New sufficient conditions for Hamiltonian paths.
Ontology highlight
ABSTRACT:
SUBMITTER: Rahman MS
PROVIDER: S-EPMC4090529 | biostudies-other | 2014
REPOSITORIES: biostudies-other
Similar Datasets
Project description:Equations of the Loewner class subject to non-constant boundary conditions along the real axis are formulated and solved giving the geodesic paths of slits growing in the upper half complex plane. The problem is motivated by Laplacian growth in which the slits represent thin fingers growing in a diffusion field. A single finger follows a curved path determined by the forcing function appearing in Loewner's equation. This function is found by solving an ordinary differential equation whose terms depend on curvature properties of the streamlines of the diffusive field in the conformally mapped 'mathematical' plane. The effect of boundary conditions specifying either piecewise constant values of the field variable along the real axis, or a dipole placed on the real axis, reveal a range of behaviours for the growing slit. These include regions along the real axis from which no slit growth is possible, regions where paths grow to infinity, or regions where paths curve back toward the real axis terminating in finite time. Symmetric pairs of paths subject to the piecewise constant boundary condition along the real axis are also computed, demonstrating that paths which grow to infinity evolve asymptotically toward an angle of bifurcation of π/5.
| S-EPMC7655755 | biostudies-literature
Project description:We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.
| S-EPMC2761313 | biostudies-literature
Project description:Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly those transforming quantum channels into CPTNI maps even when tensored with the identity supermap. We link this result to the fact that the principle of causality fails in the theory of quantum supermaps.
| S-EPMC7209144 | biostudies-literature
Project description:The emerging field of omics - large-scale data-rich biological measurements of the genome - provides new opportunities to advance and strengthen research into endocrine-disrupting chemicals (EDCs). Although some EDCs have been associated with adverse health effects in humans, our understanding of their impact remains incomplete. Progress in the field has been primarily limited by our inability to adequately estimate and characterize exposure and identify sensitive and measurable outcomes during windows of vulnerability. Evolving omics technologies in genomics, epigenomics and mitochondriomics have the potential to generate data that enhance exposure assessment to include the exposome - the totality of the lifetime exposure burden - and provide biology-based estimates of individual risks. Applying omics technologies to expand our knowledge of individual risk and susceptibility will augment biological data in the prediction of variability and response to disease, thereby further advancing EDC research. Together, refined exposure characterization and enhanced disease-risk prediction will help to bridge crucial gaps in EDC research and create opportunities to move the field towards a new vision - precision public health.
| S-EPMC7141602 | biostudies-literature
Project description:We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high-dimensional particle. Depending on its initial momentum and mass matrix, the particle evolves along a trajectory that traverses the effective nullspace, thereby producing a series of alternative models that are consistent with observations and their uncertainties. Variants of the nullspace shuttle enable hypothesis testing, for example, by adding features or by producing smoother or rougher models. Furthermore, the Hamiltonian nullspace shuttle can serve as a tunable hybrid between deterministic and probabilistic inversion methods: Choosing random initial momenta, it resembles Hamiltonian Monte Carlo; requiring misfits to decrease along a trajectory, it transforms into gradient descent. We illustrate the concept with a low-dimensional toy example and with high-dimensional nonlinear inversions of seismic traveltimes and magnetic data, respectively.
| S-EPMC6472566 | biostudies-literature
Project description:Unprecedented modern rates of warming are expected to advance boreal forest into Arctic tundra1, thereby reducing albedo2-4, altering carbon cycling4 and further changing climate1-4, yet the patterns and processes of this biome shift remain unclear5. Climate warming, required for previous boreal advances6-17, is not sufficient by itself for modern range expansion of conifers forming forest-tundra ecotones5,12-15,17-20. No high-latitude population of conifers, the dominant North American Arctic treeline taxon, has previously been documented5 advancing at rates following the last glacial maximum (LGM)6-8. Here we describe a population of white spruce (Picea glauca) advancing at post-LGM rates7 across an Arctic basin distant from established treelines and provide evidence of mechanisms sustaining the advance. The population doubles each decade, with exponential radial growth in the main stems of individual trees correlating positively with July air temperature. Lateral branches in adults and terminal leaders in large juveniles grow almost twice as fast as those at established treelines. We conclude that surpassing temperature thresholds1,6-17, together with winter winds facilitating long-distance dispersal, deeper snowpack and increased soil nutrient availability promoting recruitment and growth, provides sufficient conditions for boreal forest advance. These observations enable forecast modelling with important insights into the environmental conditions converting tundra into forest.
| S-EPMC9385489 | biostudies-literature
Project description:Although several new international brands in the information technology services industry have emerged in China, most previous research on the paths of internationalization taken by Chinese brands has focused on the manufacturing industry. Further exploration of the diversity and novel characteristics of these paths remains necessary. Taking into account the different industries and the interactions among multiple factors that are relevant in this context, supplementary research on the paths of internationalization taken by Chinese brands is also needed. Simultaneously, more research on the mechanisms underlying brand empowerment during the internationalization process is necessary. Based on a theoretical framework for brand empowerment, this article analyzes 61 representative Chinese brands using fuzzy set qualitative comparative analysis (fsQCA). This article reveals the following main findings: (1) brand penetration and brand acculturation are two key capabilities with regard to brand internationalization; (2) two modes of brand internationalization are evident in China, i.e., progressive internationalization and leapfrog internationalization; (3) four paths of internationalization can be observed with regard to Chinese brands, including two new paths, i.e., L-S-Cu and P-S-M; and (4) six additional paths are worthy of further exploration.
| S-EPMC10540969 | biostudies-literature
Project description:One in six people worldwide will experience a stroke in his/her lifetime. While people in Africa carry a disproportionately higher burden of poor stroke outcomes, compared to the rest of the world, the exact contribution of genomic factors to this disparity is unknown. Despite noteworthy research into stroke genomics, studies exploring the genetic contribution to stroke among populations of African ancestry in the United States are few. Furthermore, genomics data in populations living in Africa are lacking. The wide genomic variation of African populations offers a unique opportunity to identify genomic variants with causal relationships to stroke across different ethnic groups. The Stroke Investigative Research and Educational Network (SIREN), a component of the Human Health and Heredity in Africa (H3Africa) Consortium, aims to explore genomic and environmental risk factors for stroke in populations of African ancestry in West Africa and the United States. In this article, we review the literature on the genomics of stroke with particular emphasis on populations of African origin.
| S-EPMC4557488 | biostudies-literature
Project description:A reliable method of cell tracing is essential in evaluating potential therapeutic procedures based on stem cell transplantation. Here we present data collected using neural stem cells isolated from a transgenic mouse line Thy1-YFP. When transplanted into a stroke affected brain these cells give rise to neurons that express a fluorescent signal which can be used for their detection and tracing. Observed processes were compared with those taking place during normal embryonic neurogenesis as well as during in vitro differentiation. Since the same neurogenic patterns were observed, we confirm that neural stem cell transplantation fits well into the paradigm of neuronal birth and differentiation.
| S-EPMC5443188 | biostudies-literature
Project description:Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.
| S-EPMC5566114 | biostudies-literature