Miracle-dz/UniFAR-FTUs huggingface dataset:
Castelnuovo-Mumford regularity and the discreteness of $F$-jumping coefficients in graded rings

In this paper we show that the sets of F-jumping coefficients of ideals form discrete sets in certain graded F-finite rings. We do so by giving a criterion based on linear bounds for the growth of the Castelnuovo-Mumford regularity of certain ideals. We further show that these linear bounds exists for one-dimensional rings and for ideals of (most) two-dimensional domains. We conclude by applying our technique to prove that all sets of F-jumping coefficients of all ideals in the determinantal ring given as t he quotient by 2 × 2 minors in a 2 × 3 matrix of indeterminates form discrete sets.
Is there really a dichotomy in AGN jet power

To gain new insights into the radio-loud/radio-quiet dichotomy reported for active galactic nuclei, we examine radio loudness as a function of Eddington ratio for a previously published sample of 199 AGN from five different populations. After initially considering radio loudnesses derived using total radio luminosities, we repeat the investigation using core radio luminosities only, applying a previously established mass correction for these core luminosities. In both cases, for Eddington ratios < 1 per cent, Fanaroff-Riley type I and broad-line radio galaxies are on average more radio-loud than Seyfert and low-ionization nuclear emission-line region galaxies. However, the distribution of radio loudnesses for the mass-corrected, core-only sample is much narrower than that of the clearly bimodal total radio loudness distribution. The advantages and disadvantages of using core- or lobe-dominated radio luminosity as a measure of instantaneous jet power are discussed. We furthermore compare the core and total radio luminosities for the entire sample, as well as illustrating the importance of the mass term by comparing the AGN with a sample of black hole X-ray binaries. We conclude that if the mass-corrected core radio luminosity is a good measure of jet power, then black hole spin may have considerably less impact on jet power than previously reported, or that our sample does not include the extremes of spin. If the spread in jet power is small then we suggest that characteristics of the ambient environment and/or the radio source age could be equally as important in producing a radio-loud/radio-quiet dichotomy seen in total radio luminosity.
Modified Entropic Force

The theory of statistical thermodynamics tells us the equipartition law of energy does not hold in the limit of very low temperatures. It is found the Debye model is very successful in explaining the experimental results for most of the solid objects. Motivated by this fact, we modify the entropic force formula which is proposed very recently. Since the Unruh temperature is proportional to the strength of the gravitational field, so the modified entropic force formula is an extension of the Newtonian gravity to the weak field. On the contrary, general relativity extends Newtonian gravity to the strong field case. Corresponding to Debye temperature, there exists a Debye acceleration g{sub D}. It is found the Debye acceleration is g{sub D}=10{sup -15} N kg{sup -1}. This acceleration is very much smaller than the gravitational acceleration 10{sup -4} N kg{sup -1} which is felt by Neptune and the gravitational acceleration 10{sup -10} N kg{sup -1} felt by the Sun. Therefore, the modified entropic force can be very well approximated by the Newtonian gravity in the Solar System and in the Galaxy. With this Debye acceleration, we find the current cosmic speeding up can be explained without invoking any kind of dark energy.
Abnormal amygdala functional connectivity and deep learning classification in multifrequency bands in autism spectrum disorder: A multisite functional magnetic resonance imaging study

Previous studies have explored resting‐state functional connectivity (rs‐FC) of the amygdala in patients with autism spectrum disorder (ASD). However, it remains unclear whether there are frequency‐specific FC alterations of the amygdala in ASD and whether FC in specific frequency bands can be used to distinguish patients with ASD from typical controls (TCs). Data from 306 patients with ASD and 314 age‐matched and sex‐matched TCs were collected from 28 sites in the Autism Brain Imaging Data Exchange database. The bilateral amygdala, defined as the seed regions, was used to perform seed‐based FC analyses in the conventional, slow‐5, and slow‐4 frequency bands at each site. Image‐based meta‐analyses were used to obtain consistent brain regions across 28 sites in the three frequency bands. By combining generative adversarial networks and deep neural networks, a deep learning approach was applied to distinguish patients with ASD from TCs. The meta‐analysis results showed frequency band specificity of FC in ASD, which was reflected in the slow‐5 frequency band instead of the conventional and slow‐4 frequency bands. The deep learning results showed that, compared with the conventional and slow‐4 frequency bands, the slow‐5 frequency band exhibited a higher accuracy of 74.73%, precision of 74.58%, recall of 75.05%, and area under the curve of 0.811 to distinguish patients with ASD from TCs. These findings may help us to understand the pathological mechanisms of ASD and provide preliminary guidance for the clinical diagnosis of ASD.
Development of eosinophilic granulomatosis with polyangiitis during the clinical course of microscopic polyangiitis: A case report

Rationale: Eosinophilic granulomatosis with polyangiitis (EGPA) is belongs to the antineutrophil cytoplasmic autoantibody (ANCA)-associated vasculitis (AAV) subgroups. EGPA, unlike other subgroups of AAV, including microscopic polyangiitis (MPA) and granulomatosis with polyangiitis, has the unique feature that both ANCA and eosinophilic inflammation are involved in its pathogenesis. Although AAV often relapses, there are currently no reports of EGPA developing during other subgroups of AAV. Herein, we document a case of EGPA that developed during the clinical course of MPA. Patient concerns: A 61-year-old Japanese woman was diagnosed with MPA based on interstitial lung disease and myeloperoxidase-ANCA positivity. After starting immunosuppression therapy, including prednisolone and tacrolimus, she was expected to achieve clinical remission. Nonetheless, she occasionally experienced MPA relapse, which required an increased prednisolone dose, rituximab, intravenous cyclophosphamide, and plasma exchange. Three years after MPA onset, she developed renal amyloidosis; thus, subcutaneous tocilizumab was added to her regimen. Following clinical remission, the administration interval of her subcutaneous tocilizumab therapy was extended and immunosuppressants were discontinued. She then developed bronchial asthma and mild eosinophilia (eosinophilic count: ~1000/μL). Further, a year later, she underwent total hip replacement using a titanium implant. Subsequently, she developed abnormal sensation in both hands, numbness, and muscle weakness, as well as palpable purpura and massive eosinophilia (eosinophilic count: ~8500/μL). Diagnosis: We diagnosed the patient with EGPA based on 5 items (asthma, multiple mononeuropathies, sinus abnormality, and extravascular eosinophils) of the 1990 American College of Rheumatology classification criteria. Interventions: We administered 400 mg/kg intravenous immunoglobulin for 5 consecutive days, 300 mg mepolizumab subcutaneously every 4 weeks, and 40 mg/day prednisolone following pulsed methylprednisolone therapy (1000 mg/day for 3 consecutive days). Outcomes: After these treatments, the patient’s symptoms improved, and eosinophilic count and inflammatory markers declined. Lessons: The present case suggests that EGPA can be induced by the development of eosinophilic inflammation in other subgroups of AAV.
DISCOVERY OF FOUR GRAVITATIONALLY LENSED QUASARS FROM THE SLOAN DIGITAL SKY SURVEY

We present the discovery of four gravitationally lensed quasars selected from the spectroscopic quasar catalog of the Sloan Digital Sky Survey (SDSS). We describe imaging and spectroscopic follow-up observations that support the lensing interpretation of the following four quasars: SDSS J0832+0404 (image separation θ = 1.″98, source redshift zs = 1.115, lens redshift zl = 0.659); SDSS J1216+3529 (θ = 1.″49, zs = 2.012); SDSS J1322+1052 (θ = 2.″00, zs = 1.716); and SDSS J1524+4409 (θ = 1.″67, zs = 1.210, zl = 0.320). Each system has two lensed images. We find that the fainter image component of SDSS J0832+0404 is significantly redder than the brighter component, perhaps because of differential reddening by the lensing galaxy. The lens potential of SDSS J1216+3529 might be complicated by the presence of a secondary galaxy near the main lensing galaxy.
Topological invariants from nonrestricted quantum groups

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this case we show that these invariants are equal and extend to what we call a relative Homotopy Quantum Field Theory which is a branch of the Topological Quantum Field Theory founded by E. Witten and M. Atiyah. Our main examples of relative spherical categories are the categories of finite dimensional weight modules over non-restricted quantum groups considered by C. De Concini, V. Kac, C. Procesi, N. Reshetikhin and M. Rosso. These categories are not semi-simple and have an infinite number of non-isomorphic irreducible modules all having vanishing quantum dimensions. We also show that these categories have associated ribbon categories which gives rise to re-normalized link invariants. In the case of sl(2) these link invariants are the Alexander-type multivariable invariants defined by Y. Akutsu, T. Deguchi, and T. Ohtsuki.
The central black hole mass of the high‐σ but low‐bulge‐luminosity lenticular galaxy NGC 1332★

The masses of the most massive supermassive black holes (SMBHs) predicted by the M BH -σ and M BH -L relations appear to be in conflict. Which of the two relations is the more fundamental one remains an open question. NGC 1332 is an excellent example that represents the regime of conflict. It is a massive lenticular galaxy which has a bulge with a high velocity dispersion σ of ~320 km s -1 ; bulge-disc decomposition suggests that only 44 per cent of the total light comes from the bulge. The M BH -σ and the M BH -L predictions for the central black hole mass of NGC 1332 differ by almost an order of magnitude. We present a stellar dynamical measurement of the SMBH mass using an axisymmetric orbit superposition method. Our SINFONI integral-field unit (IFU) observations of NGC 1332 resolve the SMBH's sphere of influence which has a diameter of ~0.76 arcsec. The σ inside 0.2 arcsec reaches ~400 km s -1 . The IFU data allow us to increase the statistical significance of our results by modelling each of the four quadrants separately. We measure an SMBH mass of (1.45 ± 0.20) x 10 9 M ⊙ with a bulge mass-to-light ratio of 7.08 ± 0.39 in the R band. With this mass, the SMBH of NGC 1332 is offset from the M BH -L relation by a full order of magnitude but is consistent with the M BH -σ relation.
C*-algebras of separated graphs

The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in terms of their ideal theory and K-theory, mainly in the case of partitions by finite sets. The groups $K_0(C^*(E,C))$ and $K_1(C^*(E,C))$ are completely described via a map built from an adjacency matrix associated to $(E,C)$. One application determines the K-theory of the C*-algebras $U^{\text{nc}}_{m,n}$, confirming a conjecture of McClanahan. A reduced C*-algebra $\Cstred(E,C)$ is also introduced and studied. A key tool in its construction is the existence of canonical faithful conditional expectations from the C*-algebra of any row-finite graph to the C*-subalgebra generated by its vertices. Differences between $\Cstred(E,C)$ and $C^*(E,C)$, such as simplicity versus non-simplicity, are exhibited in various examples, related to some algebras studied by McClanahan.
Nowhere-zero flows on signed eulerian graphs

This paper is devoted to a detailed study of nowhere-zero flows on signed eulerian graphs. We generalise the well-known fact about the existence of nowhere-zero 2flows in eulerian graphs by proving that every signed eulerian graph that admits an integer nowhere-zero flow has a nowhere-zero 4-flow. We also characterise signed eulerian graphs with flow number 2, 3, and 4, as well as those that do not have an integer nowhere-zero flow. Finally, we discuss the existence of nowhere-zero A-flows on signed eulerian graphs for an arbitrary abelian group A.
Reducibility of the Cohen-Wales representation of the Artin group of type $D_n$

Using knot theory, we construct a linear representation of the CGW algebra of type $D_n$. This representation has degree $n^2-n$, the number of positive roots of a root system of type $D_n$. We show that the representation is generically irreducible, but that when the parameters of the algebra are related in a certain way, it becomes reducible. As a representation of the Artin group of type $D_n$, this representation is equivalent to the faithful linear representation of Cohen-Wales. We give a reducibility criterion for this representation as well as a conjecture on the semisimplicity of the CGW algebra of type $D_n$. Our proof is computer-assisted using Mathematica.
Oscillations and concentrations up to the boundary

Abstract. Oscillations and concentrations in sequences of gradients {∇uk}, bounded in L(Ω;R ) if p > 1 and Ω ⊂ R is a bounded domain with the extension property in W , and their interaction with local integral functionals can be described by a generalization of Young measures due to DiPerna and Majda. We characterize such DiPerna-Majda measures, thereby extending a result by Ka lamajska and Kruž́ık [13], where the full characterization was possible only for sequences subject to a fixed Dirichlet boundary condition. As an application we state a relaxation result for noncoercive multiple-integral functionals.
On the Chow motive of an abelian scheme with non-trivial endomorphisms

Let X be an abelian scheme over a base variety S with endomorphism algebra D. We prove that the relative Chow motive R(X/S) has a canonical decomposition as a direct sum of motives R (�) whereruns over an explicitly determined finite set of irreducible representations of the group D op,� , such that R (�) , seen as a functor from Chow motives to D op,� -representations, is �-isotypic. Our decomposition refines the motivic decomposition of Deninger and Murre, as well as Beauville's decomposition of the Chow group. The second main result is that we construct a canonical generalized motivic Lefschetz decomposition. Inspired by work of Looijenga and Lunts in (17), the role of sl2 in the classical theory is here replaced by a larger Lie algebra, generated by all Lefschetz and Lambda operators associated to non-degenerate line bundles. We construct an action of this larger Lie algebra on R(X/S) and deduce from this a generalized Lefschetz decomposition. We also give a precise structure result for the Lefschetz components that arise. As an application of our techniques, we provide a positive answer to a question of Claire Voisin concerning the analogue for abelian varieties of a conjecture of Beauville. AMS 2010 Mathematics subject classification: 14C15, 14K05
Torque-Induced Rotational Dynamics in Polymers: Torsional Blobs and Thinning

By using the blob theory and computer simulations, we investigate the properties of a linear polymer performing a stationary rotational motion around a long impenetrable rod. In particular, in the simulations the rotation is induced by a torque applied to the end of the polymer that is tethered to the rod. Three different regimes are found, in close analogy with the case of polymers pulled by a constant force at one end. For low torques the polymer rotates maintaining its equilibrium conformation. At intermediate torques the polymer assumes a trumpet shape, being composed by blobs of increasing size. At even larger torques the polymer is partially wrapped around the rod. We derive several scaling relations between various quantities as angular velocity, elongation, and torque. The analytical predictions match the simulation data well. Interestingly, we find a “thinning” regime where the torque has a very weak (logarithmic) dependence on the angular velocity. We discuss the origin of this behavior, which h.
Schwinger Mechanism and Hawking Radiation as Quantum Tunneling

The common interpretation of the Hawking radiation as quantum tunneling has some ambiguity such as coordinate-dependence of tunneling rate and non-invariance of the action under canonical transformations. It is shown that the tunneling process of black holes can be successfully described by Rindler coordinates in analogy with the Schwinger mechanism for pair production. We study the tunneling process of a charged black hole and a BTZ black hole.
LHCb pentaquarks as a baryon- ψ ( 2 S ) bound state: Prediction of isospin- 3 2 pentaquarks with hidden charm

The pentaquark ${P}_{c}^{+}(4450)$ recently discovered by the LHCb has been interpreted as a bound state of $\mathrm{\ensuremath{\Psi}}(2S)$ and a nucleon. The charmonium-nucleon interaction which provides the binding mechanism is given, in the heavy-quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor. In this work, we show in a model-independent way, by exploring general properties of the effective interaction, that $\mathrm{\ensuremath{\Psi}}(2S)$ can form bound states with a nucleon and $\mathrm{\ensuremath{\Delta}}$. Using the Skyrme model to evaluate the effective interaction in the large-${N}_{c}$ limit and estimate $1/{N}_{c}$ corrections, we confirm the results from prior work which were based on a different effective model (chiral quark soliton model). This shows that the interpretation of ${P}_{c}^{+}(4450)$ is remarkably robust and weakly dependent on the details of the effective theories for the nucleon energy-momentum tensor. We explore the formalism further and present robust predictions of isospin-$\frac{3}{2}$ bound states of $\mathrm{\ensuremath{\Psi}}(2S)$ and $\mathrm{\ensuremath{\Delta}}$ with masses around 4.5 GeV and widths around 70 MeV. The approach also predicts broader resonances in the $\mathrm{\ensuremath{\Psi}}(2S)\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}$ channel at 4.9 GeV with widths of the order of 150 MeV. We discuss in which reactions these new isospin-$\frac{3}{2}$ pentaquarks with hidden charm can be observed.
Secondary metabolites from Gentiana cruciata L. and their anti-inflammatory and analgesic activities

Abstract A previously unreported secoiridoid glycoside, cruciatoside (1) was isolated from the aerial parts of Gentiana cruciata L. along with ten known compounds eustomoside (2), eustomorusside (3), gentiopicroside (4), 6'-O-β-D-glucopyranosyl gentiopicroside (5), loganic acid (6), isoorientin (7), isovitexin (8), isovitexin 2''-(E)-ferulate (9), mangiferin (10), and 2-methyl-inositol (11). The chemical structures of the isolates were elucidated based on extensive 1 D and 2 D NMR experiments as well as HRMS analysis. All isolates were evaluated for their in vitro anti-inflammatory and analgesic activities. Compounds 9, 4, and 7 (200 µM) showed moderate anti-inflammatory activity by inhibiting nitrite production from LPS-induced RAW 264.7 macrophage cells, with the inhibition rates of 39.5%, 25.8% and 22.9% respectively without exhibiting substantial cytotoxicity. Besides, 1, 2, 4, and 7 exerted the highest decrease in IL-6 levels. Moreover, compound 4 showed in vitro analgesic activity by decreasing the PGE2 level comparable to the reference drugs. Graphical Abstract
An introduction to the Vainshtein mechanism

We introduce the Vainshtein mechanism which plays a crucial role in massive gravities, as well as in related theories such as Galileons and their extensions. This mechanism, also known as k-mouflage, allows to hide via nonlinear effects—typically for source distances smaller than a so-called Vainshtein radius which depends on the source and on the theory considered—some degrees of freedom whose effects are then only left important at large distances, e.g. for cosmology. It is introduced here in nonlinear Fierz–Pauli theories (massive gravities), including the dRGT theories, in their decoupling limits, as well as in other models such as the DGP model or generalized Galileons. This presentation is self-contained, and before discussing the Vainshtein mechanism we introduce some useful results and concepts concerning massive gravity, such as the vDVZ discontinuity, the decoupling limits or the Boulware–Deser ghost.
Physical Activity Trends Among Adults in a National Mobile Health Program: A Population-Based Cohort Study of 411,528 Adults

Abstract Physical inactivity is a global public health challenge, and effective, large-scale interventions are needed. We examined the effectiveness of a population-wide mobile health (mHealth) intervention in Singapore, National Steps Challenge Season 3 (NSC3) and 2 booster challenges (Personal Pledge and Corporate Challenge). The study includes 411,528 participants. We used regression discontinuity design and difference-in-difference with fixed-effects regression to examine the association of NSC3 and the additional booster challenges on daily step counts. Participants tended to be female (58.5%), with an average age of 41.5 years (standard deviation, 13.9) and body mass index (weight (kg)/height (m)2) of 23.8 (standard deviation, 4.5). We observed that NSC3 was associated with a mean increase of 1,437 steps (95% confidence interval (CI): 1,408, 1,467) per day. Enrollments in Personal Pledge and Corporate Challenge were associated with additional mean increases of 1,172 (95% CI: 1,123, 1,222) and 896 (95% CI: 862, 930) steps per day, respectively. For NSC3, the associated mean increase in the step counts across different sex and age groups varied, with greater increases for female participants and those in the oldest age group. We provide real-world evidence suggesting that NSC3 was associated with improvements in participants’ step counts. Results suggest NSC3 is an effective and appealing population-wide mHealth physical activity intervention.
Robust correlators

Context. Radio frequency interference (RFI) already limits the sensitivity of existing radio telescopes in several frequency bands and may prove to be an even greater obstacle for future generation instruments to overcome. Aims. I aim to create a structure of radio astronomy correlators which will be statistically stable (robust) in the presence of interference. Methods. A statistical analysis of the mixture of system noise + signal noise + RFI is proposed here which could be incorporated into the block diagram of a correlator. Order and rank statistics are especially useful when calculated in both temporal and frequency domains. Results. Several new algorithms of robust correlators are proposed and investigated here. Computer simulations and processing of real data demonstrate the e ﬃ cacy of the proposed algorithms.