Partition games

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can perform on a single heap. In normal play, the player with the last move wins, and the famous Sprague-Grundy theory provides a solution. We prove that several rulesets have a periodic or an arithmetic periodic Sprague-Grundy sequence (i.e. they can be partitioned into a finite number of arithmetic progressions of the same common difference). This is achieved directly for some infinite classes of games, and moreover we develop a computational testing condition, demonstrated to solve a variety of additional games. Similar results have previously appeared for various classes of games of take-and-break, for example octal and hexadecimal; see e.g. Winning Ways by Berlekamp, Conway and Guy (1982). In this context, our contribution consists of a systematic study of the subclass `break-without-take'

Spirit and Utopia: (German) Idealism as Political Theology

Can we understand (German) idealism as emancipatory today, after the new realist critique? In this paper, I argue that we can do so by identifying a political theology of revolution and utopia at the theoretical heart of German Idealism. First, idealism implies a certain revolutionary event at its foundation. Kant’s Copernicanism is ingrained, methodologically and ontologically, into the idealist system itself. Secondly, this revolutionary origin remains a “non-place” for the idealist system, which thereby receives a utopian character. I define the utopian as the ideal gap, produced by and from within the real, between the non-place of the real as origin and its reduplication as the non-place of knowledge’s closure, as well as the impulse, inherent in idealism, to attempt to close that gap and fully replace the old with the new. Based on this definition, I outline how the utopian functions in Kant, Fichte and Hegel. Furthermore, I suggest that idealism may be seen as a political-theological offshoot of realism, via the objective creation of a revolutionary condition. The origin of the ideal remains in the real, maintaining the utopian gap and the essentially critical character of idealism, both at the level of theory and as social critique

An unnoticed official: the Praepositus Saltus

The Passio Typasii survives in only one manuscript and was published for the first time in 1890. It purports to describe the trial and death of a Mauretanian martyr, a military veteran by the name of Typasius, during the Diocletianic persecution. However as recently demonstrated its literary borrowings, from the Breviarium of Eutropius and the Vita Martini of Sulpicius Severus, suggest that it is a mere fiction and that it should be dated after c. A.D. 396. It is the purpose of this note to draw attention to its preservation of an otherwise unattested title, that of the praepositus saltus, and to expand upon the significance of this title for the interpretation of the work. This title only occurs fully in one passage, being elsewhere abbreviated to praepositus, and this passage is of some interest therefore

Circum-Arctic lithosphere-basin evolution : An overview

Acknowledgements The Special Issue editors thank the contributors for their hard work and dedication in the preparation of the papers presented here, and also Victoria Pease for her active support throughout the process and in particular in co-convening the conference session giving rise to this Special Issue. In particular, we thank the Editor-in-chief, Dr. Rob Govers for his patience, guidance and valued advice throughout the process. Also, we appreciate the work of the Tectonophysics editorial and production teams for bringing the Special Issue to print. R. Ernst, G. Oakey and an anonymous reviewer provided a multitude of helpful suggestions to improve the manuscript. This Special Issue is a contribution to the Geological Survey of Canada's Geomapping for Energy and Minerals (GEM2) Program, Canada's Extended Continental Shelf Program, and the Circum-Arctic Lithosphere Evolution (CALE) network. ESS Contribution No. 20160152.Peer reviewedPostprin

The complexities of 'otherness': reflections on embodiment of a young White British woman engaged in cross-generation research involving older people in Indonesia

This article has been made available through the Brunel Open Access Publishing Fund.If interviews are to be considered embodied experiences, than the potential influence of the embodied researcher must be explored. A focus on specific attributes such as age or ethnicity belies the complex and negotiated space that both researcher and participant inhabit simultaneously. Drawing on empirical research with stroke survivors in an ethnically mixed area of Indonesia, this paper highlights the importance of considering embodiment as a specific methodological concern. Three specific interactions are described and analysed, illustrating the active nature of the embodied researcher in narrative production and development. The intersectionality of embodied features is evident, alongside their fluctuating influence in time and place. These interactions draw attention to the need to consider the researcher within the interview process and the subsequent analysis and presentation of narrative findings. The paper concludes with a reinforcement of the importance of ongoing and meaningful reflexivity in research, a need to consider the researcher as the other participant, and specifically a call to engage with and present the dynamic nature of embodiment

On the susceptibility function of piecewise expanding interval maps

We study the susceptibility function Psi(z) associated to the perturbation f_t=f+tX of a piecewise expanding interval map f. The analysis is based on a spectral description of transfer operators. It gives in particular sufficient conditions which guarantee that Psi(z) is holomorphic in a disc of larger than one. Although Psi(1) is the formal derivative of the SRB measure of f_t with respect to t, we present examples satisfying our conditions so that the SRB measure is not Lipschitz.*We propose a new version of Ruelle's conjectures.* In v2, we corrected a few minor mistakes and added Conjectures A-B and Remark 4.5. In v3, we corrected the perturbation (X(f(x)) instead of X(x)), in particular in the examples from Section 6. As a consequence, Psi(z) has a pole at z=1 for these examples.Comment: To appear Comm. Math. Phy

Mountain building in Taiwan: A thermokinematic model

The Taiwan mountain belt is classically viewed as a case example of a critical wedge growing essentially by frontal accretion and therefore submitted to distributed shortening. However, a number of observations call for a significant contribution of underplating to the growth of the orogenic wedge. We propose here a new thermokinematic model of the Taiwan mountain belt reconciling existing kinematic, thermometric and thermochronological constraints. In this model, shortening across the orogen is absorbed by slip on the most frontal faults of the foothills. Crustal thickening and exhumation are sustained by underplating beneath the easternmost portion of the wedge (Tananao Complex, TC), where the uplift rate is estimated to ~6.3 mm a^(−1), and beneath the westernmost internal region of the orogen (Hsueshan Range units, HR), where the uplift rate is estimated to ~4.2 mm a^(−1). Our model suggests that the TC units experienced a synchronous evolution along strike despite the southward propagation of the collision. It also indicates that they have reached a steady state in terms of cooling ages but not in terms of peak metamorphic temperatures. Exhumation of the HR units increases northward but has not yet reached an exhumational steady state. Presently, frontal accretion accounts for less than ~10% of the incoming flux of material into the orogen, although there is indication that it was contributing substantially more (~80%) before 4 Ma. The incoming flux of material accreted beneath the TC significantly increased 1.5 Ma ago. Our results also suggest that the flux of material accreted to the orogen corresponds to the top ~7 km of the upper crust of the underthrust Chinese margin. This indicates that a significant amount (~76%) of the underthrust material has been subducted into the mantle, probably because of the increase in density associated with metamorphism. We also show that the density distribution resulting from metamorphism within the orogenic wedge explains well the topography and the gravity field. By combining available geological data on the thermal and kinematic evolution of the wedge, our study sheds new light onto mountain building processes in Taiwan and allows for reappraising the initial structural architecture of the passive margin

The Other Side of Peirce's Phaneroscopy

Research on Peirce’s phaneroscopy has been done with and through the paradigm or the conceptual schema of “Being” — what has been critiqued by post-structuralist philosophers as the metaphysics of Being. Thus, such research is either limited to attempts to define “phaneron,” or to identify whether there is a particular and consistent meaning intention behind Peirce’s use of this term. Another problematic characteristic with such a way of engaging with phaneroscopy is the very anonymity of the schema of “Being.” While all scholars admit to the universality of “phaneron,” rarely, if ever, do we see an account of how such universality can be instantiated. In this paper, I attempt to engage with phaneroscopy differently. Instead of presenting a better version of what phaneroscopy is, or making arguments about what is the case with phaneroscopy, both of which are ways of philosophising with “being,” I attempt to enact phaneroscopy. This would mean to undertake to follow Peirce’s instructions for the phaneroscopist and report the findings. Based on the latter, I shall analogise phaneron with the possibility of understanding