Constructing Simplicial Branched Covers

Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d<=4 every closed oriented PL d-manifold is the partial unfolding of some polytopal d-sphere.Comment: 15 pages, 8 figures, typos corrected and conjecture adde

The CMA Evolution Strategy: A Tutorial

This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and from requirements of non-linear, non-convex search in continuous domain.Comment: ArXiv e-prints, arXiv:1604.xxxx

CMA-ES with Two-Point Step-Size Adaptation

We combine a refined version of two-point step-size adaptation with the covariance matrix adaptation evolution strategy (CMA-ES). Additionally, we suggest polished formulae for the learning rate of the covariance matrix and the recombination weights. In contrast to cumulative step-size adaptation or to the 1/5-th success rule, the refined two-point adaptation (TPA) does not rely on any internal model of optimality. In contrast to conventional self-adaptation, the TPA will achieve a better target step-size in particular with large populations. The disadvantage of TPA is that it relies on two additional objective functio

Algebraic models for higher categories

We introduce the notion of algebraic fibrant objects in a general model category and establish a (combinatorial) model category structure on algebraic fibrant objects. Based on this construction we propose algebraic Kan complexes as an algebraic model for oo-groupoids and algebraic quasi-categories as an algebraic model for (oo,1)-categories. We furthermore give an explicit proof of the homotopy hypothesis.Comment: 23 pages, minor change

Injecting External Solutions Into CMA-ES

This report considers how to inject external candidate solutions into the CMA-ES algorithm. The injected solutions might stem from a gradient or a Newton step, a surrogate model optimizer or any other oracle or search mechanism. They can also be the result of a repair mechanism, for example to render infeasible solutions feasible. Only small modifications to the CMA-ES are necessary to turn injection into a reliable and effective method: too long steps need to be tightly renormalized. The main objective of this report is to reveal this simple mechanism. Depending on the source of the injected solutions, interesting variants of CMA-ES arise. When the best-ever solution is always (re-)injected, an elitist variant of CMA-ES with weighted multi-recombination arises. When \emph{all} solutions are injected from an \emph{external} source, the resulting algorithm might be viewed as \emph{adaptive encoding} with step-size control. In first experiments, injected solutions of very good quality lead to a convergence speed twice as fast as on the (simple) sphere function without injection. This means that we observe an impressive speed-up on otherwise difficult to solve functions. Single bad injected solutions on the other hand do no significant harm.Comment: No. RR-7748 (2011

"Annihilation through labor": the killing of state prisoners in the Third Reich

One of the most distinctive features of Nazi society was the increasingly radical division of its members into “national comrades” and “community aliens.” The former were to be protected by the state and encouraged to procreate, while the latter were seen as political, social, racial, or eugenic threats and were to be ruthlessly eliminated from society. With the start of the Second World War, various nonlethal forms of discrimination against these “community aliens” were gradually replaced by policies geared to physical annihilation, culminating above all in the extermination of the European Jews. In view of a crime of this previously unimaginable magnitude, it is hardly surprising that when historians started in earnest to examine the genocidal policies of the Nazi dictatorship in the 1960s they focused on the development and administration of the “Final Solution of the Jewish Question,” as the Nazis called it. But in the last two decades, the fate of other “community aliens” in the Third Reich, such as the Roma and Sinti (“Gypsies”), slave laborers, and the disabled, has been investigated too. Some historians have also begun to examine those who deviated in various other ways from the norms of society, people who were often classified in the Third Reich, and indeed before, as “asocials.” There was never an agreed definition as to who these people were, and the term was used to stigmatize a vast variety of nonnormative behavior. According to a 1938 directive by the head of the German security police, Reinhard Heydrich, any person could be classified as “asocial” who “demonstrates through conduct opposed to the community . . . that he does not want to adapt to the community.” During the Third Reich, such vague statements served as the basis for the persecution of juvenile delinquents, criminal offenders, vagrants, prostitutes, and homosexuals, among many others. Certain groups were simultaneously classified as racial and social outsiders and thus suffered “dual racism.” This was true in particular for the Sinti and Roma, who had been persecuted for their way of life long before the Nazi “seizure of power” in 1933. Historical research into the fate of the “asocials” has produced some valuable insights into the treatment of members of these marginal groups in the Third Reich, many of whom died in SS concentration or extermination camps. Yet despite this growing interest, the most comprehensive of all the extermination programs directed against “asocials” in the Third Reich has never been investigated. From late 1942 onward, over twenty thousand offenders classified as “asocial” were taken out of the state penal system and transferred to the police for “annihilation through labor.” At least two-thirds of them perished in concentration camps. But in the historical literature this program has either been dealt with in passing or completely ignored. Why have historians neglected the murder of state prisoners? There appears to be a reluctance to focus on offenders against the law in the Third Reich, unless their offences can be seen in some way as forms of political or social protest. In contrast to the racially or politically persecuted, not all common criminals can be described merely as innocent victims, and the often brutal behavior of criminal Kapos in concentration camps probably further alienated historians from dealing with the criminals. Another factor that explains the poor state of research is the inaccessibility of source material. Leading officials in the Ministry of Justice made sure that most files relating to the “annihilation through labor” of state prisoners were pulped before the end of the war.8 Yet individual documents have survived, scattered around various archives in Germany. They can be complemented by information gained from individual prisoner files, as well as from unpublished documents and testimonies collected in numerous postwar legal investigations. None of these criminal investigations ever led to the conviction of the prison officials involved—another reason for the lack of historical interest. Finally, German legal history after the war spread the myth that the legal administration had rejected or even resisted the Nazi regime. State penal institutions, if dealt with at all, were described as safe havens that had “nothing to do with the concentration camps.” Thus, until today, historians have largely ignored the state prison system and its inmates. This article will first describe the origins of the decision in 1942 for the extermination of certain state prisoners. Then the actual process of transfer will be investigated in detail, examining issues such as the background of the transferred inmates and the participation of prison officials. The article will also deal with the fate of the state prisoners after their transport to the Nazi concentration camps and the radicalization of policy against the prisoners remaining in the state penal institutions. Exploring these issues contributes to our knowledge of the treatment of deviants in the Third Reich. But this article will also address some wider issues concerning the nature of the Nazi dictatorship, such as the origins of extermination policies in the Third Reich. In recent years, a number of historians have argued that it was time to move beyond the “sterile debates” between so-called intentionalist historians, who focused on the murderous will and ideology of the Nazi leaders, above all Hitler, and so-called structuralist historians, who pointed to the dynamic and uncoordinated interactions between different agencies of the Nazi dictatorship that led to a “cumulative radicalization” (Hans Mommsen). Various historians have now put forward a synthesis of both positions, while ground-breaking empirical research into the “final solution” has posed new questions and provided new answers. Still, many of the more recent studies of Nazi genocide continue to explore central issues first raised in the debates between intentionalists and structuralists such as Hitler’s role in extermination policy, the interaction between regional officials and the decision makers in Berlin, and the role of racial ideology versus more material motives in Nazi mass murder. This study of the “annihilation through labor” of state prisoners addresses some of these general issues. It will also shed new light on the relation between the judiciary and the police in the Third Reich. The postwar portrait of a passive or even anti-Nazi judiciary has not gone unchallenged. Still, many historians continue to describe the judicial authorities and the police as having been in a constant state of conflict. They describe the Third Reich as a “dual state,” split between the “prerogative state” and the “normative state.” The latter was the traditional state apparatus, ensuring that normal life was ruled by legal norms. However, in matters that were thought to touch on the interest of the state, the “prerogative state” could override these legal norms, above all through the agency of the police, locking up all political, racial, and social suspects in SS concentration camps without trial. Thus, state attorneys and the police are seen as competing institutions of prosecution, while state penal institutions and concentration camps are described as competing institutions of confinement. A detailed investigation of the transfer of state prisoners can help to establish how far this picture of the “dual state” stands up to critical scrutiny

Is boredom inevitable?

The article concerns the question whether boredom is inevitable. If, as Nietzsche claims, even the gods are at the mercy of boredom, does this mean, that boredom is something we should get used to? It is suggested, that the inevitability of boredom has several roots: The relation of the modern society to work and leisure, the existential experience of meaninglessness, modern technology and modern subjectivity. Indeed, the semantics of modern subjectivity, as Luhmann says, were born at the very moment when also the semantics of ennui emerged. The article suggests, that the consumer society not least is a reaction to the problem of boredom that stems from modern subjectivity. However, the consumer society is not able to realise the utopian situation of a world without boredom, because it does not only seek to abolish boredom but it also fuels the concept of modern subjectivity. Nevertheless, before the appearance of consumerism there already have been other tactics to cope with boredom, which also, ultimately, failed.peer-reviewe