Miracle-dz/UniFAR-FTUs huggingface dataset:
Fundamental Rate Limits of UAV-Enabled Multiple Access Channel With Trajectory Optimization

This paper studies an unmanned aerial vehicle (UAV)-enabled multiple access channel (MAC), in which multiple ground users transmit individual messages to a mobile UAV in the sky. We consider a linear topology scenario, where these users locate in a straight line and the UAV flies at a fixed altitude above the line connecting them. Under this setup, we jointly optimize the one-dimensional (1D) UAV trajectory and wireless resource allocation to reveal the fundamental rate limits of the UAV-enabled MAC, under the users’ individual maximum power constraints and the UAV’s maximum flight speed constraints. First, we consider the capacity-achieving non-orthogonal multiple access (NOMA) transmission with successive interference cancellation (SIC) at the UAV receiver. In this case, we characterize the capacity region by maximizing the average sum-rate of all users subject to a set of rate profile constraints. To optimally solve this highly non-convex problem with infinitely many UAV location variables over time, we show that any speed-constrained UAV trajectory is equivalent to the combination of a maximum-speed flying trajectory and a speed-free trajectory, and accordingly transform the original speed-constrained trajectory optimization problem into a speed-free problem that is optimally solvable via the Lagrange dual decomposition. It is rigorously proved that the optimal 1D trajectory solution follows the successive hover-and-fly (SHF) structure, i.e., the UAV successively hovers above a number of optimized locations, and flies unidirectionally among them at the maximum speed. Next, we consider two orthogonal multiple access (OMA) transmission schemes, i.e., frequency-division multiple access (FDMA) and time-division multiple access (TDMA). We maximize the achievable rate regions in the two cases by jointly optimizing the 1D trajectory design and wireless resource (frequency/time) allocation. It is shown that the optimal trajectory solutions still follow the SHF structure but with different hovering locations for each scheme. Finally, numerical results show that the proposed optimal trajectory designs achieve considerable rate gains over other benchmark schemes, and the capacity region achieved by NOMA significantly outperforms the rate regions by FDMA and TDMA.
Sensing magnetic fields with non-gaussian quantum fluctuations

The precision of a quantum sensor can overcome its classical counterpart when its constituants are entangled. In gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of non-classical states of the electronic spin $J=8$ of dysprosium atoms, created using light-induced non-linear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.
Core Loss Analysis of Soft Magnetic Composites Based on 3D Modeling under Non-sinusoidal Excitation

Based on the existing soft magnetic composite (SMC) finite element models, three-dimensional(3D) finite element simulation models of SMC single particle and magnetic ring sample were established in this paper. In view of the fact that the existing finite element models do not take into account the effect of harmonics on the hysteresis loss of SMC, based on the hysteresis loss calculation formula of Bertotti loss separation theory, an improved expression of hysteresis loss coefficient is derived by introducing the correction factor of loss coefficient. And it is applied to the model so that the model can be used to calculate the magnetic core loss under non-sinusoidal excitation. Finally, the feasibility and effectiveness of the proposed model are verified by comparing with experimental results.
Cross-intersecting integer sequences

We call $(a_1, \dots, a_n)$ an \emph{$r$-partial sequence} if exactly $r$ of its entries are positive integers and the rest are all zero. For ${\bf c} = (c_1, \dots, c_n)$ with $1 \leq c_1 \leq \dots \leq c_n$, let $S_{\bf c}^{(r)}$ be the set of $r$-partial sequences $(a_1, \dots, a_n)$ with $0 \leq a_i \leq c_i$ for each $i$ in $\{1, \dots, n\}$, and let $S_{\bf c}^{(r)}(1)$ be the set of members of $S_{\bf c}^{(r)}$ which have $a_1 = 1$. We say that $(a_1, \dots, a_n)$ \emph{meets} $(b_1, \dots, b_m)$ if $a_i = b_i \neq 0$ for some $i$. Two sets $A$ and $B$ of sequences are said to be \emph{cross-intersecting} if each sequence in $A$ meets each sequence in $B$. Let ${\bf d} = (d_1, \dots, d_m)$ with $1 \leq d_1 \leq \dots \leq d_m$. Let $A \subseteq S_{\bf c}^{(r)}$ and $B \subseteq S_{\bf d}^{(s)}$ such that $A$ and $B$ are cross-intersecting. We show that $|A||B| \leq |S_{\bf c}^{(r)}(1)||S_{\bf d}^{(s)}(1)|$ if either $c_1 \geq 3$ and $d_1 \geq 3$ or ${\bf c} = {\bf d}$ and $r = s = n$. We also determine the cases of equality. We obtain this by proving a general cross-intersection theorem for \emph{weighted} sets. The bound generalises to one for $k \geq 2$ cross-intersecting sets.
On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation

For shape optimization of fluid flows governed by the Navier–Stokes equation, we investigate effectiveness of shape gradient algorithms by analyzing convergence and accuracy of mixed finite element approximations to both the distributed and boundary types of shape gradients. We present convergence analysis with a priori error estimates for the two approximate shape gradients. The theoretical analysis shows that the distributed formulation has superconvergence property. Numerical results with comparisons are presented to verify theory and show that the shape gradient algorithm based on the distributed formulation is highly effective and robust for shape optimization.
Targeted Panel Sequencing Identifies an Intronic c.5225-3C>G Variant of the FBN1 Gene Causing Sporadic Marfan Syndrome with Annuloaortic Ectasia

Marfan syndrome (MFS) is a hereditary connective tissue disease whose clinical severity varies widely. Mutations of the FBN1 gene encoding fibrillin-1 are the most common genetic cause of Marfanoid habitus; however, about 10% of MFS patients are unaware of their genetic defects. Herein, we report a Korean patient with MFS and annuloaortic ectasia caused by an intronic c.5225-3C>G variant of the FBN1 gene identified by targeted panel sequencing. The reverse transcription analysis of FBN1 revealed that the intron 43 sequence from positions c.5297-1516 to c.5297-1 was retained at the coding sequence as a consequence of the c.5225-3C>G variant enhancing a cryptic splice acceptor site (c.5297-1518_5297-1517AG) in intron 43. The retained sequence of the part of intron 43 caused the same effect as insertion mutation (NM_000138.5:c.5297_c.5298ins5297-1516_5297-1), resulting in a frameshift mutation resulting in p.Ile1767Trpfs*3. The patient underwent an urgent modified Bentall operation with a 29 mm mechanical valve for annuloaortic ectasia and severe aortic valve regurgitation. This report emphasizes the need for functional investigations into the diagnostic workflows of certain diseases or gene panels with suspected high rates of intronic variants and potential pathogenic effects. Hence, further descriptions of individuals with intronic variants causing alternative splicing expected to have pathogenic effects at different transcript levels are crucial for improving our understanding.
Invariants and rigidity of projective hypersurfaces

We compute some invariants based on Hilbert-Poincar e series associated to Milnor algebras. These computations involve some of the classical surfaces and 3-folds with dierent congurations of isolated singularities. As a by-product of a recent result of E. Sernesi, we give examples of classical hypersurfaces which are (or are not) projectively rigid. We also include a Singular program to compute these invariants and to decide if a singular projective hypersurface is nodal and projectively rigid.
Approximating the first $L^2$-betti number of residually finite groups

We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an application we construct a finitely generated infinite residually finite torsion group with positive first $L^2$-betti number.
From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link

Author(s): Oblomkov, A; Rasmussen, J; Shende, V; Gorsky, E | Abstract: © 2018, Mathematical Sciences Publishers. All rights reserved. We conjecture an expression for the dimensions of the Khovanov-Rozansky HOMFLY homology groups of the link of a plane curve singularity in terms of the weight polynomials of Hilbert schemes of points scheme-theoretically supported on the singularity. The conjecture specializes to our previous conjecture (2012) relating the HOMFLY polynomial to the Euler numbers of the same spaces upon setting t=-1. By generalizing results of Piontkowski on the structure of compactified Jacobians to the case of Hilbert schemes of points, we give an explicit prediction of the HOMFLY homology of a (k,n) torus knot as a certain sum over diagrams. The Hilbert scheme series corresponding to the summand of the HOMFLY homology with minimal “a” grading can be recovered from the perverse filtration on the cohomology of the compactified Jacobian. In the case of (k,n) torus knots, this space furnishes the unique finite-dimensional simple representation of the rational spherical Cherednik algebra with central character k/n. Up to a conjectural identification of the perverse filtration with a previously introduced filtration, the work of Haiman and Gordon and Stafford gives formulas for the Hilbert scheme series when k=mn+1.
The Khuri-Jones Threshold Factor as an Automorphic Function

The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and $\infty$ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and $\infty$ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.
A Toponogov type triangle comparison theorem in Finsler geometry ⁄y

The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial ag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to the base point is contained in a Berwald-like region, and that the Finsler metric is convex enough in the radial directions in that region.
Decarboxylative sulfoximination of benzoic acids enabled by photoinduced ligand-to-copper charge transfer

Sulfoximines are synthetically important scaffolds and serve important roles in drug discovery. Currently, there is no solution to decarboxylative sulfoximination of benzoic acids; although thoroughly investigated, limited substrate scope and harsh reaction conditions still hold back traditional thermal aromatic decarboxylative functionalization. Herein, we realize the first decarboxylative sulfoximination of benzoic acids via photo-induced ligand to copper charge transfer (copper-LMCT)-enabled decarboxylative carbometalation. The transformation proceeds under mild reaction conditions, has a broad substrate scope, and can be applied to late-stage functionalization of complex small molecules.
Upper bound of typical ranks of m× n×((m− 1)n− 1) tensors over the real number field

Let 3 ≤ m ≤ n. We study typical ranks of m× n×((m− 1)n− 1) tensors over the real number field. The number (m− 1)n− 1 is a minimal typical rank of m× n×((m− 1)n− 1) tensors over the real number field. We show that a typical rank of m× n×((m− 1)n− 1) tensors over the real number field is less than or equal to (m− 1)n and in particular, m× n×((m− 1)n− 1) tensors over the real number field has two typical ranks (m− 1)n− 1,(m− 1)n if m ≤ ρ(n), where ρ is the HurwitzRadon function defined as ρ(n) = 2 b + 8c for nonnegative integers a, b, c such that n = (2a+ 1)2 b+4c and 0 ≤ b < 4.
Systematic Review of Complementary and Alternative Veterinary Medicine in Sport and Companion Animals: Extracorporeal Shockwave Therapy

Simple Summary Extracorporeal shockwave therapy (ECSWT) is widely used in sport and companion animals to treat disorders affecting muscles, joints, and bones. Using a shockwave generator, a probe is applied to the skin over the affected area. Typically, there are one to three treatment sessions at 1- to 3-week intervals. The scientific basis for the treatment has been queried. This systematic review evaluated the scientific literature on shockwave therapy used in horses, dogs, and cats. The review revealed that only weak scientific evidence exists for favourable effects in conditions affecting bones, ligaments, tendons, and muscles in horses and dogs. No scientific article on the use of shockwave therapy in cats was available. Reasons for the weak scientific evidence were that studies were few, most involved only a small number of animals, many had methodological problems, or, when favourable results were reported, they were not replicated in independent studies. Thus, in sport and companion animals, the scientific evidence for the clinical effects of ECSWT in horses, dogs, and cats is limited. For a few indications, notably short-term pain relief, ligament ailments, and osteoarthritis, some results appear promising, warranting further exploration in high-quality studies. Abstract Background: Extracorporeal shockwave therapy (ECSWT) is increasingly used to treat different types of musculoskeletal conditions in sport and companion animals. To explore the scientific basis for the treatment, we conducted a systematic review of the literature on ECSWT used in horses, dogs, and cats. Methods: Relevant articles published in 1980–2020 were identified from three major databases. Each article was assessed for risk of bias. Results: The review identified 27 relevant articles on the effects of ECSWT in horses, nine in dogs, but none in cats. Typically, ECSWT involved one to three treatment sessions at 1- to 3-week intervals. We identified studies on bone mass and bone healing, wound healing, navicular disease, ligament injury, desmitis, sesamoiditis, tendon injury, osteoarthritis, and short-term analgesic effects. Common to all indications was that the scientific evidence was very limited. For each separate indication, there were relatively few studies, many of which had methodological flaws. Where favorable results were reported, they were usually not replicated in independent studies. A few encouraging results were found. Conclusions: In sport and companion animals, the scientific evidence for clinical effects of ECSWT in horses, dogs, and cats is limited. For some applications, notably short-term pain relief, ligament ailments, and osteoarthritis, the results seem promising and warrant further exploration in high-quality studies.