Generalized Strong Curvature Singularities and Cosmic Censorship

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.Comment: LaTeX, 11 pages, no figures, to appear in Mod. Phys. Lett.

Coherent population oscillations with nitrogen-vacancy color centers in diamond

We present results of our research on two-field (two-frequency) microwave spectroscopy in nitrogen-vacancy (NV-) color centers in a diamond. Both fields are tuned to transitions between the spin sublevels of the NV- ensemble in the 3A2 ground state (one field has a fixed frequency while the second one is scanned). Particular attention is focused on the case where two microwaves fields drive the same transition between two NV- ground state sublevels (ms=0 -> ms=+1). In this case, the observed spectra exhibit a complex narrow structure composed of three Lorentzian resonances positioned at the pump-field frequency. The resonance widths and amplitudes depend on the lifetimes of the levels involved in the transition. We attribute the spectra to coherent population oscillations induced by the two nearly degenerate microwave fields, which we have also observed in real time. The observations agree well with a theoretical model and can be useful for investigation of the NV relaxation mechanisms.Comment: 17 page

Microwave saturation spectroscopy of nitrogen-vacancy ensembles in diamond

Negatively-charged nitrogen-vacancy (NV$^-$) centers in diamond have generated much recent interest for their use in sensing. The sensitivity improves when the NV ground-state microwave transitions are narrow, but these transitions suffer from inhomogeneous broadening, especially in high-density NV ensembles. To better understand and remove the sources of broadening, we demonstrate room-temperature spectral "hole burning" of the NV ground-state transitions. We find that hole burning removes the broadening caused by magnetic fields from $^{13}$C nuclei and demonstrate that it can be used for magnetic-field-insensitive thermometry.Comment: Main text: 5 pages, 4 figures. Supplement: 6 pages, 3 figure

Nanodiamonds carrying quantum emitters with almost lifetime-limited linewidths

Nanodiamonds (NDs) hosting optically active defects are an important technical material for applications in quantum sensing, biological imaging, and quantum optics. The negatively charged silicon vacancy (SiV) defect is known to fluoresce in molecular sized NDs (1 to 6 nm) and its spectral properties depend on the quality of the surrounding host lattice. This defect is therefore a good probe to investigate the material properties of small NDs. Here we report unprecedented narrow optical transitions for SiV colour centers hosted in nanodiamonds produced using a novel high-pressure high-temperature (HPHT) technique. The SiV zero-phonon lines were measured to have an inhomogeneous distribution of 1.05 nm at 5 K across a sample of numerous NDs. Individual spectral lines as narrow as 354 MHz were measured for SiV centres in nanodiamonds smaller than 200 nm, which is four times narrower than the best SiV line previously reported for nanodiamonds. Correcting for apparent spectral diffusion yielded a homogeneous linewith of about 200 MHz, which is close to the width limit imposed by the radiative lifetime. These results demonstrate that the direct HPHT synthesis technique is capable of producing nanodiamonds with high crystal lattice quality, which are therefore a valuable technical material

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism

This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in defining the ensemble. Ensembles are obtained by dividing a huge rock sample into many mesoscopic volumes. Because rocks are a disordered collection of grains in cohesive contact, we expect that once shear strain is applied and cracks begin to arrive in the system, the mesoscopic volumes will have a wide distribution of different crack states. These mesoscopic volumes are the members of our ensembles. We determine the probability of observing a mesoscopic volume to be in a given crack state by maximizing Shannon's measure of the emergent crack disorder subject to constraints coming from the energy-balance of brittle fracture. The laws of thermodynamics, the partition function, and the quantification of temperature are obtained for such cracking systems.Comment: 11 pages, 2 figure

Activation of JNK1 contributes to dystrophic muscle pathogenesis

AbstractDuchenne Muscular Dystrophy (DMD) originates from deleterious mutations in the dystrophin gene, with a complete loss of the protein product [1, 2]. Subsequently, the disease is manifested in severe striated muscle wasting and death in early adulthood [3]. Dystrophin provides a structural base for the assembly of an integral membrane protein complex [4]. As such, dystrophin deficiency leads to an altered mechanical integrity of the myofiber and a predisposition to contraction-induced damage [5–7]. However, the development of myofiber degeneration prior to an observed mechanical defect has been documented in various dystrophic models [8, 9]. Although activation of a detrimental signal transduction pathway has been suggested as a probable cause, a specific cellular cascade has yet to be defined. Here, it is shown that murine models of DMD displayed a muscle-specific activation of JNK1. Independent activation of JNK1 resulted in defects in myotube viability and integrity in vitro, similar to a dystrophic phenotype. In addition, direct muscle injection of an adenoviral construct containing the JNK1 inhibitory protein, JIP1, dramatically attenuated the progression of dystrophic myofiber destruction. Taken together, these results suggest that a JNK1-mediated signal cascade is a conserved feature of dystrophic muscle and contributes to the progression of the disease pathogenesis

PAX7 is required for patterning the esophageal musculature

Background The mammalian esophageal musculature is unique in that it makes a transition from smooth to skeletal muscle, with most of this process occurring after birth. In order to better understand the mechanisms that control esophageal musculature development, we investigated the roles in this process of the paired box transcription factor, PAX7, a principal regulator of skeletal myogenic progenitor cells. Previous studies showed that Pax7 is important for determining the esophageal muscle composition. Results We characterized the postnatal development of the esophageal musculature in Pax7 −/− mice by analyzing morphology, muscle composition, and the expression of markers of myogenesis, cell proliferation, and apoptosis. Pax7 −/− mice displayed megaesophagus with a severe defect in the postnatal developmental process whereby esophageal smooth muscle is replaced by skeletal muscle. Pax7 −/− esophagi have substantially reduced skeletal muscle, most likely due to diminished proliferation and premature differentiation of skeletal muscle precursor cells. This impaired the proximal-to-distal progression of skeletal myogenesis and indirectly affected the patterning of the smooth muscle-containing portion of the esophageal musculature. Conclusions Postnatal patterning of the esophageal musculature appears to require robust, PAX7-dependent cell proliferation to drive the proximal-to-distal progression of skeletal myogenesis. This process in turn influences distal smooth muscle morphogenesis and development of the mature pattern of the esophageal musculature