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Objectives:The Hepatology Committee of the European Society for Pediatric Gastroenterology, Hepatology and Nutrition (ESPGHAN) aims to educate pediatric gastroenterologists, members of ESPGHAN and professionals from other specialties promoting an exchange of clinical expertise in the field of pediatric hepatology. Herewith we have concentrated on detailing the recent advances in acute liver failure in infants and children.Methods:The 2020 ESPGHAN monothematic three-day conference on pediatric hepatology disease, entitled "acute liver failure" (ALF), was organized in Athens, Greece. ALF is a devastating disease with high mortality and most cases remain undiagnosed. As knowledge in diagnosis and treatment of ALF in infants and children has increased in the past decades, the objective was to update physicians in the field with the latest research and developments in early recognition, curative therapies and intensive care management, imaging techniques and treatment paradigms in these age groups.Results:In the first session, the definition, epidemiology, various causes of ALF, in neonates and older children and recurrent ALF (RALF) were discussed. The second session was dedicated to new aspects of ALF management including hepatic encephalopathy (HE), coagulopathy, intensive care interventions, acute on chronic liver failure, and the role of imaging in treatment and prognosis. Oral presentations by experts in various fields are summarized highlighting key learning points.Conclusions:The current report summarizes the major learning points from this meeting. It also identifies areas where there is gap of knowledge, thereby identifying the research agenda for the near future. © 2022 Lippincott Williams and Wilkins. All rights reserved.

For families of $K3$ surfaces, we establish a sufficient criterion for real or complex multiplication. Our criterion is arithmetic in nature. It may show, at first, that the generic fibre of the family has a nontrivial endomorphism field. Moreover, the endomorphism field does not shrink under specialisation. As an application, we present two explicit families of $K3$ surfaces having real multiplication by $\bbQ(\sqrt{2})$ and $\bbQ(\sqrt{5})$, respectively.

We report on the computation of invariants, covariants, and contravariants of cubic surfaces. All algorithms are implemented in the computer algebra system magma., 9 pages

Given systems of two (inhomogeneous) quadratic equations in four variables, it is known that the Hasse principle for integral points may fail. Sometimes this failure can be explained by some integral Brauer-Manin obstruction. We study the existence of a non-trivial algebraic part of the Brauer group for a family of such systems and show that the failure of the integral Hasse principle due to an algebraic Brauer-Manin obstruction is rare, as for a generic choice of a system the algebraic part of the Brauer-group is trivial. We use resolvent constructions to give quantitative upper bounds on the number of exceptions., 13 pages

We study the algebraic Brauer classes on open del Pezzo surfaces of degree $4$. I.e., on the complements of geometrically irreducible hyperplane sections of del Pezzo surfaces of degree $4$. We show that the $2$-torsion part is generated by classes of two different types. Moreover, there are two types of $4$-torsion classes. For each type, we discuss methods for the evaluation of such a class at a rational point over a $p$-adic field.

We describe a construction of plane quartics with prescribed Galois operation on the 28 bitangents, in the particular case of a Galois invariant Steiner hexad. As an application, we solve the inverse Galois problem for degree two del Pezzo surfaces in the corresponding particular case.

We describe a construction of plane quartics with prescribed Galois operation on the 28 bitangents, in the particular case of a Galois invariant Cayley octad. As an application, we solve the inverse Galois problem for degree two del Pezzo surfaces in the corresponding particular case., arXiv admin note: substantial text overlap with arXiv:1708.00071

We report on our project to find explicit examples of $K3$ surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are $p$-adic in nature.

We report on our investigations concerning algebraic and transcendental Brauer-Manin obstructions to integral points on complements of a hyperplane section in degree four del Pezzo surfaces. We discuss moreover two concepts of an obstruction at an archimedean place. Concrete examples are given of pairs of non-homogeneous quadratic polynomials in four variables representing (0,0) over Q and over Z_p for all primes p, but not over Z. By blow-up, these yield cubic polynomials in three variables all integral solutions of which satisfy a gcd condition., 39 pages

Einleitung: Studien zur Assoziation von juveniler idiopathischer Arthritis (JIA) und Zöliakie sind rar und die Ergebnisse regional unterschiedlich. Dementsprechend divergierend sind Empfehlungen zur Durchführung regelmäßiger Screeninguntersuchungen bei PatientInnen ohne Zöliakie-spezifische[zum vollständigen Text gelangen Sie über die oben angegebene URL], 43. Kongress der Deutschen Gesellschaft für Rheumatologie (DGRh); 29. Jahrestagung der Deutschen Gesellschaft für Orthopädische Rheumatologie (DGORh); 25. wissenschaftliche Jahrestagung der Gesellschaft für Kinder- und Jugendrheumatologie (GKJR)

We give an asymptotic expansion for the density of del Pezzo surfaces of degree four in a certain Birch Swinnerton-Dyer family violating the Hasse principle due to a Brauer-Manin obstruction. Under the assumption of Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups for elliptic curves, we obtain an asymptotic formula for the number of all del Pezzo surfaces in the family, which violate the Hasse principle., 27 pages

We show that, for every integer $1 \leq d \leq 4$ and every finite set $S$ of places, there exists a degree $d$ del Pezzo surface $X$ over ${\mathbb Q}$ such that ${\rm Br}(X)/{\rm Br}({\mathbb Q}) \cong {\mathbb Z}/2{\mathbb Z}$ and the Brauer-Manin obstruction works exactly at the places in $S$. For $d = 4$, we prove that in all cases, with the exception of $S = \{\infty\}$, this surface may be chosen diagonalizably over ${\mathbb Q}$.

Given a number field $k$ and a positive integer $d$, in this paper we consider the following question: does there exist a smooth diagonal surface of degree $d$ in $\mathbb{P}^3$ over $k$ which contains a line over every completion of $k$, yet no line over $k$? We answer the problem using Galois cohomology, and count the number of counter-examples using a result of Erd��s., 14 pages

We show that, over every number field, the degree four del Pezzo surfaces that violate the Hasse principle are Zariski dense in the moduli scheme., 21 pages

We construct explicit examples of $K3$ surfaces over ${\mathbb Q}$ having real multiplication. Our examples are of geometric Picard rank 16. The standard method for the computation of the Picard rank provably fails for the surfaces constructed.

We construct new examples of cubic surfaces, for which the Hasse principle fails. Thereby, we show that, over every number field, the counterexamples to the Hasse principle are Zariski dense in the moduli scheme of non-singular cubic surfaces.

For an arbitrary del Pezzo surface S, we compute alpha(S), which is the volume of a certain polytope in the dual of the effective cone of S, using Magma and Polymake. The constant alpha(S) appears in Peyre's conjecture for the leading term in the asymptotic formula for the number of rational points of bounded height on S over number fields., 11 pages, 1 figure

We study the moduli space $\widetilde{\calM}$ of marked cubic surfaces. By classical work of A.\,B. Coble, this has a compactification $\widetilde{M}$, which is linearly acted upon by the group $W(E_6)$. $\widetilde{M}$ is given as the intersection of 30 cubics in $\bP^9$. For the morphism $\widetilde{calM} \to \bP(1,2,3,4,5)$ forgetting the marking, followed by Clebsch's invariant map, we give explicit formulas. I.e., Clebsch's invariants are expressed in terms of Coble's irrational invariants. As an application, we give an affirmative answer to the inverse Galois problem for cubic surfaces over $\bbQ$.

We report on our experiments and theoretical investigations concerning weak approximation and the transcendental Brauer-Manin obstruction for special Kummer surfaces., Updated version from May 2012, Accepted for publication in the ANTS X Proceedings

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial homomorphisms in the other cases. Thereby, we follow the classification of cubic surfaces, due to A. Cayley.

We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples., Extended introduction, discussion of the example of Cassels and Guy

We test R. van Luijk's method for computing the Picard group of a $K3$ surface. The examples considered are the resolutions of Kummer quartics in $\bP^3$. Using the theory of abelian varieties, in this case, the Picard group may be computed directly. Our experiments show that the upper bounds provided by R. van Luijk's method are sharp when sufficiently many primes are used. In fact, there are a lot of primes that yield a value close to the exact one. However, for many but not all Kummer surfaces $V$ of Picard rank 18, we have $\smash{\rk\Pic(V_{\bar\bbF_{p}}) \geq 20}$ for a set of primes of density $\geq 1/2$., This article is unchanged. This is just a second trial to upload our raw data to the Data Conservancy project

We report on our project to construct non-singular cubic surfaces over $\bbQ$ with a rational line. Our method is to start with degree 4 Del Pezzo surfaces in diagonal form. For these, we develop an explicit version of Galois descent.

Let $X$ be a smooth proper variety of even dimension $d$ over a finite field. We establish a restriction on the value at $(-1)$ of the characteristic polynomial of the Frobenius on the middle-dimensional ��tale cohomology of $X$ with coefficients in ${\mathbb Q}_l(d/2)$., Revised version, several minor errors corrected

The quadruple $(1\,484\,801, 1\,203\,120, 1\,169\,407, 1\,157\,520)$ already known is essentially the only non-trivial solution of the Diophantine equation $x^4 + 2 y^4 = z^4 + 4 w^4$ for $|x|$, $|y|$, $|z|$, and $|w|$ up to one hundred million. We describe the algorithm we used in order to establish this result, thereby explaining a number of improvements to our original approach.

We present a method to construct non-singular cubic surfaces over $\bbQ$ with a Galois invariant pair of Steiner trihedra. We start with cubic surfaces in a form generalizing that of A. Cayley and G. Salmon. For these, we develop an explicit version of Galois descent.

This second section of the first ECCO pathogenesis workshop on anti-TNF therapy failures in inflammatory bowel diseases addresses the biological roles of TNFα and the effects and mechanisms of action of TNFα antagonists. Mechanisms underlying their failure, including induction of TNF-independent inflammatory pathways and phenomena of paradoxical inflammation are discussed. © 2010 European Crohn's and Colitis Organisation.

We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majority of the cases when this group is non-zero. Our approach is to associate a Brauer class with every Galois invariant double-six. We show that all order two Brauer classes may be obtained in this way. We also recover Sir Peter Swinnerton-Dyer's result that $\Br(S)/\Br(\bbQ)$ may take only five values.

We present a method to compute the geometric Picard rank of a $K3$ surface over $\bbQ$. Contrary to a widely held belief, we show it is possible to verify Picard rank $1$ using reduction only at a single prime. Our method is based on deformation theory for invertible sheaves.

We construct explicit examples of cubic surfaces over $\bbQ$ such that the 27 lines are acted upon by the index two subgroup of the maximal possible Galois group. This is the simple group of order $25 920$. Our examples are given in pentahedral normal form with rational coefficients. For such cubic surfaces, we study the discriminant and show its relation to the index two subgroup. On the corresponding parameter space, we search for rational points, discuss their asymptotic, and construct an accumulating subvariety.

We generalize L.J. Mordell's construction of cubic surfaces for which the Hasse principle fails.

We construct examples of $K3$ surfaces of geometric Picard rank $1$. Our method is a refinement of that of R. van Luijk. It is based on an analysis of the Galois module structure on ��tale cohomology. This allows to abandon the original limitation to cases of Picard rank $2$ after reduction modulo $p$. Furthermore, the use of Galois data enables us to construct examples which require significantly less computation time.

We test the methods for computing the Picard group of a $K3$ surface in a situation of high rank. The examples chosen are resolutions of quartics in $\bP^3$ having 14 singularities of type $A_1$. Our computations show that the method of R. van Luijk works well when sufficiently large primes are used.

If the cosine of a rational multiple of $��$ is a rational number then it is an integral multiple of $\frac12$. For this fact, we give a proof accessible to an interested school student. We then discuss which quadratic and cubic irrationalities are values of cosine at ratinal multiples of $��$.