After a short introduction into the history of the building of the Physics Institute of the University of Breslau, the development under Otto Lummer is sketched: influenced by the newly founded Technische Hochschule, the building as well as the faculty, were enlarged. The collection of instruments for instruction and research was built up and the cooperation with industry and with guests from abroad strengthened. Young scientists were promoted, making Lummer’s institute into one of the leading ones in optics at that (...) time. (shrink)

Empathy facilitates everyday social interactions and has often been linked in the literature to prosocial behavior. Robust evidence has been found for a positive relationship between experiencing empathy and behaving prosocially. However, empathy, and the empathy–prosocial behavior relationship in particular, has been studied mostly in combination with negative emotions. Less research has been conducted on empathy for positive emotions, and the link between positive empathy and displayed prosocial behavior has not been intensively investigated so far. The purpose of the present (...) article is thus twofold: first, we review and summarize research evidence on empathy for positive emotions, and second, we propose that people’s motivation to maintain an experienced positive affect is a viable mechanism linking positive empathy and prosocial behavior. (shrink)

Assume that the problem P0 is not solvable in polynomial time. Let T be a first-order theory containing a sufficiently rich part of true arithmetic. We characterize T∪{ConT} as the minimal extension of T proving for some algorithm that it decides P0 as fast as any algorithm B with the property that T proves that B decides P0. Here, ConT claims the consistency of T. As a byproduct, we obtain a version of Gödelʼs Second Incompleteness Theorem. Moreover, we characterize problems (...) with an optimal algorithm in terms of arithmetical theories. (shrink)

We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family . For every family of functions, this yields a notion of -fixed-parameter tractability. If is the class of all polynomially bounded functions, then -fixed-parameter tractability coincides with polynomial time decidability and if is the class of all computable functions, -fixed-parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices (...) of between these two extremes, for example the class of all singly exponential functions. In this article, we study the general theory of -fixed-parameter tractability. We introduce a generic notion of reduction and two classes -W[P] and -XP, which may be viewed as analogues of NP and EXPTIME, respectively, in the world of -fixed-parameter tractability. (shrink)

We observe that the W*-hierarchy, a variant (introduced by Downey, Fellows, and Taylor [7]) of the better known W-hierarchy, coincides with the W-hierarchy, though not level wise, but just as a whole hierarchy. More precisely, we prove that W[t] ⊆ W*[t] ⊆ W[2t − 2] for each t ≥ 2. It was known before that W[1] = W*[1] and W[2] = W*[2]. Our second main result is a new logical characterization of the W*-hierarchy in terms of "Fagin-definable problems." As a (...) by-product, we also obtain an improvement of our earlier characterization of the hierarchy in terms of model-checking problems. Furthermore, we obtain new complete problems for the classes W[3] and W*[3]. (shrink)

This research critically analyses the Israeli housing block (‘shikun’) discourse, as presented in cultural representations during 1948–1961, and its contribution to the evolution of the Israeli-Palestinian conflict. The study argues that the discursive exclusion of the shikun from Israel's socio-political history of planning and development is a central part of Israel's ethnocracy and has an essential role in exacerbating the conflict. It maintains that the shikun's exclusion is a reduction of its consequences, namely the Mizrahi population's dispersion through the shikun, (...) which stands as one of the main foundations of the Israeli ethnocratic regime. Subsequently, I identify the shikun anew as the ‘ethnocratic shikun’, and suggest that it can be a better conceptualisation to reveal how ethnic oppression, by discursive and architectural means, affects national land regimes, and thereby exacerbating regional violent conflicts. This research has two main goals. First, achieving a better understanding of Israeli society and politics by delving into a crucial component of human existence – housing, and analysing its ‘disappearance’ from public debates regarding the Middle-Eastern geopolitics. Second, the research aspires to make a methodological contribution that goes beyond Israeli housing discourse, by adding another novel layer to the Cultural Approach to Critical Discourse Analysis. (shrink)

We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define (...) the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1). (shrink)

In this article we review some of the main results of descriptive complexity theory in order to make the reader familiar with the nature of the investigations in this area. We start by presenting the characterization of automata recognizable languages by monadic second-order logic. Afterwards we explain the characterization of various logics by fIxed-point logics. We assume familiarity with logic but try to keep knowledge of complexity theory to aminimum.

Let L be one of the topological languages L t , (L ∞ω ) t and (L κω ) t . We characterize the topological spaces which are models of the L-theory of the class of ordinals equipped with the order topology. The results show that the role played in classical model theory by the property of being well-ordered is taken over in the topological context by the property of being locally compact and scattered.

We prove an extension of the Lemma of Rasiowa and Sikorski and give some applications. Moreover, we analyze the relationship to corresponding results on the omission of types.

In the last decade of the 13th century Guyart Desmoulins composed a French-language version of the Bible, the ‘Bible historiale’, based on the ‘Historia Scholastica’. In the course of the 14th century this was completed to become a full bible, and a pictorial repertoire emerged that corresponded to the work’s novel requirements. Soaring demand and the efficient production on the part of the Paris workshops resulted in a standardization of some of the pictorial elements in the times of John the (...) Good and Charles V; the usual choice of motif for the frontispiece, for example, came to be some variant of the Maiestas Domini. In complete contrast to this, miniatures were created around the year 1400 that stood out due to their iconographic originality, testifying to a more nuanced perception of the ‘Bible historiale’ and its tradition. Five examples will be presented in an examination of the interrelationship of text and image. (shrink)

When analyzing database query languages a roperty, of theories, the pseudo-finite homogeneity property, has been introduced and applied (cf. [3]). We show that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded. Moreover, we introduce the corresponding pseudo-finite saturation property and show that a theory fails to have the finite cover property if and only if it has the pseudo-finite saturation property.

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both (...) classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees. (shrink)

Let $\mathscr {C}$ be a class of finite and infinite graphs that is closed under induced subgraphs. The well-known Łoś–Tarski Theorem from classical model theory implies that $\mathscr {C}$ is definable in first-order logic by a sentence $\varphi $ if and only if $\mathscr {C}$ has a finite set of forbidden induced finite subgraphs. This result provides a powerful tool to show nontrivial characterizations of graphs of small vertex cover, of bounded tree-depth, of bounded shrub-depth, etc. in terms of forbidden (...) induced finite subgraphs. Furthermore, by the Completeness Theorem, we can compute from $\varphi $ the corresponding forbidden induced subgraphs. This machinery fails on finite graphs as shown by our results: – There is a class $\mathscr {C}$ of finite graphs that is definable in first-order logic and closed under induced subgraphs but has no finite set of forbidden induced subgraphs. – Even if we only consider classes $\mathscr {C}$ of finite graphs that can be characterized by a finite set of forbidden induced subgraphs, such a characterization cannot be computed from a first-order sentence $\varphi $ that defines $\mathscr {C}$ and the size of the characterization cannot be bounded by $f(|\varphi |)$ for any computable function f. Besides their importance in graph theory, the above results also significantly strengthen similar known theorems for arbitrary structures. (shrink)

Leonid Levin showed that every algorithm computing a function has an optimal inverter. Recently, we applied his result in various contexts: existence of optimal acceptors, existence of hard sequences for algorithms and proof systems, proofs of Gödel’s incompleteness theorems, analysis of the complexity of the clique problem assuming the nonuniform Exponential Time Hypothesis. We present all these applications here. Even though a simple diagonalization yields Levin’s result, we believe that it is worthwhile to be aware of the explicit result. The (...) purpose of this survey is to convince the reader of our view. (shrink)

The undecidability of first-order logic implies that there is no computable bound on the length of shortest proofs of valid sentences of first-order logic. Some valid sentences can only have quite long proofs. How hard is it to prove such "hard" valid sentences? The polynomial time tractability of this problem would imply the fixed-parameter tractability of the parameterized problem that, given a natural number n in unary as input and a first-order sentence φ as parameter, asks whether φ has a (...) proof of length ≤ n. As the underlying classical problem has been considered by Gödel we denote this problem by p-Gödel. We show that p-Gödel is not fixed-parameter tractable if DTIME(h O(1) ) ≠ NTIME(h O(1) ) for all time constructible and increasing functions h. Moreover we analyze the complexity of the construction problem associated with p-Gödel. (shrink)

Many parameterized problems ask, given an instance and a natural number k as parameter, whether there is a solution of size k. We analyze the relationship between the complexity of such a problem and the corresponding maximality problem asking for a solution of size k maximal with respect to set inclusion. As our results show, many maximality problems increase the parameterized complexity, while “in terms of the W-hierarchy” minimality problems do not increase the complexity. We also address the corresponding construction, (...) listing, and counting problems. (shrink)

Recognising and responding appropriately to emotions is critical to adaptive psychological functioning. Psychopathic traits (e.g. callous, manipulative, impulsive, antisocial) are related to differences in recognition and response when emotion is conveyed through facial expressions and language. Use of emotional music stimuli represents a promising approach to improve our understanding of the specific emotion processing difficulties underlying psychopathic traits because it decouples recognition of emotion from cues directly conveyed by other people (e.g. facial signals). In Experiment 1, participants listened to clips (...) of emotional music and identified the emotional content (Sample 1, N = 196) or reported on their feelings elicited by the music (Sample 2, N = 197). Participants accurately recognised (t(195) = 32.78, p <.001, d = 4.69) and reported feelings consistent with (t(196) = 7.84, p <.001, d = 1.12) the emotion conveyed in the music. However, psychopathic traits were associated with reduced emotion recognition accuracy (F(1, 191) = 19.39, p <.001) and reduced likelihood of feeling the emotion (F(1, 193) = 35.45, p <.001), particularly for fearful music. In Experiment 2, we replicated findings for broad difficulties with emotion recognition (Sample 3, N = 179) and emotional resonance (Sample 4, N = 199) associated with psychopathic traits. Results offer new insight into emotion recognition and response difficulties that are associated with psychopathic traits. (shrink)

Ebbhinghaus, H., J. Flum, and W. Thomas. 1984. Mathematical Logic. New York, NY: Springer-Verlag. Forster, T. Typescript. The significance of Yablo’s paradox without self-reference. Available from http://www.dpmms.cam.ac.uk. Gold, M. 1965. Limiting recursion. Journal of Symbolic Logic 30: 28–47. Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam.

Ebbhinghaus, H., J. Flum, and W. Thomas. 1984. Mathematical Logic. New York, NY: Springer-Verlag. Forster, T. Typescript. The significance of Yablo’s paradox without self-reference. Available from http://www.dpmms.cam.ac.uk. Gold, M. 1965. Limiting recursion. Journal of Symbolic Logic 30: 28–47. Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam.

In this paper we introduce the notion of a first order topological structure, and consider various possible conditions on the complexity of the definable sets in such a structure, drawing several consequences thereof.Our aim is to develop, for a restricted class of unstable theories, results analogous to those for stable theories. The “material basis” for such an endeavor is the analogy between the field of real numbers and the field of complex numbers, the former being a “nicely behaved” unstable structure (...) and the latter the archetypal stable structure. In this sense we try here to situate our work ono-minimal structures [PS] in a general topological context. Note, however, that thep-adic numbers, and structures definable therein, will also fit into our analysis.In the remainder of this section we discuss several ways of studying topological structures model-theoretically. Eventually we fix on the notion of a structure in which the topology is “explicitly definable” in the sense of Flum and Ziegler [FZ]. In §2 we introduce the hypothesis that every definable set is a Boolean combination of definable open sets. In §3 we introduce a “dimension rank” on definable sets. In §4 we consider structures on which this rank is defined, and for which also every definable set has a finite number of definably connected definable components. We show that prime models over sets exist under such conditions. (shrink)