Eigenvalues and simplicity of interval exchange transformations

International audienceFor a class of d-interval exchange transformations, whichwe call the symmetric class,we deÞne a new self-dual induction process in which the system is successively induced on a union ofsub-intervals. This algorithm gives rise to an underlying graph structure which reßects the dynamicalbehavior of the system, through theRokhlin towers of the induced maps. We apply it to build a wide as-sortment of explicit examples on four intervals having different dynamical properties: these include theÞrst nontrivial examples with eigenvalues (rational or irrational), the Þrst ever example of an exchangeon more than three intervals satisfying VeechÕs simplicity (though this weakening of the notion of min-imal self-joinings was designed in 1982 to be satisÞed by interval exchange transformations), and anunexpected example which is non uniquely ergodic, weakly mixing for one invariant ergodic measurebut has rational eigenvalues for the other invariant ergodic measure

Regression and the Maternal in the History of Psychoanalysis, 1900-1957

This paper examines the history of the concept of ‘regression’ as it was perceived by Sandor Ferenczi and some of his followers in the first half of the twentieth century. The first part provides a short history of the notion of ‘regression’ from the late nineteenth century to Ferenczi's work in the 1920s and 1930s. The second and third parts of the paper focus on two other thinkers on regression, who worked in Britain, under the influence of the Ferenczian paradigm – the interwar Scottish psychiatrist, Ian D. Suttie; and the British-Hungarian psychoanalyst, and Ferenczi's most important pupil, Michael Balint. Rather than a descriptive term which comes to designate a pathological mental stage, Ferenczi understood ‘regression’ as a much more literal phenomenon. For him, the mental desire to go backwards in time is a universal one, and a consequence of an inevitable traumatic separation from the mother in early childhood, which has some deep personal and cultural implications. The paper aims to show some close affinities between the preoccupation of some psychoanalysts with ‘regression’, and the growing interest in social and cultural aspects of ‘motherhood’ and ‘the maternal role’ in mid-twentieth-century British society

Linking Recent Discrimination-Related Experiences and Wellbeing via Social Cohesion and Resilience

The current study examined the relationship between recent experiences of discrimination and wellbeing and the mediating effects that social cohesion and resilience had on this relationship. Using online sampling, participants (N =255) from a South London community rated the levels of discrimination related experiences in the past 6 months, alongside measures of social cohesion, resilience, and wellbeing (happiness and depressive symptoms). Results revealed a negative relationship between recent experiences of discrimination and wellbeing which was explained by a serial mediation relationship between social cohesion and resilience, and singly by resilience alone. The study highlights how recent experiences of discrimination can lead to a depletion of personal resources and social resources (which in turn also lead to reduced personal resources) and in turn, to lower levels of wellbeing

Linking recent discrimination-related experiences and wellbeing via social cohesion and resilience

United Kingdom The current study examined the relationship between recent experiences of discrimination and wellbeing and the mediating effects that social cohesion and resilience had on this relationship. Using online sampling, participants (N= 255) from a South London community rated the levels of discrimination related experiences in the past 6 months, alongside measures of social cohesion, resilience, and wellbeing (happiness and depressive symptoms). Results revealed a negative relationship between recent experiences of discrimination and wellbeing which was explained by a serial mediation relationship between social cohesion and resilience, and singly by resilience alone. The study highlights how recent experiences of discrimination can lead to a depletion of personal resources and social resources (which in turn also lead to reduced personal resources) and in turn, to lower levels of wellbeing

Symmetries in Quantum Key Distribution and the Connection between Optimal Attacks and Optimal Cloning

We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in [Devetak and Winter, Proc. of the Roy. Soc. of London Series A, 461, 207 (2005); Kraus, Gisin and Renner, Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in d-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2, d and d+1 mutually unbiased bases where d is a prime, and show that for the protocols with 2 and d+1 MUBs the optimal attack is an optimal cloner, but for the protocols with d MUBs, it is not. Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the BB84 protocol or the 6-state protocol

Quantisations of piecewise affine maps on the torus and their quantum limits

For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the so called quantum limits, and one would like to understand which invariant measures can occur that way, thereby classifying the semiclassical behaviour of eigenfunctions. We introduce a class of maps on the torus for whose quantisations we can understand the set of quantum limits in great detail. In particular we can construct examples of ergodic maps which have singular ergodic measures as quantum limits, and examples of non-ergodic maps where arbitrary convex combinations of absolutely continuous ergodic measures can occur as quantum limits. The maps we quantise are obtained by cutting and stacking

Conduction velocities in amphibian skeletal muscle fibres exposed to hyperosmotic extracellular solutions

Early quantitative analyses of conduction velocities in unmyelinated nerve studied in a constantly iso-osmotic volume conductor were extended to an analysis of the effects of varying extracellular osmolarities on conduction velocities of surface membrane action potentials in Rana esculenta skeletal muscle fibres. Previous papers had reported that skeletal muscle fibres exposed to a wide range of extracellular sucrose concentrations resemble perfect osmometers with increased extracellular osmolarity proportionally decreasing fibre volume and therefore diminishing fibre radius, a. However, classical electrolyte theory (Robinson and Stokes 1959, Electrolyte solutions 2nd edn. Butterworth & Co. pp 41–42) would then predict that the consequent increases in intracellular ionic strength would correspondingly decrease sarcoplasmic resistivity, Ri. An extension of the original cable analysis then demonstrated that the latter would precisely offset its expected effect of alterations in a on the fibre axial resistance, ri, and leave action potential conduction velocity constant. In contrast, other reports (Hodgkin and Nakajima J Physiol 221:105–120, 1972) had suggested that Riincreased with extracellular osmolarity, owing to alterations in cytosolic viscosity. This led to a prediction of a decreased conduction velocity. These opposing hypotheses were then tested in muscle fibres subject to just-suprathreshold stimulation at a Vaseline seal at one end and measuring action potentials and their first order derivatives, dV/dt, using 5–20 MΩ, 3 M KCl glass microelectrodes at defined distances away from the stimulus sites. Exposures to hyperosmotic, sucrose-containing, Ringer solutions then reversibly reduced both conduction velocity and maximum values of dV/dt. This was compatible with an increase in Ri in the event that conduction depended upon a discharge of membrane capacitance by propagating local circuit currents through initially passive electrical elements. Conduction velocity then showed graded decreases with increasing extracellular osmolarity from 250–750 mOsm. Action potential waveforms through these osmolarity changes remained similar, including both early surface and the late after-depolarisation events reflecting transverse tubular activation. Quantitative comparisons of reduced-χ 2 values derived from a comparison of these results and the differing predictions from the two hypotheses strongly favoured the hypothesis in which Riincreased rather than decreased with hyperosmolarity

Microglia control the spread of neurotropic virus infection via P2Y12 signalling and recruit monocytes through P2Y12-independent mechanisms

Neurotropic herpesviruses can establish lifelong infection in humans and contribute to severe diseases including encephalitis and neurodegeneration. However, the mechanisms through which the brain's immune system recognizes and controls viral infections propagating across synaptically linked neuronal circuits have remained unclear. Using a well-established model of alphaherpesvirus infection that reaches the brain exclusively via retrograde transsynaptic spread from the periphery, and in vivo two-photon imaging combined with high resolution microscopy, we show that microglia are recruited to and isolate infected neurons within hours. Selective elimination of microglia results in a marked increase in the spread of infection and egress of viral particles into the brain parenchyma, which are associated with diverse neurological symptoms. Microglia recruitment and clearance of infected cells require cell-autonomous P2Y12 signalling in microglia, triggered by nucleotides released from affected neurons. In turn, we identify microglia as key contributors to monocyte recruitment into the inflamed brain, which process is largely independent of P2Y12. P2Y12-positive microglia are also recruited to infected neurons in the human brain during viral encephalitis and both microglial responses and leukocyte numbers correlate with the severity of infection. Thus, our data identify a key role for microglial P2Y12 in defence against neurotropic viruses, whilst P2Y12-independent actions of microglia may contribute to neuroinflammation by facilitating monocyte recruitment to the sites of infection