Miracle-dz/UniFAR-FTUs huggingface dataset:
Canonical Wick Rotations in 3-Dimensional Gravity

The authors develop a canonical Wick rotation-rescaling theory in 3-dimensional gravity. This includes: a simultaneous classification: this shows how maximal globally hyperbolic space times of arbitrary constant curvature, which admit a complete Cauchy surface and canonical cosmological time, as well as complex projective structures on arbitrary surfaces, are all different materializations of 'more fundamental' encoding structures; Canonical geometric correlations: this shows how space times of different curvature, that share a same encoding structure, are related to each other by canonical rescalings, and how they can be transformed by canonical Wick rotations in hyperbolic 3-manifolds, that carry the appropriate asymptotic projective structure. Both Wick rotations and rescalings act along the canonical cosmological time and have universal rescaling functions. These correlations are functorial with respect to isomorphisms of the respective geometric categories.
The spectral properties of Fermi blazars: the spectral sequence and unification of blazars

Using a large sample of blazars of the Fermi observations presented by Abdo et al., we constructed a sample of blazars including high energy peaked BL Lac objects (HBLs), low energy peaked BL Lac objects (LBLs) and flat-spectral radio quasars (FSRQs). These unique characteristics make it possible to unambiguously address the question of how HBLs, LBLs and FSRQs are related. In this paper, we investigated the relationship between X-ray and γ-ray spectral indices (αx−αγ), as well as the relationship between the broadband spectral indices (αro−αrx, αro−αox, αro−αxγ and αrx−αxγ) for this sample. The color-color diagram shows that there is a significant correlation between both quantities when all three subclasses of blazars are considered, which suggests that there is a unified scheme for blazars. On the other hand, the αx−αγ diagram reveals that three kinds of blazars have different spectral energy distributions: the trend of HBLs is different from that of FSRQs and LBLs, whereas FSRQs and LBLs have a similar trend, which hints that FSRQs and LBLs have similar spectral properties, but HBLs have distinct spectral properties. In addition, the broadband energy distributions also reveal the similar spectral properties with that of the αx−αγ diagram. The spectral properties revealed from the Fermi sample do not support the blazar sequence reported by Fossati et al. and Ghisellini et al.
Flat ring epimorphisms and universal localizations of commutative rings

We study different types of localisations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal localisation in the sense of Cohn and Schofield; and (b) when such universal localisations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialisation closed subset associated to a flat ring epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring epimorphisms are universal localisations. Moreover, it turns out that an answer to the question of when universal localisations are classical depends on the structure of the Picard group. We furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring epimorphism is a universal localisation. Finally, we explore several (counter)examples which highlight the necessity of our assumptions.
A Counterexample to the Bernhard–Jablan Unknotting Conjecture

Abstract We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at least that of the original knot, thus giving a counterexample to the Bernhard–Jablan Conjecture.
Study of the Earth’s free core nutation by tidal gravity data recorded with international superconducting gravimeters

By stacking high-precision tidal gravity observations obtained with superconducting gravimeters at six stations in China, Japan, Belgium, France, Germany and Finland, the local systematical discrepancies in the parameter fitting, caused by atmospheric, oceanic tidal loading and the other local environmental perturbations, are eliminated effectively. As a result, the resonance parameters of the Earth’s free core nutation are accurately determined. In this study, the eigenperiod of free core nutation is given as 429.0 sidereal days, which is in agreement with those published in the previous studies. It is about 30 sidereal days less than those calculated in theoretical models (about 460 sidereal days), which confirms the real ellipticity of the fluid core of the Earth to be about 5% larger than the one expected in assumption of hydrostatic equilibrium. The quality factor (Q value) of free core nutation is given as about 9543, which, compared with those determined before based on the body tide observations, is much larger, but more close to those obtained using the VLBI observations. The complex resonance strength is also determined as (−6.10×10−4, −0.01 ×10−4)°/h, which can principally describe the deformation characteristics of an anelastic mantle.
A Unified Adaptive Tensor Approximation Scheme to Accelerate Composite Convex Optimization

In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to assume any prior knowledge of the Lipschitz constants for the gradient, the Hessian and/or high-order derivatives. This is achieved by tuning the parameters used in the algorithm \textit{adaptively} in its process of progression, which has been successfully incorporated in high-order nonconvex optimization (CartisGouldToint2018, Birgin-Gardenghi-Martinez-Santos-Toint-2017). In general, we show that the adaptive high-order method has an iteration bound of $O\left( 1 / \epsilon^{1/(p+1)} \right)$ if the first $p$-th order derivative information is used in the approximation, which has the same iteration complexity as in that of the nonadaptive version in (Baes-2009, Nesterov-2018) where the Lipschitz constants are assumed to be known and the subproblems are assumed to be solved exactly. Thus, our results partially address the problem of incorporating adaptive strategies into the high-order {\it accelerated} methods raised by Nesterov in (Nesterov-2018), although our strategies cannot assure the convexity of the auxiliary problem and such adaptive strategies are already popular in high-order nonconvex optimization (CartisGouldToint2018, Birgin-Gardenghi-Martinez-Santos-Toint-2017). Our numerical experiment results show a clear effect of real acceleration displayed in the adaptive Newton's method with cubic regularization on a set of regularized logistic regression instances.
Molecular Characteristics of Atmospheric Organosulfates During Summer and Winter Seasons in Two Cities of Southern and Northern China

Organosulfates in atmospheric PM2.5 were investigated at two urban sites in Hefei and Shijiazhuang of southern and northern China during the summer and winter seasons of 2019–2020. Organic molecular composition was characterized using ultrahigh‐performance liquid chromatography coupled with Orbitrap mass spectrometry in negative electrospray ionization mode. There were overall 2,516–6,190 and 2,417–3,474 organic molecular formulas assigned on individual days in Hefei and Shijiazhuang, respectively, among which approximately 25%–41% were sulfur‐containing CHOS and CHONS compounds. The number of total organosulfates (including nitrooxy‐organosulfates) accounted for on average 84% and 79% of sulfur‐containing compounds during summer and winter in Shijiazhuang, which were much higher than those of 36% and 57% in Hefei. The higher fractions of organosulfates in the northern city of Shijiazhuang might be closely associated with the higher prevalence of SO2 and particulate sulfate. More than 96% in the peak areas of total organosulfates were present in aliphatic molecular structures instead of aromatics in both cities, suggesting the substantial contributions from biogenic precursors and anthropogenic long‐chain alkanes. The positive correlations (r: 0.33–0.96) of inorganic sulfate with the peak area abundance of organosulfates derived from isoprene and monoterpenes revealed the significant role of sulfate particles in the production of organosulfates. Particle acidity also correlated positively with these species during the winter in Hefei and summer in Shijiazhuang, yet negatively during other periods, indicating that additional reaction pathways would compete with acid‐catalyzed chemistry under atmospheric conditions limited by particle acidity or hydrocarbon precursors.
A New Strategy for Testing Structural Equation Models

One of the most important issues in structural equation modeling concerns testing model fit. We propose to retain the likelihood ratio test in combination with decision criteria that increase with sample size. Specifically, rooted in Neyman–Pearson hypothesis testing, we advocate balancing α- and β-error risks. This strategy has a number of desirable consequences and addresses several objections that have been raised against the likelihood ratio test in model evaluation. First, balancing error risks avoids logical problems with Fisher-type hypotheses tests when predicting the null hypothesis (i.e., model fit). Second, both types of statistical decision errors are controlled. Third, larger samples are encouraged (rather than penalized) because both error risks diminish as the sample size increases. Finally, the strategy addresses the concern that structural equation models cannot necessarily be expected to provide an exact description of real-world phenomena.
Markov numbers, Mather’s β function and stable norm

Fock (1997 (arXiv:dg-ga/9702018v3); Fock et al 2007 Handbook of Teichmüller Theory (Zürich: European Mathematical Society)) introduced an interesting function related to Markov numbers. We explain its relation to Federer–Gromov’s stable norm and Mather’s -function, and use this to study its properties. We prove that and its natural generalisations are differentiable at every irrational x and non-differentiable otherwise, by exploiting the relation with length of simple closed geodesics on the punctured or one-holed tori with the hyperbolic metric and the results by Bangert (1994 Calculus Variations Partial Differ. Equ. 2 49–63) and McShane–Rivin (1995 C. R. Acad. Sci. Paris I 320).
On a conjecture of Deutsch, Sagan, and Wilson

We prove a recent conjecture due to Deutsch, Sagan, and Wilson stating that the finite sequence obtained from the first p central trinomial coefficients modulo p by replacing nonzero terms by 1's is palindromic, for any prime number p > 3. Addendum: the result was proved before almost in the same way by Tony D. Noe: On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2. 7 this http URL
PMLiteDB: Streamlining Access Paths for High-Performance Persistent Memory Document Database Systems

The advent of byte-addressable persistent memory opens an important opportunity for document databases to read and write durable data fetching them into DRAM. Reaping the benefit of persistent memory is not straightforward, as existing document databases are tailored for disk storage. They assume that the disk and DRAM data movement dominates the performance. However, this paper points out that data indexing becomes the performance bottleneck when porting document databases to persistent memory. The paper proposes PMLiteDB, the first persistent memory document database with streamlined access paths. PMLiteDB introduces two techniques, direct reading and selective caching. Direct reading streamlines the translation from document IDs to the address of documents whenever possible by swizzling the IDs into persistent memory references. It guarantees to use only up-to-date persistent memory references when document movements invalidate associated references. Selective caching reduces data movements between DRAM and persistent memory by selectively caching only frequently accessed persistent memory data pages with a DRAM buffer. For other pages, the database loads data on them directly without caching. Compared to the design that adopts persistent memory as a fast disk without exploiting the byte-addressability, PMLiteDB achieves 2.33× on average and up to 6.18× speedup.
Intracranial Control With Combination BRAF and MEK Inhibitor Therapy in Patients With Metastatic Melanoma

Purpose/Objectives Combination BRAF (vemurafenib, dabrafenib, or encorafenib) plus MEK (trametinib, cobimetinib, or binimetinib) inhibitor therapy is now widely used in the treatment of metastatic melanoma. However, data for intracranial response to these drugs are limited. We aimed to evaluate the intracranial efficacy of BRAF plus MEK inhibitors in patients with BRAF-mutant melanoma with brain metastases (BM) and to determine patterns of failure of these new agents to inform optimal integration of local intracranial therapy. Materials and methods We retrospectively reviewed charts of patients with BRAF-mutant melanoma with metastasis to the brain with at least one untreated brain metastasis at the time of initiation of BRAF plus MEK inhibitors at our institution from 2006 to 2020. We collected per-patient and per-lesion data on demographics, treatment modality, and outcomes. The cumulative incidence of local (LF), distant intracranial (DF), and extracranial failure (EF) were calculated with competing risk analysis with death as a competing risk and censored at the last brain MRI follow-up. LF was calculated on a per-lesion basis while DF and EF were calculated on a per-patient basis. DF was defined as any new intracranial lesions. Overall survival (OS) was analyzed using Kaplan-Meier. Logistic regression was used to identify predictors for LF. Results We identified 10 patients with 63 untreated brain metastases. The median age was 50.5 years. The median sum of the diameters of the five largest untreated brain metastases per patient was 20 mm (interquartile range 15-39 mm) and the median diameter for all measurable lesions was 4 mm. Median follow-up time was 9.0 months (range 1.4 months-46.2 months). Median OS was 13.6 months. The one-year cumulative incidence of LF, DF, and EF was 17.1%, 88.6, and 71.4%, respectively. The median time to LF, DF, and EF from the start of BRAF plus MEK inhibitors was 9.0 months, 4.7 months, and 7.0 months, respectively. The larger size of the BM was associated with LF on univariate analysis (odds ratio 1.13 per 1 mm increase in diameter, 95% confidence interval 1.019 to 1.308, p<0.02). Two (20%) patients eventually received stereotactic radiosurgery, and 2 (20%) received whole-brain radiotherapy for intracranial progression. Conclusion Although patients with BRAF-mutant melanoma with BM had fair local control on BRAF plus MEK inhibitors, the competing risk of death and distant intracranial and extracranial progression was high. Patients with larger brain metastases may benefit from local therapy.
Integrating nephelometer with a low truncation angle and an extended calibration scheme

A resurgence of interest has arisen lately in the use of reciprocal nephelometers in aerosol instrumentation that also measures other optical properties such as extinction by the cavity ringdown method and absorption by the photoacoustic method. This paper provides fresh insight into these nephelometers from perspectives of instrument component evaluation, intra-instrument comparison and basic calibration. In particular, a 4° truncation angle reciprocal integrating nephelometer (IN) is described and demonstrated. An experimental setup for the measurement of the IN sensor cosine response is developed and described. To calibrate the IN, the sampling volume can be filled with an aerosol with negligible light absorption (e.g., ammonium sulfate), and scattering and extinction coefficients are monitored simultaneously. The performance of the IN is evaluated, at a wavelength of 532 nm, through extensive comparison with a 1° truncation angle integrating sphere integrating nephelometer (ISIN) that operates at the same wavelength. The intercomparison included measurements of ambient aerosol, kerosene soot, ammonium sulfate aerosol, NaCl aerosol and CO2 gas. Results of a linear regression analysis indicate an agreement between the IN and the ISIN within ±8%. The main advantages of the IN over the ISIN are its fast time response, relatively large signal-to-noise (S/N) ratio and design simplicity.
Hardy-Sobolev inequality with singularity a curve

We consider a bounded domain $\Omega$ of $\mathbb{R}^N$, $N\geq 3$, and $h$ a continuous function on $\Omega$. Let $\Gamma$ be a closed curve contained in $\Omega$. We study existence of positive solutions $u\in H^1_0(\Omega)$ to the equation $$ -\Delta u+h u=\rho^{-\sigma}_\Gamma u^{2^*_\sigma-1} \qquad \textrm{ in } \Omega $$ where $2^*_\sigma:=\frac{2(N-\sigma)}{N-2}$, $\sigma\in (0,2)$, and $\rho_\Gamma$ is the distance function to $\Gamma$. For $N\geq 4$, we find a sufficient condition, given by the local geometry of the curve, for the existence of a ground-state solution. In the case $N=3$, we obtain existence of ground-state solution provided the trace of the regular part of the Green of $-\Delta+h$ is positive at a point of the curve.
Using Almost-everywhere theorems from Analysis to Study Randomness

We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than \ML\ (ML) randomness. We establish several equivalences. Given a ML-random real $z$, the additional randomness strengths needed for the following are equivalent. \n (1) all effectively closed classes containing $z$ have density $1$ at $z$. \n (2) all nondecreasing functions with uniformly left-c.e. \ increments are differentiable at $z$. \n (3) $z$ is a Lebesgue point of each lower semicomputable integrable function. We also consider convergence of left-c.e. \ martingales, and convergence in the sense of Birkhoff's pointwise ergodic theorem. Lastly we study randomness notions for density of $\Pi^0_n$ and $\Sigma^1_1$ classes.
Holder estimates for solutions of integra-differential equations like the fractional laplace

We provide a purely analytical proof of Holder continuity for harmonic functions with respect to a class of integro-differential equations like the ones associated with purely jump processes. The assumptions on the operator are more flexible than in previous works. Our assumptions include the case of an operator with variable order, without any continuity assumption in that order.
Lie Calculus

We explain that general diﬀerential calculus and Lie theory have a common founda-tion: Lie Calculus is diﬀerential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher order theory naturally involves higher algebra ( n -fold groupoids).
POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES

We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geqslant 3$ , $\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$ $=f(x)$ almost everywhere with respect to Lebesgue measure for all $f\in H^{s}(\mathbb{R}^{n})$ provided that $s>(n+1)/2(n+2)$ . The proof uses linear refined Strichartz estimates. We also prove a multilinear refined Strichartz using decoupling and multilinear Kakeya.
Comparison of predicted ground-level airborne radionuclide concentrations to measured values resulting from operation of the Los Alamos Meson Physics Facility

Abstract : A comparison study of measured and predicted downwind radionuclide concentrations from the Los Alamos Meson Physics Facility (LAMPF) was performed. The radionuclide emissions consist primarily of the radioisotopes 11C, 13N, and 150. The gases, vented to the outside environment by a stack located at the facility, potentially increase the radiation exposure at the facility boundary. Emission rate, meteorological, and radiation monitoring station data were collected between September 26, 1992 and October 3, 1992. The meteorological and emission data were input to the Clean Air Act Assessment Package-1988 (CAP88-PC) computer code. The downwind radionuclide air concentrations predicted by the code were compared to the air concentrations measured by the monitoring stations. The code was found to slightly over-predict downwind concentrations during unstable atmospheric conditions. For stable atmospheric conditions, the code was not useful for predicting downwind air concentrations. This is thought to be due to an underestimation of horizontal dispersion.
ACOUSTIC LOCALIZATION IN BUBBLY LIQUID MEDIA

Acoustic wave propagation in liquid media containing many air-filled bubbles is ab initio considered. A self-consistent method is used to derive a set of coupled equations describing rigorously the multiple scattering of waves in such media. The wave transmission and backscattering are then solved exactly. The numerical results indicate localization of acoustic waves in a range of frequency.
Recent advances in responsive membrane functionalization approaches and applications

ABSTRACT In recent years, significant advances have been made in the field of functionalized membranes. With the functionalization using various materials, such as polymers and enzymes, membranes can exhibit property changes in response to an environmental stimulation, such as heat, light, ionic strength, or pH. The resulting responsive nature allows for an increased breadth of membrane uses, due to the developed functionalization properties, such as smart-gating filtration for size-selective water contaminant removal, self-cleaning antifouling surfaces, increased scalability options, and highly sensitive molecular detection. In this review, new advances in both fabrication and applications of functionalized membranes are reported and summarized, including temperature-responsive, pH-responsive, light-responsive, enzyme-functionalized, and two-dimensional material-functionalized membranes. Specific emphasis was given to the most recent technological improvements, current limitations, advances in characterization techniques, and future directions for the field of functionalized membranes.
ON ITERATED TWISTED TENSOR PRODUCTS OF ALGEBRAS

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors and give some examples of algebras that can be described within our theory. We prove a certain result (called "invariance under twisting") for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrel.