Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Generalized Quantum Theory: Overview and Latest Developments

The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.Comment: 14 pages, update in reference

Distinguishing between pre- and post-incision under general anesthesia by spectral and recurrence analysis of EEG data

International audienceNowadays, surgical operations are impossible to imagine without general anaesthesia, which involves loss of consciousness, immobility, amnesia and analgesia. Understanding mechanisms underlying each of these effects guarantees well-controlled medical treatment.Our work focuses on analgesia effect of general anaesthesia, more specifically, on patients reaction on nociception stimuli. The study was conducted on dataset consisting of 230 EEG signals: pre- and post-incisional recordings for 115 patients, who received desflurane and propofol [1].Initial analysis was performed by power spectral analysis, which is a widespread approach in signal processing. Power spectral information was described by fitting the background activity and measuring power contained in delta and alpha bands according to power of background activity. The fact that power spectrum of background activity decays as frequency increasing is well known and thoroughly studied [2]. Here, traditional 1/f^α behaviour of the decay was replaced by a Lorentzian model to describe the power spectrum of background activity.Due to observed non-stationary nature of EEG signals spectral analysis does not suffice to reveal significant changes between two states. A further improvement was done by expanding spectra with time information. To obtain time-frequency representations of the signals conventional spectrograms were used as well as a spectrogram reassignment technique [3]. The latter allows to ameliorate readability of a spectrogram by reassigning energy contained in spectrogram to more precise positions.Subsequently, obtained spectrograms were used in recurrence analysis [4] and its quantification by complexity measure. Recurrence analysis allows to describe and visualise dynamics of a system and discover structural patterns contained in the data. Structure of each recurrence plot is characterised by Lempel–Ziv complexity measure [5], which shows a difference between pre- and post-incision.References:1. James W. Sleigh, Leslie, K. & Voss, L. The effect of skin incision on the electroencephalogram during general anesthesia maintained with propofol or desflurane. Journal of clinical monitoring and computing 24, 307–18 (2010), 10.1007/s10877-010-9251-32. Bédard, C. & Destexhe, A. Macroscopic Models of Local Field Potentials and the Apparent 1/f Noise in Brain Activity. Biophysical Journal 96, 2589–2603 (2009), 10.1016/j.bpj.2008.12.39513. Auger, F. et al. Time-Frequency Reassignment and Synchrosqueezing: An Overview. IEEE Signal Processing Magazine 30, 32–41 (2013), 10.1109/MSP.2013.22653164. Marwan, N., Carmenromano, M., Thiel, M. & Kurths, J. Recurrence plots for the analysis of complex systems. Physics Reports 438, 237–329 (2007), 10.1016/j.physrep.2006.11.0015. Zhang, X.-S., Roy, R. J. & Jensen, E. W. EEG complexity as a measure of depth of anesthesia for patients. Biomedical Engineering, IEEE Transactions on 48, 1424–1433 (2001), 10.1109/10.96660

Epistemic Entanglement due to Non-Generating Partitions of Classical Dynamical Systems

Quantum entanglement relies on the fact that pure quantum states are dispersive and often inseparable. Since pure classical states are dispersion-free they are always separable and cannot be entangled. However, entanglement is possible for epistemic, dispersive classical states. We show how such epistemic entanglement arises for epistemic states of classical dynamical systems based on phase space partitions that are not generating. We compute epistemically entangled states for two coupled harmonic oscillators.Comment: 13 pages, no figures; International Journal of Theoretical Physics, 201

The genetic basis of endometriosis and comorbidity with other pain and inflammatory conditions

Endometriosis is a common condition associated with debilitating pelvic pain and infertility. A genome-wide association study meta-analysis, including 60,674 cases and 701,926 controls of European and East Asian descent, identified 42 genome-wide significant loci comprising 49 distinct association signals. Effect sizes were largest for stage 3/4 disease, driven by ovarian endometriosis. Identified signals explained up to 5.01% of disease variance and regulated expression or methylation of genes in endometrium and blood, many of which were associated with pain perception/maintenance (SRP14/BMF, GDAP1, MLLT10, BSN and NGF). We observed significant genetic correlations between endometriosis and 11 pain conditions, including migraine, back and multisite chronic pain (MCP), as well as inflammatory conditions, including asthma and osteoarthritis. Multitrait genetic analyses identified substantial sharing of variants associated with endometriosis and MCP/migraine. Targeted investigations of genetically regulated mechanisms shared between endometriosis and other pain conditions are needed to aid the development of new treatments and facilitate early symptomatic intervention

Empirical Research on Sovereign Debt and Default

The long history of sovereign debt and the associated enforcement problem have attracted researchers in many fields. In this paper, we survey empirical work by economists, historians, and political scientists. As we review the empirical literature, we emphasize parallel developments in the theory of sovereign debt. One major theme emerges. Although recent research has sought to balance theoretical and empirical considerations, there remains a gap between theories of sovereign debt and the data used to test them. We recommend a number of steps that researchers can take to improve the correspondence between theory and data

The genetic basis of endometriosis and comorbidity with other pain and inflammatory conditions

Endometriosis is a common condition associated with debilitating pelvic pain and infertility. A genome-wide association study meta-analysis, including 60,674 cases and 701,926 controls of European and East Asian descent, identified 42 genome-wide significant loci comprising 49 distinct association signals. Effect sizes were largest for stage 3/4 disease, driven by ovarian endometriosis. Identified signals explained up to 5.01% of disease variance and regulated expression or methylation of genes in endometrium and blood, many of which were associated with pain perception/maintenance (SRP14/BMF, GDAP1, MLLT10, BSN and NGF). We observed significant genetic correlations between endometriosis and 11 pain conditions, including migraine, back and multisite chronic pain (MCP), as well as inflammatory conditions, including asthma and osteoarthritis. Multitrait genetic analyses identified substantial sharing of variants associated with endometriosis and MCP/migraine. Targeted investigations of genetically regulated mechanisms shared between endometriosis and other pain conditions are needed to aid the development of new treatments and facilitate early symptomatic intervention