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We present the results of Phase I of an ongoing review of Monte Carlo tools relevant for low-energy hadronic cross sections. This includes a detailed comparison of Monte Carlo codes for electron-positron scattering into a muon pair, pion pair, and electron pair, for scan and radiative-return experiments. After discussing the various approaches that are used and effects that are included, we show differential cross sections obtained with AfkQed, BabaYaga@NLO, KKMC, MCGPJ, McMule, Phokhara, and Sherpa, for scenarios that are inspired by experiments providing input for the dispersive evaluation of the hadronic vacuum polarisation., Comment: RadioMonteCarLow 2 Working Group report Phase I, 67 pages, 34 figures

We consider solutions to parametrized systems of generalized polynomial equations (with real exponents) in $n$ positive variables, involving $m$ monomials with positive parameters; that is, $x\in\mathbb{R}^n_>$ such that ${A \, (c \circ x^B)=0}$ with coefficient matrix $A\in\mathbb{R}^{l \times m}$, exponent matrix $B\in\mathbb{R}^{n \times m}$, parameter vector $c\in\mathbb{R}^m_>$, and componentwise product $\circ$. As our main result, we characterize the existence of a unique solution (modulo an exponential manifold) for all parameters in terms of the relevant geometric objects of the polynomial system, namely the $\textit{coefficient polytope}$ and the $\textit{monomial dependency subspace}$. We show that unique existence is equivalent to the bijectivity of a certain moment/power map, and we characterize the bijectivity of this map using Hadamard's global inversion theorem. Furthermore, we provide sufficient conditions in terms of sign vectors of the geometric objects, thereby obtaining a multivariate Descartes' rule of signs for exactly one solution.

We present our SageMath package elementary_vectors for computing elementary and sign vectors of real subspaces. In this setting, elementary vectors are support-minimal vectors that can be determined from maximal minors of a real matrix representing a subspace. By applying the sign function, we obtain the cocircuits of the corresponding oriented matroid, which in turn allow the computation of all sign vectors of a real subspace. As an application, we discuss sign vector conditions for existence and uniqueness of complex-balanced equilibria of chemical reaction networks with generalized mass-action kinetics. The conditions are formulated in terms of sign vectors of two subspaces arising from the stoichiometric coefficients and the kinetic orders of the reactions. We discuss how these conditions can be checked algorithmically, and we demonstrate the functionality of our package sign_vector_conditions in several examples., Comment: 10 pages, ICMS 2024

We develop a general toolbox to study $W^{1,p}$ solutions of differential inclusions $\nabla u \in K$ for unbounded sets $K$. A key notion is the concept that a subset $K$ of the space $\mathbb{R}^{d \times m}$ of $d \times m$ matrices can be reduced to another set $K'$. We then use this framework to show that the product rigidity for Sobolev maps fails for $p<2$, and also apply our toolbox to simplify several examples from the literature., Comment: Dedicated to Professor Vladimir \v Sver\'ak on the occasion of his 65th birthday

Let $M$ be a smooth, compact, connected, oriented Riemannian manifold, and let $\imath: M \to \mathbb R^d$ be an isometric embedding. We show that a Sobolev map $f: M \to M$ which has the property that the differential $df(q)$ is close to the set $SO(T_q M, T_{f(q)} M)$ of orientation preserving isometries (in an $L^p$ sense) is already $W^{1,p}$ close to a global isometry of $M$. More precisely we prove for $p \in (1,\infty)$ the optimal linear estimate $$\inf_{\phi \in \mathrm{Isom}_+(M)} \| \imath \circ f - \imath \circ \phi\|_{W^{1,p}}^p \le C E_p(f)$$ where $$ E_p(f) := \int_M {\rm dist}^p(df(q), SO(T_q M, T_{f(q)} M)) \, d{\rm vol}_M$$ and where $\mathrm{Isom}_+(M)$ denotes the group of orientation preserving isometries of $M$. This extends the Euclidean rigidity estimate of Friesecke-James-M\"uller [Comm. Pure Appl. Math. {\bf 55} (2002), 1461--1506] to Riemannian manifolds. It also extends the Riemannian stability result of Kupferman-Maor-Shachar [Arch. Ration. Mech. Anal. {\bf 231} (2019), 367--408] for sequences of maps with $E_p(f_k) \to 0$ to an optimal quantitative estimate. The proof relies on the weak Riemannian Piola identity of Kupferman-Maor-Shachar, a uniform $C^{1,\alpha}$ approximation through the harmonic map heat flow, and a linearization argument which reduces the estimate to the well-known Riemannian version of Korn's inequality.

Chemical reactions can be understood as transformations of multigraphs (molecules) that preserve vertex labels (atoms) and degrees (sums of bonding and non-bonding electrons), thereby implying the atom-atom map of a reaction. The corresponding reaction mechanism is often described by an electron pushing diagram that explains the transformation by consecutive local relocations of invidudal edges (electron pairs). Here, we show that every degree-preserving map between multigraphs, and thus every atom-atom map, can be generated by cyclic electron pushing. Moreover, it is always possible to decompose such an explanation into electron pushing diagrams involving only four electron pairs. This in turn implies that every reaction can be decomposed into a sequence of elementary reactions that involve at most two educt molecules and two product molecules. Hence, the requirement of a mechanistic explantion in terms of electron pushing and small imaginary transition states does not impose a combinatorial constraint on the feasibility of hypothetical chemical reactions.

The PSI Positron Production (P$^3$ or P-cubed) experiment is a demonstrator for a e+ source and capture system with potential to improve the state-of-the-art e+ yield by an order of magnitude. The experiment is driven by the FCC-ee injector study and will be hosted in the SwissFEL facility at the Paul Scherrer Institute in Switzerland. This paper is an overview of the P$^3$ design at an advanced stage, with a particular emphasis on a novel e+ capture system and its associated beam dynamics. Additionally, a concept for the experiment diagnostics is presented, as well as the key points of the ongoing installation works.

We provide fundamental results on positive solutions to parametrized systems of generalized polynomial $\textit{inequalities}$ (with real exponents and positive parameters), including generalized polynomial $\textit{equations}$. In doing so, we also offer a new perspective on fewnomials and (generalized) mass-action systems. We find that geometric objects, rather than matrices, determine generalized polynomial systems: a bounded set/"polytope" $P$ (arising from the coefficient matrix) and two subspaces representing monomial differences and dependencies (arising from the exponent matrix). The dimension of the latter subspace, the monomial dependency $d$, is crucial. As our main result, we rewrite $\textit{polynomial inequalities}$ in terms of $d$ $\textit{binomial equations}$ on $P$, involving $d$ monomials in the parameters. In particular, we establish an explicit bijection between the original solution set and the solution set on $P$ via exponentiation. (i) Our results apply to any generalized polynomial system. (ii) The dependency $d$ and the dimension of $P$ indicate the complexity of a system. (iii) Our results are based on methods from linear algebra and convex/polyhedral geometry, and the solution set on $P$ can be further studied using methods from analysis such as sign-characteristic functions (introduced in this work). We illustrate our results (in particular, the relevant geometric objects) through three examples from real fewnomial and reaction network theory. For two mass-action systems, we parametrize the set of equilibria and the region for multistationarity, respectively, and even for univariate trinomials, we offer new insights: We provide a "solution formula" involving discriminants and "roots"., Comment: arXiv admin note: substantial text overlap with arXiv:2304.05273. author note: this manuscript and arXiv:2304.05273 are parallel works; there is no overlap regarding examples. there is overlap in the outline of the underlying theory for a self-contained presentation

We consider positive solutions to parametrized systems of generalized polynomial equations (with real exponents and positive parameters). By a fundamental result obtained in parallel work, polynomial systems are determined by geometric objects, rather than matrices: a polytope $P$ (arising from the coefficient matrix) and two subspaces representing monomial differences and dependencies (arising from the exponent matrix). The dimension of the latter subspace, the monomial dependency $d$, is crucial. Indeed, we rewrite $\textit{polynomial}$ equations in terms of $d$ $\textit{binomial}$ equations on the coefficient polytope $P$, involving $d$ monomials in the parameters. We further study the solution set on $P$ using methods from analysis such as sign-characteristic functions and Wronskians. In this work, we present first applications to fewnomial systems through five (classes of) examples. In particular, we study (i) $n$ trinomials involving ${n+2}$ monomials in $n$ variables, having dependency $d=1$, and (ii) one trinomial and one $t$-nomial (with $t\ge3$) in two variables, having $d=t-1\ge2$. For (i), we bound the number of positive solutions using the number of roots of a univariate polynomial of degree at most $n$. We also show that this number is always less than or equal to the number of sign changes in an optimal Descartes' rule given in Bihan et al. (2021). For (ii), we improve upper bounds given in Li et al. (2003) and Koiran et al. (2015). Further, for two trinomials ($t=3$), we refine the known upper bound of five in terms of the exponents, and we find an example with five positive solutions that is even simpler than the smallest "Haas system"., Comment: author note: this manuscript and arXiv:2306.13916 are parallel works; there is overlap in the outline of the underlying theory, required for a self-contained presentation. more specifically, in this manuscript, we apply results from arXiv:2306.13916

Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written in this form. Previous results have focused on existence and uniqueness of special steady states (complex-balanced equilibria) for all rate constants, thereby ruling out multiple (special) steady states. Recently, necessary conditions for linear stability have been obtained. In this work, we provide sufficient conditions for the linear stability of complex-balanced equilibria for all rate constants (and also for the non-existence of other steady states). In particular, via sign-vector conditions (on the stoichiometric coefficients and kinetic orders), we guarantee that the Jacobian matrix is a $P$-matrix. Technically, we use a new decomposition of the graph Laplacian which allows to consider orders of (generalized) monomials. Alternatively, we use cycle decomposition which allows a linear parametrization of all Jacobian matrices. In any case, we guarantee stability without explicit computation of steady states. We illustrate our results in examples from chemistry and biology: generalized Lotka-Volterra systems and SIR models, a two-component signaling system, and an enzymatic futile cycle.

The journal impact factor (JIF) is often equated with journal quality and the quality of the peer review of the papers submitted to the journal. We examined the association between the content of peer review and JIF by analysing 10,000 peer review reports submitted to 1,644 medical and life sciences journals. Two researchers hand-coded a random sample of 2,000 sentences. We then trained machine learning models to classify all 187,240 sentences as contributing or not contributing to content categories. We examined the association between ten groups of journals defined by JIF deciles and the content of peer reviews using linear mixed-effects models, adjusting for the length of the review. The JIF ranged from 0.21 to 74.70. The length of peer reviews increased from the lowest (median number of words 185) to the JIF group (387 words). The proportion of sentences allocated to different content categories varied widely, even within JIF groups. For thoroughness, sentences on 'Materials and Methods' were more common in the highest JIF journals than in the lowest JIF group (difference of 7.8 percentage points; 95% CI 4.9 to 10.7%). The trend for 'Presentation and Reporting' went in the opposite direction, with the highest JIF journals giving less emphasis to such content (difference -8.9%; 95% CI -11.3 to -6.5%). For helpfulness, reviews for higher JIF journals devoted less attention to 'Suggestion and Solution' and provided fewer Examples than lower impact factor journals. No, or only small differences were evident for other content categories. In conclusion, peer review in journals with higher JIF tends to be more thorough in discussing the methods used but less helpful in terms of suggesting solutions and providing examples. Differences were modest and variability high, indicating that the JIF is a bad predictor for the quality of peer review of an individual manuscript., Comment: 44 pages

We provide a new decomposition of the Laplacian matrix (for labeled directed graphs with strongly connected components), involving an invertible $\textit{core matrix}$, the vector of tree constants, and the incidence matrix of an auxiliary graph, representing an order on the vertices. Depending on the particular order, the core matrix has additional properties. Our results are graph-theoretic/algebraic in nature. As a first application, we further clarify the binomial structure of (weakly reversible) mass-action systems, arising from chemical reaction networks. Second, we extend a classical result by Horn and Jackson on the asymptotic stability of special steady states (complex-balanced equilibria). Here, the new decomposition of the graph Laplacian allows us to consider regions in the positive orthant with given $\textit{monomial evaluation orders}$ (and corresponding polyhedral cones in logarithmic coordinates). As it turns out, all dynamical systems are asymptotically stable that can be embedded in certain $\textit{binomial differential inclusions}$. In particular, this holds for complex-balanced mass-action systems, and hence we also obtain a polyhedral-geometry proof of the classical result.

Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$ of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$ into a multiset $Y'\subseteq X$ of products. RNs are equivalent to directed hypergraphs. However, not all RNs necessarily admit a chemical interpretation. Instead, they might contradict fundamental principles of physics such as the conservation of energy and mass or the reversibility of chemical reactions. The consequences of these necessary conditions for the stoichiometric matrix $\mathbf{S} \in \mathbb{R}^{X\times\mathscr{R}}$ have been discussed extensively in the literature. Here, we provide sufficient conditions for $\mathbf{S}$ that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively. Chemically plausible RNs allow neither a perpetuum mobile, i.e., a "futile cycle" of reactions with non-vanishing energy production, nor the creation or annihilation of mass. Such RNs are said to be thermodynamically sound and conservative. For finite RNs, both conditions can be expressed equivalently as properties of $\mathbf{S}$. The first condition is vacuous for reversible networks, but it excludes irreversible futile cycles and - in a stricter sense - futile cycles that even contain an irreversible reaction. The second condition is equivalent to the existence of a strictly positive reaction invariant. Furthermore, it is sufficient for the existence of a realization in terms of sum formulas, obeying conservation of "atoms". In particular, these realizations can be chosen such that any two species have distinct sum formulas, unless $\mathbf{S}$ implies that they are "obligatory isomers". In terms of structural formulas, every compound is a labeled multigraph, in essence a Lewis formula, and reactions comprise only a rearrangement of bonds such that the total bond order is preserved.

Motivated by experiments and formal asymptotic expansions in the physics literature, Maor and Shachar (J. Elasticity 134 (2019), 149-173) studied the behaviour of a model elastic energy of maps between manifolds with incompatible metrics. For thin objects they analysed the scaling of the minimal elastic energy as a function of the thickness. In particular they showed that for maps from a ball of radius h in an oriented Riemannian manifold to Euclidean space, the infimum of a model elastic energy per unit volume scales like the fourth power of h and after rescaling one gets convergence to a quadratic expression in the curvature tensor R(p), where p denotes the centre of the ball. In this paper we show the same result for general compact oriented Riemannian targets with R(p) replaced by a suitable difference of the curvature tensors in the target and the domain, thus answering Open Question 1 in the paper by Maor and Shachar. The result extends noncompact targets provided they satisfy a uniform regularity condition. A key idea in the proof is to use Lipschitz approximations to define a suitable notion of convergence., Comment: Typos corrected, exposition slightly expanded, reference [2] added

Let $\Omega \subset \mathbb{R}^3$ be an open and bounded set with Lipschitz boundary and outward unit normal $\nu$. For $11 \quad \text{if $p = \frac32$.}$$ Specifically, there exists a constant $c=c(p,\Omega,r)>0$ such that the inequality \[ \|P \|_{L^p}\leq c\,\left(\|\operatorname{sym} P \|_{L^p} + \|\operatorname{dev}\operatorname{sym} \operatorname{Curl} P \|_{L^{r}}\right) \] holds for all tensor fields $P\in W^{1,\,p, \, r}_0(\operatorname{dev}\operatorname{sym}\operatorname{Curl})$. Here, $\operatorname{dev} X := X -\frac13 \operatorname{tr}(X)\,\mathbb{1}$ denotes the deviatoric (trace-free) part of a $3 \times 3$ matrix $X$ and the boundary condition is understood in a suitable weak sense., Comment: Ref.numbers are now visible

Systems for the automatic recognition and detection of automotive parts are crucial in several emerging research areas in the development of intelligent vehicles. They enable, for example, the detection and modelling of interactions between human and the vehicle. In this paper, we quantitatively and qualitatively explore the efficacy of deep learning architectures for the classification and localisation of 29 interior and exterior vehicle regions on three novel datasets. Furthermore, we experiment with joint and transfer learning approaches across datasets and point out potential applications of our systems. Our best network architecture achieves an F1 score of 93.67 % for recognition, while our best localisation approach utilising state-of-the-art backbone networks achieve a mAP of 63.01 % for detection. The MuSe-CAR-Part dataset, which is based on a large variety of human-car interactions in videos, the weights of the best models, and the code is publicly available to academic parties for benchmarking and future research., Comment: Demonstration and instructions to obtain data and models: https://github.com/lstappen/GoCarD

We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, "formal balance", and the new notion of "cycle balance" are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic (non-algebraic) proofs of a previous result (detailed balance = complex balance + formal balance), our main result (detailed balance = complex balance + cycle balance), and a corresponding result in the setting of continuous-time Markov chains.

We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti, M\"uller, Ortiz, Arch.\ Ration.\ Mech.\ Anal.\ 229, 79-123, 2018. The main focus of this paper concerns the formulation of a suitable framework in which the Data-Driven problem of finite elasticity is well-posed in the sense of existence of solutions. We confine attention to deformation gradients $F \in L^p(\Omega;\mathbb{R}^{n\times n})$ and first Piola-Kirchhoff stresses $P \in L^q(\Omega;\mathbb{R}^{n\times n})$, with $(p,q)\in(1,\infty)$ and $1/p+1/q=1$. We assume that the material behavior is described by means of a material data set containing all the states $(F,P)$ that can be attained by the material, and develop germane notions of coercivity and closedness of the material data set. Within this framework, we put forth conditions ensuring the existence of solutions. We exhibit specific examples of two- and three-dimensional material data sets that fit the present setting and are compatible with material frame indifference.

We study gradient field models on an integer lattice with non-convex interactions. These models emerge in distinct branches of physics and mathematics under various names. In particular, as zero-mass lattice (Euclidean) quantum field theory, models of random interfaces, and as mass-string models of nonlinear elasticity.Our attention is mostly devoted to the latter with random vector valued fields as displacements for atoms of crystal structures,where our aim is to prove the strict convexity of the free energy as a function of affine deformations for low enough temperatures and small enough deformations. This claim can be interpreted as a form of verification of the Cauchy-Born rule at small non-vanishing temperatures for a class of these models. We also show that the scaling limit of the Laplace transform of the corresponding Gibbs measure (under a proper rescaling) corresponds to the Gaussian gradient field with a particular covariance. The proofs are based on a multi-scale (renormalisation group analysis) techniques needed in view of strong correlations of studied gradient fields. To cover sufficiently wide class of models, we extend these techniques from the standard case with rotationally symmetric nearest neighbour interaction to a more general situation with finite range interactions without any symmetry. Our presentation is entirely self-contained covering the details of the needed renormalisation group methods.

We study the problem of existence and uniqueness of strong solutions to a degenerate quasilinear parabolic non-Newtonian thin-film equation. Originating from a non-Newtonian Navier--Stokes system the equation is derived by lubrication theory and under the assumption that capillarity is the only driving force. The fluid's shear-thinning rheology is described by the so-called Ellis constitutive law. For flow behaviour exponents $\alpha \geq 2$ the corresponding initial boundary value problem fits into the abstract setting of [4,Thm. 12.1]. Due to a lack of regularity this is not true for flow behaviour exponents $\alpha \in (1,2)$. For this reason we prove an existence theorem for abstract quasilinear parabolic evolution problems with H\"older continuous dependence. This result provides existence of strong solutions to the non-Newtonian thin-film problem in the setting of fractional Sobolev spaces and (little) H\"older spaces. Uniqueness of strong solutions is derived by energy methods and by using the particular structure of the equation., Comment: 20 pages

We consider problems of static equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to equilibrium constraints. A necessary and sufficient condition for the sequential lower-semicontinuity of such functionals is symmetric ${\rm div}$-quasiconvexity, a special case of Fonseca and M\"uller's $A$-quasiconvexity with $A = {\rm div}$ acting on $R^{n\times n}_{sym}$. We specifically consider the example of the static problem of plastic limit analysis and seek to characterize its relaxation in the non-standard case of a non-convex elastic domain. We show that the symmetric ${\rm div}$-quasiconvex envelope of the elastic domain can be characterized explicitly for isotropic materials whose elastic domain depends on pressure $p$ and Mises effective shear stress $q$. The envelope then follows from a rank-$2$ hull construction in the $(p,q)$-plane. Remarkably, owing to the equilibrium constraint the relaxed elastic domain can still be strongly non-convex, which shows that convexity of the elastic domain is not a requirement for existence in plasticity.

It is well known that, for mass-action systems, complex-balanced equilibria are asymptotically stable. For generalized mass-action systems, even if there exists a unique complex-balanced equilibrium (in every stoichiometric class and for all rate constants), it need not be stable. We first discuss several notions of matrix stability (on a linear subspace) such as D-stability and diagonal stability, and then we apply our abstract results to complex-balanced equilibria of generalized mass-action systems. In particular, we show that linear stability (on the stoichiometric subspace and for all rate constants) implies uniqueness. For cyclic networks, we characterize linear stability (in terms of D-stability of the Jacobian matrix); and for weakly reversible networks, we give necessary conditions for linear stability (in terms of D-semistability of the Jacobian matrices of all cycles in the network). Moreover, we show that, for classical mass-action systems, complex-balanced equilibria are not just asymptotically stable, but even diagonally stable (and hence linearly stable). Finally, we recall and extend characterizations of D-stability and diagonal stability for matrices of dimension up to three, and we illustrate our results by examples of irreversible cycles (of dimension up to three) and of reversible chains and S-systems (of arbitrary dimension)., Comment: 18 pages

Physics at a multi-TeV muon collider needs a change of perspective for the detector design due to the large amount of background induced by muon beam decays. Preliminary studies, based on simulated data, on the composition and the characteristics of the particles originated from the muon decays and reaching the detectors are presented here. The reconstruction performance of the physics processes $H\to b\bar b$ and $Z\to b\bar b$ has been investigated for the time being without the effect of the machine induced background. A preliminary study of the environment hazard due to the radiation induced by neutrino interactions with the matter is presented using the FLUKA simulation program.

We prove an optimal order error bound in the discrete $H^2(\Omega)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n \in \{2,\dots,7\}$, whose generalized solution belongs to the Sobolev space $H^s(\Omega) \cap H^2_0(\Omega)$, for $\frac{1}{2} \max(5,n) < s \leq 4$, where $\Omega = (0,1)^n$. The result extends the range of the Sobolev index $s$ in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of $H^s(\Omega)$ into $C(\overline\Omega)$ in $n$ space dimensions.

We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including generalized monomial and monotonic (not necessarily continuous) maps. In fact, monotonic maps are special cases of {\em component-wise affine} maps. Further, we study compositions of maps with a matrix and other composed maps, in particular, rational functions. Our framework covers classical injectivity criteria based on mean value theorems for vector-valued maps and recent results obtained in the study of chemical reaction networks.

The field of nuclear astrophysics is devoted to the study of the creation of the chemical elements. By nature, it is deeply intertwined with the physics of the Sun. The nuclear reactions of the proton-proton cycle of hydrogen burning, including the 3He({\alpha},{\gamma})7Be reaction, provide the necessary nuclear energy to prevent the gravitational collapse of the Sun and give rise to the by now well-studied pp, 7Be, and 8B solar neutrinos. The not yet measured flux of 13N, 15O, and 17F neutrinos from the carbon-nitrogen-oxygen cycle is affected in rate by the 14N(p,{\gamma})15O reaction and in emission profile by the 12C(p,{\gamma})13N reaction. The nucleosynthetic output of the subsequent phase in stellar evolution, helium burning, is controlled by the 12C({\alpha},{\gamma})16O reaction. In order to properly interpret the existing and upcoming solar neutrino data, precise nuclear physics information is needed. For nuclear reactions between light, stable nuclei, the best available technique are experiments with small ion accelerators in underground, low-background settings. The pioneering work in this regard has been done by the LUNA collaboration at Gran Sasso/Italy, using a 0.4 MV accelerator. The present contribution reports on a higher-energy, 5.0 MV, underground accelerator in the Felsenkeller underground site in Dresden/Germany. Results from {\gamma}-ray, neutron, and muon background measurements in the Felsenkeller underground site in Dresden, Germany, show that the background conditions are satisfactory for nuclear astrophysics purposes. The accelerator is in the commissioning phase and will provide intense, up to 50{\mu}A, beams of 1H+, 4He+ , and 12C+ ions, enabling research on astrophysically relevant nuclear reactions with unprecedented sensitivity., Comment: Submitted to the Proceedings of the 5th International Solar Neutrino Conference, Dresden/Germany, 11-14 June 2018, to appear on World Scientific -- updated version (Figure 2 and relevant discussion updated, co-author A. Domula added)

We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (ii) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ-OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness (ACR), as we demonstrate for the EnvZ-OmpR pathway., Comment: 23 pages, 0 figures

An embedding $\varphi \colon (M_1, \omega_1) \to (M_2, \omega_2)$ (of symplectic manifolds of the same dimension) is called $\epsilon$-symplectic if the difference $\varphi^* \omega_2 - \omega_1$ is $\epsilon$-small with respect to a fixed Riemannian metric on $M_1$. We prove that if a sequence of $\epsilon$-symplectic embeddings converges uniformly (on compact subsets) to another embedding, then the limit is $E$-symplectic, where the number $E$ depends only on $\epsilon$ and $E (\epsilon) \to 0$ as $\epsilon \to 0$. This generalizes $C^0$-rigidity of symplectic embeddings, and answers a question in topological quantum computing by Michael Freedman. As in the symplectic case, this rigidity theorem can be deduced from the existence and properties of symplectic capacities. An $\epsilon$-symplectic embedding preserves capacity up to an $\epsilon$-small error, and linear $\epsilon$-symplectic maps can be characterized by the property that they preserve the symplectic spectrum of ellipsoids (centered at the origin) up to an error that is $\epsilon$-small. We sketch an alternative proof using the shape invariant, which gives rise to an analogous characterization and rigidity theorem for $\epsilon$-contact embeddings., Comment: 17 pages

We start from a parametrized system of $d$ generalized polynomial equations (with real exponents) for $d$ positive variables, involving $n$ generalized monomials with $n$ positive parameters. Existence and uniqueness of a solution for all parameters and for all right-hand sides is equivalent to the bijectivity of (every element of) a family of generalized polynomial/exponential maps. We characterize the bijectivity of the family of exponential maps in terms of two linear subspaces arising from the coefficient and exponent matrices, respectively. In particular, we obtain conditions in terms of sign vectors of the two subspaces and a nondegeneracy condition involving the exponent subspace itself. Thereby, all criteria can be checked effectively. Moreover, we characterize when the existence of a unique solution is robust with respect to small perturbations of the exponents or/and the coefficients. In particular, we obtain conditions in terms of sign vectors of the linear subspaces or, alternatively, in terms of maximal minors of the coefficient and exponent matrices. Finally, we present applications to chemical reaction networks with (generalized) mass-action kinetics.

We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the square and the edges and corners of the cube. The main idea is to transfer estimates for the continuous bilaplacian using a new discrete compactness argument and a discrete version of the Cacciopoli (or reverse Poincar\'e) inequality. One application that we have in mind is the study of entropic repulsion for the membrane model from statistical physics.

The discovery of ferroelectric properties of binary oxides revitalized the interest in ferroelectrics and bridged the scaling gap between the state-of-the-art semiconductor technology and ferroelectric memories. However, before hitting the markets, the origin of ferroelectricity and in-depth studies of device characteristics are needed. Establishing a correlation between the performance of the device and underlying physical mechanisms is the first step toward understanding the device and engineering guidelines for a novel, superior device. Therefore, in this paper a holistic modeling approaches which lead to a better understanding of ferroelectric memories based on hafnium and zirconium oxide is addressed. Starting from describing the stabilization of the ferroelectric phase within the binary oxides via physical modeling the physical mechanisms of the ferroelectric devices are reviewed. Besides, limitations and modeling of the multilevel operation and switching kinetics of ultimately scaled devices as well as the necessity for Landau-Khalatnikov approach are discussed. Furthermore, a device-level model of ferroelectric memory devices that can be used to study the array implementation and their operational schemes are addressed. Finally, a circuit model of the ferroelectric memory device is presented and potential further applications of ferroelectric devices are outlined.