Miracle-dz/UniFAR-FTUs huggingface dataset:
Global rough solution for $L^2$-critical semilinear heat equation in the negative Sobolev space

In this paper, we consider the Cauchy global problem for the $L^2$-critical semilinear heat equations $\partial_t h=\Delta h\pm |h|^{\frac4d}h, $ with $h(0,x)=h_0$, where $h$ is an unknown real function defined on $ \R^+\times\R^d$. In most of the studies on this subject, the initial data $h_0$ belongs to Lebesgue spaces $L^p(\R^d)$ for some $p\ge 2$ or to subcritical Sobolev space $H^{s}(\R^d)$ with $s>0$. We here prove that there exists some positive constant $\varepsilon_0$ depending on $d$, such that the Cauchy problem is locally and globally well-posed for any initial data $h_0$ which is radial, supported away from origin and in the negative Sobolev space $\dot H^{-\varepsilon_0}(\R^d)$ including $L^p(\R^d)$ with certain $p<2$ as subspace. Furthermore, unconditional uniqueness, and $L^2$-estimate both as time $t\to0$ and $t\to +\infty$ were considered.
Blow-up lemmas for sparse graphs

The blow-up lemma states that a system of super-regular pairs contains all bounded degree spanning graphs as subgraphs that embed into a corresponding system of complete pairs. This lemma has far-reaching applications in extremal combinatorics. We prove sparse analogues of the blow-up lemma for subgraphs of random and of pseudorandom graphs. Our main results are the following three sparse versions of the blow-up lemma: one for embedding spanning graphs with maximum degree $\Delta$ in subgraphs of $G(n,p)$ with $p=C(\log n/n)^{1/\Delta}$; one for embedding spanning graphs with maximum degree $\Delta$ and degeneracy $D$ in subgraphs of $G(n,p)$ with $p=C_\Delta\big(\log n/n\big)^{1/(2D+1)}$; and one for embedding spanning graphs with maximum degree $\Delta$ in $(p,cp^{\max(4,(3\Delta+1)/2)}n)$-bijumbled graphs. We also consider various applications of these lemmas.
Neuroprotective effects of Scrophularia buergeriana extract against glutamate-induced toxicity in SH-SY5Y cells

The aim of this study was to investigate the antioxidant and anti-apoptotic activities, as well as the underlying mechanisms of action, of Scrophularia buergeriana (S. buergeriana) extract (SBE) in glutamate-induced SH-SY5Y cell death. The roots of S. buergeriana were extracted with 70% ethanol, and standardized SBE was used in this study. To induce cytotoxicity, the SH-SY5Y cells were exposed to glutamate for 3 h, or pre-treated with SBE for 1 h, and subsequently incubated with glutamate for 3 h. The neuro-protective effects were assessed by measuring cell viability and the total glutathione contents using commercial kits. The antioxidant and anti-apoptotic mechanisms of action of SBE were evaluated by western blot analysis. The results confirmed that glutamate-induced toxicity was caused by reactive oxygen species (ROS) production, leading to oxidative stress and DNA damage, thus leading to cell death. However, treatment of the SH-SY5Y cells with SBE significantly increased the viability of the cells exposed to glutamate by upregulating the levels of antioxidant proteins, such as superoxide dismutase (SOD)1, SOD2 and glutathione peroxidase-1 (GPx-1), and directly enhancing the total glutathione contents. Furthermore, SBE attenuated DNA impairment and decreased B-cell lymphoma-2 (Bcl-2)-associated X protein (Bax), cleaved caspase-3 and cleaved poly(adenosine diphosphate (ADP)-ribose) polymerase (PARP) activation. In addition, SBE upregulated Bcl-2 expression via p38 mitogen-activated protein kinases (MAPKs). On the whole, the findings of this study demonstrated that SBE exerts neuroprotective effects against glutamate-induced cell toxicity through its antioxidant and anti-apoptotic activities.
Financial literacy and behavioural biases of individual investors: empirical evidence of Pakistan stock exchange

Purpose Financial literacy is a crucial element of financial decision-making, exerting significant influence on the behaviour of individual investors, while making budgetary, house financing, stock investing and retirement planning decisions. So, the purpose of this research is to determine the relationship between financial literacy and behavioural biases of individual investors in Pakistan. Design/methodology/approach In this research paper, a sample of 300 observations was obtained through questionnaires from individual investors residing in Lahore and invested in Pakistan Stock Exchange. The data obtained, was passed through Cronbach’s Alpha and Exploratory Factor Analysis (EFA). The hypothesis developed for the research was tested by Pearson’s Chi-square and Ordinal Regression Analysis. Findings The hypothesis testing of the research concluded that there is a negative association between financial literacy and behavioural biases of individual investors. So, it means; with an increase in level of financial literacy, the likelihood of investor facing behavioural biases reduces. It also appeared that male respondents have more financial literacy than female respondents Originality/value Previous studies in the field of finance, identified different factors causing the financial behaviour of individual investor of Pakistan, and also focused on level of financial literacy in Pakistan, but these studies have not emphasized the crucial relationship between financial literacy and behavioural biases of individual investors. Thus, the unique empirical analysis developed in this paper has accentuated the financial literacy as a factor that mitigates behavioural biases of individual investor.
LOW-RANK AND SPARSE MATRIX RECOVERY FROM NOISY OBSERVATIONS VIA 3-BLOCK ADMM ALGORITHM

Recovering low-rank and sparse matrix from a given matrix arises in many applications, such as image processing, video background substrac-tion, and so on. The 3-block alternating direction method of multipliers (ADMM) has been applied successfully to solve convex problems with 3-block variables. However, the existing sufficient conditions to guarantee the convergence of the 3-block ADMM usually require the penalty parameter γ to satisfy a certain bound, which may affect the performance of solving the large scale problem in practice. In this paper, we propose the 3-block ADMM to recover low-rank and sparse matrix from noisy observations. In theory, we prove that the 3-block ADMM is convergent when the penalty parameters satisfy a certain condition and the objective function value sequences generated by 3-block ADMM converge to the optimal value. Numerical experiments verify that proposed method can achieve higher performance than existing methods in terms of both efficiency and accuracy.
ROLE OF ACUTE PHASE REACTANTS: STUDY IN DIABETIC AND NON DIABETIC PATIENTS SUFFERING FROM SEPSIS IN INDIA

Background: In the modern era of critical care management, sepsis remains a serious problem accounting for thousands of death per year with noteworthy morbidity and mortality. Sepsis results in multi-organ dysfunction secondary to culture-positive or negative infection. In diabetes mellitus (DM), the major problem is vurnerable infection or sometimes development of sepsis and septic shock. Researchers showed DM has reduced bacterial clearance as hyperglycemia decreases polymorphonuclear function and less production of inflammatory cytokines. Thus DM creates a comorbid condition in sepsis. The mechanism of the inter-twining of diabetes, infection and inflammatory response in sepsis is quite unclear. Research methods: Our objective remains in clarifying the reliability of acute phase biomarkers as diagnostic tool (Procalcitonin; PCT and C-reactive protein; CRP) in diabetic patient in comparison to non-diabetic patients with sepsis. A total of 40 subjects, (20 patients had sepsis with DM, 20 patients had sepsis without DM) were enrolled. PCT, CRP, and other laboratory testing (WBC count, ESR, serum lactate, albumin) were done for all subjects at admission. Subjects were managed according to hospital protocol and followed up till remedy. Acute phase biomarker status was assessed based on their stratified concentration in groups. Results: Compared with non-DM group, PCT and CRP in DM group were significantly high (all P < 0.05) and associated with bad outcome. Conclusion: PCT level ( 40 ng/mL; odds ratio 1) and CRP level (100 mg/L; odds ratio 1) proved to be a reliable acute phase marker of sepsis patients with DM in Indian population.
Molecular Profiling Defines Evolutionarily Conserved Transcription Factor Signatures of Major Vestibulospinal Neuron Groups

Abstract Vestibulospinal neurons are organized into discrete groups projecting from brainstem to spinal cord, enabling vertebrates to maintain proper balance and posture. The two largest groups are the lateral vestibulospinal tract (LVST) group and the contralateral medial vestibulospinal tract (cMVST) group, with different projection lateralities and functional roles. In search of a molecular basis for these differences, we performed RNA sequencing on LVST and cMVST neurons from mouse and chicken embryos followed by immunohistofluorescence validation. Focusing on transcription factor (TF)-encoding genes, we identified TF signatures that uniquely distinguish the LVST from the cMVST group and further parse different rhombomere-derived portions comprising the cMVST group. Immunohistofluorescence assessment of the CNS from spinal cord to cortex demonstrated that these TF signatures are restricted to the respective vestibulospinal groups and some neurons in their immediate vicinity. Collectively, these results link the combinatorial expression of TFs to developmental and functional subdivisions within the vestibulospinal system.
Diagnosis and Management of Gastroesophageal Reflux Disease in Infants and Children: from Guidelines to Clinical Practice

The diagnosis and management of gastro-esophageal reflux (GER) and GER disease (GERD) in infants and children remains a challenge. Published guidelines and position papers, along with Embase, MEDLINE, and the Cochrane Database were reviewed and summarized with the intent to propose a practical approach and management of GER and GERD for healthcare providers and to standardize and improve the quality of care for infants and children. For this purpose, 2 algorithms were developed, 1 for infants <12 months of age and the other for older children. None of the signs and symptoms of GER and GERD are specific and there is no gold standard diagnostic test or tool. Nutritional management is recommended as a first-line approach in infants, while in children, a therapeutic trial with antacid medication is advised for early management. The practical recommendations from this review are intended to optimize the management of GER in infants and older children and reduce the number of investigations and inappropriate use of medication.
Observations of Red Giants with Suspected Massive Companions

Motivated by the existence of binary systems where a stellar-mass black hole is bound to a normal star, we selected four red giants with large radial velocity (RV) variation from the survey of Space Interferometry Mission (SIM) grid stars and monitored their RVs for several months. None turned out to contain a massive companion above 2.5 solar masses. The red giant TYC 9299-1080-1 with a large RV and a large proper motion is a single-lined spectroscopic binary with a period of 81 days. It is an extreme halo object moving at 350 km s−1 almost directly toward the Galactic center. HD 206092 is a double-lined binary with a short period of 4.37 days. It belongs to the rare class of active RS CVn-type binaries with evolved primary components, apparently undergoing mass transfer. The X-ray luminosity of HD 206092 is about twice as high as the most luminous coronal X-ray emitters observed by ROSAT, including II Peg and the prototype star RS CVn. HD 318347 has a variable double-peaked emission-line spectrum (not a giant), while HD 324668 has a constant RV. Despite the overall good quality of the SIM survey data confirmed by a comparison with Gaia Data Release 2 (DR2) mean RVs, the few large RV variations are explained, mostly, by erroneous data. We discuss the significance of the non-detection of massive companions in the SIM grid sample and the associated work.
Friedelane-type triterpene cyclase in celastrol biosynthesis from Tripterygium wilfordii and its application for triterpenes biosynthesis in yeast.

Celastrol is a promising bioactive compound isolated from Tripterygium wilfordii and has been shown to possess many encouraging preclinical applications. However, the celastrol biosynthetic pathway is poorly understood, especially the key oxidosqualene cyclase (OSC) enzyme responsible for cyclisation of the main scaffold. Here, we report on the isolation and characterisation of three OSCs from T. wilfordii: TwOSC1, TwOSC2 and TwOSC3. Both TwOSC1 and TwOSC3 were multiproduct friedelin synthases, while TwOSC2 was a β-amyrin synthase. We further found that TwOSC1 and TwOSC3 were involved in the biosynthesis of celastrol and that their common product, friedelin, was a precursor of celastrol. We then reconstituted the biosynthetic pathway of friedelin in engineered yeast constructed by the CRISPR/Cas9 system, with protein modification and medium optimisation, leading to heterologous production of friedelin at 37.07 mg l-1 in a shake flask culture. Our study was the first to identify the genes responsible for biosynthesis of the main scaffold of celastrol and other triterpenes in T. wilfordii. As friedelin has been found in many plants, the results and approaches described here have laid a solid foundation for further explaining the biosynthesis of celastrol and related triterpenoids. Moreover, our results provide insights for metabolic engineering of friedelane-type triterpenes.
On Partially Ordered Patterns of Length 4 and 5 in Permutations

Partially ordered patterns (POPs) generalize the notion of classical patterns studied widely in the literature in the context of permutations, words, compositions and partitions. In an occurrence of a POP, the relative order of some of the elements is not important. Thus, any POP of length $k$ is defined by a partially ordered set on $k$ elements, and classical patterns correspond to $k$-element chains. The notion of a POP provides a convenient language to deal with larger sets of permutation patterns. This paper contributes to a long line of research on classical permutation patterns of length 4 and 5, and beyond, by conducting a systematic search of connections between sequences in the Online Encyclopedia of Integer Sequences (OEIS) and permutations avoiding POPs of length 4 and 5. As the result, we (i) obtain 13 new enumerative results for classical patterns of length 4 and 5, and a number of results for patterns of arbitrary length, (ii) collect under one roof many sporadic results in the literature related to avoidance of patterns of length 4 and 5, and (iii) conjecture 6 connections to the OEIS. Among the most intriguing bijective questions we state, 7 are related to explaining Wilf-equivalence of various sets of patterns, e.g. 5 or 8 patterns of length 4, and 2 or 6 patterns of length 5.
1,25-Dihydroxy-Vitamin D3 induces macrophage polarization to M2 by upregulating T-cell Ig-mucin-3 expression

Macrophage polarization serves an important role in immune regulation that is regulated by T-cell immunoglobulin-mucin-3 (Tim-3). The objective of the present study was to explore the role of 1,25-dihydroxy-vitamin D3 [1,25(OH)2D3] in macrophage polarization. Plasmid transfection techniques were applied to prepare RAW264.7 cells with silenced or overexpressed Tim-3 gene. ELISAs were used to examine the level of inflammatory factors secreted by macrophages. Proteins levels were determined by western blot analysis. mRNAs expression levels were assessed using reverse transcription quantitative polymerase chain reaction. It was identified that 1,25(OH)2D3 upregulated Tim-3 levels and promoted the secretion of interleukin (IL)-10. 1,25(OH)2D3 was also observed to increase the level of transforming growth factor-β and to inhibit tumor necrosis factor-α and IL-6. The results also suggested that Tim-3 gene silencing induced macrophages polarization to classically activated macrophages (M1), and that overexpression of the Tim-3 gene induced macrophage polarization to alternatively activated macrophages (M2). 1,25(OH)2D3 treatment upregulated the expression level of Tim-3 in macrophages, which promoted cell polarization to M2 and inhibited polarization to M1. The data from the present study indicated that Tim-3 may induce macrophage polarization to M2, and that 1,25(OH)2D3 produced immunosuppressive effects by upregulating Tim-3.
Save Environment by Replace Plastic, The Case of PepsiCola

Pepsi-Cola is one of the largest multinational food and beverage brand in the world. In 1902 Pepsi-Cola Company was founded in the United State. It has continuously developed during the past 118 years. Our Report is about replacing Plastic bottle to Reusable Plastic to develop and change the company product to be better. The issue of environmental pollution especially plastic pollution is becoming serious; it is damaging the ecological environment. This had triggered the attention of organization on the environment and some of them take their responsibility to work hard on sustainability a strong environmental profile.
Variational Bayesian modelling of mixed-effects

This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple subjects. When approached from a bayesian perspective, such mixed-effects models typically rely upon a hierarchical generative model of the data, whereby both within- and between-subject effects contribute to the overall observed variance. The ensuing VB scheme can be used to assess statistical significance at the group level and/or to capture inter-individual differences. Alternatively, it can be seen as an adaptive regularization procedure, which iteratively learns the corresponding within-subject priors from estimates of the group distribution of effects of interest (cf. so-called "empirical bayes" approaches). We outline the mathematical derivation of the ensuing VB scheme, whose open-source implementation is available as part the VBA toolbox.
Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics

Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance -- the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180 degrees flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed vs Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon Acoustic Oscillations where the covariance matrix of the power spectrum is lower by only 20% compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogs.
Cross-Dataset Transfer Driver Expression Recognition via Global Discriminative and Local Structure Knowledge Exploitation in Shared Projection Subspace

Facial expression is one of the important characteristics of drivers during driving. It is very useful in safe driving detection. Recognizing drivers’ expressions by the facial images can be solved with machine learning classification strategies. To obtain a reliable reorganization performance, most of approaches assume that the facial images in the training and testing datasets are independently and identically distributed. However, for real time drivers’ facial expression recognition, due to vehicle motion, changes in illumination, noise and head movement, the features displayed for the training dataset may be not valid for the testing dataset. To solve this problem, a novel approach is proposed for cross-dataset transfer driver expression recognition via global discriminative and local structure knowledge exploitation in shared projection subspace (GD-LS-SS). By leaning a shared common subspace, GD-LS-SS utilizes the local geometrical structure of data by exploiting the knowledge of graph topology, meanwhile exploiting the global discriminative information by using the pairwise constrained knowledge between the source and labeled target data. Taking advantage of kernel trick, the kernel version of GD-LS-SS is proposed to learn the kernel projection for handling nonlinear cross-dataset transfer and to further promote the recognition accuracy. Experiments on the KMU-FED dataset show that the satisfactory recognition performance of GD-LS-SS outperforms several traditional non-transfer and related transfer approaches.
Instability of Thin Concrete Walls with a Single Layer of Reinforcement under Cyclic Loading: Numerical Simulation and Improved Equivalent Boundary Element Model for Assessment

ABSTRACT Thin reinforced concrete walls may fail due to out-of-plane instability when subjected to seismic loading. While previous numerical studies on wall instability have focused on the behaviour of members with two layers of vertical reinforcement, this work addresses the response of walls with a single layer of rebars. Such walls are particular prone to out-of-plane failure when subjected to cyclic in-plane loading. The numerical investigations herein performed simulate the aforementioned local behaviour and validate it against experimental measurements. A parametric study on the effect of boundary conditions shows that imposing an out-of-plane displacement or a rotation at the storey height increases the vulnerability to instability. It is also seen that the storey height itself is an influencing variable. The second part of this study proposes an improved equivalent boundary element model for the assessment of wall instability. Existing mechanical models, based on pinned-pinned boundary conditions, represent the boundary element over the height of the plastic hinge. This work shows that such models often underestimate the critical tensile strain triggering out-of-plane failure. A new equivalent boundary element model is proposed where a bilinear axial displacement profile defined a priori is applied. The latter is shown to satisfactorily approximate the vertical strain profile in wall boundary elements and to lead to better estimates of the critical strain triggering out-of-plane failure.