Miracle-dz/UniFAR-FTUs huggingface dataset:
Symplectic realizations of holomorphic Poisson manifolds

Symplectic realization is a longstanding problem which can be traced back to Sophus Lie. In this paper, we present an explicit solution to this problem for an arbitrary holomorphic Poisson manifold. More precisely, for any holomorphic Poisson manifold $(X, \pi)$, we prove that there exists a holomorphic symplectic structure in a neighborhood $Y$ of the zero section of $T^*X$ such that the projection map is a symplectic realization of the given Poisson manifold, and moreover the zero section is a holomorphic Lagrangian submanifold. We describe an explicit construction for such a new holomorphic symplectic structure on $Y \subseteq T^*X$.
On semi‐isogenous mixed surfaces

Let C be a smooth projective curve and G be a finite subgroup of Aut (C)2⋊Z2 whose action is mixed, i.e. there are elements in G exchanging the two isotrivial fibrations of C×C . Let G0◃G be the index two subgroup G∩ Aut (C)2 . If G0 acts freely, then X:=(C×C)/G is smooth and we call it semi‐isogenous mixed surface. In this paper we give an algorithm to determine semi‐isogenous mixed surfaces with given geometric genus, irregularity and self‐intersection of the canonical class. As an application we classify irregular semi‐isogenous mixed surfaces with K2>0 and geometric genus equal to the irregularity; the regular case is subjected to some computational restrictions. In this way we construct new examples of surfaces of general type with χ=1 . We provide an example of a minimal surface of general type with K2=7 and pg=q=2 .
The Semiclassical Einstein Equation on Cosmological Spacetimes

The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the stress-energy tensor and the semiclassical Einstein equation. Basic notions of differential geometry, topology, functional and microlocal analysis, causality and general relativity will be summarised, and the algebraic approach to QFT on curved spacetime will be reviewed. Apart from these foundations, the original research of the author and his collaborators will be presented: Together with Fewster, the author studied the up and down structure of permutations using their decomposition into so-called atomic permutations. The relevance of these results to this thesis is their application in the calculation of the moments of quadratic quantum fields. In a work with Pinamonti, the author showed the local and global existence of solutions to the semiclassical Einstein equation in flat cosmological spacetimes coupled to a scalar field by solving simultaneously for the quantum state and the Hubble function in an integral-functional equation. The theorem is proved with a fixed-point theorem using the continuous functional differentiability and boundedness of the integral kernel of the integral-functional equation. In another work with Pinamonti the author proposed an extension of the semiclassical Einstein equations which couples the moments of a stochastic Einstein tensor to the moments of the quantum stress-energy tensor. In a toy model of a Newtonianly perturbed exponentially expanding spacetime it is shown that the quantum fluctuations of the stress-energy tensor induce an almost scale-invariant power spectrum for the perturbation potential and that non-Gaussianties arise naturally.
Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this work, we combine such variational formulas with functional inequalities (Poincar{e}, $\log$-Sobolev, Liapunov functions) to derive explicit uncertainty quantification bounds for time-averaged observables, comparing a Markov process to a second (not necessarily Markov) process. These bounds are well-behaved in the infinite-time limit and apply to steady-states of both discrete and continuous-time Markov processes.
Star Formation Rate and AGN in Barred Galaxies

We investigate the dependence of star formation rate and Active Galaxy Nuclei (AGN) frequency on the bar properties, especially the bar strength, using SDSS DR6. To better represent the bar strength, we divided the bars into 6 classes according to their length and axial ratios. There seems to be a fairly good correlation between the star formation rate derived from emission lines and the bar strength, whereas there is no apparent correlation between the AGN activity and the bar strength. We interpret that the former correlation is due to the dependence of bar-driven gas inflow on the strength of bar. The lack of correlation between AGN and bar properties suggests that the accretion of gas onto a supermassive black hole (SMBH) is regulated by the interplay between the bar and SMBH. The frequency of AGN seems to be dependent on the background density but the star formation rate does not. It suggests that star formation is a localized phenomenon that is mostly determined by the gas density in a galaxy, while AGN activity is more closely related to the host property such as mass and luminosity that are thought to be dependent on the environment through the density-luminosity relation.
Construction of R-matrices for symmetric tensor representations related to U q ( sl n ˆ )

In this paper we construct a new factorized representation of the R-matrix related to the affine algebra U q ( sl n ^ ) for symmetric tensor representations with arbitrary weights. Using the 3D approach we obtain explicit formulas for the matrix elements of the R-matrix and give a simple proof that a ‘twisted’ R-matrix is stochastic. We also discuss symmetries of the R-matrix, its degenerations and compare our formulas with other results available in the literature.
A global perspective to connections on principal 2-bundles

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen–Messing. This provides a consistent, global perspective to higher gauge theory.
Counting restricted orientations of random graphs

We count orientations of G(n,p) avoiding certain classes of oriented graphs. In particular, we study Tr(n,p) , the number of orientations of the binomial random graph G(n,p) in which every copy of Kr is transitive, and Sr(n,p) , the number of orientations of G(n,p) containing no strongly connected copy of Kr . We give the correct order of growth of logTr(n,p) and logSr(n,p) up to polylogarithmic factors; for orientations with no cyclic triangle, this significantly improves a result of Allen, Kohayakawa, Mota, and Parente. We also discuss the problem for a single forbidden oriented graph, and state a number of open problems and conjectures.
The localic Istropy group of a topos

It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the group of points of a localic group object, called the localic isotropy group, which also acts on every object, and in fact also on every internal locales and on every T-topos. This new localic isotropy group has better functoriality and stability property than the original version and shed some lights on the phenomenon of higher isotropy observed for the ordinary isotropy group. We prove in particular using a localic version of the isotropy quotient that any geometric morphism can be factored uniquely as a connected atomic geometric morphism followed by a so called "essentially anisotropic" geometric morphism, and that connected atomic morphism are exactly the quotient by an open isotropy action.
Normed symmetric monoidal categories

Let $G$ be a finite group. In this paper, we study $G$-categories equipped with an ordinary symmetric monoidal structure, together with a set of specified norm maps. We give an example and explain how the Hill-Hopkins-Ravenel norm functors arise from it, and then we generalize the Kelly-Mac Lane coherence theorem to include the present structures. As an application, we obtain finite presentations of $N_\infty$-$G$-categories for any $G$-indexing system.
Identities for the Lie algebra gl(2) over an infinite field of characteristic two

In 1970 Vaughan-Lee established that over an infinite field of characteristic two the ideal T[gl(2)] of all polynomial identities for the Lie algebra gl(2) is not finitely generated as a T-ideal. But a generating set for this ideal of polynomial identities was not found. We establish some generating set for the T-ideal T[gl(2)].
Nonlocal Kirchhoff Superlinear Equations with Indefinite Nonlinearity and Lack of Compactness

Abstract We study the following Kirchhoff equation: (K) −1+b∫ℝ3|∇u|2dxΔu+V(x)u=f(x,u),x∈ℝ3. $$ - \left({1 + b\int_{{{\mathbb R}^3}} |\nabla u{|^2}dx} \right)\Delta u + V(x)u = f(x, u), \quad x \in {{\mathbb R}^3}. $$ A feature of this paper is that the nonlinearity f$f$ and the potential V$V$ are indefinite, hence sign-changing. Under some appropriate assumptions on V$V$ and f$f$ , we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.
On the existence of $W^{1,2}_{p}$ solutions for fully nonlinear parabolic equations under either relaxed or no convexity assumptions

We establish the existence of solutions of fully nonlinear parabolic second-order equations like $\partial_{t}u+H(v,Dv,D^{2}v,t,x)=0$ in smooth cylinders without requiring $H$ to be convex or concave with respect to the second-order derivatives. Apart from ellipticity nothing is required of $H$ at points at which $|D^{2}v|\leq K$, where $K$ is any fixed constant. For large $|D^{2}v|$ some kind of relaxed convexity assumption with respect to $D^{2}v$ mixed with a VMO condition with respect to $t,x$ are still imposed. The solutions are sought in Sobolev classes. We also establish the solvability without almost any conditions on $H$, apart from ellipticity, but of a "cut-off" version of the equation $\partial_{t}u+H(v,Dv,D^{2}v,t,x)=0$.
Ground states and semiclassical states of nonlinear Choquard equations involving Hardy-Littlewood-Sobolev critical growth

We are concerned with the existence of ground states for nonlinear Choquard equations involving a critical nonlinearity in the sense of Hardy-Littlewood-Sobolev. Our result complements previous results by Moroz and Van Schaftingen where the subcritical case was considered. Then, we focus on the existence of semi-classical states and by using a truncation argument approach, we establish the existence and concentration of single peak solutions concentrating around minima of the Schr\"odinger potential, as the Planck constant goes to zero. The result is robust in the sense that the nonlinearity is not required to satisfy monotonicity conditions nor the Ambrosetti-Rabinowitz condition.
Fermion condensation and super pivotal categories

We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call "m-type" and "q-type" particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations in fermionic topological phases. We then prove a series of results relating data in condensed theories to data in their parent theories; for example, if $\mathcal{C}$ is a modular tensor category containing a fermion, then the tube category of the condensed theory satisfies $\textbf{Tube}(\mathcal{C}/\psi) \cong \mathcal{C} \times (\mathcal{C}/\psi)$. We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the $SO(3)_6$ theory, and the $\frac{1}{2}\text{E}_6$ theory, and compute the quasiparticle excitation spectrum in each of these examples.
Liquid Drops on a Rough Surface

We consider a liquid drop sitting on a rough solid surface at equilibrium, a volume‐constrained minimizer of the total interfacial energy. The large‐scale shape of such a drop strongly depends on the microstructure of the solid surface. Surface roughness enhances hydrophilicity and hydrophobicity properties of the surface, altering the equilibrium contact angle between the drop and the surface. Our goal is to understand the shape of the drop with fixed small‐scale roughness. To achieve this, we develop a quantitative description of the drop and its contact line in the context of periodic homogenization theory, building on the qualitative theory of Alberti and DeSimone. © 2018 Wiley Periodicals, Inc.
Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras

The aim of this paper is to introduce the notions of Hom Gel'fand-Dorfman bialgebra and Hom-Lie conformal algebra. In this paper, we give four constructions of Hom Gel'fand-Dorfman bialgebras. Also, we provide a general construction of Hom-Lie conformal algebras from Hom-Lie algebras. Finally, we prove that a Hom Gel'fand-Dorfman bialgebra is equivalent to a Hom-Lie conformal algebra of degree 2.
Intersection cohomology of moduli spaces of vector bundles over curves

We compute the intersection cohomology of the moduli spaces $M(r,d)$ of semistable vector bundles of arbitrary rank $r$ and degree $d$ over a curve. To do this, we introduce new invariants, called Donaldson-Thomas invariants of a curve, which can be effectively computed by methods going back to Harder, Narasimhan, Desale and Ramanan. Our main result relates the Hodge-Euler polynomial of the intersection cohomology of $M(r,d)$ to the Donaldson-Thomas invariants. More generally, we introduce Donaldson-Thomas classes in the Grothendieck group of mixed Hodge modules over $M(r,d)$ and relate them to the class of the intersection complex of $M(r,d)$. Our methods can be applied to the moduli spaces of objects in arbitrary hereditary categories.
Recipe for Inferring Subsurface Solar Magnetism via Local Mode Coupling Using Slepian Basis Functions

Direct seismic imaging of subsurface flow, sound speed, and magnetic field is crucial for predicting flux-tube emergence on the solar surface, an important ingredient for space weather. The sensitivity of helioseismic mode-amplitude cross-correlation to p- and f-mode oscillations enables formal inversion of such subphotospheric perturbations. It is well known that such problems are written in the form of an integral equation that connects the perturbations to the observations via sensitivity kernels. While the sensitivity kernels for flow and sound speed have been known for decades and have been used extensively, formulating kernels for general magnetic perturbations had been elusive. A recent study proposed sensitivity kernels for Lorentz stresses corresponding to global magnetic fields of general geometry. The present study is devoted to proposing kernels for inferring Lorentz stresses as well as the solenoidal magnetic field in a local patch on the Sun via Cartesian mode coupling. Moreover, for the first time in solar physics, Slepian functions are employed to parameterize perturbations in the horizontal dimension. This is shown to increase the number of data constraints in the inverse problem, implying an increase in the precision of inferred parameters. This paves the path to reliably imaging subsurface solar magnetic features in, e.g., supergranules and (emerging) active regions.
Low-Cost Prototype Multidiameter Measurement for Vertical Cylinder Tank

The vertical cylinder tank can serve as a measuring tool and as a storage device. When the vertical cylinder tank is used as a measuring instrument, it needs to be calibrated. In this process, measuring the diameter of the vertical cylinder tank is the most important step. The diameter of the tank is divided into several parts, the first part is referred to as a reference, where the results of the reference measurement will be used in the measurement of other parts. To conduct this measurement, a prototype consisting of two sensors, namely, laser distance and rotary encoder, is build. The prototype was tested using five variations in standard tube diameters measured using a steel ruler. The results of this test produce an average correction of +0.17 mm with an error of 0.59%. Furthermore, the prototype is used to measure the diameter of the vertical cylinder tank, which is compared with the certificate of the results of tank measurements using a theodolite. Testing the prototype with a vertical cylindrical tank produces a correction of +8.73 mm with an error of 0.03%. This error value is within the error limit according to the OIML International Recommendation of R-071 for vertical tanks.
Three-Dimensional UAV-Based Atmospheric Tomography

AbstractThis paper presents a method for tomographically reconstructing spatially varying three-dimensional atmospheric temperature profiles and wind velocity fields based on passive acoustic travel time measurements between a small unmanned aerial vehicle (UAV) and ground-based microphones. A series of simulations are presented to provide an indication of the performance of the technique. The parametric fields are modeled as the weighted sum of radial basis functions (RBFs) or Fourier series, which also allow local meteorological measurements made at the UAV and ground receivers to supplement any time delay observations. The technique has potential for practical applications such as boundary layer meteorology and theories of atmospheric turbulence and wave propagation through a turbulent atmosphere.
Agroforestry Farming System: Measuring its Development in Financial Feasibility Aspects

Paradigm contradictions, conflicts of interest, and the synchronization of agricultural development that occurs also affect the irregularity of progress, which creates an agricultural system that is less environmentally friendly. Thus, the presence of the Agroforestry paradigm provides alternative solutions that are synthesized on economic, social, and environmental sustainability. The purpose of the study was to determine the financial feasibility of several combined agroforestry patterns. The study was conducted in Boalemo Regency in April 2018. The data were analyzed based on the value of NPV, BCR, and IRR (16.23%). The results show that the combinations that are feasible with NPV, BCR and IRR values are Food-Plantation-Forestry (Rp.388,425,185), (1.77), (87.65%); Food-Plantation-Forestry-Horticulture (Rp.1,253,822,148), (4.50), (216.58%); Plantation-Forestry (Rp.144,707,388), (1.52), (56.48%); Plantation-Forestry-Horticulture (Rp.718,374,087), (3.77), (129.57%) and those that are not suitable for cultivation are Food-Forestry combinations (Rp.- 52,006,231), (0.49), and (5.71%). To make it feasible to cultivate, farmers can choose types of plants that have commercial value. This indicates that the accuracy in choosing the pattern of plant combinations and the suitability of adapting to the agroecosystem will increase the success of the applied agroforestry system.
Ramsey Problems for Berge Hypergraphs

For a graph $G$, a hypergraph $\mathcal{H}$ is a Berge copy of $G$ (or a Berge-$G$ in short), if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for each $e \in E(G)$ we have $e \subseteq f(e)$. We denote the family of $r$-uniform hypergraphs that are Berge copies of $G$ by $B^rG$. For families of $r$-uniform hypergraphs $\mathbf{H}$ and $\mathbf{H}'$, we denote by $R(\mathbf{H},\mathbf{H}')$ the smallest number $n$ such that in any blue-red coloring of $\mathcal{K}_n^r$ (the complete $r$-uniform hypergraph on $n$ vertices) there is a monochromatic blue copy of a hypergraph in $\mathbf{H}$ or a monochromatic red copy of a hypergraph in $\mathbf{H}'$. $R^c(\mathbf{H})$ denotes the smallest number $n$ such that in any coloring of the hyperedges of $\mathcal{K}_n^r$ with $c$ colors, there is a monochromatic copy of a hypergraph in $\mathbf{H}$. In this paper we initiate the general study of the Ramsey problem for Berge hypergraphs, and show that if $r> 2c$, then $R^c(B^rK_n)=n$. In the case $r = 2c$, we show that $R^c(B^rK_n)=n+1$, and if $G$ is a non-complete graph on $n$ vertices, then $R^c(B^rG)=n$, assuming $n$ is large enough. In the case $r < 2c$ we also obtain bounds on $R^c(B^rK_n)$. Moreover, we also determine the exact value of $R(B^3T_1,B^3T_2)$ for every pair of trees $T_1$ and $T_2$.
The Absolute Magnitudes of Type IA Supernovae

Absolute magnitudes in the B, V, and I bands are derived for nine well-observed Type Ia supernovae, using host galaxy distances estimated via the surface brightness fluctuations or Tully-Fisher methods. These data indicate that there is a significant intrinsic dispersion in the absolute magnitudes at maximum light of Type Ia supernovae, amounting to +/- 0.8 mag in B, +/- 0.6 mag in V, and +/- 0.5 mag in I. Moreover, the absolute magnitudes appear to be tightly correlated with the initial rate of decline of the B light curve, with the slope of the correlation being steepest in B and becoming progressively flatter in the V and I bands. This implies that the intrinsic B - V colors of Type Ia supernovae at maximum light are not identical, with the fastest declining light curves corresponding to the intrinsically reddest events. Certain spectroscopic properties may also be correlated with the initial decline rate. These results are most simply interpreted as evidence for a range of progenitor masses, although variations in the explosion mechanism are also possible. Considerable care must be exercised in employing Type Ia supernovae as cosmological standard candles, particularly at large redshifts where Malmquist bias could be an important effect.
A Stochastic Line Search Method with Convergence Rate Analysis

For deterministic optimization, line-search methods augment algorithms by providing stability and improved efficiency. We adapt a classical backtracking Armijo line-search to the stochastic optimization setting. While traditional line-search relies on exact computations of the gradient and values of the objective function, our method assumes that these values are available up to some dynamically adjusted accuracy which holds with some sufficiently large, but fixed, probability. We show the expected number of iterations to reach a near stationary point matches the worst-case efficiency of typical first-order methods, while for convex and strongly convex objective, it achieves rates of deterministic gradient descent in function values.