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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)