Miracle-dz/UniFAR-FTUs huggingface dataset:
Embedded symbiosis: an institutional approach to government-business relationships in the Chinese internet industry

ABSTRACT Studies on the Chinese internet mostly focus on how the government censors content and regulate digital platforms. We rarely know how internet companies understand, respond to and negotiate the relationship with the government. This study examines Danlan, the company that runs the world’s largest gay dating app Blued. We approach the interaction between Danlan and the government with an institutional perspective, treating them both as organizations seeking resources and legitimacy. Drawing on fieldwork, we develop the concept of embedded symbiosis, which characterizes the collaborative government-business relationship, and explore how Danlan, the seemingly weak side in this relationship, plays an active role in initiating, negotiating, and maintaining such relations at different stages of embeddedness. Danlan endeavors to form a symbiosis with the government to pursue its survival and development, yet eventually risks alienating from the gay community and colluding with the state in governing homosexuality. The case of Danlan shows the possibility for internet companies to seek legitimacy in an ever-changing political environment through working closely with the authorities and even becoming part of the governmental system itself.
Exact Hausdorff and packing measures of Cantor sets with overlaps

Let $K$ be the attractor of a linear iterated function system (IFS) $S_{j}(x)={\it\rho}_{j}x+b_{j},j=1,\ldots ,m$, on the real line $\mathbb{R}$ satisfying the generalized finite type condition (whose invariant open set ${\mathcal{O}}$ is an interval) with an irreducible weighted incidence matrix. This condition was recently introduced by Lau and Ngai [A generalized finite type condition for iterated function systems. Adv. Math.208 (2007), 647–671] as a natural generalization of the open set condition, allowing us to include many important overlapping cases. They showed that the Hausdorff and packing dimensions of $K$ coincide and can be calculated in terms of the spectral radius of the weighted incidence matrix. Let ${\it\alpha}$ be the dimension of $K$. In this paper, we state that $$\begin{eqnarray}{\mathcal{H}}^{{\it\alpha}}(K\cap J)\leq |J|^{{\it\alpha}}\end{eqnarray}$$ for all intervals $J\subset \overline{{\mathcal{O}}}$, and $$\begin{eqnarray}{\mathcal{P}}^{{\it\alpha}}(K\cap J)\geq |J|^{{\it\alpha}}\end{eqnarray}$$ for all intervals $J\subset \overline{{\mathcal{O}}}$ centered in $K$, where ${\mathcal{H}}^{{\it\alpha}}$ denotes the ${\it\alpha}$-dimensional Hausdorff measure and ${\mathcal{P}}^{{\it\alpha}}$ denotes the ${\it\alpha}$-dimensional packing measure. This result extends a recent work of Olsen [Density theorems for Hausdorff and packing measures of self-similar sets. Aequationes Math.75 (2008), 208–225] where the open set condition is required. We use these inequalities to obtain some precise density theorems for the Hausdorff and packing measures of $K$. Moreover, using these density theorems, we describe a scheme for computing ${\mathcal{H}}^{{\it\alpha}}(K)$ exactly as the minimum of a finite set of elementary functions of the parameters of the IFS. We also obtain an exact algorithm for computing ${\mathcal{P}}^{{\it\alpha}}(K)$ as the maximum of another finite set of elementary functions of the parameters of the IFS. These results extend previous ones by Ayer and Strichartz [Exact Hausdorff measure and intervals of maximum density for Cantor sets. Trans. Amer. Math. Soc.351 (1999), 3725–3741] and by Feng [Exact packing measure of Cantor sets. Math. Natchr.248–249 (2003), 102–109], respectively, and apply to some new classes allowing us to include Cantor sets in $\mathbb{R}$ with overlaps.
Menger algebras of $n$-place functions

It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups and semigroups, and to algebras of functions closed with respect natural relations defined on their domains.
Analysis of large urn models with local mean-field interactions

The stochastic models investigated in this paper describe the evolution of a set of $F_N$ identical balls scattered into $N$ urns connected by an underlying symmetrical graph with constant degree $h_N$. After some exponentially distributed amount of time {\em all the balls} of one of the urns are redistributed locally, among the $h_N$ urns of its neighborhood. The allocation of balls is done at random according to a set of weights which depend on the state of the system. The main original features of this context is that the cardinality $h_N$ of the range of interaction is not necessarily linear with respect to $N$ as in a classical mean-field context and, also, that the number of simultaneous jumps of the process is not bounded due to the redistribution of all balls of an urn at the same time. The approach relies on the analysis of the evolution of the local empirical distributions associated to the state of urns in the neighborhood of a given urn. Under some convenient conditions, by taking an appropriate Wasserstein distance and by establishing appropriate technical estimates for local empirical distributions, we are able to establish a mean-field convergence result. Convergence results of the corresponding invariant distributions are obtained for several allocation policies. For the class of power of $d$ choices policies for the allocations of balls, we show that the invariant measure of the corresponding McKean-Vlasov process has an asymptotic finite support property when the average load per urn gets large. This result differs somewhat from the classical double exponential decay property usually encountered in the literature for power of $d$ choices policies. This finite support property has interesting consequences in practice.
Predicting Path Loss Distributions of a Wireless Communication System for Multiple Base Station Altitudes from Satellite Images

It is expected that unmanned aerial vehicles (UAVs) will play a vital role in future communication systems. Optimum positioning of UAVs, serving as base stations, can be done through extensive field measurements or ray tracing simulations when the 3D model of the region of interest is available. In this paper, we present an alternative approach to optimize UAV base station altitude for a region. The approach is based on deep learning; specifically, a 2D satellite image of the target region is input to a deep neural network to predict path loss distributions for different UAV altitudes. The neural network is designed and trained to produce multiple path loss distributions in a single inference; thus, it is not necessary to train a separate network for each altitude.
EFFECTIVE EQUIDISTRIBUTION OF CLOSED HOROCYCLES FOR GEOMETRICALLY FINITE SURFACES

For a complete hyperbolic surface whose fundamental group is finitely generated and has critical exponent bigger than 1 2 , we obtain an effective equidistribution of closed horocycles in its unit tangent bundle. This extends a result of Sarnak in 1981 for surfaces of finite area. We also discuss applications in Affine sieves.
Picard numbers of quintic surfaces

We solve the Picard number problem for complex quintic surfaces by proving that every number between 1 and 45 occurs as Picard number of a quintic surface over Q . Our main technique consists in arithmetic deformations of Delsarte surfaces, but we also use K3 surfaces and wild automorphisms.
Domain Knowledge-Based Human Capital Strategy in Manufacturing AI

As the Industry 4.0 paradigm accelerates, the importance of artificial intelligence (AI) in manufacturing industry is increasing. Manufacturing AI requires balanced capabilities between industry-specific domain knowledge and AI capability. Nevertheless, many manufacturing AI startups are mainly focusing on human capital based on AI or data science capability. This article focused on the importance of human capital based on domain knowledge for the success of manufacturing AI. In this article, the relationship between domain knowledge and corporate performance was analyzed for 127 global manufacturing AI startups. Furthermore, the moderating effects of educational level and cofounder size for domain knowledge were analyzed. In addition, an expanded analysis was conducted on effect between domain knowledge, educational level, cofounder size, and corporate performance by business model. This article has new implications for and provides practical contributions to the human capital strategy for manufacturing AI corporates.
Negligibity of elliptic elements in ascending HNN-extensions of

Abstract We study ascending HNN-extensions G of finitely generated free abelian groups: examples of such G include soluble Baumslag–Solitar groups and fundamental groups of orientable prime 3-manifolds modeled on Sol geometry. In particular, we study the elliptic subgroup consisting of all elements that stabilize a point in the Bass–Serre tree of G. We consider the density of A with respect to ball counting measures corresponding to finite generating sets of G, and we show that A is exponentially negligible in G with respect to such sequences of measures. As a consequence, we show that the set of tuples such that the -fold simple commutator vanishes, is exponentially negligible in with respect to sequences of ball counting measures.
Gabriel’s theorem and birational geometry

Extending work of Meinhardt and Partsch, we prove that two varieties are isomorphic in codimension c if and only if certain quotients of their categories of coherent sheaves are equivalent. This result interpolates between Gabriel's reconstruction theorem and the fact that two varieties are birational if and only if they have the same function field.
Data transmission through lasers

In the current era technology in science has recently attracted owing the advancement of applications in lasers. A project on the applications of the laser introduced. The application part of the laser has been applied by simple laser communication system which evolved in its working with the support of solar panel, differential grating. It also provides the information how the data is transmitted through lasers.
Moderate deviations for Ewens-Pitman exchangeable random partitions

Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of different types and the number of types appearing in the sample with a fixed frequency are important statistics. In this paper we establish the moderate deviation principles for these quantities. The corresponding rate functions are explicitly identified, which help revealing a critical scale and understanding the exact role of the parameters. Conditional, or posterior, counterparts of moderate deviation principles are also established.
The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.
Orbifold equivalence: structure and new examples

Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general category-theoretic language, we focus on the most explicit setting in terms of matrix factorisations, where orbifold equivalences arise from defects with special properties. Examples are relatively difficult to construct, but we uncover some structural features that distinguish orbifold equivalences -- most notably a finite perturbation expansion. We use those properties to devise a search algorithm, then present some new examples including Arnold singularities.
Categorical structures on bundle gerbes and higher geometric prequantisation

We present a construction of a 2-Hilbert space of sections of a bundle gerbe, a suitable candidate for a prequantum 2-Hilbert space in higher geometric quantisation. We introduce a direct sum on the morphism categories in the 2-category of bundle gerbes and show that these categories are cartesian monoidal and abelian. Endomorphisms of the trivial bundle gerbe, or higher functions, carry the structure of a rig-category, which acts on generic morphism categories of bundle gerbes. We continue by presenting a categorification of the hermitean metric on a hermitean line bundle. This is achieved by introducing a functorial dual that extends the dual of vector bundles to morphisms of bundle gerbes, and constructing a two-variable adjunction for the aforementioned rig-module category structure on morphism categories. Its right internal hom is the module action, composed by taking the dual of higher functions, while the left internal hom is interpreted as a bundle gerbe metric. Sections of bundle gerbes are defined as morphisms from the trivial bundle gerbe to a given bundle gerbe. The resulting categories of sections carry a rig-module structure over the category of finite-dimensional Hilbert spaces. A suitable definition of 2-Hilbert spaces is given, modifying previous definitions by the use of two-variable adjunctions. We prove that the category of sections of a bundle gerbe fits into this framework, thus obtaining a 2-Hilbert space of sections. In particular, this can be constructed for prequantum bundle gerbes in problems of higher geometric quantisation. We define a dimensional reduction functor and show that the categorical structures introduced on bundle gerbes naturally reduce to their counterparts on hermitean line bundles with connections. In several places in this thesis, we provide examples, making 2-Hilbert spaces of sections and dimensional reduction very explicit.
2‐Selmer parity for hyperelliptic curves in quadratic extensions

We study the 2‐parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove the conjecture over quadratic extensions of the base field. The proof proceeds via a generalisation of a formula of Kramer and Tunnell relating local invariants of the curve, which may be of independent interest. A new feature of this generalisation is the appearance of terms which govern whether or not the Cassels–Tate pairing on the Jacobian is alternating, which first appeared in work of Poonen–Stoll. We establish the local formula in many instances and show that in remaining cases, it follows from standard global conjectures.
Smallest not $C_{2l+1}$-colourable graphs of odd-girth $2k+1$

Gr\"otzsch introduced his famous graph as a triangle-free graph which is not 3-colourable. Harary showed that any such graph must be of order at least 11 and Chv\'atal proved that the Gr\"otzsch graph is the only such graph on 11 vertices. As a generalization, Ngoc and Tuza asked about the order of a smallest graph of odd-girth $2k+1$ which is not 3-colourable, a question which, despite several partial results, remains open. Viewing 3-colouring as a homomorphism to the 3-cycle, along this line of work, we ask more generally: What is the smallest order $\eta(k,l)$ of a graph of odd-girth $2k+1$ that admits no homomorphism to the cycle $C_{2l+1}$? In this work, we determine the value of $\eta(k,l)$ for $l\leq k\leq\frac{3l+i-3}{2}$ ($2k=i\bmod 3$) and for $(k,l)=(3,2)$. More precisely, we show that $\eta(k,l)$=$4k$ for $l\leq k\leq\frac{3l+i-3}{2}$ ($2k=i\bmod 3$) and that $\eta(3,2)=15$. The latter is to say that a smallest graph of odd-girth 7 not admitting a homomorphism to the 5-cycle is of order 15 (there are 10 such graphs on 15 vertices).
Perpetual integral functionals as hitting and occupation times

Let $X$ be a linear diffusion and $f$ a non-negative, Borel measurable function. We are interested in finding conditions on $X$ and $f$ which imply that the perpetual integral functional $$ I^X_\infty(f):=\int_0^\infty f(X_t) dt $$ is identical in law with the first hitting time of a point for some other diffusion. This phenomenon may often be explained using random time change. Because of some potential applications in mathematical finance, we are considering mainly the case when $X$ is a Brownian motion with drift $\mu>0,$ denoted $\{B^{(\mu)}_t: t\geq 0\},$ but it is obvious that the method presented is more general. We also review the known examples and give new ones. In particular, results concerning one-sided functionals $$ \int_0^\infty f(B^{(\mu)}_t) {\bf 1}_{\{B^{(\mu)}_t<0\}} dt\quad {\rm and}\quad \int_0^\infty f(B^{(\mu)}_t) {\bf 1}_{\{B^{(\mu)}_t>0\}} dt $$ are presented. This approach generalizes the proof, based on the random time change techniques, of the fact that the Dufresne functional (this corresponds to $f(x)=\exp(-2x)),$ playing quite an important r\^ole in the study of geometric Brownian motion, is identical in law with the first hitting time for a Bessel process. Another functional arising naturally in this context is %associated to the function $$ \int_0^\infty \big(a+\exp(B^{(\mu)}_t)\big)^{-2} dt, $$ which is seen, in the case $\mu=1/2,$ to be identical in law with the first hitting time for a Brownian motion with drift $\mu=a/2. $ The paper is concluded by discussing how the Feynman-Kac formula can be used to find the distribution of a perpetual integral functional.
Toward Terrain Effects on GNSS Interferometric Reflectometry Snow Depth Retrievals: Geometries, Modeling, and Applications

Accurate and high temporal–spatial resolution snow depth retrieval using the global navigation satellite system interferometric reflectometry (GNSS-IR) has become a popular topic. The terrain is a significant issue affecting GNSS-IR snow depth retrieval. This study explores detailed information about the problems and new solutions to this issue. The main conclusions include but are not limited to the following aspects: 1) reflections from below the antenna (RBA) is the primary geometrical relationship of the GNSS multipath signal for snow depth retrieval; 2) the proposed GSnow_TERR model considers the terrain effects by incorporating the surface tilt angle (<inline-formula> <tex-math notation="LaTeX">$\gamma$ </tex-math></inline-formula>) into the derivative of the multipath relative phase (<inline-formula> <tex-math notation="LaTeX">$\varphi$ </tex-math></inline-formula>) with respect to the satellite elevation angle (<inline-formula> <tex-math notation="LaTeX">$e$ </tex-math></inline-formula>); unlike the previous region-by-region solutions, the new model has a definite physical meaning, which considers <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> as an independent nonnegligible variable; 3) the new model performs well for repeatable and nonrepeatable GNSS tracks. The former agrees with the plate boundary observatory (PBO) H2O product with <inline-formula> <tex-math notation="LaTeX">$r^{2} =0.97$ </tex-math></inline-formula> and a slightly 1–2 cm improvement in the root mean square error (RMSE). The latter agrees with the baseline two-step clustering method for GLObal NAvigation Satellite System (GLONASS), Galileo, and BeiDou Navigation Satellite System (BDS), with <inline-formula> <tex-math notation="LaTeX">$r^{2} =0.96$ </tex-math></inline-formula> and root mean square difference (RMSD) = 1.11 cm. The rate of data utilization increases by a mean value of 38.21% for nonrepeatable tracks. The performance of the model in practical applications is consistent with theoretical analysis. The findings of this study provide a valuable reference for future GNSS-IR snow depth research and applications.
Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds

We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and give its applications to intersection forms with local coefficients of 4-manifolds. The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients. The second is a local coefficient version of Furuta's 10/8-inequality. As a corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's theorem and the 10/8-inequality.
Vector Spaces of Generalized Linearizations for Rectangular Matrix Polynomials

The complete eigenvalue problem associated with a rectangular matrix polynomial is typically solved via the technique of linearization. This work introduces the concept of generalized linearizations of rectangular matrix polynomials. For a given rectangular matrix polynomial, it also proposes vector spaces of rectangular matrix pencils with the property that almost every pencil is a generalized linearization of the matrix polynomial which can then be used to solve the complete eigenvalue problem associated with the polynomial. The properties of these vector spaces are similar to those introduced in the literature for square matrix polynomials and in fact coincide with them when the matrix polynomial is square. Further, almost every pencil in these spaces can be `trimmed' to form many smaller pencils that are strong linearizations of the matrix polynomial which readily yield solutions of the complete eigenvalue problem for the polynomial. These linearizations are easier to construct and are often smaller than the Fiedler linearizations introduced in the literature for rectangular matrix polynomials. Additionally, a global backward error analysis applied to these linearizations shows that they provide a wide choice of linearizations with respect to which the complete polynomial eigenvalue problem can be solved in a globally backward stable manner.
Boundary of the Relative Outer Space

Let $\mathcal{A} = {A_1, . , A_k}$ be a system of free factors of $F_n$. The group of relative automorphisms $\mathrm{Aut}(F_n; \mathcal{A})$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The group of relative outer automorphisms is defined as $\mathrm{Out}(F_n; \mathcal{A}) = \mathrm{Aut}(F_n; \mathcal{A}) / \mathrm{Inn}(F_n)$, where $\mathrm{Inn (F_n)$ is the normal subgroup of $\mathrm{Aut}(F_n)$ given by all the inner automorphisms. This group acts on the relative outer space $\mathrm{CV}_n(\mathcal{A})$. We prove that the dimension of the boundary of the relative outer space is $\mathrm{dim}(\mathrm{CV}_n(\mathcal{A}))-1$.