Miracle-dz/UniFAR-FTUs huggingface dataset:
11. Point-plane incidences and some applications in positive characteristic

The point-plane incidence theorem states that the number of incidences between $n$ points and $m\geq n$ planes in the projective three-space over a field $F$, is $$O\left(m\sqrt{n}+ m k\right),$$ where $k$ is the maximum number of collinear points, with the extra condition $n 0$. This theorem also underlies a state-of-the-art Szemer\'edi-Trotter type bound for point-line incidences in $F^2$, due to Stevens and de Zeeuw. This review focuses on some recent, as well as new, applications of these bounds that lead to progress in several open geometric questions in $F^d$, for $d=2,3,4$. These are the problem of the minimum number of distinct nonzero values of a non-degenerate bilinear form on a point set in $d=2$, the analogue of the Erd\H os distinct distance problem in $d=2,3$ and additive energy estimates for sets, supported on a paraboloid and sphere in $d=3,4$. It avoids discussing sum-product type problems (corresponding to the special case of incidences with Cartesian products), which have lately received more attention.
Monadic representability of certain binary relations

Call a relation R⊆A2 (A some non-empty set) monadically representable when there exist F, G⊆A such that R = {(x, y) | x ∈ F ∘ y ∈ G} for some truth-functional connective ∘. This note finds a first-order condition on R which is necessary and sufficient for R to be monadically representable.
Fractional Cone Splines and Hex Splines

We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain $s$-dimensional meshes and include as special cases the three-directional box splines \cite{article:condat} and hex splines \cite{article:vandeville} previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex B-splines defined in \cite{article:ub,article:fbu} and investigated in, e.g., \cite{article:fm,article:mf}. Explicit time domain representations are derived for these splines on $3$-directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span.
A conjugate subgradient algorithm with adaptive preconditioning for LASSO minimization

This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion of ill-conditioned linear problems, in particular for computed tomography with the dictionary learning method. A comparison with other state-of-art methods shows a significant reduction of the number of iterations, which makes this algorithm appealing for practical use.
Unstructured Business Processes Improvement using Process Mining Techniques

Executing loosely structured processes generate unstructured behaviours. Thus, an Unstructured Business Process (UBP) still has more issues that are difficult to be analysed and to be understood due to its complexity and variability. Moreover, the need of an instantiate response is clearly appeared in operational systems. Therefore, it is required to study related challenges that can be acquired during the transition from the structured BP to the unstructured one. In this context, process mining plays a dominant role to understand business process complexity using event data resulted from business process execution. Mainly, this paper treats three challenges related to unstructured BPs. The first challenge is how to support UBPs at runtime using process mining techniques. The second challenge is how to manage UBP variability taking into consideration variant conditions. The third challenge is how to adapt dynamically UBPs according to the company business rules and conditions.
Ionospheric delay gradient monitoring for GBAS by GPS stations near Suvarnabhumi airport, Thailand

Ground‐based augmentation system (GBAS) is an important augmentation system that provides the differential corrections and integrity information from the reference stations to the aircrafts for precision approach and landing. It is known that the nonuniform ionospheric characteristics called “ionospheric delay gradient” can cause the errors in differential corrections degrading the accuracy and safety level if they are undetected by the reference stations. Since the characteristics of the ionosphere are different for each region, the ionospheric delay gradient observations in equatorial and low‐latitude regions are necessary for developing the suitable ionospheric threat models. The purpose of this work is to analyze the ionospheric delay gradients observed by three GPS stations near Suvarnabhumi airport in Bangkok, Thailand, which is located in the low‐latitude region. The ionospheric irregularities in this region are mainly caused by the plasma bubble, which usually occurs after sunset. The GPS data with plasma bubble occurrence during the September equinox 2011 and 2012 are therefore analyzed. In addition, the data analysis procedure utilizing the rate of total electron content change index for this region is proposed. The results show that the ionospheric delay gradients observed in the west‐east direction appear higher than the south‐north direction, varying from 28 to 178 mm/km during plasma bubble occurrences.
Rationale and Design of LAPIS: A Multicenter Prospective Cohort Study to Investigate the Efficacy and Safety of Low-Dose Aspirin in Elderly Chinese Patients

Purpose Although aspirin can effectively reduce the occurrence of atherothrombosis, it is significantly associated with increased bleeding, with elderly individuals being at increased risk of cardiovascular diseases(CVDs) and hemorrhage. While the adverse effects of aspirin can be reduced by using the lowest effective dose, its optimal dose remains undetermined in the elderly Chinese population with both higher cardiovascular and bleeding risks. This study aims to assess the current status of aspirin therapy in real-world clinical settings as well as investigate the efficacy and safety of different doses of aspirin intake (≤ 50 mg/d and > 50 mg/d) for CVD prevention and management in elderly Chinese individuals. Patients and Methods The Low-dose Aspirin for Primary and Secondary Prevention of Cardiovascular Disease in the Elderly Study (LAPIS) is a multicenter, prospective, observational cohort study. At least 10,000 people aged ≥ 60 years who require long-term aspirin therapy will be recruited. The effectiveness outcome is a composite of major cardiovascular events(MACEs), including nonfatal myocardial infarction, unstable angina, arteriosclerotic disease requiring surgery or intervention, nonfatal stroke, transient ischemic attack, or cardiovascular death (excluding intracranial hemorrhage). The safety outcome is a composite of the first occurrence of fatal bleeding, major bleeding and minor bleeding. Information on the incidence of aspirin-associated gastrointestinal adverse events will also be collected for safety analyses. Outcome measurements will be performed at intervals of 30 days, 3 months, 6 months and then every 6 months for the next 3 years. Conclusion The results of the LAPIS study will ascertain the efficacy and safety of different doses of aspirin for the prevention and management of CVD, thereby providing evidence to determine the optimal evidence-based dose of aspirin therapy in Chinese elderly individuals. Trial Registration ChiCTR1900021980 (chictr.org.cn). Registered on March 19, 2019.
Virasoro Action and Virasoro Constraints on Integrable Hierarchies of the $r$-Matrix Type

For a large class of hierarchies of integrable equations admitting a classical $r-$matrix, we propose a construction for the Virasoro algebra actionon the Lax operators which commutes with the hierarchy flows. The construction relies on the existence of dressing transformations associated to the $r$-matrix and does not involve the notion of a tau function. The dressing-operator form of the Virasoro action gives the corresponding formulation of the Virasoro constraints on hierarchies of the $r-$matrix type. We apply the general construction to several examples which include KP, Toda and generalized KdV hierarchies, the latter both in scalar and the Drinfeld-Sokolov formalisms. We prove the consistency of Virasoro action on the scalar and matrix (Drinfeld-Sokolov) Lax operators, and make an observation on the difference in the form of string equations in the two formalisms.
Construction of a $C^2$ class finite element based on the Clough-Tocher subdivision

In this paper, we construct a $C^2$ finite element based on the Clough-Tocher subdivision. We use derivatives order up to two at the vertices and cross boundary derivatives order up to two along the exterior edges of the triangle. The centroid of the triangle is just evaluated. The interpolant used is globally $C^2,$ has local support, is piecewise polynomial of degree less or equal to 5.
Extinction and the Allee effect in an age structured Ricker population model with inter-stage interaction

We study the evolution in discrete time of certain age-structured populations, such as adults and juveniles, with a Ricker fitness function. We determine conditions for the convergence of orbits to the origin (extinction) in the presence of the Allee effect and time-dependent vital rates. We show that when stages interact, they may survive in the absence of interior fixed points, a surprising situation that is impossible without inter-stage interactions. We also examine the shift in the interior Allee equilibrium caused by the occurrence of interactions between stages and find that the extinction or Allee threshold does not extend to the new boundaries set by the shift in equilibrium, i.e. no interior equilibria are on the extinction threshold.
A Robust Observer-Based Fault Tolerant Control Scheme for Underwater Vehicles

This paper proposes an actuator failure tolerant robust control scheme for underwater vehicles. A state observer is introduced first, aimed at estimating velocities. In order to solve the tracking problem for vehicle positions, a sliding mode control (SMC) law is developed using the available position measurements and the velocity estimates provided by the observer. Detection of thruster faults based on the check of any deviation of the observed sliding surfaces, and an isolation policy for the failed thruster are proposed. Finally, control reconfiguration is performed exploiting the inherent redundancy of actuators. An extensive simulation study has been performed, supporting the effectiveness of the proposed approach.
A first guide to the character theory of finite groups of Lie type

This survey article is an introduction to some of Lusztig's work on the character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power of a prime~$p$. It is partly based on two series of lectures given at the Centre Bernoulli (EPFL) in July 2016 and at a summer school in Les Diablerets in August 2015. Our focus here is on questions related to the parametrization of the irreducible characters and on results which hold without any assumption on~$p$ or~$q$.
Homotopy invariants of covers and KKM type lemmas

With any (open or closed) cover of a space T we associate certain homotopy classes of maps T into n-spheres. These homotopy invariants can be considered as obstructions for extensions of covers of a subspace A to a space X. We using these obstructions for generalizations of the classic KKM (Knaster-Kuratowski-Mazurkiewicz) and Sperner lemmas. In particular, we show that in the case when A is a k-sphere and X is a (k+1)-disk there exist KKM type lemmas for covers by n+2 sets if and only if the k-homotopy group of n-sphere is not zero.
Coordination Control of Wind Farm Integrated Cascaded Hybrid HVDC System in Weak Grids

Combing the benefits of line-commutated converter (LCC) and modular multilevel converter (MMC), the hybrid high-voltage direct-current (HVDC) system is a viable option for the long-distance transmission of large-scale wind power. However, as renewable energy becomes more prevalent, the inertia of power networks will decrease, possibly leading to instability problems. In this scenario, the conventional grid following (GFL) control scheme is no longer applicable, and suitable coordination control strategies are required. This paper proposes two coordinated grid forming (GFM) control strategies for the cascaded hybrid system and evaluates the control performance of different control types. Firstly, the conventional control scheme of the cascaded hybrid HVDC system and problems under weak AC power systems integration are introduced. Then, coordinated grid forming control strategies are proposed, and the control performance of the GFL and GFM control schemes are compared. Finally, the cascaded hybrid HVDC system's electromagnetic transient model is constructed in PSCAD/EMTDC to confirm the efficacy of the proposed coordinated control strategies.
Jordan blocks of cuspidal representations of symplectic groups

Let $G$ be a symplectic group over a nonarchimedean local field of characteristic zero and odd residual characteristic. Given an irreducible cuspidal representation of G, we determine its Langlands parameter (equivalently, its Jordan blocks in the language of Moeglin) in terms of the local data from which the representation is explicitly constructed, up to a possible unramified twist in each block of the parameter. We deduce a Ramification Theorem for $G$, giving a bijection between the set of endo-parameters for $G$ and the set of restrictions to wild inertia of discrete Langlands parameters for $G$, compatible with the local Langlands correspondence. The main tool consists in analysing the intertwining Hecke algebra of a good cover, in the sense of Bushnell--Kutzko, for parabolic induction from a cuspidal representation of $G\times\mathrm{GL}_n$, seen as a maximal Levi subgroup of a bigger symplectic group, in order to determine its (ir)reducibility; a criterion of Moeglin then relates this to Langlands parameters.
PATRICIA Bridges

A radix sort tree arises when storing distinct infinite binary words in the leaves of a binary tree such that for any two words their common prefixes coincide with the common prefixes of the corresponding two leaves. If one deletes the out-degree $1$ vertices in the radix sort tree and "closes up the gaps", then the resulting PATRICIA tree maintains all the information that is necessary for sorting the infinite words into lexicographic order. We investigate the PATRICIA chains -- the tree-valued Markov chains that arise when successively building the PATRICIA trees for the collection of infinite binary words $Z_1,\ldots, Z_n$, $n=1,2,\ldots$, where the source words $Z_1, Z_2,\ldots$ are independent and have a common diffuse distribution on $\{0,1\}^\infty$. It turns out that the PATRICIA chains share a common collection of backward transition probabilities and that these are the same as those of a chain introduced by R\'emy for successively generating uniform random binary trees with larger and larger numbers of leaves. This means that the infinite bridges of any PATRICIA chain (that is, the chains obtained by conditioning a PATRICIA chain on its remote future) coincide with the infinite bridges of the R\'emy chain. The infinite bridges of the R\'emy chain are characterized concretely in Evans, Gr\"ubel, and Wakolbinger 2017 and we recall that characterization here while adding some details and clarifications.
Convex Ramsey matrices and non-amenability of automophism groups of generic structures

In this paper we prove that the automorphism groups of certain countable generic structures are not amenable. For doing that, we first prove the existence of particular matrices that do not satisfy the convex Ramsey condition. For a pair of elements in a smooth class, we introduce the property of forming a free-pseudoplane in the generic structure. We then prove the non-amenability of the automorphism group of a generic structure obtained from a smooth class with a pair that forms a free-pseudoplane. As an application we show that the automorphism group of an ab-initio generic structure that is constructed using a pre-dimension function with irrational coefficients is not amenable.
Averaging over Heegner points in the hyperbolic circle problem

For $\Gamma={\hbox{PSL}_2( {\mathbb Z})}$ the hyperbolic circle problem aims to estimate the number of elements of the orbit $\Gamma z$ inside the hyperbolic disc centered at $z$ with radius $\cosh^{-1}(X/2)$. We show that, by averaging over Heegner points $z$ of discriminant $D$, Selberg's error term estimate can be improved, if $D$ is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindel\"of conjecture for twists of the $L$-functions attached to Maa{\ss} cusp forms.
Random matrices: Universality of local spectral statistics of non-Hermitian matrices

It is a classical result of Ginibre that the normalized bulk k-point correlation functions of a complex n×n Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process on C with kernel K∞(z,w):=1πe−|z|2/2−|w|2/2+zw¯ in the limit n→∞. In this paper, we show that this asymptotic law is universal among all random n×n matrices Mn whose entries are jointly independent, exponentially decaying, have independent real and imaginary parts and whose moments match that of the complex Gaussian ensemble to fourth order. Analogous results at the edge of the spectrum are also obtained. As an application, we extend a central limit theorem for the number of eigenvalues of complex Gaussian matrices in a small disk to these more general ensembles. These results are non-Hermitian analogues of some recent universality results for Hermitian Wigner matrices. However, a key new difficulty arises in the non-Hermitian case, due to the instability of the spectrum for such matrices. To resolve this issue, we the need to work with the log-determinants log|det(Mn−z0)| rather than with the Stieltjes transform 1ntr(Mn−z0)−1, in order to exploit Girko’s Hermitization method. Our main tools are a four moment theorem for these log-determinants, together with a strong concentration result for the log-determinants in the Gaussian case. The latter is established by studying the solutions of a certain nonlinear stochastic difference equation. With some extra consideration, we can extend our arguments to the real case, proving universality for correlation functions of real matrices which match the real Gaussian ensemble to the fourth order. As an application, we show that a real n×n matrix whose entries are jointly independent, exponentially decaying and whose moments match the real Gaussian ensemble to fourth order has 2nπ−−√+o(n√) real eigenvalues asymptotically almost surely.
Intersection numbers on the relative Hilbert schemes of points on surfaces

We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the non-relative Hilbert schemes. In particular, we obtain a relative version of the explicit formula found by Carlsson-Okounkov for the Euler class of the twisted tangent bundle of the Hilbert schemes.
Ferromagnetic-paramagnetic phase diagram of the Kondo lattice

A theory which can easily be used to discuss the competition between ferromagnetic order and the Kondo effect is presented in this paper. The magnetic order parameters of conduction and localized electrons as well as the hybridization term describing the Kondo effect are introduced simultaneously in a Kondo lattice model using the functional integral method. At zero temperature, quite a complete phase diagram of ferromagnetic and paramagnetic (Kondo) states is obtained in the static saddle-point approximation. At finite temperatures, the dependences of the Curie temperature and the total magnetization on the exchange-coupling strength |J| for various concentrations of conduction electrons, are also given by the theory. The main results are in qualitative agreement with experimental observations in heavy-fermion ferromagnets.
Protected Vertices in Motzkin trees

In this paper we find recurrence relations for the asymptotic probability a vertex is $k$ protected in all Motzkin trees. We use a similar technique to calculate the probabilities for balanced vertices of rank $k$. From this we calculate upper and lower bounds for the probability a vertex is balanced and upper and lower bounds for the expected rank of balanced vertices.
Sublogarithmic fluctuations for internal DLA

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of order log(radius) [resp. , log2(radius)]. Using the same approach, we improve the upper bound on the inner fluctuation to log(radius)−−−−−−−−−√ when d is larger than or equal to three. The inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation.
Connectifying a space by adding one point

It is a classical theorem of Alexandroff that a locally compact Hausdorff space has a one-point Hausdorff compactification if and only if it is non-compact. The one-point Hausdorff compactification is indeed obtained by adding the so called "point at infinity. " Here we consider the analogous problem of existence of a one-point connectification, and keeping analogy, we prove that a locally connected normal space has a one-point normal connectification if and only if it has no compact component.
Quasiinvariants of Coxeter groups and m-harmonic polynomials

The space of m-harmonic polynomials related to a Coxeter group G and a multiplicity function m on its root system is defined as the joint kernel of the properly gauged invariant integrals of the corresponding generalised quantum Calogero-Moser problem. The relation between this space and the ring of all quantum integrals of this system (which is isomorphic to the ring of corresponding quasiinvariants) is investigated.
Behavior of the drift mobility in the glass transition region of some hole‐transporting amorphous organic films

Drift mobility in prototypical hole‐transporting organic glasses is observed to undergo a relatively abrupt, but fully reversible, decrease in activation energy during rate heating near Tg. Sensitivity of charge transport to the dynamic phenomena peculiar to the glass transition process is therefore indicated. No significant hysteresis of the drift mobility is observed during rate heating and subsequent rate cooling through the Tg region. The latter contrasts sharply with the behavior observed in amorphous chalcogenides. It is suggested that absence of mobility hysteresis is a consequence of the fact that electonic states which control transport arise from incorporated chemical species and not, as in the chalcogenides, from structural defects.