On Signature Transition and Compactification in Kaluza-Klein Cosmology

We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative cosmological constant and a Robertson-Walker type metric. It is shown that the solutions to Einstein field equations have degenerate metric and exhibit transitioins from a Euclidean to a Lorentzian domain. We then suggest a mechanism, based on signature transition which leads to compactification of the internal space in the Lorentzian region as $a \sim |\Lambda|^{1/2}$. With the assumption of a very small value for the cosmological constant we find that the size of the universe $R$ and the internal scale factor $a$ would be related according to $Ra\sim 1$ in the Lorentzian region. The corresponding Wheeler-DeWitt equation has exact solution in the mini-superspace giving rise to a quantum state which peaks in the vicinity of the classical solutions undergoing signature transition.Comment: 13 pages, 3 figure

Quaternionic Salkowski Curves and Quaternionic Similar Curves

In this paper, we give the definitions and characterizations of quaternionic Salkowski, quaternionic anti-Salkowski and quaternionic similar curves in the Euclidean spaces E^3 and E^4. We obtain relationships between these curves and some special quaternionic curves such as quaternionic slant helices and quaternionic B2-slant helices.Comment: 17 page

Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background

The effective potential for a dynamical Wick field (dynamical signature) induced by the quantum effects of massive fields on a topologically non-trivial $D$ dimensional background is considered. It is shown that when the radius of the compactified dimension is very small compared with $\Lambda^{1/2}$ (where $\Lambda$ is a proper-time cutoff), a flat metric with Lorentzian signature is preferred on ${\bf R}^4 \times {\bf S}^1$. When the compactification radius becomes larger a careful analysis of the 1-loop effective potential indicates that a Lorentzian signature is preferred in both $D=6$ and $D=4$ and that these results are relatively stable under metrical perturbations

Diffeomorphism algebra of two dimensional free massless scalar field with signature change

We study a model of free massless scalar fields on a two dimensional cylinder with metric that admits a change of signature between Lorentzian and Euclidean type (ET), across the two timelike hypersurfaces (with respect to Lorentzian region). Considering a long strip-shaped region of the cylinder, denoted by an angle \theta, as the signature changed region it is shown that the energy spectrum depends on the angle \theta and in a sense differs from ordinary one for low energies. Morever diffeomorphism algebra of corresponding infinite conserved charges is different from '' Virasoro'' algebra and approaches to it at higher energies. The central term is also modified but does not approach to the ordinary one at higher energies.Comment: 18 pages, Latex, 2 ps figure

Non-Riemannian Gravity and the Einstein-Proca System

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

On Applications of Campbell's Embedding Theorem

A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found. The local nature of Campbell's theorem is highlighted by studying the embedding of some lower-dimensional spaces.Comment: 17 pages, standard Latex sourc

Low disorder and high valley splitting in silicon

The electrical characterisation of classical and quantum devices is a critical step in the development cycle of heterogeneous material stacks for semiconductor spin qubits. In the case of silicon, properties such as disorder and energy separation of conduction band valleys are commonly investigated individually upon modifications in selected parameters of the material stack. However, this reductionist approach fails to consider the interdependence between different structural and electronic properties at the danger of optimising one metric at the expense of the others. Here, we achieve a significant improvement in both disorder and valley splitting by taking a co-design approach to the material stack. We demonstrate isotopically-purified, strained quantum wells with high mobility of 3.14(8)$\times$10$^5$ cm$^2$/Vs and low percolation density of 6.9(1)$\times$10$^{10}$ cm$^{-2}$. These low disorder quantum wells support quantum dots with low charge noise of 0.9(3) $\mu$eV/Hz$^{1/2}$ and large mean valley splitting energy of 0.24(7) meV, measured in qubit devices. By striking the delicate balance between disorder, charge noise, and valley splitting, these findings provide a benchmark for silicon as a host semiconductor for quantum dot qubits. We foresee the application of these heterostructures in larger, high-performance quantum processors

Mouse nuclear myosin I knock-out shows interchangeability and redundancy of myosin isoforms in the cell nucleus.

Nuclear myosin I (NM1) is a nuclear isoform of the well-known "cytoplasmic" Myosin 1c protein (Myo1c). Located on the 11(th) chromosome in mice, NM1 results from an alternative start of transcription of the Myo1c gene adding an extra 16 amino acids at the N-terminus. Previous studies revealed its roles in RNA Polymerase I and RNA Polymerase II transcription, chromatin remodeling, and chromosomal movements. Its nuclear localization signal is localized in the middle of the molecule and therefore directs both Myosin 1c isoforms to the nucleus. In order to trace specific functions of the NM1 isoform, we generated mice lacking the NM1 start codon without affecting the cytoplasmic Myo1c protein. Mutant mice were analyzed in a comprehensive phenotypic screen in cooperation with the German Mouse Clinic. Strikingly, no obvious phenotype related to previously described functions has been observed. However, we found minor changes in bone mineral density and the number and size of red blood cells in knock-out mice, which are most probably not related to previously described functions of NM1 in the nucleus. In Myo1c/NM1 depleted U2OS cells, the level of Pol I transcription was restored by overexpression of shRNA-resistant mouse Myo1c. Moreover, we found Myo1c interacting with Pol II. The ratio between Myo1c and NM1 proteins were similar in the nucleus and deletion of NM1 did not cause any compensatory overexpression of Myo1c protein. We observed that Myo1c can replace NM1 in its nuclear functions. Amount of both proteins is nearly equal and NM1 knock-out does not cause any compensatory overexpression of Myo1c. We therefore suggest that both isoforms can substitute each other in nuclear processes

A large scale hearing loss screen reveals an extensive unexplored genetic landscape for auditory dysfunction

The developmental and physiological complexity of the auditory system is likely reflected in the underlying set of genes involved in auditory function. In humans, over 150 non-syndromic loci have been identified, and there are more than 400 human genetic syndromes with a hearing loss component. Over 100 non-syndromic hearing loss genes have been identified in mouse and human, but we remain ignorant of the full extent of the genetic landscape involved in auditory dysfunction. As part of the International Mouse Phenotyping Consortium, we undertook a hearing loss screen in a cohort of 3006 mouse knockout strains. In total, we identify 67 candidate hearing loss genes. We detect known hearing loss genes, but the vast majority, 52, of the candidate genes were novel. Our analysis reveals a large and unexplored genetic landscape involved with auditory function