Miracle-dz/UniFAR-FTUs huggingface dataset:
Reducing sub-modules of the Bergman module $\mathbb A^{(\lambda)}(\mathbb D^n)$ under the action of the symmetric group

The weighted Bergman spaces on the polydisc, $\mathbb A^{(\lambda)}(\mathbb D^n)$, $\lambda>0,$ splits into orthogonal direct sum of subspaces $\mathbb P_{\boldsymbol p}\big(\mathbb A^{(\lambda)}(\mathbb D^n)\big)$ indexed by the partitions $\boldsymbol p$ of $n,$ which are in one to one correspondence with the equivalence classes of the irreducible representations of the symmetric group on $n$ symbols. In this paper, we prove that each sub-module $\mathbb P_{\boldsymbol p}\big(\mathbb A^{(\lambda)}(\mathbb D^n)\big)$ is a locally free Hilbert module of rank equal to square of the dimension $\chi_{\boldsymbol p}(1)$ of the corresponding irreducible representation. It is shown that given two partitions $\boldsymbol p$ and $\boldsymbol q$, if $\chi_{\boldsymbol p}(1) \ne \chi_{\boldsymbol q}(1),$ then the sub-modules $\mathbb P_{\boldsymbol p}\big (\mathbb A^{(\lambda)}(\mathbb D^n)\big )$ and $\mathbb P_{\boldsymbol q}\big (\mathbb A^{(\lambda)}(\mathbb D^n)\big )$ are not equivalent. We prove that for the trivial and the sign representation corresponding to the partitions $\boldsymbol p = (n)$ and $\boldsymbol p = (1,\ldots,1)$, respectively, the sub-modules $\mathbb P_{(n)}\big(\mathbb A^{(\lambda)}(\mathbb D^n)\big)$ and $\mathbb P_{(1,\ldots,1)}\big(\mathbb A^{(\lambda)}(\mathbb D^n)\big)$ are inequivalent. In particular, for $n=3$, we show that all the sub-modules in this decomposition are inequivalent.
On the {\L}ojasiewicz Exponent of the Quadratic Sphere Constrained Optimization Problem

In this paper, we prove that the global version of the Łojasie wicz gradient inequality holds for the quadratic sphere con strained optimization problem with exponent θ = 3 4 . An example from [ 29] inspired by [4] shows thatθ = 3 4 is tight. This is the first Łojasiewicz gradient inequality established for the sphere constrained optimiz ation problem with a linear term.
Locally standard torus actions and h'-vectors of simplicial posets

We consider the orbit type filtration on a manifold $X$ with locally standard action of a compact torus and the corresponding homological spectral sequence $(E_X)^r_{*,*}$. If all proper faces of the orbit space $Q=X/T$ are acyclic, and the free part of the action is trivial, this spectral sequence can be described in full. The ranks of diagonal terms are equal to the $h'$-numbers of the Buchsbaum simplicial poset $S_Q$ dual to $Q$. Betti numbers of $X$ depend only on the orbit space $Q$ but not on the characteristic function. If $X$ is a slightly different object, namely the model space $X=(P\times T^n)/\sim$ where $P$ is a cone over Buchsbaum simplicial poset $S$, we prove that $\dim (E_X)^{\infty}_{p,p} = h''_p(S)$. This gives a topological evidence for the fact that $h''$-numbers of Buchsbaum simplicial posets are nonnegative.
Effects of Irvingia gabonensis Extract on Metabolism, Antioxidants, Adipocytokines, Telomere Length, and Aerobic Capacity in Overweight/Obese Individuals

We investigated the effects of Irvingia gabonensis (IG) kernel extract on the metabolism, adiposity indices, redox status, inflammation, adipocytokines, blood leukocyte relative telomere length (RTL), and aerobic capacity of overweight/obese individuals. All participants used the first 12-week phase to monitor body weight. They were then randomly divided into two groups: (1) 300 mg IG or (2) placebo (PLA). Both groups took one tablet per day for 12 weeks. The variables were measured before supplementation and after 3, 6, and 12 weeks of supplementation. RTL and aerobic capacity were measured before and after 12 weeks. Compared with the PLA, the IG increased plasma vitamin C after supplementation at 6 (p < 0.01) and 12 weeks (p < 0.05) and serum adiponectin after 3 weeks (p < 0.05). Compared with before supplementation, plasma malondialdehyde in the IG and serum leptin in the PLA were decreased after 12-week supplementation, without any differences between the groups. There were no differences between groups with respect to metabolism, inflammation, RTL, and aerobic capacity after the supplementation. We suggest that 12-week daily IG supplementation improved plasma vitamin C and adiponectin. The findings show the possible mechanism contributing to the effect of IG supplementation on a reduction in obesity-related complications.
Riesz bases, Meyer's quasicrystals, and bounded remainder sets

We consider systems of exponentials with frequencies belonging to simple quasicrystals in $\mathbb{R}^d$. We ask if there exist domains $S$ in $\mathbb{R}^d$ which admit such a system as a Riesz basis for the space $L^2(S)$. We prove that the answer depends on an arithmetical condition on the quasicrystal. The proof is based on the connection of the problem to the discrepancy of multi-dimensional irrational rotations, and specifically, to the theory of bounded remainder sets. In particular it is shown that any bounded remainder set admits a Riesz basis of exponentials. This extends to several dimensions (and to the non-periodic setting) the results obtained earlier in dimension one.
Imprimitivity theorems for weakly proper actions of locally compact groups

In a recent paper the authors introduced universal and exotic generalized fixed-point algebras for weakly proper group actions on $C^{\ast }$-algebras. Here we extend the notion of weakly proper actions to actions on Hilbert modules. As a result we obtain several imprimitivity theorems establishing important Morita equivalences between universal, reduced, or exotic crossed products and appropriate universal, reduced, or exotic fixed-point algebras, respectively. In particular, we obtain an exotic version of Green’s imprimitivity theorem and a very general version of the symmetric imprimitivity theorem by weakly proper actions of product groups $G\times H$. In addition, we study functorial properties of generalized fixed-point algebras for equivariant categories of $C^{\ast }$-algebras based on correspondences.
Motivic and p-adic Localization Phenomena

In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the $p$-adic pushforward of the Haar measure under a hypertoric moment map $\mu$. This leads to an explicit formula for the Igusa zeta function $\FI_\mu(s)$ of $\mu$, and in particular to a small set of candidate poles for $\FI_\mu(s)$. We also study various properties of the residue at the largest pole of $\FI_\mu(s)$. Finally, if $\mu$ is constructed out of a quiver $\Gamma$ we give a conjectural description of this residue in terms of indecomposable representations of $\Gamma$ over finite depth rings. The connections between these different results is the method of proof. At the heart of each theorem lies a motivic or $p$-adic volume computation, which is only possible due to some surprising cancellations. These cancellations are reminiscent of a result in classical symplectic geometry by Duistermaat and Heckman on the localization of the Liouville measure, hence the title of the thesis.
Hitchin Pairs for non-compact real Lie groups

Hitchin pairs on Riemann surfaces are generalizations of Higgs bundles, allowing the Higgs field to be twisted by an arbitrary line bundle. We consider this generalization in the context of $G$-Higgs bundles for a real reductive Lie group $G$. We outline the basic theory and review some selected results, including recent results by Nozad and the author arXiv:1602.02712 [math.AG] on Hitchin pairs for the unitary group of indefinite signature $\mathrm{U}(p,q)$.
Feedback Nash Equilibrium With Packet Dropouts in Networked Control Systems

This brief is concerned with the feedback Nash equilibrium for networked control systems (NCSs) with packet dropouts. The packet dropouts occur when the state information is transformed via a wireless network, causing the fall that the state information is unavailable to design the feedback Nash equilibrium. The main contribution of this brief is that the necessary and sufficient condition for the existence of feedback Nash equilibrium is presented. The key is that by decoupling solving the forward and backward difference equations (FBDEs), the analytical solutions of the two controllers are given in terms of the two coupled Riccati equations.
A Max-Cut approximation using a graph based MBO scheme

The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the vertex set of G into two disjoint subsets. For an unweighted graph, the size of the cut is the number of edges that have one vertex on either side of the partition; we also consider a weighted version of the problem where each edge contributes a nonnegative weight to the cut. We introduce the signless Ginzburg-Landau functional and prove that this functional Gamma-converges to a Max-Cut objective functional. We approximately minimize this functional using a graph based signless Merriman-Bence-Osher scheme, which uses a signless Laplacian. We show experimentally that on some classes of graphs the resulting algorithm produces more accurate maximum cut approximations than the current state-of-the-art approximation algorithm. One of our methods of minimizing the functional results in an algorithm with a time complexity of O(|E|), where |E| is the total number of edges on G.
Application of Exogenous Silicon for Alleviating Photosynthetic Inhibition in Tomato Seedlings under Low−Calcium Stress

To address the low Ca−induced growth inhibition of tomato plants, the mitigation effect of exogenous Si on tomato seedlings under low−Ca stress was investigated using different application methods. We specifically analyzed the effects of root application or foliar spraying of 1 mM Si on growth conditions, leaf photosynthetic properties, stomatal status, chlorophyll content, chlorophyll fluorescence, ATP activity and content, Calvin cycle−related enzymatic activity, and gene expression in tomato seedlings under low vs. adequate calcium conditions. We found that the low−Ca environment significantly affected (reduced) these parameters, resulting in growth limitation. Surprisingly, the application of 1 mM Si significantly increased plant height, stem diameter, and biomass accumulation, protected photosynthetic pigments, improved gas exchange, promoted ATP production, enhanced the activity of Calvin cycle key enzymes and expression of related genes, and ensured efficient photosynthesis to occur in plants under low−Ca conditions. Interestingly, when the same amount of Si was applied, the beneficial effects of Si were more pronounced under low−Ca conditions that under adequate Ca. We speculate that Si might promote the absorption and transport of calcium in plants. The effects of Si also differed depending on the application method; foliar spraying was better in alleviating photosynthetic inhibition in plants under low−Ca stress, whereas root application of Si significantly promoted root growth and development. Enhancing the photosynthetic capacity by foliar Si application is an effective strategy for ameliorating the growth inhibition of plants under low−Ca stress.
Pointwise multiplication of Besov and Triebel--Lizorkin spaces

It is shown that para-multiplication applies to a certain product $\pi(u,v)$ defined for appropriate temperate distributions $u$ and $v$. Boundedness of $\pi(\cdot,\cdot)$ is investigated for the anisotropic Besov and Triebel--Lizorkin spaces, more precisely for $B^{M,s}_{p,q}$ and $F^{M,s}_{p,q}$ with $s\in\mathbb{R}$ and $p$ and $q\in\,]0,\infty]$, though $p 0$. For generic isotropic spaces $F^{s_0}_{p_0,q_0}\oplus F^{s_1}_{p_1,q_1}$ the receiving $F^{s}_{p,q}$ spaces are characterised. It is proved that $\pi(f,g)=f\cdot g$ holds for functions $f$ and $g$ when $f\cdot g$ is locally integrable, roughly speaking. In addition, $\pi(f,u)=fu$ when $f$ is of polynomial growth and $u$ is temperate. Moreover, for an arbitrary open set $\Omega$ in Euclidean space, a product $\pi_\Omega(\cdot,\cdot)$ is defined by lifting to $\mathbb{R}^n$. Boundedness of $\pi$ on $\mathbb{R}^n$ is shown to carry over to $\pi_\Omega$ in general.
Swift Observations of High-Redshift Radio-loud Quasars

We report on Swift observations of four z > 2 radio-loud quasars (0212+735, 0537-286, 0836+710, and 2149-307), classified as blazars. The sources, well-known emitters at soft-to-medium X-rays, were detected at >5 σ with the BAT experiment in 15-150 keV. No flux variability was detected within the XRT and BAT exposures, with the exception of 0836+710, which shows an increase by a factor of 4 in the 15-150 keV flux on a timescale of 1 month. The 0.3-10 keV spectra are well fitted by power-law models, with rather hard continua (photon indices ΓXRT ~ 1.3-1.5); similarly, the 15-150 keV spectra are described by power laws with ΓBAT ~ 1.3-1.8. The XRT data exhibit spectral curvature, which can be modeled in terms of either excess absorption along the line of sight or a downward-curved broken power law. In the former case, if the excess NH is at the rest frame of the source, columns of N = (0.3-6) × 1022 cm-2 are measured. Modeling of the SEDs of the four quasars shows that the emission at the higher frequencies, ≳10 16 Hz, is dominated by the jet, while the steep optical-to-UV continua, observed with the UVOT, can be attributed to thermal emission from the accretion disk. The disk luminosity is between 1% and 10% of the jet power, similar to other powerful blazars.
On Certain Positive Semidefinite Matrices of Special Functions

Special functions are often defined as a Fourier or Laplace transform of a positive measure, and the positivity of the measure manifests as positive definiteness of certain matrices. The purpose of this expository note is to give a sample of such positive definite matrices to demonstrate this connection for some well-known special functions such as Gamma, Beta, hypergeometric, theta, elliptic, zeta and basic hypergeometric functions.
Nanoparticle-Based Bivalent Swine Influenza Virus Vaccine Induces Enhanced Immunity and Effective Protection against Drifted H1N1 and H3N2 Viruses in Mice

Swine influenza virus (SIV) circulates worldwide, posing substantial economic loss and disease burden to humans and animals. Vaccination remains the most effective way to prevent SIV infection and transmission. In this study, we evaluated the protective efficacy of a recombinant, baculovirus-insect cell system-expressed bivalent nanoparticle SIV vaccine in mice challenged with drifted swine influenza H1N1 and H3N2 viruses. After a prime-boost immunization, the bivalent nanoparticle vaccine (BNV) induced high levels of hemagglutination inhibition (HAI) antibodies, virus-neutralization (VN) antibodies, and antigen-specific IgG antibodies in mice, as well as more efficient cytokine levels. The MF59 and CPG1 adjuvant could significantly promote both humoral and cellular immunity of BNV. The MF59 adjuvant showed a balanced Th1/Th2 immune response, and the CPG1 adjuvant tended to show a Th1-favored response. The BALB/c challenge test showed that BNV could significantly reduce lung viral loads and feces viral shedding, and showed fewer lung pathological lesions than those in PBS and inactivated vaccine groups. These results suggest that this novel bivalent nanoparticle swine influenza vaccine can be used as an efficacious vaccine candidate to induce robust immunity and provide broad protection against drifted subtypes in mice. Immune efficacy in pigs needs to be further evaluated.
Quantum Symmetries of Graph C *-algebras

Abstract The study of graph ${{C}^{*}}$ -algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have not yet been computed. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple edges acts maximally on the corresponding graph ${{C}^{*}}$ -algebra. This shows that the quantum symmetry of a graph coincides with the quantum symmetry of the graph ${{C}^{*}}$ -algebra. In our result, we use the definition of quantum automorphism groups of graphs as given by Banica in 2005. Note that Bichon gave a different definition in 2003; our action is inspired from his work. We review and compare these two definitions and we give a complete table of quantum automorphism groups (with respect to either of the two definitions) for undirected graphs on four vertices.
Twisted Affine Lie Algebras, Fusion Algebras, and Congruence Subgroups

The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an $SL(2,\mathbb{Z})$-closure of the space of characters. Analogous to the untwisted affine Lie algebra case, we construct a commutative associative algebra (fusion algebra) structure on this space through the use of the Verlinde formula and study important quotients. Unlike the untwisted cases, some of these algebras and their quotients, which relate to the trace of diagram automorphisms on conformal blocks, have negative structure constants with respect to the (usual) basis indexed by the dominant integral weights of the Lie algebra. We give positivity conjectures for the new structure constants and prove them in some illuminating cases. We then compute formulas for the action of congruence subgroups on these character spaces and give explicit descriptions of the quotients using the affine Weyl group.
Adaptive Chinese Pinyin IME for Most Similar Representation

Many neural-network approaches are used for Pinyin-to-character (P2C) conversion in Chinese input method engines (IMEs). However, in previous research, the conversion effectiveness of neural network P2C models relies on adequate training data. Unfortunately, neural networks cannot maintain high performance with conversions across users and domains. In this study, we propose a method for improving the efficiency of model conversion and tracking user behavior based on dynamic storage and representations that can be updated using historical information from user input. Our experimental results show that our technique tracks user behavior and has strong domain adaptability without requiring additional training. For the cross-domain datasets Touchpal, cMedQA1.0, CAIL2019, compared with the direct use of neural network, its indicators, Top-1 MIU-Acc, CA and KySS, are improved by at least 20.0%, 8.1%, 18.3%, respectively, and the results are close to the in-domain training of the model. Furthermore, compared with the traditional methods On-OMWA and Google IME, this method improves at least 7.8%, 2.0%, 11.9% and 3.2%, 0.7%, 13.9% in Top-1 MIU-Acc, CA and Kyss, respectively. This demonstrates that the proposed method is superior to existing models in terms of conversion accuracy and generality, and can point a new path for P2C platforms.
Comparison of iCOR and Rayleigh atmospheric correction methods on Sentinel-3 OLCI images for a shallow eutrophic reservoir

Remote sensing of inland waters is challenging, but also important, due to the need to monitor the ever-increasing harmful algal blooms (HABs), which have serious effects on water quality. The Ocean and Land Color Instrument (OLCI) of the Sentinel-3 satellites program is capable of providing images for the monitoring of such waters. Atmospheric correction is a necessary process in order to retrieve the desired surface-leaving radiance signal and several atmospheric correction methods have been developed through the years. However, many of these correction methods require programming language skills, or function as commercial software plugins, limiting their possibility of use by end users. Accordingly, in this study, the free SNAP software provided by the European Space Agency (ESA) was used to evaluate the possible differences between a partial atmospheric correction method accounting for Rayleigh scattering and a full atmospheric correction method (iCOR), applied on Sentinel-3 OLCI images of a shallow, highly eutrophic water reservoir. For the complete evaluation of the two methods, in addition to the comparison of the band reflectance values, chlorophyll (CHL) and cyanobacteria (CI) indices were also calculated and their values were intercompared. The results showed, that although the absolute values between the two correction methods did not coincide, there was a very good correlation between the two methods for both bands’ reflectance (r > 0.73) and the CHL and CI indices values (r > 0.95). Therefore, since iCOR correction image processing time is 25 times longer than Rayleigh correction, it is proposed that the Rayleigh partial correction method may be alternatively used for seasonal water monitoring, especially in cases of long time-series, enhancing time and resources use efficiency. Further comparisons of the two methods in other inland water bodies and evaluation with in situ chlorophyll and cyanobacteria measurements will enhance the applicability of the methodology.
An alternative globalization strategy for unconstrained optimization

Abstract We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a sequence of representative models of the objective function. Using the new information gathered from those multiple points, a local step is gradually improved by updating its direction as well as its length. We give a global convergence result and also provide the parallel implementation details accompanied with a numerical study. Our numerical study shows that the proposed algorithm is a promising alternative as a globalization strategy.
On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate

We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the possibility of finding a shape functional able to quantify the torsional instability of the plate, namely how prone is the plate to transform longitudinal oscillations into torsional ones. This functional should obey several rules coming from both theoretical and practical evidences. We show that a simple functional obeying all the required rules does not exist and that the functionals available in literature are not reliable.
Synthetic Post-Contrast Imaging through Artificial Intelligence: Clinical Applications of Virtual and Augmented Contrast Media

Contrast media are widely diffused in biomedical imaging, due to their relevance in the diagnosis of numerous disorders. However, the risk of adverse reactions, the concern of potential damage to sensitive organs, and the recently described brain deposition of gadolinium salts, limit the use of contrast media in clinical practice. In recent years, the application of artificial intelligence (AI) techniques to biomedical imaging has led to the development of ‘virtual’ and ‘augmented’ contrasts. The idea behind these applications is to generate synthetic post-contrast images through AI computational modeling starting from the information available on other images acquired during the same scan. In these AI models, non-contrast images (virtual contrast) or low-dose post-contrast images (augmented contrast) are used as input data to generate synthetic post-contrast images, which are often undistinguishable from the native ones. In this review, we discuss the most recent advances of AI applications to biomedical imaging relative to synthetic contrast media.