Miracle-dz/UniFAR-FTUs huggingface dataset:
Derived smooth stacks and prequantum categories

The Weil-Kostant integrality theorem states that given a smooth manifold endowed with an integral complex closed 2-form, then there exists a line bundle with connection on this manifold with curvature the given 2-form. It also characterises the moduli space of line bundles with connection that arise in this way. This theorem was extended to the case of p-forms by Gajer in [Ga]. In this paper we provide a generalization of this theorem where we replace the original manifold by a derived smooth Artin stack. Our derived Artin stacks are geometric stacks on the \'etale (\infty,1)-site of affine derived smooth manifolds. We introduce the notion of a n-shifted p-preplectic derived smooth Artin stack in analogy with the algebraic case constructed by Pantev-To\"en-Vaqui\'e-Vezzosi in [PTVV]. This is a derived smooth Artin stack endowed with a complex closed (p+1)-form which has been cohomologically shifted by degree n. It is a far reaching generalization of a p-preplectic manifold which includes orbifolds and other highly singular objects. We then show that when its n-shifted p-preplectic form is integral, then there exists a (p+n-1)-gerbe with p-connection data and curvature corresponding to the original p-preplectic form. We also provide the characterization of the moduli stack of gerbes with connections arising in this context. We construct a canonical functor from the (\infty,1)-category of integral n-shifted p-preplectic derived smooth Artin stacks to the (\infty,1)-category of linear (\infty,p+n-1)-categories. When n=0 and p=1, this functor can be thought of like a cohomology functor in that it associates to a derived presymplectic smooth Artin stack a linear invariant in the form of a differential graded module. In the general case we obtain higher prequantum categories which requires the machinery of linear (\infty,n)-categories.
The variety of three-dimensional real Jordan algebras

In this paper, we study the variety $Jor_{3}$ of three-dimensional Jordan algebras over the field of real numbers. We establish the list of $26$ non-isomorphic Jordan algebras and describe the irreducible components of $Jor_{3}$ proving that it is the union of Zariski closure of the orbits of $8$ rigid algebras.
Optimized Deep Neural Model-Based Intrusion Detection and Mitigation System for Vehicular Ad-Hoc Network

Abstract In this research work, a novel Intrusion Detection and Mitigation System (IDMS) is modeled based on the optimization assisted deep learning technique. The two major phases are: feature extraction, attack detection and mitigation. In the feature extraction phases, the features related to the traffic flow and the vehicle position gets extracted. Then, these extracted features are subjected to attack detection phase, where the weight optimized Deep Neural Network detects the presence/absence of attack in the network. For the tuning purpose, a new Improved Particle Swarm Optimization (IPSO) algorithm is introduced in this work. The presented method overcomes the traditional PSO's drawbacks, such as easily falling into local optima, and improves its performance. Once the attack behavior is identified, it is very important to mitigate the attacker from the network. For this, BAIT based mitigation process is used in this work. Finally, the performance of the proposed IDMS is evaluated over the extant techniques in terms of certain performance measures. The proposed work’s UR is 13% better than the current SVM, 9% better than PSO + DNN, 6.6% better than NB, 8.6% better than I-GHSOM, and 16.6% better than SLnO + DNN.
Academic Cyberslacking: Why Do Students Engage in Non-Academic Internet Access During Lectures?

Introduction University students, as members of the digital generation, often access the internet for non-academic purposes while attending lectures in the classroom. Internet access for non-academic purposes during lectures is known as academic cyberslacking. This study aims to test the effects of media multitasking, self-efficacy, self-regulation, social media engagement, and Attention, Relevance, Confidence, and Satisfaction (ARCS) motivation, on the engagement in academic cyberslacking by university students. Methods The participants were 1485 university students, who had previously engaged in academic cyberslacking during lectures. The research instruments in this study were an academic cyberslacking scale, a media multitasking self-efficacy scale, a self-regulation scale, a social media engagement scale, and an ARCS motivation scale. The research model and hypotheses are tested using structural equation model (SEM) by Lisrel. Confirmatory factor analysis (CFA) is also used to analyze all the instruments. The respondents’ demographic data were analyzed using SPSS. Results The results showed that it is only media multitasking self-efficacy and social media engagement which have any significant effects regarding academic cyberslacking. Self-regulation and ARCS motivation do not have direct association with academic cyberslacking. Conclusion Students do academic cyberslacking during lectures. Media multitasking self-efficacy and social media engagement can predict students’ academic cyberslacking. It is recommended that students direct their involvement in the digital environment to more constructive efforts during lectures.
Rational vs transcendental points on analytic Riemann surfaces

Let $(X,L)$ be a polarized variety over a number field. We suppose that $L$ is an hermitian line bundle. Let $M$ be a non compact Riemann Surface and $U\subset M$ be a relatively compact open set. Let $\varphi:M\to X({\Bbb C})$ be a holomorphic map. For every positive real number $T$, let $A_U(T)$ be the cardinality of the set of $z\in U$ such that $\varphi (z)\in X(K)$ and $h_L(\varphi(z))\leq T$. After a revisitation of the proof of the sub exponential bound for $A_U(T)$, obtained by Bombieri and Pila , we show that there are intervals of $T$'s as big as we want for which $A_U(T)$ is upper bounded by a polynomial in $T$. We then introduce subsets of type $S$ with respect of $\varphi$. These are compact subsets of $M$ for which an inequality similar to Liouville inequality on algebraic points holds. We show that, if $M$ contains a subset of type $S$, then, {\it for every value of $T$} the number $A_U(T)$ is bounded by a polynomial in $T$. As a consequence, we show that if $M$ is a smooth leaf of a foliation in curves then $A_U(T)$ is bounded by a polynomial in $T$. Let $S(X)$ be the subset (full for the Lebesgue measure) of points which verify some kind of Liouville inequalities. In the second part we prove that $\varphi^{-1}(S(X))\neq\emptyset$ if and only if $\varphi^{-1}(S(X))$ is full for the Lebesgue measure on $M$.
Homeomorphisms, homotopy equivalences and chain complexes

This thesis concerns the relationship between bounded and controlled topology and how these can be used to recognise which homotopy equivalences of reasonable topological spaces are homotopic to homeomorphisms. Let $f:X\to Y$ be a simplicial map of finite-dimensional locally finite simplicial complexes. We prove that $f$ has contractible point inverses if and only if it is an $\epsilon$-controlled homotopy equivalences for all $\epsilon>0$, if and only if $f\times\mathrm{id}:X\times\mathbb{R} \to Y\times\mathbb{R}$ is a homotopy equivalence bounded over the open cone $O(Y^+)$ of Pedersen and Weibel. This approach can be generalised to algebra using geometric categories: the $X$-controlled categories $\mathbb{A}^*(X)$, $\mathbb{A}_*(X)$ of Ranicki and Weiss together with the bounded categories $\mathcal{C}_M(\mathbb{A})$ of Pedersen and Weibel. Analogous to the barycentric subdivision of a simplicial complex, we define the algebraic subdivision of a chain complex over that simplicial complex. The main theorem of the thesis is that a chain complex $C$ is chain contractible in $\mathbb{A}(X)$ if and only if $\textit{"}C\otimes\mathbb{Z}\textit{"}\in\mathbb{A}(X\times\mathbb{R})$ is boundedly chain contractible when measured in $O(X^+)$ for a functor $\textit{"}-\otimes\mathbb{Z}\textit{"}$ defined appropriately using algebraic subdivision and for $\mathbb{A}=\mathbb{A}^*$ or $\mathbb{A}_*$. We prove a squeezing result: a chain complex with a small enough chain contraction has arbitrarily small chain contractions. We conclude with consequences for Poincar\'e Duality spaces. Squeezing tells us that a $PL$ Poincar\'e duality space with small enough Poincar\'e duality is a homology manifold and the main theorem tells us that a $PL$ Poincar\'e duality space $X$ is a homology manifold if and only if $X\times\mathbb{R}$ has bounded Poincar\'e duality when measured in the open cone $O(X^+)$.
Some applications of localization to enumerative problems.

A simple corollary of the localization theorem (due to the author and, independently, to Lian-Liu-Yau) is applied to several problems in enumerative geometry. New formulas for Schubert calculus on flag manifolds, due to Kong, and a new reconstruction theorem for genus-zero Gromov-Witten invariants, due to Bertram-Kley, are discussed, as well as some simple functorial properties of Givental's J-function. This paper will appear in the issue of the Michigan Mathematical Journal dedicated to Bill Fulton.
Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions

We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable ("tail" estimates). These results specify and extend some results by Kusuoka and Stroock [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1--76], but our approach is substantially different and based on a technique to estimate the Fourier transform inspired from Fournier [Electron. J. Probab. 13 (2008) 135--156] and Bally [Integration by parts formula for locally smooth laws and applications to equations with jumps I (2007) The Royal Swedish Academy of Sciences]. This study is motivated by existing models for financial securities which rely on SDEs with non-Lipschitz coefficients. Indeed, we apply our results to a square root-type diffusion (CIR or CEV) with coefficients depending on the state variable, that is, a situation where standard techniques for density estimation based on Malliavin calculus do not apply. We establish the existence of a smooth density, for which we give exponential estimates and study the behavior at the origin (the singular point).
Triality in so(4,4), characteristic classes, D4 and G2 singularities

We recall the construction of triality automorphism of so(8) given by E. Cartan and we give a matrix representation for the real form so(4,4). We compute the induced results on the characteristic classes. Paralelly we study the triality automorphism of the singularity D4 (in Arnolds classification of smooth functions) and its miniversal deformation. The similarity with Lie theory leads us to a definition of G2 singularity.
Evaluation of Machine Learning Interatomic Potentials for the Properties of Gold Nanoparticles

We have investigated Machine Learning Interatomic Potentials in application to the properties of gold nanoparticles through the DeePMD package, using data generated with the ab-initio VASP program. Benchmarking was carried out on Au20 nanoclusters against ab-initio molecular dynamics simulations and show we can achieve similar accuracy with the machine learned potential at far reduced cost using LAMMPS. We have been able to reproduce structures and heat capacities of several isomeric forms. Comparison of our workflow with similar ML-IP studies is discussed and has identified areas for future improvement.
FatigueView: A Multi-Camera Video Dataset for Vision-Based Drowsiness Detection

Although vision-based drowsiness detection approaches have achieved great success on empirically organized datasets, it remains far from being satisfactory for deployment in practice. One crucial issue lies in the scarcity and lack of datasets that represent the actual challenges in real-world applications, e.g. tremendous variation and aggregation of visual signs, challenges brought on by different camera positions and camera types. To promote research in this field, we introduce a new large-scale dataset, FatigueView, that is collected by both RGB and infrared (IR) cameras from five different positions. It contains real sleepy driving videos and various visual signs of drowsiness from subtle to obvious, e.g. with 17,403 different yawning sets totaling more than 124 million frames, far more than recent actively used datasets. We also provide hierarchical annotations for each video, ranging from spatial face landmarks and visual signs to temporal drowsiness locations and levels to meet different research requirements. We structurally evaluate representative methods to build viable baselines. With FatigueView, we would like to encourage the community to adapt computer vision models to address practical real-world concerns, particularly the challenges posed by this dataset.
$ADE$ bundles over $ADE$ singular surfaces and flag varieties of $ADE$ type

Based on the Brieskorn-Slodowy-Grothendieck diagram, we write the holomorphic structures (or filtrations) of the ADE Lie algebra bundles over the corresponding type ADE flag varieties, over the cotangent bundles of these flag varieties, and over the corresponding type $ADE$ singular surfaces. The main tool is the cohomology of line bundles over flag varieties and their cotangent bundles.
Scalar oscillatory integrals in smooth spaces of homogeneous type

We consider a generalization of the notion of spaces of homogeneous type, inspired by recent work of Street (2011) on the multi-parameter Carnot–Caratheodory geometry, which endows such spaces with differential structure. The setting allows one to formulate estimates for scalar oscillatory integrals on these spaces which are uniform and respect the underlying geometry of both the space and the phase function. As a corollary we obtain a generalization of a theorem of Bruna, Nagel, and Wainger (1988) on the asymptotic behavior of scalar oscillatory integrals with smooth, convex phase of finite type.
$J$-holomorphic disks with pre-Lagrangian boundary conditions

The purpose of this paper is to carry out a classical construction of a non-constant holomorphic disk with boundary on (the suspension of) a Lagrangian submanifold in R 2 n in the case the Lagrangian is the lift of a coisotropic (a.k.a. pre-Lagrangian) submanifold in (a subset U of) R 2 n − 1 . We show that the positive lower and ﬁnite upper bounds for the area of such a disk (which are due to M. Gromov and J.-C. Sikorav and F. Laudenbach-Sikorav for general Lagrangians) depend on the coisotropic submanifold only but not on its lift to the symplectization. The main application is to a C 0 -characterization of contact embeddings in terms of coisotropic embeddings in another paper by the present author. Moreover, we prove a version of Gromov’s non-existence of exact Lagrangian embeddings into standard R 2 n for coisotropic embeddings into S 1 × R 2 n . This allows us to distinguish diﬀerent contact structures on the latter by means of the (modiﬁed) contact shape invariant. As in the general Lagrangian case, all of the existence results are based on Gromov’s theory of J -holomorphic curves and his compactness theorem (or persistence principle). Analytical diﬃculties arise mainly at the ends of the cone R + × U .
Boundary amenability of $Out(F_N)$

We prove that $Out(F_N)$ is boundary amenable. This also holds more generally for $Out(G)$, where $G$ is either a toral relatively hyperbolic group or a right-angled Artin group. As a consequence, all these groups satisfy the Novikov conjecture on higher signatures.
K3 surfaces associated to Abelian Fourfolds of Mumford's Type

Mumford constructed a family of abelian fourfolds with special stucture not characterized by endomorphism ring. Galluzzi showed that the weight 2 Hodge structure of such a variety decomposes into Hodge substructures via the action of Mumford-Tate group, one of which is of K3 type with Hodge number (1,7,1). We will compute the intersection form of such a Hodge structure and provide a canonical integral Hodge structure on this subspace. Furthermore, we shall show two applications of this invariant. Firstly, using the above formula we shall show that every K3 surface obtained in this way will admit an elliptic fibration. Comparing them with the list by Shimada, we will show that the Mordell-Weil group of all elliptic fibrations have either 2-torsion or trivial torsion group, and the conditions of the occurance of 2-torsions can be specified. Secondly, we shall use it to determine the quaternion that gives a special CM abelian fourfold that is derived equivalent to the Shioda fourfold.
Conditional measure on the Brownian path and other random sets

Let $B$ denote the range of the Brownian motion in $\mathbb{R}^{d}$ ($d\geq3$). For a deterministic Borel measure $\nu$ on $\mathbb{R}^{d}$ we wish to find a random measure $\mu$ such that the support of $\mu$ is contained in $B$ and it is a solution to the equation $E(\mu(A))=\nu(A)$ for every Borel set $A$. We discuss when exactly we can find such a solution $\mu$. We study several properties of $\mu$ such as the probability of $\mu\neq0$ and we establish a formula for the expectation of the double integral with respect to $\mu\times\mu$. We calculate $\mu$ in terms of the occupation measure when $\nu$ is the Lebesgue measure. We generalise the theory for more general random sets in complete separable metric spaces.
Adaptive Tracking Control for a Quadrotor System Subject to Internal and External Uncertainties

In this brief, the estimates of the upper bound of disturbance and all physical parameters of attitude dynamics of quadrotor system are considered, respectively. By virtue of the estimation result of the upper bound, any prior information of disturbance are not required in the construction of quadrotor controller. To compensate for saturation effect, an adaptive second-order saturation auxiliary system based on the parameter estimation result is proposed. Furthermore, a robust attitude trajectory tracking controller based on sliding mode approach is presented to guarantee that the defined tracking error is stabilized asymptotically. The bound of real transient attitude tracking error in terms of $L_{2}$ norm is derived by designing an auxiliary equation. Finally, simulations are carried out to illustrate the effectiveness of the proposed controller.
Compact Dual-Band Filtenna With Controllable Radiation Nulls for Vehicle Application

This paper presents a compact dual-band filtenna with controllable radiation nulls for Shark-Fin scenarios. The proposed filtenna is composed of three quarter-wavelength dual-band resonators. The resonator in the middle is fed by the probe. The other resonators on both sides of the middle resonator are coupled by the mixed electromagnetic (EM) field. Since the electric and magnetic couplings can be cancelled, the mixed EM coupling can be used to obtain more radiation nulls with less order than the other coupling mechanisms. Thus, the proposed antenna is straightforward and compact. Furthermore, the dual-band Quasi-elliptical responses are realized. Four radiation nulls are realized on both sides of two pass-bands, and the positions can be flexibly adjusted in dual bands. Without extra filtering circuits, high radiation efficiency can be achieved. To analyze and guide antenna design, the RLC equivalent circuit and extraction method are provided. For demonstration, the proposed filtenna is implement-ed. Radiation efficiency is about 64% and 83% within 2.4–2.5 GHz and 5.0–5.88 GHz, respectively. Moreover, the out-of-band supp-ression is over 20 dB. Compared with the traditional antenna, the in-band radiation performance of the proposed antenna is almost maintained, whereas out-of-band suppression is significantly enhanced. The proposed filtenna is suitable for Shark-Fin scenar-ios where multiple antennas operating at different frequency bands coexist. The interference from antennas at adjacent bands is reduced significantly due to the out-of-band suppression. Specially, the isolation between the proposed dual-band filtenna and antennas operating at the other bands can be improved by about 21 dB.
Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations

In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E7(7) which is parabolically related to the CLA E7(−25). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so(n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so(n − 1,1) and its analogs so(p − 1, q − 1). Further we consider the algebras sl(2n, ℝ) and for n = 2k the algebras su* (4k) which are parabolically related to the CLA su(n,n). Further we consider the algebras sp(r,r) which are parabolically related to the CLA sp(2r, ℝ). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14),
Linearized stability for a multi-dimensional free boundary problem modelling two-phase tumour growth

This paper is concerned with a multi-dimensional free boundary problem modelling the growth of a tumour with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By using the Fourier expansion of functions on unit sphere via spherical harmonics, we establish some decay estimates for the solution of the linearized system of this tumour model at the radial stationary solution, so proving that the radial stationary solution is linearly asymptotically stable when neglecting translations.