Miracle-dz/UniFAR-FTUs huggingface dataset:
Pivotal, cluster, and interface measures for critical planar percolation

This work is the first in a series of papers devoted to the construction and study of scaling limits of dynamical and near-critical planar percolation and related objects like invasion percolation and the Minimal Spanning Tree. We show here that the counting measure on the set of pivotal points of critical site percolation on the triangular grid, normalized appropriately, has a scaling limit, which is a function of the scaling limit of the percolation configuration. We also show that this limit measure is conformally covariant, with exponent 3/4. Similar results hold for the counting measure on macroscopic open clusters (the area measure), and for the counting measure on interfaces (length measure). Since the aforementioned processes are very much governed by pivotal sites, the construction and properties of the "local time"-like pivotal measure are key results in this project. Another application is that the existence of the limit length measure on the interface is a key step towards constructing the so-called natural time-parametrization of the SLE(6) curve. The proofs make extensive use of coupling arguments, based on the separation of interfaces phenomenon. This is a very useful tool in planar statistical physics, on which we included a self-contained Appendix. Simple corollaries of our methods include ratio limit theorems for arm probabilities and the rotational invariance of the two-point function.
A note on the Hanson-Wright inequality for random vectors with dependencies

We prove that quadratic forms in isotropic random vectors $X$ in $\mathbb{R}^n$, possessing the convex concentration property with constant $K$, satisfy the Hanson-Wright inequality with constant $CK$, where $C$ is an absolute constant, thus eliminating the logarithmic (in the dimension) factors in a recent estimate by Vu and Wang. We also show that the concentration inequality for all Lipschitz functions implies a uniform version of the Hanson-Wright inequality for suprema of quadratic forms (in the spirit of the inequalities by Borell, Arcones-Gine and Ledoux-Talagrand). Previous results of this type relied on stronger isoperimetric properties of $X$ and in some cases provided an upper bound on the deviations rather than a concentration inequality. In the last part of the paper we show that the uniform version of the Hanson-Wright inequality for Gaussian vectors can be used to recover a recent concentration inequality for empirical estimators of the covariance operator of $B$-valued Gaussian variables due to Koltchinskii and Lounici.
Pointwise Estimation of Density of Heteroscedastistic Response in Regression

In fitting a regression model, we often encounter data sets which do not follow Gaussian distribution and/or do not have equal variance. In this case estimation of the conditional density of a response variable at a given design point is hardly solved by a standard least squares method. To solve this problem, we propose a simple method to estimate the distribution of the fitted vales under heteroscedasticity using the idea of quantile regression and the histogram techniques. Application of this method to a real data sets is given.
Spectra of random graphs with given expected degrees

In the study of the spectra of power-law graphs, there are basically two competing approaches. One is to prove analogues of Wigner's semicircle law, whereas the other predicts that the eigenvalues follow a power-law distribution. Although the semicircle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matrices. We will prove that (under certain mild conditions) the eigenvalues of the (normalized) Laplacian of a random power-law graph follow the semicircle law, whereas the spectrum of the adjacency matrix of a power-law graph obeys the power law. Our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants. Of interest are a number of (new) values for the exponent β, where phase transitions for eigenvalue distributions occur. The spectrum distributions have direct implications to numerous graph algorithms such as, for example, randomized algorithms that involve rapidly mixing Markov chains.
Dynamics of closed singularities

Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in the dynamical properties of the flow, we obtain also smoothing for long time for generic initial conditions. When combined with our earlier paper this allows us to show that, in an important special case, the singularities are the simplest possible. We take here the first steps towards understanding the dynamics of the flow. The question of the dynamics of a singularity has two parts. One is: What are the dynamics near a singularity? The second is: What is the long time behavior of the flow of things close to the singularity. That is, if the flow leaves a neighborhood of a singularity, is it possible for the flow to re-enter the same neighborhood at a much later time? The first part is addressed in this paper, while the second will be addressed elsewhere.
The Mediating Role of Organizational Agility on the Relationship between Environmental Uncertainty and Innovation in Hotels

Organizational agility leads to many positive outcomes for hotels, such as adapting to and surviving in a volatile, uncertain, and dynamic environment, increasing product or service quality, etc. In addition, agility has become essential for different types of innovation. As agility is of crucial importance for hotels, they must be aware of its effects. Thus, this study aimed at determining the degree of environmental uncertainty (EU) in hotels; assessing the agility and innovation in hotels; investigating how the EU influences innovation dimensions, and finally examining the effect of agility as a mediating variable on the relationship between EU and innovation in hotels. The research population was the department managers and supervisors in five-star hotels in Greater Cairo. The convenience sampling method was adopted to attain the objectives of this research. A total of 480 questionnaire forms were handed out to the respondents. The questionnaires valid for analysis were 420, with a response rate of 87.5 percent. To analyze these forms, descriptive analysis, correlation analysis, and multiple regression analysis were used. The main results revealed that the EU has a positive effect on the four dimensions of hotel innovation (i.e., product innovation, process innovation, organizational innovation, and marketing innovation). Additionally, the results showed that organizational agility fully mediates the impact of the EU on the four dimensions of hotel innovation. Hence, it was recommended that hotels should continue with the best practices of organizational agility.
A numerical simulation of PM 2.5 concentration using the WRF-Chem model during a high air pollution episode in 2019 in Jakarta, Indonesia

Jakarta, as a megapolitan city, is always crowded with thousands of vehicles every day which results in decreased air quality due to combustion emissions and may have a significant impact on human health. Particulate matter (PM 2.5 ) is a pollutant that has an aerodynamic diameter of fewer than 2.5 micrometers and very easy to enter the human respiratory system so it can affect health. In the dry season, rain as the main natural mechanism for reducing PM 2.5 occurs very rarely, causing an accumulation of PM 2.5 concentrations in the atmosphere. The weather research and forecasting model coupled with chemistry (WRF-Chem) model is a dynamic model that works with atmospheric chemistry combined with meteorological variables simultaneously. This study aims to simulate the concentration of PM 2.5 in Jakarta during the high air pollution episode from 20 to 29 June 2019 with the WRF-Chem model based on the T1-MOZCART chemical scheme. Spatial analysis was conducted to determine the distribution of PM 2.5 concentrations during high air pollution episodes in Jakarta. Validation of the simulation model was based on three observation sites, one in South Jakarta and two in Central Jakarta. The results showed that the highest correlation is 0.3 and the lowest root mean square error (RMSE) is 26.4, while the simulations still tend to overestimate the PM 2.5 concentration.
Polarization Apparatus for Interference Microscopy and Macroscopy of Isotropic Transparent Objects

The various instruments to be described are based on the following principle: a wave front which has been deformed by optical path difference variations in the object is doubled into two identical wave fronts by means of a birefringent system. The interference phenomena between these two wave fronts bring out the path difference variations in the object. By this means the transparent object is made visible. The birefringent systems employed are mainly of the Savart polariscope and Wollaston prism types. They can be equally well used in microscopy or macroscopy. These instruments can be used, by means of adequate modifications, without any collimation. In the latter case they are extremely luminous. They are of particular interest in microscopy where they permit the measure of refractive indexes and of thicknesses of small details in preparations. We shall describe a very simple differential observation method which places in evidence the gradient of the optical path. The sensitivity of the method depends on the width of the object. It is of the order of λ/50 for an object 1 mm wide. This sensitivity can therefore be very large for very small objects.
On unconditional well-posedness of modified KdV

Bourgain(1993) proved that the periodic modified KdV equation (mKdV) is locally well-posed in Sobolev spave H^s(T), s >= 1/2, by introducing new weighted Sobolev spaces X^s,b, where the uniqueness holds conditionally, namely in the intersection of C([0, T]; H^s) and X^s,b. In this paper, we establish unconditional well-posedness of mKdV in H^s(T), s >= 1/2, i.e. we in addition establish unconditional uniqueness in C([0, T]; H^s), s >= 1/2, of solutions to mKdV. We prove this result via differentiation by parts. For the endpoint case s = 1/2, we perform careful quinti- and septi-linear estimates after the second differentiation by parts.
Statistical Analysis of the Mixed Fractional Ornstein--Uhlenbeck Process

This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent and asymptotically normal in the large-sample limit, using some recent results on the canonical representation and spectral structure of mixed processes.
Inhomogeneous phase-type distributions and heavy tails

Abstract We extend the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable the carrying over of fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavy-tail phenomena. We also illustrate the versatility and parsimony of the proposed approach in modelling a real-world heavy-tailed fire insurance dataset.
A proof of the instability of AdS for the Einstein-null dust system with an inner mirror

In 2006, Dafermos and Holzegel formulated the so-called AdS instability conjecture, stating that there exist arbitrarily small perturbations to AdS initial data which, under evolution by the Einstein vacuum equations for $\Lambda<0$ with reflecting boundary conditions on conformal infinity, lead to the formation of black holes. The numerical study of this conjecture in the simpler setting of the spherically symmetric Einstein--scalar field system was initiated by Bizon and Rostworowski, followed by a vast number of numerical and heuristic works by several authors. In this paper, we provide the first rigorous proof of the AdS instability conjecture in the simplest possible setting, namely for the spherically symmetric Einstein--massless Vlasov system, in the case when the Vlasov field is moreover supported only on radial geodesics. This system is equivalent to the Einstein--null dust system, allowing for both ingoing and outgoing dust. In order to overcome the break down of this system occuring once the null dust reaches the centre $r=0$, we place an inner mirror at $r=r_{0}>0$ and study the evolution of this system on the exterior domain $\{r\ge r_{0}\}$. The structure of the maximal development and the Cauchy stability properties of general initial data in this setting are studied in our companion paper. The statement of the main theorem is as follows: We construct a family of mirror radii $r_{0\epsilon}>0$ and initial data $\mathcal{S}_{\epsilon}$, $\epsilon\in(0,1]$, converging to the AdS initial data in a suitable norm, such that, for any $\epsilon>0$, the maximal development $(\mathcal{M}_{\epsilon},g_{\epsilon})$ of $\mathcal{S}_{\epsilon}$ contains a black hole region. Our proof is based on purely physical space arguments.
The Heston stochastic volatility model in Hilbert space

ABSTRACT We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein–Uhlenbeck process with itself. The volatility process is then defined by a Cholesky decomposition of the variance process. We define a Hilbert-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this stochastic volatility, and compute the characteristic functional and covariance operator of this process. This process is then applied to the modeling of forward curves in energy and commodity markets. Finally, we compute the dynamics of the tensor Heston volatility model when the generator is bounded, and study its projection down to the real line for comparison with the classical Heston dynamics.
Interleaving Distance as a Limit

Persistent homology is a way of determining the topological properties of a data set. It is well known that each persistence module admits the structure of a representation of a finite totally ordered set. In previous work, the authors proved an analogue of the isometry theorem of Bauer and Lesnick for representations of a certain class of finite posets. The isometry was between the interleaving metric of Bubenik, de Silva and Scott and a bottleneck metric which incorporated algebraic information. The key step in both isometry theorems was proving a matching theorem, that an interleaving gives rise to a matching of the same height. In this paper we continue this work, restricting to those posets which arise from data while making more general the choice of metrics. We first show that while an interleaving always produces a matching, for an arbitrary choice of weights it will not produce one of the same height. We then show that although the matching theorem fails in this sense, one obtains a "shifted" matching (of the correct height) from an interleaving by enlarging the category. We then prove an isometry theorem on this extended category. As an application, we make precise the way in which representations of finite partially ordered sets approximate persistence modules. Specifically, given two finite point clouds of data, we associate a generalized sequence (net) of algebras over which the persistence modules for both data sets can be compared. We recover the classical interleaving distance uniformly by taking limits.
SU(2) graph invariants, Regge actions and polytopes

We revisit the the large spin asymptotics of 15j symbols in terms of cosines of the 4d Euclidean Regge action, as derived by Barrett and collaborators using a saddle point approximation. We bring it closer to the perspective of area-angle Regge calculus and twisted geometries, and compute explicitly the Hessian and phase offsets. We then extend it to more general SU(2) graph invariants associated to nj-symbols. We find that saddle points still exist for special boundary configurations, and that these have a clear geometric interpretation, but there is a novelty: configurations with two distinct saddle points admit a conformal shape-mismatch of the geometry, and the cosine asymptotic behaviour oscillates with a generalisation of the Regge action. The allowed mismatch correspond to angle-matched twisted geometries, 3d polyhedral tessellations with adjacent faces matching areas and 2d angles, but not their diagonals. We study these geometries, identify the relevant subsets corresponding to 3d Regge data and 4d flat polytope data, and discuss the corresponding Regge actions emerging in the asymptotics. Finally, we also provide the first numerical confirmation of the large spin asymptotics of the 15j symbol. We show that the agreement is accurate to the per cent level already at spins of order 10, and the next-to-leading order oscillates with the same frequency and same global phase.
Effect of smooth moving punch in an initially stressed monoclinic magnetoelastic crystalline medium due to shear wave propagation

This work studies the effect of a semi-infinite smooth moving punch on the shear wave propagation in an initially stressed magnetoelastic monoclinic strip. The closed form expression of dynamic stress concentration due to the punch for the force of a constant intensity has been established. The speed of moving punch associated with shear wave speed in the medium, vertical compressive initial stress, vertical tensile initial stress and monoclinic magnetoelastic coupling parameter have a substantial effect on the dynamic stress concentration owing to a semi-infinite smooth moving punch. Numerical computation and graphical demonstration has been carried out for quartz crystal with monoclinic symmetry to observe the profound effect of these affecting parameters on dynamic stress concentration. In order to highlight some of the important peculiarities of the problem, a comparative study of dynamic stress concentration in an initially stressed magnetoelastic monoclinic strip and initially stressed magnetoelastic isotropic strip has been made. Weiner-Hopf technique indicated by Matczynski has been adopted to solve the problem. In particular, some special cases have been deduced from the obtained expression of dynamic stress concentration due to the smooth moving punch.
Stationary vacuum black holes in 5 dimensions

Abstract We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in 5-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a prime 3-manifold of positive Yamabe type, namely the 3-sphere S3, the ring , or the lens space L(p, q). The Einstein vacuum equations reduce to an axially symmetric harmonic map with prescribed singularities from into the symmetric space . In this paper, we solve the problem for all possible topologies, and in particular the first candidates for smooth vacuum non-degenerate black lenses are produced. In addition, a generalization of this result is given in which the spacetime is allowed to have orbifold singularities. We also formulate conditions for the absence of conical singularities which guarantee a physically relevant solution.
Intrinsic regular surfaces of low codimension in Heisenberg groups

In this paper we study intrinsic regular submanifolds of $\mathbb{H}^n$, of low co-dimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for one co-dimensional $\mathbb{H}$-regular surfaces, characterizing uniformly intrinsic differentiable functions $\phi$ acting between two complementary subgroups of the Heisenberg group $\mathbb{H}^n$, with target space horizontal of dimension $k$, with $1 \leq k \leq n$, in terms of the Euclidean regularity of its components with respect to a family of non linear vector fields $\nabla^{\phi_j}$. Moreover, we show how the area of the intrinsic graph of $\phi$ can be computed through the component of the matrix identifying the intrinsic differential of $\phi$.
Minimizing the Influence of Item Parameter Estimation Errors in Test Development: A Comparison of Three Selection Procedures

Abstract In test development, item response theory (IRT) is a method to determine the amount of information that each item (i.e., item information function) and combination of items (i.e., test information function) provide in the estimation of an examinee's ability. Studies investigating the effects of item parameter estimation errors over a range of ability have demonstrated an overestimation of information when the most discriminating items are selected (i.e., item selection based on maximum information). In the present study, the authors examined the influence of item parameter estimation errors across 3 item selection methods—maximum no target, maximum target, and theta maximum—using the 2- and 3-parameter logistic IRT models. Tests created with the maximum no target and maximum target item selection procedures consistently overestimated the test information function. Conversely, tests created using the theta maximum item selection procedure yielded more consistent estimates of the test information function and, at times, underestimated the test information function. Implications for test development are discussed.
ROSAT Survey Diffuse X-Ray Background Maps. II.

This paper presents new maps of the soft X-ray background from the ROSAT all-sky survey. These maps represent a significant improvement over the previous version in that (1) the position resolution of the PSPC has been used to improve the angular resolution from ~2° to 12', (2) there are six energy bands that divide each of the previous three into two parts, and (3) the contributions of point sources have been removed to a uniform source flux level over most of the sky. These new maps will be available in electronic format later in 1997. In this paper we also consider the bright emission in the general direction of the Galactic center in the 0.5-2.0 keV band, and the apparent absorption trough that runs through it along the Galactic plane. We find that while the northern hemisphere data are confused by emission from Loop I, the emission seen south of the plane is consistent with a bulge of hot gas surrounding the Galactic center (in our simple model, a cylinder with an exponential fall-off of density with height above the plane). The cylinder has a radial extent of ~5.6 kpc. The X-ray emitting gas has a scale height of 1.9 kpc, an in-plane electron density of ~0.0035 cm-3, a temperature of ~106.6 K, a thermal pressure of ~28,000 cm-3 K, and a total luminosity of ~2 × 1039 ergs s-1 using a collisional ionization equilibrium (CIE) plasma emission model.