Miracle-dz/UniFAR-FTUs huggingface dataset:
On the energy variant of the sum-product conjecture

We prove new exponents for the energy version of the Erdős-Szemeredi sum-product conjecture, raised by Balog and Wooley. They match the previously established milestone values for the standard formulation of the question, both for general fields and the special case of real or complex numbers, and appear to be the best ones attainable within the currently available technology. Further results are obtained about multiplicative energies of additive shifts and a strengthened energy version of the "few sums, many products" inequality of Elekes and Ruzsa. The latter inequality enables us to obtain a minor improvement of the state-of the art sum-product exponent over the reals due to Konyagin and the second author, up to $\frac{4}{3}+\frac{1}{1509}$. An application of energy estimates to an instance of arithmetic growth in prime residue fields is presented.
Open-closed Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric DM stacks

Abstract We study open-closed orbifold Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric Deligne-Mumford stacks (with possibly nontrivial generic stabilisers K and semi-projective coarse moduli spaces) relative to Lagrangian branes of Aganagic-Vafa type. An Aganagic-Vafa brane in this paper is a possibly ineffective $C^\infty $ orbifold that admits a presentation $[(S^1\times \mathbb {R} ^2)/G_\tau ]$ , where $G_\tau $ is a finite abelian group containing K and $G_\tau /K \cong \boldsymbol {\mu }_{\mathfrak {m}}$ is cyclic of some order $\mathfrak {m}\in \mathbb {Z} _{>0}$ . 1. We present foundational materials of enumerative geometry of stable holomorphic maps from bordered orbifold Riemann surfaces to a 3-dimensional Calabi-Yau smooth toric DM stack $\mathcal {X}$ with boundaries mapped into an Aganagic-Vafa brane $\mathcal {L}$ . All genus open-closed Gromov-Witten invariants of $\mathcal {X}$ relative to $\mathcal {L}$ are defined by torus localisation and depend on the choice of a framing $f\in \mathbb {Z} $ of $\mathcal {L}$ . 2. We provide another definition of all genus open-closed Gromov-Witten invariants in (1) based on algebraic relative orbifold Gromov-Witten theory, which agrees with the definition in (1) up to a sign depending on the choice of orientation on moduli of maps in (1). This generalises the definition in [57] for smooth toric Calabi-Yau 3-folds and specifies an orientation on moduli of maps in (1) compatible with the canonical orientation on moduli of relative stable maps determined by the complex structure. 3. When $\mathcal {X}$ is a toric Calabi-Yau 3-orbifold (i.e., when the generic stabiliser K is trivial), so that $G_\tau =\boldsymbol {\mu }_{\mathfrak {m}}$ , we define generating functions $F_{g,h}^{\mathcal {X},(\mathcal {L},f)}$ of open-closed Gromov-Witten invariants of arbitrary genus g and number h of boundary circles; it takes values in $H^*_{ {\mathrm {CR}} }(\mathcal {B} \boldsymbol {\mu }_{\mathfrak {m}}; \mathbb {C} )^{\otimes h}$ , where $H^*_{ {\mathrm {CR}} }(\mathcal {B} \boldsymbol {\mu }_{\mathfrak {m}}; \mathbb {C} )\cong \mathbb {C} ^{\mathfrak {m}}$ is the Chen-Ruan orbifold cohomology of the classifying space $\mathcal {B} \boldsymbol {\mu }_{\mathfrak {m}}$ of $\boldsymbol {\mu }_{\mathfrak {m}}$ . 4. We prove an open mirror theorem that relates the generating function $F_{0,1}^{\mathcal {X},(\mathcal {L},f)}$ of orbifold disk invariants to Abel-Jacobi maps of the mirror curve of $\mathcal {X}$ . This generalises a conjecture by Aganagic-Vafa [6] and Aganagic-Klemm-Vafa [5] (proved in full generality by the first and the second authors in [33]) on the disk potential of a smooth semi-projective toric Calabi-Yau 3-fold.
A Novel Peptide from Polypedates megacephalus Promotes Wound Healing in Mice

Amphibian skin contains wound-healing peptides, antimicrobial peptides, and insulin-releasing peptides, which give their skin a strong regeneration ability to adapt to a complex and harsh living environment. In the current research, a novel wound-healing promoting peptide, PM-7, was identified from the skin secretions of Polypedates megacephalus, which has an amino acid sequence of FLNWRRILFLKVVR and shares no structural similarity with any peptides described before. It displays the activity of promoting wound healing in mice. Moreover, PM-7 exhibits the function of enhancing proliferation and migration in HUVEC and HSF cells by affecting the MAPK signaling pathway. Considering its favorable traits as a novel peptide that significantly promotes wound healing, PM-7 can be a potential candidate in the development of novel wound-repairing drugs.
Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic $3$-manifolds

In this paper, it is shown that every closed hyperbolic 3-manifold contains an immersed quasi-Fuchsian closed subsurface of odd Euler characteristic. The construction adopts the good pants method, and the primary new ingredient is an enhanced version of the connection principle, which allows one to connect any two frames with a path of frames in a prescribed relative homology class of the frame bundle. The existence result is applied to show that every uniform lattice of $\mathrm{PSL}(2,\mathbb{C})$ admits an exhausting nested sequence of sublattices with exponential homological torsion growth. However, the constructed sublattices are not normal in general.
RESOLVED CO GAS INTERIOR TO THE DUST RINGS OF THE HD 141569 DISK

The disk around HD 141569 is one of a handful of systems whose weak infrared emission is consistent with a debris disk, but still has a significant reservoir of gas. Here we report spatially resolved millimeter observations of the CO(3-2) and CO(1-0) emission as seen with the Submillimeter Array and CARMA. We find that the excitation temperature for CO is lower than expected from cospatial blackbody grains, similar to previous observations of analogous systems, and derive a gas mass that lies between that of gas-rich primordial disks and gas-poor debris disks. The data also indicate a large inner hole in the CO gas distribution and an outer radius that lies interior to the outer scattered light rings. This spatial distribution, with the dust rings just outside the gaseous disk, is consistent with the expected interactions between gas and dust in an optically thin disk. This indicates that gas can have a significant effect on the location of the dust within debris disks.
Xiphinema index-resistant grapevine materials derived from muscadine are also resistant to a population of X. diversicaudatum

Grapevine is severely affected by two major nepoviruses that cause grapevine degeneration: the grapevine fanleaf virus (GFLV) and the arabis mosaic virus (ArMV), specifically transmitted by the dagger nematodes Xiphinema index and X. diversicaudatum, respectively. While natural resistance to X. index has been shown to be a promising alternative for controlling X. index and GFLV transmission, the resistance interaction between X. diversicaudatum and grapevine has not yet been documented. In the present study, we evaluated the host suitability to X. diversicaudatum in materials previously characterised for their resistance to X. index. Two X. index-resistant accessions VRH8771 (F1 hybrid) and Nemadex Alain Bouquet (BC1 hybrid) derived from muscadine, together with the X. index-susceptible reference accession V. vinifera cv. Cabernet-Sauvignon and the X. index-resistant reference accession V. riparia ‘10128’, were challenged with a X. diversicaudatum population obtained from woody host plants and a reference isolate of X. index. The reproduction factors of X. diversicaudatum and its numbers per gram of roots paralleled those of X. index, showing a resistance interaction to the population of the former species and suggesting that resistance determinants to both nematode vectors might be the same or linked. Nevertheless, these two criteria illustrated a poorer host suitability of grapevine materials to this X. diversicaudatum population than to X. index.
Maximum Likelihood Duality for Determinantal Varieties

In a recent paper, Hauenstein, Sturmfels, and the second author discovered a conjectural bijection between critical points of the likelihood func- tion on the complex variety of matrices of rank r and critical points on the complex variety of matrices of co-rank r 1. In this paper, we prove that conjecture for rectangular matrices and for symmetric matrices, as well as a variant for skew-symmetric matrices.
Local contributions to Donaldson-Thomas invariants

Let $C$ be a smooth curve embedded in a smooth quasi-projective threefold $Y$, and let $Q^n_C=\textrm{Quot}_n(\mathscr I_C)$ be the Quot scheme of length $n$ quotients of its ideal sheaf. We show the identity $\tilde\chi(Q^n_C)=(-1)^n\chi(Q^n_C)$, where $\tilde\chi$ is the Behrend weighted Euler characteristic. When $Y$ is a projective Calabi-Yau threefold, this shows that the DT contribution of a smooth rigid curve is the signed Euler characteristic of the moduli space. This can be rephrased as a DT/PT wall-crossing type formula, which can be formulated for arbitrary smooth curves. In general, the formula is shown to be equivalent to a certain Behrend function identity.
Stability of Steady Solutions to Reaction-Hyperbolic Systems for Axonal Transport

This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the reaction-hyperbolic systems and show the time-asymptotic stability of steady solutions or relaxation boundary-layers.
The Optimization of Faecalibacterium prausnitzii Extracellular Vesicle Concentrations on PPARγ and FIAF Expression in the Caco-2 Cell Culture Model

extracellular (EVs) a novel communication between microbiota the are capable of imposing positive effects on the host. Recently, EV-based treatments have been evaluated in different studies, and using EVs derived from microbiota has been recommended in recent studies as post-vaccination adjuvants. Accordingly, in the present study, the effects of various EV concentrations on the mRNA expression of peroxisome proliferator-activated receptor γ ( PPARγ ) and fasting-induced adipose factor (FIAF) genes were evaluated and optimized in the human epithelial colorectal adenocarcinoma (Caco-2) cell line. Methods: The effects of the extracted EVs from F. prausnitzii on the PPARγ and FIAF gene expression were investigated in the Caco-2 cell line via cell culture and quantitative real-time PCR. The obtained outcomes were then compared with those of our previous study (concentrations of 50 and 100 µg/ml). Results: It was shown that F. prausnitzii EVs (150 µg/ml) significantly increased PPARγ and FIAF gene expression in the Caco-2 cell line, relative to previous studies conducted by our team. Conclusion: Considering the positive impact of F. Prausnitzii EVs on the studied genes’ expression in the present study, the EVs of the bacterium will be proposed as new post-vaccination adjuvants in people suffering from intestinal barrier disorders such as inflammatory bowel disease patients. However, more studies should be performed in this respect.
Nutrient mobilization and crop assimilation as influenced by nutrient management strategies under direct seeded basmati rice (Oryza sativa) – based cropping systems

The field experiment was carried out for two consecutive years (2014–2016) in split-plot design to investigate the effect of integrated nutrient management and crop diversification through inclusion of legume and vegetable crops in direct seeded basmati rice (Oryza sativa L.)–based cropping systems (DSRB) on nutrient availability for crop uptake. The study involved four cropping systems (CS) in main plots (DSBR‒wheat‒fallow (CS1), DSBR‒wheat‒greengram (CS2), DSBR‒cabbage‒greengram (CS3) and DSBR‒cabbage‒onion (CS4) and four nutrient management strategies under subplots (unfertilized (NS0), 100% recommended dose of fertilizers (RDF) (NS1), 50% RDF + 25% recommended dose of nitrogen (RDN) through leaf compost (LC) + biofertilizer (NS2), 50% RDF + 25% RDN through vermicompost (VC) + biofertilizer (NS3)). The results revealed that diversification of rice–wheat system with legume (greengram) or vegetable (cabbage and onion) crops and integrated nutrient management strategies had positive effect on nutrient uptake and available nutrient status in the soil. Significantly higher uptake of N, P and K in all crops and Zn, Fe, Mn and Cu in rice and wheat were observed with NS2 and NS3 as compared to NS0. Available N, P and K status were significantly higher in NS2 and NS3 as against NS0 and NS1. Inclusion of cereal crops in the cropping systems showed a negative apparent N balance, but inclusion of vegetable crops in the cropping systems exhibited positive apparent N balance under different nutrient management strategies except NS0. The highest positive apparent N balance was observed in NS1 treatment. The apparent P balance was found to be positive in all the cropping systems with all the nutrients sources except NS0. Apparent K balance was found negative in all the cropping systems under different nutrient management strategies. Thus, cropping systems with summer greengram, cabbage and onion (CS2, CS3 and CS4) under integrated nutrient management practices (NS2 and NS3) were found more sustainable after two years of cropping cycle and can be advocated by the farmers of IGP.
(M-theory-)Killing spinors on symmetric spaces

We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow \Lambda^*(TM)$ is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e. $(M,g,F)$ with $(M,g)$ a symmetric space and $F$ an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.
A quantum waveguide with Aharonov–Bohm magnetic field

In a previous study, we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disk window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We proved that such system exhibits discrete eigenvalues below the essential spectrum for any a > 0. In the present work, we study the effect of the presence of a magnetic field of Aharonov–Bohm type on this system. Precisely, we prove that in the presence of such field, there is some critical values of a0>0, for which we have absence of the discrete spectrum for 0
NanoSQUID magnetometry of individual cobalt nanoparticles grown by focused electron beam induced deposition

We demonstrate the operation of low-noise nano superconducting quantum interference devices (SQUIDs) based on the high critical field and high critical temperature superconductor YBa2Cu3O7 (YBCO) as ultra-sensitive magnetometers for single magnetic nanoparticles (MNPs). The nanoSQUIDs exploit the Josephson behavior of YBCO grain boundaries and have been patterned by focused ion beam milling. This allows us to precisely define the lateral dimensions of the SQUIDs so as to achieve large magnetic coupling between the nanoloop and individual MNPs. By means of focused electron beam induced deposition, cobalt MNPs with a typical size of several tens of nm have been grown directly on the surface of the sensors with nanometric spatial resolution. Remarkably, the nanoSQUIDs are operative over extremely broad ranges of applied magnetic field (–1 T < μ 0 H < 1 T) and temperature (0.3 K < T < 80 K). All these features together have allowed us to perform magnetization measurements under different ambient conditions and to detect the magnetization reversal of individual Co MNPs with magnetic moments (1–30) × 10 6 μ B . Depending on the dimensions and shape of the particles we have distinguished between two different magnetic states yielding different reversal mechanisms. The magnetization reversal is thermally activated over an energy barrier, which has been quantified for the (quasi) single-domain particles. Our measurements serve to show not only the high sensitivity achievable with YBCO nanoSQUIDs, but also demonstrate that these sensors are exceptional magnetometers for the investigation of the properties of individual nanomagnets.
Computer-Assisted Annotation of Digital H&E/SOX10 Dual Stains Generates High-Performing Convolutional Neural Network for Calculating Tumor Burden in H&E-Stained Cutaneous Melanoma

Deep learning for the analysis of H&E stains requires a large annotated training set. This may form a labor-intensive task involving highly skilled pathologists. We aimed to optimize and evaluate computer-assisted annotation based on digital dual stains of the same tissue section. H&E stains of primary and metastatic melanoma (N = 77) were digitized, re-stained with SOX10, and re-scanned. Because images were aligned, annotations of SOX10 image analysis were directly transferred to H&E stains of the training set. Based on 1,221,367 annotated nuclei, a convolutional neural network for calculating tumor burden (CNNTB) was developed. For primary melanomas, precision of annotation was 100% (95%CI, 99% to 100%) for tumor cells and 99% (95%CI, 98% to 100%) for normal cells. Due to low or missing tumor-cell SOX10 positivity, precision for normal cells was markedly reduced in lymph-node and organ metastases compared with primary melanomas (p < 0.001). Compared with stereological counts within skin lesions, mean difference in tumor burden was 6% (95%CI, −1% to 13%, p = 0.10) for CNNTB and 16% (95%CI, 4% to 28%, p = 0.02) for pathologists. Conclusively, the technique produced a large annotated H&E training set with high quality within a reasonable timeframe for primary melanomas and subcutaneous metastases. For these lesion types, the training set generated a high-performing CNNTB, which was superior to the routine assessments of pathologists.
Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials

This paper analyzes the numerical solution of a class of nonlinear Schrodinger equations by Galerkin finite elements in space and a mass and energy conserving variant of the Crank–Nicolson method due to Sanz-Serna in time. The novel aspects of the analysis are the incorporation of rough, discontinuous potentials in the context of weak and strong disorder, the consideration of some general class of nonlinearities, and the proof of convergence with rates in L∞(L2) under moderate regularity assumptions that are compatible with discontinuous potentials. For sufficiently smooth potentials, the rates are optimal without any coupling condition between the time step size and the spatial mesh width.
Weighted restriction estimates using polynomial partitioning

We use the polynomial partitioning method of Guth [J. Amer. Math. Soc. 29 (2016) 371–413] to prove weighted Fourier restriction estimates in R3 with exponents p that range between 3 and 3.25, depending on the weight. As a corollary to our main theorem, we obtain new (non‐weighted) local and global restriction estimates for compact C∞ surfaces S⊂R3 with strictly positive second fundamental form. For example, we establish the global restriction estimate ∥Ef∥Lp(R3)≲∥f∥Lq(S) in the full conjectured range of exponents for p>3.25 (up to the sharp line), and the global restriction estimate ∥Ef∥Lp(Ω)≲∥f∥L2(S) for p>3 and certain sets Ω⊂R3 of infinite Lebesgue measure. As a corollary to our main theorem, we also obtain new results on the decay of spherical means of Fourier transforms of positive compactly supported measures on R3 with finite α ‐dimensional energies.
An upper boundary in the mass-metallicity plane of exo-Neptunes

With the progress of detection techniques, the number of low-mass and small-size exoplanets is increasing rapidly. However their characteristics and formation mechanisms are not yet fully understood. The metallicity of the host star is a critical parameter in such processes and can impact the occurence rate or physical properties of these planets. While a frequency-metallicity correlation has been found for giant planets, this is still an ongoing debate for their smaller counterparts. Using the published parameters of a sample of 157 exoplanets lighter than 40 Mearth, we explore the mass-metallicity space of Neptunes and Super-Earths. We show the existence of a maximal mass that increases with metallicity, that also depends on the period of these planets. This seems to favor in situ formation or alternatively a metallicity-driven migration mechanism. It also suggests that the frequency of Neptunes (between 10 and 40 Mearth) is, like giant planets, correlated with the host star metallicity, whereas no correlation is found for Super-Earths (<10 Mearth).
Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction

We look at the general SU(2) invariant spin-1 Heisenberg model. This family includes the well-known Heisenberg ferromagnet and antiferromagnet as well as the interesting nematic (biquadratic) and the largely mysterious staggered-nematic interaction. Long range order is proved using the method of reflection positivity and infrared bounds on a purely nematic interaction. This is achieved through the use of a type of matrix representation of the interaction making clear several identities that would not otherwise be noticed. Using the reflection positivity of the antiferromagnetic interaction one can then show that the result is maintained if we also include an antiferromagnetic interaction that is sufficiently small.
AN ASTROMETRIC SEARCH FOR A SUB-STELLAR COMPANION OF THE M8.5 DWARF TVLM 513−46546 USING VERY LONG BASELINE INTERFEROMETRY

We conducted multi-epoch very long baseline interferometry observations to search for astrometric reflex motion that would be caused by a sub-stellar companion of the M8.5 dwarf TVLM 513−46546. The observations yield an absolute parallax corresponding to a distance of 10.762 ± 0.027 pc and a proper motion of 78.09 ± 0.17 mas yr−1. The averaged flux density per epoch varies by a factor of at least three. From the absence of significant residual motion, we place an upper limit on any reflex motion caused by a companion, extending the parameter space covered by previous near-infrared direct-imaging searches. The data exclude a phase space of companion masses and orbital periods ranging from 3.8 MJup with an orbital radius of ∼0.05 AU (and an orbital period of 16 days) to 0.3 MJup with an orbital radius of ∼0.7 AU (and an orbital period of 710 days).
Can AGN feedback-driven star formation explain the size evolution of massive galaxies?

Observations indicate that massive galaxies at z~2 are more compact than galaxies of comparable mass at z~0, with effective radii evolving by a factor of ~3-5. This implies that galaxies grow significantly in size but relatively little in mass over the past ~10 Gyr. Two main physical models have been proposed in order to explain the observed evolution of massive galaxies: "mergers" and "puffing-up" scenarios. Here we introduce another possibility, and discuss the potential role of the central active galactic nucleus (AGN) feedback on the evolution of its host galaxy. We consider triggering of star formation, due to AGN feedback, with radiation pressure on dusty gas as the driving feedback mechanism. In this picture, stars are formed in the feedback-driven outflow at increasingly larger radii and build up the outer regions of the host galaxy. The resulting increase in size and stellar mass can be compared with the observed growth of massive galaxies. Star formation in the host galaxy is likely obscured due to dust extinction and reddening. We suggest a number of observational predictions of our model, and discuss possible implications for AGN feedback-driven star formation.