University of Graz

About: University of Graz is a education organization based out in Graz, Steiermark, Austria. It is known for research contribution in the topics: Population & Quantum chromodynamics. The organization has 17934 authors who have published 37489 publications receiving 1110980 citations. The organization is also known as: Carolo Franciscea Graecensis & Karl Franzens Universität.

What people regard as unjust: Types and structures of everyday experiences of injustice.

Abstract: The present research was designed to identify types of events in everyday life that people regard as unjust and to find a meaningful structural representation of these types of events. Two hundred and eighty descriptions of unjust events were collected from various student samples using different methodologies. Interestingly, a considerable proportion of the injustices which were reported did not concern distributional or procedural issues in the narrow sense but referred to the manner in which people were treated in interpersonal interactions and encounters. An intuitive classification of the descriptions by two experts led to 22 different types of unjust events. Subsequently, a sample of 84 descriptions was selected and sorted by naive subjects into similar groupings. The grouping data were then subjected to cluster and multidimensional scaling analyses. A nineteen-cluster solution reproduced the intuitively defined main types of unjust events very well. An eight-cluster solution, which provided the most meaningful higher level grouping, and the MDS results indicated that a meaningful structural representation of types of injustices has to consider the particular content of unjust events as well as the social setting where they occur. With regard to the latter aspect, injustices in task-oriented relationships of unequal power and impersonal short-term encounters are distinguished from injustices occurring in personal, long-term, social-emotional relationships of equal power.

Crystal structure of human β2‐glycoprotein I: implications for phospholipid binding and the antiphospholipid syndrome

Abstract: The high affinity of human plasma beta2-glycoprotein I (beta(2)GPI), also known as apolipoprotein-H (ApoH), for negatively charged phospholipids determines its implication in a variety of physiological pathways, including blood coagulation and the immune response. beta(2)GPI is considered to be a cofactor for the binding of serum autoantibodies from antiphospholipid syndrome (APS) and correlated with thrombosis, lupus erythematosus and recurrent fetal loss. We solved the beta(2)GPI structure from a crystal form with 84% solvent and present a model containing all 326 amino acid residues and four glycans. The structure reveals four complement control protein modules and a distinctly folding fifth C-terminal domain arranged like beads on a string to form an elongated J-shaped molecule. Domain V folds into a central beta-spiral of four antiparallel beta-sheets with two small helices and an extended C-terminal loop region. It carries a distinct positive charge and the sequence motif CKNKEKKC close to the hydrophobic loop composed of residues LAFW (313-316), resulting in an excellent counterpart for interactions with negatively charged amphiphilic substances. The beta(2)GPI structure reveals potential autoantibody-binding sites and supports mutagenesis studies where Trp316 and CKNKEKKC have been found to be essential for the phospholipid-binding capacity of beta(2)GPI.

Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control

Abstract: Nonlinear Dynamical System Let V and H be real separable Hilbert spaces and suppose that V is dense in H with compact embedding. By 〈· , ·〉H we denote the inner product in H. The inner product in V is given by a symmetric bounded, coercive, bilinear form a : V × V → IR: 〈φ,ψ〉V = a(φ,ψ) for all φ,ψ ∈ V (10.16) with associated norm given by ‖ · ‖V = √ a(· , ·). Since V is continuously injected into H, there exists a constant cV > 0 such that ‖φ‖H ≤ cV ‖φ‖V for all φ ∈ V. (10.17) We associate with a the linear operator A: 〈Aφ,ψ〉V ′,V = a(φ,ψ) for all φ,ψ ∈ V, where 〈· , ·〉V ′,V denotes the duality pairing between V and its dual. Then, by the Lax-Milgram lemma, A is an isomorphism from V onto V ′. Alternatively, A can be considered as a linear unbounded self-adjoint operator in H with domain D(A) = {φ ∈ V : Aφ ∈ H}. By identifying H and its dual H ′ it follows that 10 POD: Error Estimates and Suboptimal Control 269 D(A) ↪→ V ↪→ H = H ′ ↪→ V ′, each embedding being continuous and dense, when D(A) is endowed with the graph norm of A. Moreover, let F : V × V → V ′ be a bilinear continuous operator mapping D(A) × D(A) into H. To simplify the notation we set F (φ) = F (φ,φ) for φ ∈ V . For given f ∈ C([0, T ];H) and y0 ∈ V we consider the nonlinear evolution problem d dt 〈y(t), φ〉H + a(y(t), φ) + 〈F (y(t)), φ〉V ′,V = 〈f(t), φ〉H (10.18a) for all φ ∈ V and t ∈ (0, T ] a.e. and y(0) = y0 in H. (10.18b) Assumption (A1). For every f ∈ C([0, T ];H) and y0 ∈ V there exists a unique solution of (10.18) satisfying y ∈ C([0, T ];V ) ∩ L(0, T ;D(A)) ∩H(0, T ;H). (10.19) Computation of the POD Basis Throughout we assume that Assumption (A1) holds and we denote by y the unique solution to (10.18) satisfying (10.19). For given n ∈ IN let 0 = t0 < t1 < . . . < tn ≤ T (10.20) denote a grid in the interval [0, T ] and set δtj = tj − tj−1, j = 1, . . . , n. Define ∆t = max (δt1, . . . , δtn) and δt = min (δt1, . . . , δtn). (10.21) Suppose that the snapshots y(tj) of (10.18) at the given time instances tj , j = 0, . . . , n, are known. We set V = span {y0, . . . , y2n}, where yj = y(tj) for j = 0, . . . , n, yj = ∂ty(tj−n) for j = n + 1, . . . , 2n with ∂ty(tj) = (y(tj)−y(tj−1))/δtj , and refer to V as the ensemble consisting of the snapshots {yj} j=0, at least one of which is assumed to be nonzero. Furthermore, we call {tj}j=0 the snapshot grid. Notice that V ⊂ V by construction. Throughout the remainder of this section we let X denote either the space V or H. 270 Michael Hinze and Stefan Volkwein Remark 10.2.1 (compare [KV01, Remark 1]). It may come as a surprise at first that the finite difference quotients ∂ty(tj) are included into the set V of snapshots. To motivate this choice let us point out that while the finite difference quotients are contained in the span of {yj} j=0, the POD bases differ depending on whether {∂ty(tj)}j=1 are included or not. The linear dependence does not constitute a difficulty for the singular value decomposition which is required to compute the POD basis. In fact, the snapshots themselves can be linearly dependent. The resulting POD basis is, in any case, maximally linearly independent in the sense expressed in (P ) and Proposition 10.2.5. Secondly, in anticipation of the rate of convergence results that will be presented in Section 10.3.3 we note that the time derivative of y in (10.18) must be approximated by the Galerkin POD based scheme. In case the terms {∂ty(tj)}j=1 are included in the snapshot ensemble, we are able to utilize the estimate