Miracle-dz/UniFAR-FTUs huggingface dataset:
MULTIPLICITY ONE AT FULL CONGRUENCE LEVEL

Abstract Let $F$ be a totally real field in which $p$ is unramified. Let $\overline{r}:G_{F}\rightarrow \text{GL}_{2}(\overline{\mathbf{F}}_{p})$ be a modular Galois representation that satisfies the Taylor–Wiles hypotheses and is tamely ramified and generic at a place $v$ above $p$ . Let $\mathfrak{m}$ be the corresponding Hecke eigensystem. We describe the $\mathfrak{m}$ -torsion in the $\text{mod}\,p$ cohomology of Shimura curves with full congruence level at $v$ as a $\text{GL}_{2}(k_{v})$ -representation. In particular, it only depends on $\overline{r}|_{I_{F_{v}}}$ and its Jordan–Hölder factors appear with multiplicity one. The main ingredients are a description of the submodule structure for generic $\text{GL}_{2}(\mathbf{F}_{q})$ -projective envelopes and the multiplicity one results of Emerton, Gee and Savitt [Lattices in the cohomology of Shimura curves, Invent. Math. 200(1) (2015), 1–96].
Analysis of Mobile Phone Dependence among Students in Higher Vocational Institutions

Students’ motivation for using mobile phones is mainly entertainment, followed by a sense of achievement and finally social interaction. Mobile phone dependency is a real problem for students in higher vocational institutions and accounts for up to 90% of the population. Students’ mobile phone dependence is influenced by their motivation to use, and the result is that the individual is physically and mentally impaired, which has some negative impact on their social functioning. In tests of students’ mobile phone dependence, the results are out of control > avoidance > wariness > inefficiency. Three ways of intervention are recommended: by actively guiding students in the scientific use of mobile phones, by strengthening control over classroom order management and by establishing a harmonious teacher-student connection through mobile phones.
Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs

In this note, we address the following question: Why certain nonassociative algebra structures emerge in the regularity theory of elliptic type PDEs and also in constructing nonclassical and singular solutions? The aim of the paper is twofold. Firstly, to give a survey of diverse examples on nonregular solutions to elliptic PDEs with emphasis on recent results on nonclassical solutions to fully nonlinear equations. Secondly, to define an appropriate algebraic formalism which makes the analytic part of the construction of nonclassical solutions more transparent.
Quantum computation with noisy operations

In this paper, we show how to use low-fidelity operations to control the dynamics of quantum systems. Noisy operations usually drive a system to evolve into a mixed state and damage the coherence. Sometimes frequent noisy operations result in the coherent evolution of a subsystem, and the dynamics of the subsystem is controlled by tuning noisy operations. Based on this, we find that universal quantum computation can be carried out by low-fidelity (fidelity $<90\%$) operations.
Representations of right 3-Nakayama algebras

In this paper we study the category of finitely generated modules over a right $3$-Nakayama artin algebra. First we give a characterization of right $3$-Nakayama artin algebras and then we give a complete list of non-isomorphic finitely generated indecomposable modules over any right $3$-Nakayama artin algebra. Also we compute all almost split sequences for the class of right $3$-Nakayama artin algebras. Finally, we classify finite dimensional right $3$-Nakayama algebras in terms of their quivers with relations.
Compositionality in Computational Linguistics

Neural models greatly outperform grammar-based models across many tasks in modern computational linguistics. This raises the question of whether linguistic principles, such as the Principle of Compositionality, still have value as modeling tools. We review the recent literature and find that while an overly strict interpretation of compositionality makes it hard to achieve broad coverage in semantic parsing tasks, compositionality is still necessary for a model to learn the correct linguistic generalizations from limited data. Reconciling both of these qualities requires the careful exploration of a novel design space; we also review some recent results that may help in this exploration. Expected final online publication date for the Annual Review of Linguistics, Volume 9 is January 2023. Please see http://www.annualreviews. org/page/journal/pubdates for revised estimates.
Instability of the abstract Rayleigh–Taylor problem and applications

Based on a bootstrap instability method, we prove the existence of unstable strong solutions in the sense of [Formula: see text]-norm to an abstract Rayleigh–Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates. In the proof we develop a method to modify the initial data of the linearized abstract RT problem by exploiting the existence theory of a unique solution to the stratified (steady) Stokes problem and an iterative technique, such that the obtained modified initial data satisfy the necessary compatibility conditions on boundary of the original (nonlinear) abstract RT problem. Applying an inverse transform of Lagrangian coordinates to the obtained unstable solutions and taking then proper values of the parameters, we can further obtain unstable solutions of the RT problem in viscoelastic, magnetohydrodynamics (MHD) flows with zero resistivity and pure viscous flows (with/without interface intension) in Eulerian coordinates.
DIFFUSIVE NUCLEAR BURNING OF HELIUM ON NEUTRON STARS

Diffusive nuclear burning (DNB) of H by an underlying material capable of capturing protons can readily consume H from the surface of neutron stars (NSs) during their early cooling history. In the absence of subsequent accretion, it will be depleted from the photosphere. We now extend DNB to He, motivated by the recent observation by Ho & Heinke of a carbon atmosphere on the NS in the Cassiopeia A supernova remnant. We calculate the equilibrium structure of He on an underlying α capturing material, accounting for thermal, mass defect, and Coulomb corrections on the stratification of material with the same zeroth order μe = A/Z. We show that Coulomb corrections dominate over thermal and mass defect corrections in the highly degenerate part of the envelope. We also show that the bulk of the He sits deep in the envelope rather than near the surface. Thus, even if the photospheric He abundance is low, the total He column could be substantially larger than the photospheric column, which may have implications for rapid surface evolution (≈1 yr timescales) of NSs. When nuclear reactions are taken into account, we find that for base temperatures ≳1.6 × 108 K, He is readily captured onto C. As these high temperatures are present during the early stages of NS evolution, we expect that the primordial He is completely depleted from the NS surface like the case for primordial H. We also find that magnetic fields ≲1012 G do not affect our conclusions. Armed with the results of this work and our prior efforts, we expect that primordial H and He are depleted, and so any observed H or He on the surfaces of these NS must be due to subsequent accretion (with or without spallation). If this subsequent accretion can be prevented, the underlying mid-Z material would be exposed.
Nonlinear parabolic equations with soft measure data

In this paper we prove existence and uniqueness results for nonlinear parabolic problems with Dirichlet boundary values whose model is \[ \left\{ \begin{aligned} b\mbox{in }(0,T)\times\Omega,\\ b\mbox{in }\Omega,\\ u\mbox{on }(0,T)\times\partial\Omega. \end{aligned} \right. \] where $\Delta_{p}u=\text{div}(|\nabla u|^{p-2}\nabla u)$ is the usual $p-$Laplace operator, $b$ is a increasing $C^{1}-$function and $\mu$ is a finite measure which does not charge sets of zero parabolic $p-$capacity, and we discuss their main properties.
Computing the stochastic $H^\infty$-norm

The stochastic $H^\infty$-norm is defined as the $L^2$-induced norm of the input-output operator of a stochastic linear system. Like the deterministic $H^\infty$-norm it is characterised by a version of the bounded real lemma, but without a frequency domain description or a Hamiltonian condition. Therefore, we base its computation on a parametrised algebraic Riccati-type matrix equation.
Enhancing Topology Identification of Distribution Power Systems Using Multi-Rate Voltage Measurements

An accurate system topology is essential for distribution system monitoring and operation. This paper presents a novel approach to distribution system topology identification (DSTI). The proposed method identifies the topology of the distribution network in real-time by applying Linear Discriminant Analysis (LDA) and Regularized Diagonal Quadratic Discriminant Analysis (RDQDA) to the voltage magnitudes collected by distribution grid sensors. The results show that this method can utilize noisy voltage magnitude readings from load buses to identify distribution system reconfiguration between radial topologies during operation under changing loads in an accurate manner. Furthermore, the approach has shown good results for DSTI utilizing available multi-rate voltage measurements and for reduced-dimensionality input data using principal component analysis. The proposed DSTI approaches have outperformed convolution neural networks under limited training data.
Distribution of Eigenvalues in Electromagnetic Scattering on an Arbitrarily Shaped Dielectric

We study the distribution of eigenvalues for the Green operator occurring in the scattering of electromagnetic waves by an arbitrarily shaped dielectric medium. It is revealed that the totality of eigenvalues (counting multiplicities) can be enumerated as a sequence $ \{\lambda_s\}_{s=1}^N,N\leq\aleph_0$, with only two possible accumulation points $ \{0,-1/2\}$, and the following spectral series converges: $ \sum_{s=1}^N|\lambda_s|^2|1+2\lambda_s|^4<+\infty$.
Electron waves in chemically substituted graphene

We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.
IMC-NET: Learning Implicit Field with Corner Attention Network for 3D Shape Reconstruction

Learning implicit field as shape representation brings a revolution in 3D shape single view reconstruction, while it suffers from over-smoothness of corners and details. Many involve 2D supervision to solve corners and details. However, they are limited by the number of views and the accuracy of the renderer. Thus, we propose IMC-NET, an IMplicit field with Corner attention NETwork, to reconstruct details and corners of 3D shapes without any 2D supervision. In IMC-NET, we designed a corner attention branch to predict detailed corners of 3D shape under hand-crafted 3D corner points supervision. Then, an aggregation module was presented to differentiably merge the shape corners and implicit fields using a corner weight prediction. In addition, to help further shape reconstruction work on corners and details, we released a new dataset based on Shapenet models, named Shape-CornerNet, including 43784 3D shapes in 13 categories with detailed corner points. Afterward, we quantitatively and qualitatively evaluated our model on Shape-CornerNet. Our IMC-NET achieved state-of-the-art performance on Shape-CornerNet.
Neutral meson oscillations in the Standard Model and beyond from Nf=2 Twisted Mass Lattice QCD

We present the ETMC results for the bag parameters describing the neutral kaon mixing in the Standard Model and beyond and preliminary results for the bag parameters controlling the short distance contributions in the D^0-\bar{D}^0 oscillations. We also present preliminary results for the B_{Bd}, B_{Bs}, B_{Bs}/B_{Bd} and \xi -parameter controlling B^0_-\bar{B}^0 oscillations in the Standard Model employing the so-called ratio method. Using Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve both O(a)-improvement and continuum like renormalization pattern. Simulations are performed at three-values of the lattice spacing and several values of quark masses in the light, strange, charm region and above charm up to ~2. 5m_c. Our results are extrapolated to the continuum limit and extrapolated/interpolated to the physical quark masses.
A Novel Fractional Analytical Technique for the Time-space Fractional Equations Appearing in Oil Pollution

the of outreached the as initial and boundary conditions for a mathematical model of oil diffusion and alteration in As it involves the hyperbolic (advection/wave) component of the equation, the most reasonable choices are diffusion and Allen–Cahn (AC) equations, which are to solve numerically. Equations of diffusion and Allen-Cahn were solved with different degrees of fractional derivatives (α= 0.25, α=0.5, α=0.75 and α=0.75), and the oil pollution concentration was obtained at a specific time and place. This study adopts the homotopy perturbation method (HPM) for nonlinear Allen–Cahn (AC) equation and time fractional diffusion equation to express oil pollution in the water. Fractional derivatives are portrayed in the sense of Caputo. Two presented examples illustrate the applicability and validity of the proposed method. Pollution concentrations in flow field over an interval of time and space for different degrees of fractional derivation are shown. At lower fraction derivative degrees, the pollution concentration behavior is nonlinear, and as the degree of fraction derivation increases to one, the nonlinear behavior of the pollution concentration decreases. The results produced by the suggested technique compared to the exact solutions shows that it is efficient and convenient; it is also reduces computational time.
Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1

Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with the natural involution defined by (E,\Phi)\mapsto (E,-\Phi). We study the fixed point locus of this involution. In [GM], this moduli space with involution was identified with the moduli space of hyperpolygons equipped with a certain natural involution. Here we identify the fixed point locus with the moduli spaces of polygons in Minkowski 3-space. This identification yields information on the connected components of the fixed point locus.
Almost sure scattering for the energy critical nonlinear wave equation

abstract:We study the defocusing energy critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random perturbations of the initial data. The random perturbation is defined through a microlocal randomization, which is based on a unit-scale decomposition in physical and frequency space. In contrast to the previous literature, we do not require the spherical symmetry of the perturbation.The main novelty lies in a wave packet decomposition of the random linear evolution. Through this decomposition, we can adaptively estimate the interaction between the rough and regular components of the solution. Our argument relies on techniques from restriction theory, such as Bourgain's bush argument and Wolff's induction on scales.
On the spectral moment of trees with given degree sequences

Let $A(G)$ be the adjacency matrix of graph $G$ with eigenvalues $\lambda_1(G), \lambda_2(G),. , \lambda_n(G)$ in non-increasing order. The number $S_k(G):=\sum_{i=1}^{n}\lambda_i^{k}(G)\, (k=0, 1,., n-1)$ is called the $k$th spectral moment of $G$. Let $S(G) = (S_0(G), S_1(G),. , S_{n-1}(G))$ be the sequence of spectral moments of $G. $ For two graphs $G_1, G_2$, we have $G_1\prec_{s}G_2$ if for some $k \in \{1,2,3,. ,n-1\}$, we have $S_i(G_1) = S_i(G_2)\, ,\, i = 0, 1,. , k-1$ and $S_k(G_1)<S_k(G_2). $ In this paper, the last $n$-vertex tree with a given degree sequence in an $S$-order is determined. Consequently, we also obtain the last trees in an $S$-order in the sets of all trees of order $n$ with the largest degree, the leaves number, the independence number and the matching number, respectively.
On the assumption of Gaussianity for cosmological two-point statistics and parameter dependent covariance matrices

In this brief paper we revisit the Fisher information content of cosmological power spectra or two-point functions of Gaussian fields in order to comment on the assumption of Gaussian estimators and the use of parameter-dependent covariance matrices for parameter inference in the context of precision cosmology. Even though the assumption of a Gaussian likelihood is motivated by the central limit theorem, we discuss that it leads to Fisher information content that violates the Cram\'er-Rao bound if used consistently, owing to independent but artificial information from the parameter-dependent covariance matrix. At any fixed multipole, this artificial term is shown to become dominant in the case of a large number of correlated fields. While the distribution of the estimators does indeed tend to a Gaussian with a large number of modes, it is shown, however, that its Fisher information content does not, in the sense that their covariance matrix never carries independent information content, precisely because of the non-Gaussian shape of the distribution. In this light, we discuss the use of parameter-dependent covariance matrices with Gaussian likelihoods for parameter inference from two-point statistics. As a rule of thumb, Gaussian likelihoods should always be used with a covariance matrix fixed in parameter space, since only this guarantees that conservative information content is assigned to the observables, and at the same time prevents biases appearing.
Manufacturing of Soft Contact Lenses Using Reusable and Reliable Cyclic Olefin Copolymer Moulds

We present experimental evidence of reusable, reliable cyclic olefin copolymer (COC) moulds in soft contact lens manufacturing. The moulds showed high performance surface roughness characteristics despite >20 kW exposure to 365 nm ultraviolet (UV) light from repeated use. Ultra-precision manufacturing techniques were used to fabricate transparent COC mould inserts and to produce soft contact lenses from liquid monomer compositions. Both polymer and silicone hydrogels were fabricated with more than 60 individual uses of the moulds. White light interferometry measured the surface roughness (Sa) of the COC moulds to be almost unchanged before and after repeated use (Sa 16.3 nm before vs. 16.6 nm after). The surface roughness of the prototyped lenses and that of commercially available soft contact lenses were then compared by white light interferometry. The surface roughness of the lenses was also nearly unchanged, despite undergoing more than 60 uses of the COC moulds (lens Sa 24.4 nm before vs. after Sa 26.5 nm). By comparison the roughness of the commercial lenses ranged from 9.3–28.5 nm, including conventional and silicone lenses, indicating that the reusable COC moulds produced competitive surface properties. In summary, COC moulds have potential as reusable and reliable mould inserts in the manufacturing of soft contact lenses, yet maintain high quality optical surfaces even after sustained exposure to UV light.
QCD Phase Transition in a Strong Magnetic Background

We investigate the properties of the deconfining/chiral restoring transition for two flavor QCD in presence of a uniform background magnetic field. We adopt a standard staggered discretization of the fermion action and a lattice spacing of the order of 0.3 fm. We explore different values of the bare quark mass, corresponding to pion masses in the range 200 - 480 MeV, and magnetic fields up to |e|B ~ 0.75 GeV^2. The deconfinement and chiral symmetry restoration temperatures remain compatible with each other and rise very slightly (< 2 % for our largest magnetic field) as a function of the magnetic field. On the other hand, the transition seems to become sharper as the magnetic field increases.
Origin of the blackhole information paradox

It is argued that the blackhole information paradox originates from treating the blackhole geometry as strictly classical. It is further argued that the theory of quantum fields in a classical curved space with a horizon is an ill posed problem. If the geometry is allowed to fluctuate quantum mechanically, then the horizon effectively disappears. The sharp horizon emerges only in the classical limit when the ratio of the Compton wavelength of the black hole to its Schwarzschild radius vanishes. The region of strong gravity that develops when matter collapses to form the blackhole remains visible to the whole of spacetime and has to be described by a microscopic theory of strong gravity. The arguments imply that the information paradox is demoted from a paradox involving fundamental principles of physics to the problem of describing how matter at the highest densities gravitates.
Modes of asymmetry: The application of harmonic analysis to symmetric quantum dynamics and quantum reference frames

Finding the consequences of symmetry for open-system quantum dynamics is a problem with broad applications, including describing thermal relaxation, deriving quantum limits on the performance of amplifiers, and exploring quantum metrology in the presence of noise. The symmetry of the dynamics may reflect a symmetry of the fundamental laws of nature or a symmetry of a low-energy effective theory, or it may describe a practical restriction such as the lack of a reference frame. In this paper, we apply some tools of harmonic analysis together with ideas from quantum information theory to this problem. The central idea is to study the decomposition of quantum operations\char22{}in particular, states, measurements, and channels\char22{}into different modes, which we call modes of asymmetry. Under symmetric processing, a given mode of the input is mapped to the corresponding mode of the output, implying that one can only generate a given output if the input contains all of the necessary modes. By defining monotones that quantify the asymmetry in a particular mode, we also derive quantitative constraints on the resources of asymmetry that are required to simulate a given asymmetric operation. We present applications of our results for deriving bounds on the probability of success in nondeterministic state transitions, such as quantum amplification, and a simplified formalism for studying the degradation of quantum reference frames.