several conditions for the product to be Toeplitz.
SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)

ABSTRACT Sdpnal+ is a MATLAB software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented Lagrangian method, here we designed it within an inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating direction method of multipliers/augmented Lagrangian method) framework for the purpose of deriving simpler stopping conditions and closing the gap between the practical implementation of the algorithm and the theoretical algorithm. The basic code is written in MATLAB, but some subroutines in C language are incorporated via Mex files. We also design a convenient interface for users to input their SDP models into the solver. Numerous problems arising from combinatorial optimization and binary integer quadratic programming problems have been tested to evaluate the performance of the solver. Extensive numerical experiments conducted in [L.Q. Yang, D.F. Sun, and K.C. Toh, SDPNAL+: A majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints, Math. Program. Comput. 7 (2015), pp. 331–366] show that the proposed method is quite efficient and robust, in that it is able to solve 98.9% of the 745 test instances of SDP problems arising from various applications to the accuracy of in the relative KKT residual.
Zero map between obstruction spaces: subvarieties versus cycles.

In 1970s, for local complete intersections, Spencer Bloch [2] constructed the semi-regularity map $\pi: H^{1}(\mathcal{N}_{Y/X}) \to H^{q+1}(\Omega_{X/k}^{q-1})$. As an analogue, we construct a map $\pi: H^{1}(\mathcal{N}_{Y/X}) \to H^{q+1}(\Omega_{X/\mathbb{Q}}^{q-1})$, without assuming local complete intersections. While semi-regularity asks for injectivity, our map is a zero map. We use this zero map to interpret how to eliminate obstructions of deformation of cycles, an idea by Mark Green and Phillip Griffiths in [7].
Fractional Perimeter and Nonlocal Minimal Surfaces

This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give full detailed proofs for all the Theorems contained in the article "Nonlocal Minimal Surfaces" by Caffarelli, Roquejoffre and Savin, where these s-minimal sets were introduced and studied for the first time.
A triangular gap of size two in a sea of dimers on a $60^\circ$ angle

We consider a triangular gap of side two in a $60^\circ$ angle on the triangular lattice whose sides are zig-zag lines. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its five images in the sides of the angle. This provides a new aspect of the parallel between the correlation of gaps in dimer packings and electrostatics developed by the first author in previous work.
control strategies for flotation

: Flotation is a difficult process to run efficiently. One way to make flotation performance better is to improve cell level control. However, controlling pulp levels in flotation cells is a complex control task because of strong interactions between the levels in flotation cells. Therefore advanced controllers are needed to give good level control. This paper deals with a model of six flotation cells in series. Simulations are performed to compare different control strategies. Four control strategies are considered: one SISO controller and three different MIMO controllers including a new multivariable controller. It is shown that level control performances of the MIMO controllers are significantly better than that of the classical SISO controller.
An expectation-based metric for NFL field goal kickers

The standard metric for American football field goal kickers is simply the percentage of attempts successfully converted. Due to variance in distance of attempts and other conditions (weather, altitude, defense, etc.), we argue that field goal percentage is an insufficient measure of kicker performance. Using three seasons of NFL data, we construct a multivariate logistic regression model for the success probability of a given attempt. This leads naturally to metrics in which a kicker’s performance is compared to model expectations, if a replacement-level player was attempting the same kicks. Player salaries correlate only weakly with our measures of field goal kicking success. We find that those kickers selected to the Pro Bowl and All-Pro teams were rather mediocre by our metrics, over the seasons studied. The relative difficulty of kicking in various stadiums is also considered. Finally, we discuss the degree to which field goal kicking is a skill that can be maintained over multiple seasons.
Polynomial growth of subharmonic functions in a strongly symmetric Riemannian manifold

In this article we have studied some properties of subharmonic functions in a strongly symmetric Riemannian manifold with a pole. As a generalization of polynomial growth of a function we have introduced the notion of polynomial growth of some degree of a function with respect to a real function and proved that any non-negative twice differentiable subharmonic functions in an $n$-dimensional manifold always admit polynomial growth of degree $1$ with respect to a non-negative real valued subharmonic function on real line. We have also given a lower bound of the integration of a convex function in a geodesic ball.
Photovoltaic Characteristics of Phthalocyanine-Polysilane Composite Films

Poly[p-(methylphenylsilanylene)anthrylene] (PMPSA) which introduced anthracene into the Si–Si backbone structure of poly(methylphenylsilanylene) (PMPS) was synthesized. Schottky barrier photovoltaic cells consisting of semitransparent aluminum and phthalocyanine (H2Pc) dispersed in PMPSA were fabricated (H2Pc-PMPSA). The effects of a binder polymer and annealing of PMPSA on the photovoltaic characteristics were investigated. Since the conductivity of H2Pc-PMPSA composite films increases by the introduction of anthracene and the annealing, the photovoltaic property of H2Pc-PMPSA improves markedly. It is found that the power conversion efficiency becomes a maximum for H2Pc-PMPSA with a copolymerization ratio (1:1) at the annealing temperature of 160°C for 2 h. The photovoltaic parameters have the following values: the power conversion efficiency η is 4.42%, the fill factor F.F. is 0.30, the open circuit voltage Voc is 0.84 V and the short circuit photocurrent Jsc is 0.71 µA/cm2. Furthermore, the carrier transport mechanisms of H2Pc-PMPSA composite films are discussed.
Broad-band properties of the CfA Seyfert galaxies. III - Ultraviolet variability

A total of 657 archived IUE spectra are used to study the UV variability properties of six members of the CfA Seyfert I galaxy sample. All show strong evidence for continuum and line variations and a tendency for less luminous objects to be more strongly variable. Most objects show a clear correlation at zero lag between UV spectral index and luminosity, evidence that the variable component is an accretion disk around a black hole which is systematically smaller in less luminous sources. No correlation is seen between the continuum luminosity and equivalent width of the C IV, Mg II, and semiforbidden C III emission lines when the entire sample is examined, but a clear anticorrelation is present when only repeated observations of individual objects are considered. This is due to a combination of light-travel time effects in the broad-line region and the nonlinear responses of lines to continuum fluctuations. 51 refs.
Locally definable and approximate subgroups of semialgebraic groups

We prove the following instance of a conjecture stated in arXiv:1103.4770. Let $G$ be an abelian semialgebraic group over a real closed field $R$ and let $X$ be a semialgebraic subset of $G$. Then the group generated by $X$ contains a generic set and in particular is divisible. More generally, the same result holds when $X$ is definable in any o-minimal expansion of $R$ which is elementarily equivalent to $\mathbb R_{an,exp}$. We observe that the above statement is equivalent to saying: there exists an $m$ such that $\Sigma_{i=1}^m(X-X)$ is an approximate subgroup of $G$.
Additive Chow groups of schemes

We show how to make the additive Chow groups of Bloch-Esnault, Ruelling and Park into a graded module for Bloch's higher Chow groups, in the case of a smooth projective variety over a field. This yields a a projective bundle formula as well as a blow-up formula for the additive Chow groups of a smooth projective variety. In case the base-field admits resolution of singularieties, these properties allow us to apply the technique of Guille'n and Navarro Aznar to define the additive Chow groups "with log poles at infinity" for an arbitrary finite-type k-scheme X. This theory has the usual properties of a Borel-Moore theory on finite type k-schemes: it is covariantly functorial for projective morphisms, contravariantly functorial for morphisms of smooth schemes, and has a projective bundle formula, homotopy property, Mayer-Vietoris and localization sequences. Finally, we show that the regulator map defined by Park from the additive Chow groups of 1-cycles to the modules of absolute Kaehler differentials of an algebraically closed field of characteristic zero is surjective, giving an evidence of conjectured isomorphism between these two groups.
A Simple Adaptive Step-size Choice for Iterative Optimization Methods

We suggest a simple adaptive step-size procedure for a general class of iterative optimization methods, which does not require any line-search, and prove convergence of a general method under mild assumptions. This procedure maintains the basic convergence properties, but reduce the implementation cost of each iteration essentially. We describe its applications in the gradient projection method for nonlinear optimization problems and in the projection method for variational inequalities. Preliminary results of computational experiments confirm efficiency of the proposed modification.
PERFECTOID SPACES AND THE HOMOLOGICAL CONJECTURES

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct summand conjecture are included. One then portrays the progresses made with these (and related) techniques on the so-called homological conjectures.