Unknown Quantum States: The Quantum de Finetti Representation

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an ``unknown quantum state'' in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point.Comment: 30 pages, 2 figure

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page

Martingale Models for Quantum State Reduction

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations experienced by the expectation of the observable during the course of the reduction process and an upper bound is established for the ensemble average of the greatest fluctuations incurred. We consider the general projection postulate of L\"uders applicable in the case of a possibly degenerate eigenvalue spectrum, and derive this result rigorously from the underlying stochastic dynamics for state reduction in the case of both a pure and a mixed initial state. We also analyse the associated Lindblad equation for the evolution of the density matrix, and obtain an exact time-dependent solution for the state reduction that explicitly exhibits the transition from a general initial density matrix to the L\"uders density matrix. Finally, we apply Girsanov's theorem to derive a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.Comment: 30 pages LaTeX. Submitted to Journal of Physics

Gestational Weight Gain and Body Mass Index in Children: Results from Three German Cohort Studies

Previous studies suggested potential priming effects of gestational weight gain (GWG) on offspring's body composition in later life. However, consistency of these effects in normal weight, overweight and obese mothers is less clear. We combined the individual data of three German cohorts and assessed associations of total and excessive GWG (as defined by criteria of the Institute of Medicine) with offspring's mean body mass index (BMI) standard deviation scores (SDS) and overweight at the age of 5-6 years (total: n = 6,254). Quantile regression was used to examine potentially different effects on different parts of the BMI SDS distribution. All models were adjusted for birth weight, maternal age and maternal smoking during pregnancy and stratified by maternal pre-pregnancy weight status. In adjusted models, positive associations of total and excessive GWG with mean BMI SDS and overweight were observed only in children of non- overweight mothers. For example, excessive GWG was associated with a mean increase of 0.08 (95% CI: 0.01, 0.15) units of BMI SDS (0.13 (0.02, 0.24) kg/m(2) of 'real' BMI) in children of normal-weight mothers. The effects of total and excessive GWG on BMI SDS increased for higher- BMI children of normal-weight mothers. Increased GWG is likely to be associated with overweight in offspring of non-overweight mothers

Bmp4 Is Essential for the Formation of the Vestibular Apparatus that Detects Angular Head Movements

Angular head movements in vertebrates are detected by the three semicircular canals of the inner ear and their associated sensory tissues, the cristae. Bone morphogenetic protein 4 (Bmp4), a member of the Transforming growth factor family (TGF-β), is conservatively expressed in the developing cristae in several species, including zebrafish, frog, chicken, and mouse. Using mouse models in which Bmp4 is conditionally deleted within the inner ear, as well as chicken models in which Bmp signaling is knocked down specifically in the cristae, we show that Bmp4 is essential for the formation of all three cristae and their associated canals. Our results indicate that Bmp4 does not mediate the formation of sensory hair and supporting cells within the cristae by directly regulating genes required for prosensory development in the inner ear such as Serrate1 (Jagged1 in mouse), Fgf10, and Sox2. Instead, Bmp4 most likely mediates crista formation by regulating Lmo4 and Msx1 in the sensory region and Gata3, p75Ngfr, and Lmo4 in the non-sensory region of the crista, the septum cruciatum. In the canals, Bmp2 and Dlx5 are regulated by Bmp4, either directly or indirectly. Mechanisms involved in the formation of sensory organs of the vertebrate inner ear are thought to be analogous to those regulating sensory bristle formation in Drosophila. Our results suggest that, in comparison to sensory bristles, crista formation within the inner ear requires an additional step of sensory and non-sensory fate specification

Gamma Power Is Phase-Locked to Posterior Alpha Activity

Neuronal oscillations in various frequency bands have been reported in numerous studies in both humans and animals. While it is obvious that these oscillations play an important role in cognitive processing, it remains unclear how oscillations in various frequency bands interact. In this study we have investigated phase to power locking in MEG activity of healthy human subjects at rest with their eyes closed. To examine cross-frequency coupling, we have computed coherence between the time course of the power in a given frequency band and the signal itself within every channel. The time-course of the power was calculated using a sliding tapered time window followed by a Fourier transform. Our findings show that high-frequency gamma power (30–70 Hz) is phase-locked to alpha oscillations (8–13 Hz) in the ongoing MEG signals. The topography of the coupling was similar to the topography of the alpha power and was strongest over occipital areas. Interestingly, gamma activity per se was not evident in the power spectra and only became detectable when studied in relation to the alpha phase. Intracranial data from an epileptic subject confirmed these findings albeit there was slowing in both the alpha and gamma band. A tentative explanation for this phenomenon is that the visual system is inhibited during most of the alpha cycle whereas a burst of gamma activity at a specific alpha phase (e.g. at troughs) reflects a window of excitability

Task-related modulation of anterior theta and posterior alpha EEG reflects top-down preparation

<p>Abstract</p> <p>Background</p> <p>Prestimulus EEG alpha activity in humans has been considered to reflect ongoing top-down preparation for the performance of subsequent tasks. Since theta oscillations may be related to poststimulus top-down processing, we investigated whether prestimulus EEG theta activity also reflects top-down cognitive preparation for a stimulus.</p> <p>Results</p> <p>We recorded EEG data from 15 healthy controls performing a color and shape discrimination task, and used the wavelet transformation to investigate the time course and power of oscillatory activity in the signals. We observed a relationship between both anterior theta and posterior alpha power in the prestimulus period and the type of subsequent task.</p> <p>Conclusions</p> <p>Since task-differences were reflected in both theta and alpha activities prior to stimulus onset, both prestimulus theta (particularly around the anterior region) and prestimulus alpha (particularly around the posterior region) activities may reflect prestimulus top-down preparation for the performance of subsequent tasks.</p

Suppression of p75 Neurotrophin Receptor Surface Expression with Intrabodies Influences Bcl-xL mRNA Expression and Neurite Outgrowth in PC12 Cells

Background: Although p75 neurotrophin receptor (p75NTR) is the first neurotrophin receptor isolated, its diverse physiological functions and signaling have remained elusive for many years. Loss-of-function phenotypic analyses for p75NTR were mainly focused at the genetic level; however these approaches were impacted by off-target effect, insufficient stability, unspecific stress response or alternative active splicing products. In this study, p75NTR surface expression was suppressed for the first time at the protein level by endoplasmic reticulum (ER) retained intrabodies. Results: Three monoclonal recombinant antibody fragments (scFv) with affinities in the low nanomolar range to murine p75NTR were isolated by antibody phage display. To suppress p75NTR cell surface expression, the encoding genes of these scFvs extended by the ER retention peptide KDEL were transiently transfected into the neuron-like rat pheochromocytoma cell line PC12 and the mouse neuroblastoma x mouse spinal cord hybrid cell line NSC19. The ER retained intrabody construct, SH325-G7-KDEL, mediated a downregulation of p75NTR cell surface expression as shown by flow cytometry. This effect was maintained over a period of at least eight days without activating an unfolded protein response (UPR). Moreover, the ER retention of p75NTR resulted in downregulation of mRNA levels of the anti-apoptotic protein Bcl-xL as well as in strong inhibition of NGF-induced neurite outgrowth in PC12 cells. Conclusion: The ER retained intrabody SH325-G7-KDEL not only induces phenotypic knockdown of this p75NTR but als

Dynamic Changes in the MicroRNA Expression Profile Reveal Multiple Regulatory Mechanisms in the Spinal Nerve Ligation Model of Neuropathic Pain

Neuropathic pain resulting from nerve lesions or dysfunction represents one of the most challenging neurological diseases to treat. A better understanding of the molecular mechanisms responsible for causing these maladaptive responses can help develop novel therapeutic strategies and biomarkers for neuropathic pain. We performed a miRNA expression profiling study of dorsal root ganglion (DRG) tissue from rats four weeks post spinal nerve ligation (SNL), a model of neuropathic pain. TaqMan low density arrays identified 63 miRNAs whose level of expression was significantly altered following SNL surgery. Of these, 59 were downregulated and the ipsilateral L4 DRG, not the injured L5 DRG, showed the most significant downregulation suggesting that miRNA changes in the uninjured afferents may underlie the development and maintenance of neuropathic pain. TargetScan was used to predict mRNA targets for these miRNAs and it was found that the transcripts with multiple predicted target sites belong to neurologically important pathways. By employing different bioinformatic approaches we identified neurite remodeling as a significantly regulated biological pathway, and some of these predictions were confirmed by siRNA knockdown for genes that regulate neurite growth in differentiated Neuro2A cells. In vitro validation for predicted target sites in the 3′-UTR of voltage-gated sodium channel Scn11a, alpha 2/delta1 subunit of voltage-dependent Ca-channel, and purinergic receptor P2rx ligand-gated ion channel 4 using luciferase reporter assays showed that identified miRNAs modulated gene expression significantly. Our results suggest the potential for miRNAs to play a direct role in neuropathic pain