Miracle-dz/UniFAR-FTUs huggingface dataset:
DEGENERATE PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS TO PROBABILITY THEORY AND FOUNDATIONS OF MATHEMATICAL FINANCE

OF THE DISSERTATION Degenerate Partial Differential Equations and Applications to Probability Theory and Foundations of Mathematical Finance by Camelia Alexandra Pop Dissertation Director: Professor Paul M. N. Feehan In the first part of our thesis, we prove existence, uniqueness and regularity of solutions for a certain class of degenerate parabolic partial differential equations on the half space which are a generalization of the Heston operator. We use these results to show that the martingale problem associated with the differential operator is well-posed and we build generalized Heston-like processes which match the one-dimensional probability distributions of a certain class of Ito processes. The second part of our thesis is concerned with the study of regularity of solutions to the variational equation associated to the elliptic Heston operator. With the aid of weighted Sobolev spaces, we prove supremum bounds, a Harnack inequality, and Holder continuity near the boundary for solutions to elliptic variational equations defined by the Heston partial differential operator. Finally, we establish stochastic representations of solutions to elliptic and parabolic boundary value problems and obstacle problems associated to the Heston generator. In mathematical finance, solutions to parabolic obstacle problems correspond to value functions for American-style options.
A systematic review on whether regenerative agriculture improves animal welfare: A qualitative analysis with a One Welfare perspective

The welfare of animals in food-production systems is a cause of concern to the public. Regenerative agriculture was first used by the Rodale Institute and proposes to regenerate degraded components of ecosystems, aiming to be more than just sustainable. However, despite animal welfare being pushed to be part of the SDG agenda for 2030, there is no clarity on how regenerative agriculture impacts animal welfare. It is challenging to determine regenerative agriculture impacts on animal welfare, since it is not entirely defined. One Welfare could help define entry points for future research by studying animal welfare in connection with human welfare and environmental conservation. We aimed to analyse the extent to which positive animal welfare outcomes characterise regenerative agriculture systems in peer-reviewed articles and whether the narratives of such articles support that regenerative agriculture promotes animal welfare directly or indirectly by improving human welfare and environmental conservation. We searched papers including ‘regenerative agriculture’ using PRISMA-P, selecting animal welfare, human welfare, environment conservation terms, developed themes, and carried out analysis using Atlas.Ti8 and Causal Loop Diagram. We found that papers mainly linked animal welfare to animal health, human welfare to financial farm status and farmer’s self-awareness, and environmental conservation to soil improvement. Causal Loop Diagram indicated that regenerative agriculture had the potential to improve the health and nutrition components of animal welfare by enhancing financial farmers’ status/self-awareness (human welfare), and the soil (environmental conservation), reflecting that the processes that affect human welfare and environmental conservation could also affect animal welfare. However, information in papers remains insufficient to determine how regenerative agriculture impacts on animal welfare and research into regenerative agriculture needs to extend its focus on animal welfare and elucidate the regenerative agriculture principles leading to animal welfare.
Application of Shuffling Techniques within Watermarking

In recent years, digital watermarking has been widely used in copyright protection for digital images, and a large number of schemes have been proposed. In this paper, the application of shuffling techniques within watermarking and present criterion measure on shuffling degree is extensively studied. The criterion measure is helpful to decide how far to shuffle a image in order to obtain the best robustness. As examples, two novel applications within watermarking system are presented and compared. Experimental results indicate that these techniques are very effective in respect of keeping resilience to cropping attack.
FINITE HOPF-GALOIS COEXTENSIONS

Let H be a finite dimensional Hopf algebra, C a right H -module coalgebra and R=C/CH + Suppose that C/R is an H -Galois coextension,and both R and R  H * satisfy Krull-Schmidt property for injective comodules. We show that C is a crossed coproduct if and only if C_R is free.
Redefining Autoimmune Disorders’ Pathoetiology: Implications for Mood and Psychotic Disorders’ Association with Neurodegenerative and Classical Autoimmune Disorders

Although previously restricted to a limited number of medical conditions, there is a growing appreciation that ‘autoimmune’ (or immune-mediated) processes are important aspects of a wide array of diverse medical conditions, including cancers, neurodegenerative diseases and psychiatric disorders. All of these classes of medical conditions are associated with alterations in mitochondrial function across an array of diverse cell types. Accumulating data indicate the presence of the mitochondrial melatonergic pathway in possibly all body cells, with important consequences for pathways crucial in driving CD8+ T cell and B-cell ‘autoimmune’-linked processes. Melatonin suppression coupled with the upregulation of oxidative stress suppress PTEN-induced kinase 1 (PINK1)/parkin-driven mitophagy, raising the levels of the major histocompatibility complex (MHC)-1, which underpins the chemoattraction of CD8+ T cells and the activation of antibody-producing B-cells. Many factors and processes closely associated with autoimmunity, including gut microbiome/permeability, circadian rhythms, aging, the aryl hydrocarbon receptor, brain-derived neurotrophic factor (BDNF) and its receptor tyrosine receptor kinase B (TrkB) all interact with the mitochondrial melatonergic pathway. A number of future research directions and novel treatment implications are indicated for this wide collection of poorly conceptualized and treated medical presentations. It is proposed that the etiology of many ‘autoimmune’/‘immune-mediated’ disorders should be conceptualized as significantly determined by mitochondrial dysregulation, with alterations in the mitochondrial melatonergic pathway being an important aspect of these pathoetiologies.
Model Selection and Forward Validation

Traditionally we fit one model at a time to our data, compute some measure of the model fit adjusted for the number of parameters and then we compare different models and optimize. However, the very selection of a model may substantially change the statistical properties of the measures we are optimizing. We here suggest a selection and validation procedure for regressive time series models and linear regression which takes into account these effects of the model selection. The procedure is based on weighted sums of squared recursive prediction errors for models which are selected at each step of time. The measures provided by this method are compared with conventional measures in a multivariate time series example.
Complete solutions of a family of cubic Thue equations

Dans cet article, nous utilisons la methode de Baker, basee sur les formes lineaires en logarithmes, pour resoudre une famille d'equations de Thue liee a une famille de corps de nombres de degre 3. Nous obtenons toutes les solutions de l'equation de Thue Φ n (x, y) = x 3 + (n 8 + 2n 6 - 3n 5 + 3n 4 - 4n 3 + 5n 2 - 3n + 3)x 2 y - (n 3 - )n 2 xy 2 -y 3 =±1, pour n ≥ 0.
Single Image Reflection Removal Based on Dark Channel Sparsity Prior

The major task of reflection removal methods is to restore a reflection-free image from a reflection-contaminated image taken through glass. We propose an algorithm to remove reflections from a single image by means of the <inline-formula> <tex-math notation="LaTeX">$l_{0}$ </tex-math></inline-formula>-regularized dark channel sparsity prior and an <inline-formula> <tex-math notation="LaTeX">$l_{0}$ </tex-math></inline-formula> gradient sparsity prior. In addition, we analyze the difference between the dark channel map in the reflection-contaminated image and the reflection-free image empirically and mathematically. Moreover, a new data fidelity term is introduced to handle strong reflections and preserve high-frequency details in the recovered transmission image. Different from the model used in most state-of-the-art methods, our reflection removal model does not rely on the assumption of out-of-focus objects in the reflection layer. Quantitative evaluation on several publicly available real-world image datasets including ground-truth demonstrates the high accuracy of our algorithm. Qualitative evaluation of extensive experimental results on real-world images shows the competitive performance of the proposed method compared with the state-of-the-art reflection removal methods.
Spontaneous pattern formation in primary visual cortex

The primary visual cortex (V1) is the first cortical area to receive visual information transmitted by ganglion cells of the retina via the lateral geniculate nucleus (LGN) of the thalmus to the back of the brain (see figure 1.1). A fundamental property of the functional architecture of V1 is an orderly retinotopic mapping of the visual field onto the surface of cortex, with the left and right halves of visual field mapped onto the right and left cortices respectively. Except close to the fovea (centre of the visual field), this map can be approximated by the complex logarithm (see figure 1.2). Let rR = {rR, θR} be a point in the visual field represented in polar coordinates and let r = {x, y} be the corresponding point in the cortex given in Cartesian coordinates. Under the retino-cortical map, r = {log rR, θR}. Evidently, if we introduce the complex representation of rR, zR = rReR then z = log zR = log rR + iθR = x + iy generates the complex cortical representation. One of the interesting properties of the retino-cortical map is that the action of rotations and dilatations in the visual field correspond to translations in the x and y directions, respectively, in cortex. Superimposed upon the retinotopic map are a number of additional feature maps reflecting the fact that neurons respond preferentially to stimuli with particular features [38, 43, 55]. For example, most cortical cells signal the local orientation of a contrast edge or bar—they are tuned to
Pediatric Posterior Fossa ATRT: A Case Report, New Treatment Strategies and Perspectives

Posterior fossa atypical teratoid rhabdoid tumor (ATRT) is a rare childhood tumor usually associated with a dismal prognosis. Although upfront surgical gross total resection (GTR) has classically been the first line of treatment, new multimodal treatments, including two-stage surgery, are showing promising results in terms of overall survival (OS) and complication rate. We present a case of a 9-month-old child treated with two-staged surgery and chemotherapy. When deemed risky, multimodal treatments, including staged surgeries, can be a safe alternative to reduce surgical mortality and morbidity. At 23 months old, the patient had normal global development and no major impact on quality of life. We, therefore, discuss the most recent advancements from a treatment perspective, including molecular targeting.
Tides in Close Binary Systems

We consider three aspects of tidal interactions in close binary systems. 1) We first develop a framework for predicting and interpreting photometric observations of eccentric binaries, which we term tidal asteroseismology. In such systems, the Fourier transform of the observed lightcurve is expected to consist of pulsations at harmonics of the orbital frequency. We use linear stellar perturbation theory to predict the expected pulsation amplitude spectra. Our numerical model does not assume adiabaticity, and accounts for stellar rotation in the traditional approximation. We apply our model to the recently discovered Kepler system KOI-54, a 42-day face-on stellar binary with e=0.83. Our modeling yields pulsation spectra that are semi-quantitatively consistent with observations of KOI-54. KOI-54's spectrum also contains several nonharmonic pulsations, which can be explained by nonlinear three-mode coupling. 2) We next consider the situation of a white dwarf (WD) binary inspiraling due to the emission of gravitational waves. We show that resonance locks, previously considered in binaries with an early-type star, occur universally in WD binaries. In a resonance lock, the orbital and spin frequencies evolve in lockstep, so that the tidal forcing frequency is approximately constant and a particular normal mode remains resonant, producing efficient tidal dissipation and nearly synchronous rotation. We derive analytic formulas for the tidal quality factor and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We apply our analysis to the 13-minute double-WD binary J0651, and show that our predictions are roughly consistent with observations. 3) Lastly, we examine the general dynamics of resonance locking in more detail. Previous analyses of resonance locking, including my own earlier work, invoke the adiabatic (a.k.a. Lorentzian) approximation for the mode amplitude, valid only in the limit of relatively strong mode damping. We relax this approximation, analytically derive conditions under which the fixed point associated with resonance locking is stable, and further check our analytic results with numerical integration of the coupled mode, spin, and orbital evolution equations. These show that resonance locking can sometimes take the form of complex limit cycles or even chaotic trajectories. We also show that resonance locks can accelerate the course of tidal evolution in eccentric systems.
Validation of a Disease-Free Survival Prediction Model Using UBE2C and Clinical Indicators in Breast Cancer Patients

Objective To explore the validation of a disease-free survival (DFS) model for predicting disease progression based on the combination of ubiquitin-conjugating enzyme E2 C (UBE2C) levels and clinical indicators in breast cancer patients. Methods We enrolled 121 patients with breast cancer, collected their baseline characteristics and follow-up data, and analyzed the UBE2C levels in tumor tissues. We studied the relationship between UBE2C expression in tumor tissues and disease progression events of patients. We used the Kaplan-Meier method for identifying the disease-free survival rate of patients, and the multivariate Cox regression analysis to study the risk factors affecting the prognosis of patients. We sought to develop and validate a model for predicting disease progression. Results We found that the level of expression of UBE2C could effectively distinguish the prognosis of patients. In the Receiver Operating Characteristic (ROC) curve analysis, the Area under the ROC Curve (AUC) = 0.826 (0.714–0.938) indicating that high levels of UBE2C was a high-risk factor for poor prognosis. After evaluating different models using the ROC curve, Concordance index (C-index), calibration curve, Net Reclassification Index (NRI), Integrated Discrimination Improvement Index (IDI), and other methods, we finally developed a model for the expression of Tumor-Node (TN) staging using Ki-67 and UBE2C, which had an AUC=0.870, 95% CI of 0.786–0.953. The traditional TN model had an AUC=0.717, and 95% CI of 0.581–0.853. Decision Curve Analysis (DCA) and Clinical Impact Curve (CIC) analysis indicated that the model had good clinical benefits and it was relatively simple to use. Conclusion We found that high levels of UBE2C was a high-risk factor for poor prognosis. The use of UBE2C in addition to other breast cancer-related indicators effectively predicted the possible disease progression, thus providing a reliable basis for clinical decision-making.
Nifuroxazide induces the apoptosis of human non‑small cell lung cancer cells through the endoplasmic reticulum stress PERK signaling pathway

The aim of the present study was to investigate the molecular mechanism of nifuroxazide (NFZ) in the induction of apoptosis of NCI-H1299 human non-small cell lung cancer (NSCLC) cells through the reactive oxygen species (ROS)/Ca2+/protein kinase R-like ER kinase (PERK)-activating transcription factor 4 (ATF4)-DNA damage inducible transcript 3 (CHOP) signaling pathway. Morphological changes of cells were observed by microscopy, and the apoptosis and intracellular ROS levels of cells were observed by inverted fluorescence microscopy. Cell viability after the addition of the PERK inhibitor, GSK2606414, were detected by Cell Counting Kit-8 assay. Annexin V-FITC was used to detect cell apoptosis, Brite 670 was used to detect intracellular ROS and Fura Red AM was used to detect Ca2+ content. Western blotting was used to detect PERK, phosphorylated (P)-PERK, ATF4, CHOP, P-Janus kinase 2 and P-signal transducer and activator of transcription 3 expression levels. Compared with the dimethyl sulfoxide control group, NFZ inhibited the survival activity in the H1299 NSCLC cell line, in a time- and dose-dependent manner. However, GSK2606414 inhibited the NFZ-induced apoptosis of H1299 cells. GSK2606414 also inhibited the increase in ROS and Ca2+ in H1299 cells induced by NFZ. Western blotting results demonstrated that NFZ significantly increased the expression levels of P-PERK, ATF4 and CHOP, whereas GSK2606414 significantly reduced the NFZ-induced increase in these protein expression levels. In conclusion, NFZ may induce the apoptosis of H1299 NSCLC cells through the ROS/Ca2+/PERK-ATF4-CHOP signaling pathway.
S-VIO: Exploiting Structural Constraints for RGB-D Visual Inertial Odometry

Vision-based localization is an essential problem for autonomous systems while the performance of vision-based odometry degrades in the challenging scenario. This letter presents S-VIO, an RGB-D visual inertial odometry (VIO) which fully uses multi-sensor measurements (i.e. depth, RGB and IMU), heterogeneous landmarks (i.e. points, lines and planes) and structural regularity of the environment to obtain a robust and accurate localization result. In order to detect the underlying structural regularity of the environment, a two-step Atlanta world inference method is proposed. Leveraging the gravity direction estimated by the VIO system, the proposed algorithm first generates horizontal Atlanta axis hypotheses from a set of recently optimized plane landmarks. Then the following plane landmarks and line clusters are used to filter out the occasionally observed axes based on the persistence of the observation. The remaining axes will survive and be saved in the Atlanta map for future re-observations. Particularly, an efficient mined-and-stabbed (MnS) method is applied to classify the structural line and extract the vanishing point from each line cluster. In addition, a closed-form initialization method for the structural line feature is proposed, which leverages the known direction to obtain a better initial estimation. Integrated with the above novelties, S-VIO is tested on two public real-world RGB-D inertial datasets. Experiments demonstrate that S-VIO has better accuracy and robustness compared to state-of-the-art VIO and RGB-D VIO algorithms.
A New Microarchitecture-Based Parameter to Predict the Micromechanical Properties of Bone Allografts

Scaffolds are an essential component of bone tissue engineering. They provide support and create a physiological environment for cells to proliferate and differentiate. Bone allografts extracted from human donors are promising scaffolds due to their mechanical and structural characteristics. Bone microarchitecture is well known to be an important determinant of macroscopic mechanical properties, but its role at the microscopic, i.e., the trabeculae level is still poorly understood. The present study investigated linear correlations between microarchitectural parameters obtained from X-ray computed tomography (micro-CT) images of bone allografts, such as bone volume fraction (BV/TV), degree of anisotropy (DA), or ellipsoid factor (EF), and micromechanical parameters derived from micro-finite element calculations, such as mean axial strain (εz) and strain energy density (We). DAEF, a new parameter based on a linear combination of the two microarchitectural parameters DA and EF, showed a strong linear correlation with the bone mechanical characteristics at the microscopic scale. Our results concluded that the spatial distribution and the plate-and-rod structure of trabecular bone are the main determinants of the mechanical properties of bone at the microscopic level. The DAEF parameter could, therefore, be used as a tool to predict the level of mechanical stimulation at the local scale, a key parameter to better understand and optimize the mechanism of osteogenesis in bone tissue engineering.
The role of surface tension on the elastic decohesion of polymeric filaments

We simulate the rapid extension of polymeric filaments between parallel plates with special attention to the role of surface tension in the symmetry breaking azimuthal instability that may occur near the end plates. The instability is viewed as a precursor to the breakup into separate fibrils and the eventual elastic decohesion of the filament from the plate. It is demonstrated that high Deborah numbers are needed to initiate the instability and that surface tension provides a wave number selection. Moreover, the surface tension has a stabilizing effect on the end plate instability.
Modelling the onset of dynamic friction : A study of rupture velocities

The onset of dynamic dry friction between two blocks of PMMA has recently been studied experimentally. Technological advances enable the study of the onset of sliding at high temporal resolutions, resulting in new insights regarding how slip occurs at a local scale along the interface. In this thesis, spring-block models are used to study the onset of dynamic dry friction. These models have been used to study earthquakes for a long time, and have later been adopted to study friction on a laboratory scale. The agreement with the mentioned experimental results has, however, up until now been rather poor. In these models, which are fully resolved in time, the local friction law has to be imposed. Using a local Amontons–Coulomb friction law, the one-dimensional model shows qualitative agreement with the experimental results. A quantitative comparison, however, reveals serious discrepancies. Studies reveal the importance of dimensionality to the kinetics, i.e. the states where slip nucleates and arrests, of the system. An example is the length of precursors as a function of the applied tangential load, which appears to be improved by including two-dimensional effects in the one-dimensional model. Both dimensionality and the local friction law are seen to be crucial for the dynamics of the system, e.g. micro-slip front propagation. In the one-dimensional model, a specific relationship between the rupture velocity, the initial shear to normal stress ratio and the local friction coefficients is derived. This reveals the importance of the interfacial strength to the rupture velocities in addition to the stress ratio which has been suggested in the experimental papers. A (2 + 0)D model, where both horizontal dimensions of the system are included, is also studied. It is shown that details of how the driving force is applied are crucial. As an illustration, a precursor has in a (2 + 0)D system both a length and a size. The development of these two quantities as a function of the applied tangential load can significantly deviate from each other depending on how the driving force is applied. The lack of experimental results studying these effects, however, makes the analysis difficult.