States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution

A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and semiclassical equations, based on general properties of quantum moments.Comment: 23 page

Group Theoretical Quantization and the Example of a Phase Space S1×R+S^{1} \times R^{+}

The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group actions. A systematic strategy for finding admissible group actions for particular subbundles of cotangent spaces is developed, two-dimensional prototypes of which are T^*R^+ and S^1 x R^+ (interpreted as restrictions of T^*R and T^*S^1 to positive coordinate and momentum, respectively). In this framework (and under an additional, natural condition) an SO_+(1,2)-action on S^1 x R^+ results as the unique admissible group action. For symplectic manifolds which are (specific) parts of phase spaces with known quantum theory a simple projection method of quantization is formulated. For T^*R^+ and S^1 x R^+ equivalent results to those of more established (but more involved) quantization schemes are obtained. The approach may be of interest, e.g., in attempts to quantize gravity theories where demanding nondegenerate metrics of a fixed signature imposes similar constraints

Symplectic Cuts and Projection Quantization

The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor

Group Theoretical Quantization of a Phase Space S1xR+S^{1} x R^{+} and the Mass Spectrum of Schwarzschild Black Holes in D Space-Time Dimensions

The symplectic reduction of pure spherically symmetric (Schwarzschild) classical gravity in D space-time dimensions yields a 2-dimensional phase space of observables consisting of the Mass M (>0) and a canonically conjugate (Killing) time variable T. Imposing (mass-dependent) periodic boundary conditions in time on the associated quantum mechanical plane waves which represent the Schwarzschild system in the period just before or during the formation of a black hole, yields an energy spectrum of the hole which realizes the old Bekenstein postulate that the quanta of the horizon A_{D-2} are multiples of a basic area quantum. In the present paper it is shown that the phase space of such a Schwarzschild black hole in D space-time dimensions is symplectomorphic to a symplectic manifold S={(phi in R mod 2 pi, p = A_{D-2} >0)} with the symplectic form d phi wedge d p. As the action of the group SO_+(1,2) on that manifold is transitive, effective and Hamiltonian, it can be used for a group theoretical quantization of the system. The area operator p for the horizon corresponds to the generator of the compact subgroup SO(2) and becomes quantized accordingly: The positive discrete series of the irreducible unitary representations of SO_+(1,2) yields an (horizon) area spectrum proportional k+n, where k = 1,2,... characterizes the representation and n = 0,1,2,... the number of area quanta. If one employs the unitary representations of the universal covering group of SO_+(1,2) the number k can take any fixed positive real value (theta-parameter). The unitary representations of the positive discrete series provide concrete Hilbert spaces for quantum Schwarzschild black holes

Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries

Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of the PSM in the literature are not globally well-defined for non-parallelizable Poisson manifolds and propose a covariant definition of them as left action of some finite-dimensional Lie algebroid. Our approach allows to avoid complications arising in the infinite dimensional super-geometry of the BV- and AKSZ-formalism. This preprint is a starting point in a series of papers meant to introduce Yang-Mills type gauge theories of Lie algebroids, which include and generalize the standard YM theory, the PSM, and gerbes.Comment: 24 page

Safety, Health and Environmental Annual Report 2011

This report is the integrated Safety, Health and Environmental Annual Report 2011 of the Institute for Energy and Transport (IET) of the JRC at the Petten site. The report is split in a health and safety part and an environmental part. The report includes a description of the organisational systems and structures together with the planned activities and the achieved goals. The environmental part contains in addition an assessment of the environmental impact of the Institute. This report only refers to the activities of the JRC-Petten site of the Institute. The Institute has implemented a Quality Management System of which Environmental and Safety Management is an integral part. Internal audits and external inspections by Dutch authorities have not identified a significant deviation from legal requirements. The institute will continue to improve the environmental and safety system in 2012 and will amongst other things focus on improving energy performance of the institute.JRC.F.1 - Site Managemen

Integrated optical sensors for disposable microfluidics

Optical chemical sensors are established process monitoring tools in industry and research laboratories. Optical chemical sensors basically comprise of luminescent indicator dye based in a host polymer. They are easy to integrate, non-invasive, do not need any reference element and can be read-out contactless from outside. However, to fully exploit the potential in microfluidic or organ-on- chip devices, the sensors have to fulfil several demands including high brightness, capability to be applied as thin film, excellent photo-stability, cheap and accurate read-out systems, ease in use (simple calibration and drift free), simple mass production compatible preparation steps, compatibility with the chip materials, resistance towards γ-sterilisation and no toxicity. We present sensors for oxygen and pH fulfilling these demands. Our sensors can be excited with red-light and emit light in the near infra-red range (\u3c700 nm). This suppresses background fluorescence and scattering from biological material. Sensor layers or spots are deposited with inkjet-based micro-dispensing or air-brush spraying with good adherence on glass or polymeric materials. A modified miniaturized phase-fluorimeter in a foot-print of a memory stick enables the read-out of sensor sizes below 100 micrometers. The sensor enable dynamic cell culturing and monitoring of cell metabolism in a microfluidic environment. We will give examples of oxygen sensors in a organ-on-chip model and pH sensors in cell cultures. Please click Additional Files below to see the full abstract

Uncovering convolutional neural network decisions for diagnosing multiple sclerosis on conventional MRI using layer-wise relevance propagation

Machine learning-based imaging diagnostics has recently reached or even superseded the level of clinical experts in several clinical domains. However, classification decisions of a trained machine learning system are typically non-transparent, a major hindrance for clinical integration, error tracking or knowledge discovery. In this study, we present a transparent deep learning framework relying on convolutional neural networks (CNNs) and layer-wise relevance propagation (LRP) for diagnosing multiple sclerosis (MS). MS is commonly diagnosed utilizing a combination of clinical presentation and conventional magnetic resonance imaging (MRI), specifically the occurrence and presentation of white matter lesions in T2-weighted images. We hypothesized that using LRP in a naive predictive model would enable us to uncover relevant image features that a trained CNN uses for decision-making. Since imaging markers in MS are well-established this would enable us to validate the respective CNN model. First, we pre-trained a CNN on MRI data from the Alzheimer's Disease Neuroimaging Initiative (n = 921), afterwards specializing the CNN to discriminate between MS patients and healthy controls (n = 147). Using LRP, we then produced a heatmap for each subject in the holdout set depicting the voxel-wise relevance for a particular classification decision. The resulting CNN model resulted in a balanced accuracy of 87.04% and an area under the curve of 96.08% in a receiver operating characteristic curve. The subsequent LRP visualization revealed that the CNN model focuses indeed on individual lesions, but also incorporates additional information such as lesion location, non-lesional white matter or gray matter areas such as the thalamus, which are established conventional and advanced MRI markers in MS. We conclude that LRP and the proposed framework have the capability to make diagnostic decisions of..

Micromechanical characterization of the interphase layer in semi-crystalline polyethylene

The interphase layer in semi-crystalline polyethylene is the least known constituent, compared to the amorphous and crystalline phases, in terms of mechanical properties. In this study, the Monte Carlo molecular simulation results for the interlamellar domain (i.e. amorphous+ interphases), reported in (Macromolecules 2006, 39, 439–447) are employed. The amorphous elastic properties are adopted from the literature and then two distinct micromechanical homogenization approaches are utilized to dissociate the interphase stiffness from that of the interlamellar region. The results of the two micromechanical approaches match perfectly. Interestingly, the dissociated interphase stiffness lacks the common feature of positive definiteness, which is attributed to its nature as a transitional domain between two coexisting phases. The sensitivity analyses reveal that this property is insensitive to the non-orthotropic components of the interlamellar stiffness and the uncertainties existing in the interlamellar and amorphous stiffnesses. Finally, using the dissociated interphase stiffness, its effective Young's modulus is calculated, which compares well with the effective interlamellar Young's modulus for highly crystalline polyethylene, reported in an experimental study. This satisfactory agreement along with the identical results produced by the two micromechanical approaches confirms the validity of the new information about the interphase elastic properties in addition to making the proposed dissociation methodology quite reliable when applied to similar problems