Miracle-dz/UniFAR-FTUs huggingface dataset:
A single exponential bound for the redundant vertex Theorem on surfaces

Let s1, t1,. sk, tk be vertices in a graph G embedded on a surface \sigma of genus g. A vertex v of G is "redundant" if there exist k vertex disjoint paths linking si and ti (1 \lequal i \lequal k) in G if and only if such paths also exist in G - v. Robertson and Seymour proved in Graph Minors VII that if v is "far" from the vertices si and tj and v is surrounded in a planar part of \sigma by l(g, k) disjoint cycles, then v is redundant. Unfortunately, their proof of the existence of l(g, k) is not constructive. In this paper, we give an explicit single exponential bound in g and k.
Non-commutative Hodge structures: Towards matching categorical and geometric examples

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the periodic cyclic homology viewed as a bundle over the punctured formal disk. Our main result says that for the category of matrix factorizations of a polynomial the formulas reproduce, up to a certain shift, a well-known connection on the associated twisted de Rham cohomology which plays a central role in the geometric approach to the Hodge theory of isolated singularities.
Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings

In this paper we study the $w^*$-fixed point property for nonexpansive mappings. First we show that the dual space $X^*$ lacks the $w^*$-fixed point property whenever $X$ contains an isometric copy of the space $c$. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in $\ell_1$ space. This result allows us to obtain a characterization of all separable Lindenstrauss spaces $X$ inducing the failure of $w^*$-fixed point property in $X^*$.
Sniffing out Stingray Noses: The Functional Morphology of Batoid Olfaction

Synopsis Batoid fishes (rays, skates, sawfishes, and guitarfishes) are macrosmatic, meaning they rely on their sense of smell as one of the primary senses for survival and reproduction. Olfaction is important for long-distance tracking and navigation, predator and prey recognition, and conspecific signaling. However, the mechanisms by which batoids harness odorants is unknown. Without a direct pump-like system, it is hypothesized that batoids irrigate their nostrils via one or a combination of the following: the motion pump, buccopharyngeal pump, pressure (ex. pitot-like mechanism), or a shearing force (ex. viscous entrainment). These mechanisms rely on the size, shape, and position of the nostrils with respect to the head and to each other. Batoids are united as a group by their dorsoventrally compressed body plans, with nostrils on the ventral side of their body. This position presents several challenges for odor capture and likely limits the effectivity of the motion pump. Batoid fishes display an expansive nasal morphology, with inlet nostrils ranging from thin, vertical slits to wide, horizontal ovals to protruding, tube-like funnels, and more. In this paper, a morphometric model is developed to quantify the vast diversity in batoid nose shapes, sizes, and positions on the head in an ecological and functional framework. Specifically, swimming mode, lifestyle, habitat, and diet are examined for correlations with observed nasal morphotypes. Morphometric measurements were taken on all 4 orders present in Batoidea to broadly encompass batoid nasal diversity (Rhinopristiformes 4/5 families; Rajiformes 2/4 families; Torpediniformes 4/4 families; Myliobatiformes 8/11 families). All batoid external nasal diversity was found to be categorized into 5 major morphological groups and were termed: flush nare [circle, comma, intermediate], open nare, and protruding nare. Several morphometric traits remained significant when accounting for shared ancestry, including the position and angle of the nostril on the head, the width of the inlet hole, and the spacing of the nostrils from each other. These measurements were found to be closely correlated and statistically significant with the swimming mode of the animal. This study provides the first crucial step in understanding batoid olfaction, by understanding the diversity of the morphology of the system. Because odor capture is a strictly hydrodynamic process, it may be that factors relating more directly to the fluid dynamics (i.e., swimming mode, velocity, Reynolds number) may be more important in shaping the evolution of the diversity of batoid noses than other ecological factors like habitat and diet.
Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections

The behavior of the gradient descent (GD) algorithm is analyzed for a deep neural network model with skip-connections. It is proved that in the over-parametrized regime, for a suitable initialization, with high probability GD can find a global minimum exponentially fast. Generalization error estimates along the GD path are also established. As a consequence, it is shown that when the target function is in the reproducing kernel Hilbert space (RKHS) with a kernel defined by the initialization, there exist generalizable early-stopping solutions along the GD path. In addition, it is also shown that the GD path is uniformly close to the functions given by the related random feature model. Consequently, in this "implicit regularization" setting, the deep neural network model deteriorates to a random feature model. Our results hold for neural networks of any width larger than the input dimension.
A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing

The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of the underlying Markov process, and branches onto another particle at each killing time. The consistency of this method in the large population limit was the subject of several recent articles. In the present paper, we go one step forward and prove a central limit theorem for the law of the Fleming-Viot particle system at a given time under two conditions: a “soft killing” assumption and a boundedness condition involving the “carré du champ” operator of the underlying Markov process. Index Terms — Sequential Monte Carlo, Interacting particle systems, Process with killing 2010 Mathematics Subject Classification: 82C22, 82C80, 65C05, 60J25, 60K35, 60K37 This work was partially supported by the French Agence Nationale de la Recherche, under grant ANR-14-CE23-0012, and by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement number 614492. Corresponding author.
Error analysis of a finite volume element method for fractional order evolution equations with nonsmooth initial data

In this paper, a finite volume element (FVE) method is considered for spatial approximations of time-fractional diffusion equations involving a Riemann-Liouville fractional derivative of order $\alpha \in (0,1)$ in time. Improving upon earlier results (Karaa {\it et al.}, IMA J. Numer. Anal. 2016), optimal error estimates in $L^2(\Omega)$- and $H^1(\Omega)$-norms for the semidiscrete problem with smooth and middly smooth initial data, i.e., $v\in H^2(\Omega)\cap H^1_0(\Omega)$ and $v\in H^1_0(\Omega)$ are established. For nonsmooth data, that is, $v\in L^2(\Omega)$, the optimal $L^2(\Omega)$-error estimate is shown to hold only under an additional assumption on the triangulation, which is known to be satisfied for symmetric triangulations. Superconvergence result is also proved and as a consequence, a quasi-optimal error estimate is established in the $L^\infty(\Omega)$-norm. Further, two fully discrete schemes using convolution quadrature in time generated by the backward Euler and the second-order backward difference methods are analyzed, and error estimates are derived for both smooth and nonsmooth initial data. Based on a comparison of the standard Galerkin finite element solution with the FVE solution and exploiting tools for Laplace transforms with semigroup type properties of the FVE solution operator, our analysis is then extended in a unified manner to several time-fractional order evolution problems. Finally, several numerical experiments are conducted to confirm our theoretical findings.
Optimal Treatment Duration of Bevacizumab as Front-Line Therapy for Advanced Ovarian Cancer: AGO-OVAR 17 BOOST/GINECO OV118/ENGOT Ov-15 Open-Label Randomized Phase III Trial

PURPOSE To compare standard versus extended duration of bevacizumab treatment in combination with front-line chemotherapy in women with newly diagnosed stage IIB-IV ovarian cancer. METHODS In this multicenter, open-label, randomized phase III trial (ClinicalTrials.gov identifier: NCT01462890), patients with newly diagnosed International Federation of Gynecology and Obstetrics stage IIB-IV epithelial ovarian, fallopian tube, or peritoneal cancer underwent primary cytoreductive surgery followed by six cycles of chemotherapy (paclitaxel 175 mg/m2 plus carboplatin area under the curve 5 once every 3 weeks) and bevacizumab (15 mg/kg once every 3 weeks). Patients were randomly assigned 1:1 to receive bevacizumab for either 15 or 30 months, stratified by International Federation of Gynecology and Obstetrics stage/residual tumor. The primary end point was investigator-assessed progression-free survival (PFS) according to RECIST version 1.1. Secondary end points included overall survival (OS), safety, and tolerability. RESULTS Between November 11, 2011, and August 6, 2013, 927 women were randomly assigned. There was no difference in PFS between treatment arms (hazard ratio, 0.99; 95% CI, 0.85 to 1.15; unstratified log-rank P = .90). Median PFS was 24.2 versus 26.0 months with standard versus extended duration of bevacizumab, respectively; restricted mean PFS was 39.5 versus 39.3 months, respectively. There was no OS difference between treatment arms (hazard ratio, 1.04; 95% CI, 0.87 to 1.23; P = .68). Serious/nonserious adverse events of special interest occurred in 29% versus 34% of patients in the standard versus experimental arms, respectively, and were consistent with the known safety profile of standard bevacizumab. CONCLUSION Longer treatment duration with bevacizumab for up to 30 months did not improve PFS or OS in patients with primary epithelial ovarian, fallopian tube, or peritoneal cancer. A bevacizumab treatment duration of 15 months remains the standard of care.
Paley Graphs and Their Generalizations

Acknowledgment I would like to offer my deepest gratitude and thankfulness to Prof. Dr. F. Grunewald for suggesting the topics of this thesis, for his kind supervision, and for his invaluable help during the progress of present work. I owe my deepest gratitude and special thankfulness to Prof. Dr. E. Klimenko who offered me a great help in understanding the topics and to get this document into its present shape. Many thanks for her stimulating discussion, sincere advice, incisive comments, and careful reading of the manuscript. Naturally, all the mistakes that can still be found in this thesis are mine. If you ever find a word that is spelled correctly, it must have been Prof. Dr. E. Klimenko dropping me a line. I want also to thank my family for their support and for keeping me going.
$\mathcal{C}^{\infty}$-hypoellipticity and extension of $CR$ functions

Let $M$ be a $CR$ submanifold of a complex manifold $X$. The main result of this article is to show that $CR$-hypoellipticity at $p_0\in{M}$ is necessary and sufficient for holomorphic extension of all germs of $CR$ functions to an ambient neighborhood in $X$. As an application, we obtain that $CR$-hypoellipticity implies the existence of generic embeddings and prove holomorphic extension for a large class of $CR$ manifolds satisfying a higher order Levi pseudoconcavity condition.
An inverse problem for Maxwell’s equations with Lipschitz parameters

We consider an inverse boundary value problem for Maxwell’s equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric permittivity, and magnetic permeability are uniquely determined by knowledge of all tangential electric and magnetic fields on the boundary of the body at a fixed frequency.
Typicality of recurrence for Lorentz gases

It is a safe conjecture that most (not necessarily periodic) two-dimensional Lorentz gases with finite horizon are recurrent. Here we formalize this conjecture by means of a stochastic ensemble of Lorentz gases, in which independent identically distributed random scatterers are placed in each cell of a co-compact lattice in the plane. We prove that the typical Lorentz gas, in the sense of Baire, is recurrent, and give results in the direction of showing that recurrence is an almost sure property (including a zero--one law that holds in every dimension). A few toy models illustrate the extent of these results.
A mouse pancreatic organoid model to compare PD-L1 blocking antibodies

ABSTRACT Immune checkpoint inhibitors (ICIs) have changed the therapeutic landscape for cancer patients, but diabetes, a rare, severe immune-related endocrinopathy, is linked to ICI therapy. It is unclear whether glycosylation of ICIs may play a role in the development of this adverse event and how the physiological effects of different ICIs on pancreatic cells should be evaluated. We used a mouse pancreatic organoid model to compare three PD-L1 blocking antibodies in the presence or absence of IFNγ using a metabolic bioanalyzer. Modulation of ICI glycosylation altered its metabolic effects on mouse pancreatic organoids, suggesting that this model could be used to monitor and compare ICIs and to study the mechanisms underlying the development of IC-mediated diabetes.
Modified future diurnal variability of the global surface ocean CO2 system

Our understanding of how increasing atmospheric CO2 and climate change influences the marine CO2 system and in turn ecosystems has increasingly focused on perturbations to carbonate chemistry variability. This variability can affect ocean‐climate feedbacks and has been shown to influence marine ecosystems. The seasonal variability of the ocean CO2 system has already changed, with enhanced seasonal variations in the surface ocean pCO2 over recent decades and further amplification projected by models over the 21st century. Mesocosm studies and CO2 vent sites indicate that diurnal variability of the CO2 system, the amplitude of which in extreme events can exceed that of mean seasonal variability, is also likely to be altered by climate change. Here, we modified a global ocean biogeochemical model to resolve physically and biologically driven diurnal variability of the ocean CO2 system. Forcing the model with 3‐h atmospheric outputs derived from an Earth system model, we explore how surface ocean diurnal variability responds to historical changes and project how it changes under two contrasting 21st‐century emission scenarios. Compared to preindustrial values, the global mean diurnal amplitude of pCO2 increases by 4.8 μatm (+226%) in the high‐emission scenario but only 1.2 μatm (+55%) in the high‐mitigation scenario. The probability of extreme diurnal amplitudes of pCO2 and [H+] is also affected, with 30‐ to 60‐fold increases relative to the preindustrial under high 21st‐century emissions. The main driver of heightened pCO2 diurnal variability is the enhanced sensitivity of pCO2 to changes in temperature as the ocean absorbs atmospheric CO2. Our projections suggest that organisms in the future ocean will be exposed to enhanced diurnal variability in pCO2 and [H+], with likely increases in the associated metabolic cost that such variability imposes.
Inapproximability of actions and Kazhdan's property (T)

We construct p.m. p. group actions that are not local-global limits of sequences of finite graphs. Moreover, they do not weakly contain any sequence of finite labeled graphs. Our methods are based on the study of almost automorphisms of sofic approximations: We show that the set of epsilon-automorphisms of a sufficiently good sofic approximation of a Kazhdan group by expanders form a group in a natural way.
Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts

Consider a topologically transitive countable Markov shift and, let $f$ be a summable potential with bounded variation and finite Gurevic pressure. We prove that there exists an equilibrium state $\mu_{tf}$ for each $t > 1$ and that there exists accumulation points for the family $(\mu_{tf})_{t>1}$ as $t \to \infty$. We also prove that the Kolmogorov-Sinai entropy is continuous at $\infty$ with respect to the parameter $t$, that is $\lim_{t \to \infty} h(\mu_{tf})=h(\mu_{\infty})$, where $\mu_{\infty}$ is an accumulation point of the family $(\mu_{tf})_{t>1}$. These results do not depend on the existence of Gibbs measures and, therefore, they extend results of \cite{MaUr01} and \cite{Sar99} for the existence of equilibrium states without the BIP property, \cite{JMU05} for the existence of accumulation points in this case and, finally, we extend completely the result of \cite{Mor07} for the entropy zero temperature limit beyond the finitely primitive case.
Subexponential growth rates in functional differential equations

This paper determines the rate of growth to infinity of a scalar autonomous nonlinear functional differential equation with finite delay, where the right hand side is a positive continuous linear functional of $f(x)$. We assume $f$ grows sublinearly, and is such that solutions should exhibit growth faster than polynomial, but slower than exponential. Under some technical conditions on $f$, it is shown that the solution of the functional differential equation is asymptotic to that of an auxiliary autonomous ordinary differential equation with righthand side proportional to $f$ (with the constant of proportionality equal to the mass of the finite measure associated with the linear functional), provided $f$ grows more slowly than $l(x)=x/\log x$. This linear--logarithmic growth rate is also shown to be critical: if $f$ grows more rapidly than $l$, the ODE dominates the FDE; if $f$ is asymptotic to a constant multiple of $l$, the FDE and ODE grow at the same rate, modulo a constant non--unit factor.
Evaluation of online interprofessional simulation workshops for obstetric and neonatal emergencies

Objectives To explore student perceptions of learning and interprofessional aspects of obstetric and neonatal emergencies through online simulation-based workshops. Methods This qualitative study was conducted at Monash University, Australia. Data were obtained from six separate online Obstetric Neonatal Emergency Simulation workshops held between May 2020 and August 2021. A total of 385 students attended and were invited to participate in the study by completing an online survey two-three weeks later. Of the attendees, 144 students completed the survey (95 medical, 45 midwifery), equating to a response rate of 37%. Survey responses were downloaded from online survey platform and separated into medical and midwifery responses. Thematic analysis of data was performed using a coding framework, resulting in development of themes and subthemes. Results Main themes were adaptability, connectivism, preparedness for practice, experiential learning, learning through modelling and dynamics of online interaction. Students reported that online workshop was a useful alternative method to experience simulation-based learning, increase their readiness for clinical practice and foster positive interprofessional relationships. Consistent with existing literature evaluating similar in-person programs, midwifery students were most interested in interprofessional interaction (predominant theme: dynamics of online interaction), whilst medical students were more concerned with developing clinical skills (predominant themes: learning through modelling, experiential learning). Conclusions Online learning may be a useful and convenient way of delivering interprofessional simulation-based education during the pandemic, in remote areas and as an adjunct to in-person teaching. Future studies should evaluate the impact of online learning with a mixed methods study and in comparison, to in-person programs.
Isomorphisms of algebras of convolution operators

For $p,q\in [1,\infty)$, we study the isomorphism problem for the $p$- and $q$-convolution algebras associated to locally compact groups. While it is well known that not every group can be recovered from its group von Neumann algebra, we show that this is the case for the algebras $\mathrm{CV}_p(G)$ of $p$-convolvers and $\mathrm{PM}_p(G)$ of $p$-pseudomeasures, for $p\neq 2$. More generally, we show that if $\mathrm{CV}_p(G)$ is isometrically isomorphic to $\mathrm{CV}_q(H)$, with $p,q\neq 2$, then $G$ must be isomorphic to $H$ and $p$ and $q$ are either equal or conjugate. This implies that there is no $L^p$-version of Connes' uniqueness of the hyperfinite II$_1$-factor. Similar results apply to the algebra $\mathrm{PF}_p(G)$ of $p$-pseudofunctions, generalizing a classical result of Wendel. We also show that other $L^p$-rigidity results for groups can be easily recovered and extended using our main theorem. Our results answer questions originally formulated in the work of Herz in the 70's. Moreover, our methods reveal new information about the Banach algebras in question. As a non-trivial application, we verify the reflexivity conjecture for all Banach algebras lying between $\mathrm{PF}_p(G)$ and $\mathrm{CV}_p(G)$: if any such algebra is reflexive and amenable, then $G$ is finite.
Critical soil moisture thresholds of plant water stress in terrestrial ecosystems

Plant water stress occurs at the point when soil moisture (SM) limits transpiration, defining a critical SM threshold (θcrit). Knowledge of the spatial distribution of θcrit is crucial for future projections of climate and water resources. Here, we use global eddy covariance observations to quantify θcrit and evaporative fraction (EF) regimes. Three canonical variables describe how EF is controlled by SM: the maximum EF (EFmax), θcrit, and slope (S) between EF and SM. We find systematic differences of these three variables across biomes. Variation in θcrit, S, and EFmax is mostly explained by soil texture, vapor pressure deficit, and precipitation, respectively, as well as vegetation structure. Dryland ecosystems tend to operate at low θcrit and show adaptation to water deficits. The negative relationship between θcrit and S indicates that dryland ecosystems minimize θcrit through mechanisms of sustained SM extraction and transport by xylem. Our results further suggest an optimal adaptation of local EF-SM response that maximizes growing-season evapotranspiration and photosynthesis.
What Makes Dependency on Homecare Bearable? A Phenomenological Study

Becoming dependent on homecare in old age is a radical life change that requires complex adaption. The purpose of this study was to explore the existential dimension of being dependent on homecare with a particular focus on what makes dependency bearable. In total, 15 older people living in Denmark or Norway were interviewed using a phenomenological approach. The material was analyzed employing Max van Manen’s meaning-giving approach coined “Phenomenology of practice. ” During the analysis, four themes emerged: pure acceptance of an inevitable situation, acting independently as much as possible, negotiating to receive good care, and gratitude toward caring caregivers. The results point to a need for respectful and individualized homecare leveling out the subordinate position in which dependency on homecare tends to place older people.