Measuring the size of a Schroedinger cat state

We propose a measure for the "size" of a Schroedinger cat state, i.e. a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties, by counting how many single-particle operations are needed to map one state onto the other. This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- and right-circulating supercurrent states and find this Schroedinger cat to be surprisingly small.Comment: 5 pages, 3 figure

Descartes' Theory of Passions

Descartes not only had a theory of passions, but one that deserves a place among contemporary debates on emotions. The structure of this dissertation attempts to make explicit the unity of that theory. The study of the passions by the physicien (who not only studies matter and motion but also human nature) [Chapter 2] appears to be the "foundations" (as he tells Chanut) of morals [Chapters 1 and 4] insofar as their main function [Chapter 3] is to dispose us to act in ways which directly affect our natural happiness. In other words, Descartes is in the Passions of the Soul (1649) climbing the very tree of philosophy he presented two years earlier in the Preface to French Edition of the Principles of Philosophy: the trunk (in this case a section of it: our nature) leads us to the highest of the three branches (morals) when we study human passions. Human passions constitute the only function of the mind-body union that can guide us in the pursuit of our (natural) happiness. They do this (1) by informing the soul about the current state of perfection both of the body and, most importantly, of the mind-body union; (2) by discriminating what is relevant in the world regarding our perfection; and (3) by proposing (to the will) possible ways of action (i.e. by disposing us to act). The virtuous (the generous) are those who have achieved "contentment" not by impeding the arousal of their passions but by living them according to reason, that is, by following freely the dispositions to act (brought about by them) which can increase our perfection—i.e. the disposition to join true goods and to avoid true evils. Regarding current debates on emotions [Chapter 5], Descartes' perceptual model not only provides a satisfactory answer to the major challenges faced today both by feeling theories (intentionality) and judgment theories (feelings and the passivity of emotions) but it can also help advance those debates by, on one hand, bringing into them new or neglected ideas, and, on the other, providing a solid overall framework to think about passions

P3b reflects periodicity in linguistic sequences

Temporal predictability is thought to affect stimulus processing by facilitating the allocation of attentional resources. Recent studies have shown that periodicity of a tonal sequence results in a decreased peak latency and a larger amplitude of the P3b compared with temporally random, i.e., aperiodic sequences. We investigated whether this applies also to sequences of linguistic stimuli (syllables), although speech is usually aperiodic. We compared aperiodic syllable sequences with two temporally regular conditions. In one condition, the interval between syllable onset was fixed, whereas in a second condition the interval between the syllables’ perceptual center (p-center) was kept constant. Event-related potentials were assessed in 30 adults who were instructed to detect irregularities in the stimulus sequences. We found larger P3b amplitudes for both temporally predictable conditions as compared to the aperiodic condition and a shorter P3b latency in the p-center condition than in both other conditions. These findings demonstrate that even in acoustically more complex sequences such as syllable streams, temporal predictability facilitates the processing of deviant stimuli. Furthermore, we provide first electrophysiological evidence for the relevance of the p-center concept in linguistic stimulus processing

The Redox Couple of the Cytochrome \u3cem\u3ec\u3c/em\u3e Cyanide Complex: The Contribution of Heme Iron Ligation to the Structural Stability, Chemical Reactivity, and Physiological Behavior of Horse Cytochrome \u3cem\u3ec\u3c/em\u3e

Contrary to most heme proteins, ferrous cytochrome c does not bind ligands such as cyanide and CO. In order to quantify this observation, the redox potential of the ferric/ferrous cytochrome c–cyanide redox couple was determined for the first time by cyclic voltammetry. Its E0′ was −240 mV versus SHE, equivalent to −23.2 kJ/mol. The entropy of reaction for the reduction of the cyanide complex was also determined. From a thermodynamic cycle that included this new value for the cyt c cyanide complex E0′, the binding constant of cyanide to the reduced protein was estimated to be 4.7 × 10−3 LM−1 or 13.4 kJ/mol (3.2 kcal/mol), which is 48.1 kJ/mol (11.5 kcal/mol) less favorable than the binding of cyanide to ferricytochrome c. For coordination of cyanide to ferrocytochrome c, the entropy change was earlier experimentally evaluated as 92.4 Jmol−1K−1 (22.1 e.u.) at 25 K, and the enthalpy change for the same net reaction was calculated to be 41.0 kJ/mol (9.8 kcal/mol). By taking these results into account, it was discovered that the major obstacle to cyanide coordination to ferrocytochrome c is enthalpic, due to the greater compactness of the reduced molecule or, alternatively, to a lower rate of conformational fluctuation caused by solvation, electrostatic, and structural factors. The biophysical consequences of the large difference in the stabilities of the closed crevice structures are discussed

On Irrelevance and Algorithmic Equality in Predicative Type Theory

Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model.Comment: 36 pages, superseds the FoSSaCS 2011 paper of the first author, titled "Irrelevance in Type Theory with a Heterogeneous Equality Judgement

Neuronal representation of intrinsic cochlear sound signals in the colliculus inferior of the mongolian gerbil

Die vorliegende Arbeit untersucht die neuronale Repräsentation von cochleären Verzerrungsprodukten im auditorischen Mittelhirn der Wüstenrennmaus. Die hohe Sensitivität und die gute Frequenzauflösung des Hörorgans der Säugetiere basiert auf einer aktiven mechanischen Verstärkung der schallinduzierten Basilarmembranschwingung im Innenohr. Die äußeren Haarsinneszellen, die während des Transduktionsprozesses zyklisch ihre Länge ändern und dabei zusätzliche Schwingungsenergie in das System zurückführen, sind der zugrunde liegende Motor des aktiven cochleären Verstärkers. Die stark nichtlinearen Eigenschaften dieses Verstärkers führen allerdings bei gleichzeitiger Verstärkung mehrerer Frequenzkomponenten zur Generierung von Kombinationsschwingungen, welche im Ursprungssignal nicht vorhanden sind. Wird das Ohr beispielsweise durch zwei Töne mit den Frequenzen f1 und f2 stimuliert (f1f1), DPs are generated in the region of overlap of the two stimulus travelling waves and the most distinct distortion products are the quadratic distortion-tone (f2-f1) and the cubic distortion-tone (2f1-f2). From their generation site they propagate via the cochlear fluid space in both directions, i.e. both towards the base of the cochlear where they are reversely transmitted via the middle ear into the ear channel and towards the apex of the cochlea to their characteristic frequency site where they may activate the sound transduction process and subsequent neuronal processing. In the ear channel the distortion product energy can be measured as distortion product otoacoustic emission (DPOAEs). Neuronal correlates of cochlear DPs can be measured in several brain regions along the auditory pathway. In the present Phd-thesis the neuronal correlates and the otoacoustic emissions of cochlear distortion products were measured simultaneously. By comparing the neuronal responses with the peripheral DPOAE measures possible changes of the neuronal representation of cochlear DPs should be revealed. For this purpose the electrical activity of 91 neurons in the colliculus inferior of the Mongolian gerbil was recorded while the contra lateral ear was stimulated with two high frequency stimuli and DPOAE were measured. The frequencies of the stimulus tones (f1 and f2) where chosen such that the frequency of a resulting DP (f2-f1 or 2f1-f2) matched the characteristic frequency of the recorded auditory neuron. In 95~% of all measurements a strong neuronal response could be measured during two tone stimulation which can be attributed to the intracochlear stimulation by a distinct DP. The stimulation with one of the two stimuli alone did not induce any neuronal response. In a subset of the measurements the neuronal response during two tone stimulation could be successfully canceled by a third phase adjusted tone with a frequency equal to the DP frequency what provides evidence for the intra cochlear DP as source of the neuronal response. While at DP frequencies above 1.3 kHz the neuronal responses near threshold could be well described by the DPOAE level, at lower frequencies an increasing discrepancy between intra cochlear DP level and the DPOAE level in the ear channel is obvious. Part of the low frequency neurons already responded during stimulation with the high frequency stimuli with stimulus levels at or below the neuronal threshold. Again, high intracochlear DP-levels were verified by the cancellation of the neuronal DP-response with a third phase-adjusted tone stimulus at the DP frequency. A frequency-specific reduction of middle ear gain at low frequencies is possibly involved in the reduction of DPOAE level. The results indicate that pitch-related properties of complex stimuli may be produced partially by high intracochlear f2-f1 distortion levels