Higher Derivative Fermionic Field Equation in the First Order Formalism

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found which extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and non-minimal (anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first order equation has been obtained.Comment: 16 pages, title changed, new section, appendixes, and references adde

Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale

We provide a set of probabilistic laws for range-based estimation of integrated variance of a continuous semi-martingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for non-parametric measurement of return variation. Assuming the entire sample path realization of the log-price process is available - and given weak technical conditions - we prove that the high-low statistic converges in probability to the integrated variance. Moreover, with slightly stronger condi- tions, in particular a zero drift-term, we ¯nd an asymptotic distribution theory. To relax the mean-zero constraint, we modify the estimator using an adjusted range. A weak law of large numbers and central limit theorem is then derived under more general assump- tions about drift. In practice, inference about integrated variance is drawn from discretely sampled data. Here, we split the sampling period into sub-intervals containing the same number of price recordings and estimate the true range. In this setting, we also prove consistency and asymptotic normality. Finally, we analyze our framework in the presence of microstructure noise. JEL Classification: C10; C22; C80

Quantitative biology: where modern biology meets physical sciences

Quantitative methods and approaches have been playing an increasingly important role in cell biology in recent years. They involve making accurate measurements to test a predefined hypothesis in order to compare experimental data with predictions generated by theoretical models, an approach that has benefited physicists for decades. Building quantitative models in experimental biology not only has led to discoveries of counterintuitive phenomena but has also opened up novel research directions. To make the biological sciences more quantitative, we believe a two-pronged approach needs to be taken. First, graduate training needs to be revamped to ensure biology students are adequately trained in physical and mathematical sciences and vice versa. Second, students of both the biological and the physical sciences need to be provided adequate opportunities for hands-on engagement with the methods and approaches necessary to be able to work at the intersection of the biological and physical sciences. We present the annual Physiology Course organized at the Marine Biological Laboratory (Woods Hole, MA) as a case study for a hands-on training program that gives young scientists the opportunity not only to acquire the tools of quantitative biology but also to develop the necessary thought processes that will enable them to bridge the gap between these disciplines

Intrahippocampal pathways involved in learning/memory mechanisms are affected by intracerebral infusions of amyloid-beta25-35 peptide and hydrated fullerene C60 in rats

Primary memory impairments associated with increased level of amyloid-beta (Аβ) in the brain have been shown to be linked, partially, with early pathological changes in the entorhinal cortex (EC) which spread on the whole limbic system. While the hippocampus is known to play a key role in learning and memory mechanisms, it is as yet unclear how its structures are involved in the EC pathology. In this study, changes in memory and neuronal morphology in male Wistar rats intrahippocampally injected with Аβ25–35 were correlated on days 14 and 45 after the injection to reveal specific cognitive - structural associations. The main focus was on the dentate gyrus (DG) and hippocampal areas of CA1 and CA3 because of their involvement in afferent flows from EC to the hippocampus through tri-synaptic (EC DG CA3 CA1) and/or mono-synaptic (EC CA1) pathways. Evident memory impairments were observed at both time points after Аβ25–35 injection. However, on day 14, populations of morphological intact neurons were decreased in CA3 and, drastically, in CA1, and the DG supramedial bundle was significantly damaged. On day 45, this bundle largely and СА1 neurons partially recovered, whereas CA3 neurons remained damaged. We suggest that Аβ25–35 primarily affects the tri-synaptic pathway, destroying the granular cells in the DG supramedial area and neurons in CA3 and, through the Schaffer collaterals, in CA1. Intrahippocampal pretreatment with hydrated fullerene С60 allows the neurons and their connections to survive the amyloidosis, thus supporting the memory mechanisms

Validating Vegetable Production Unit (VPU) Plants, Protocols, Procedures and Requirements (P3R) using Currently Existing Flight Resources

Validating Vegetable Production Unit (VPU) Plants, Protocols, Procedures and Requirements (P3R) Using Currently Existing Flight Resources (Lada-VPU-P3R) is a study to advance the technology required for plant growth in microgravity and to research related food safety issues. Lada-VPU-P3R also investigates the non-nutritional value to the flight crew of developing plants on-orbit. The Lada-VPU-P3R uses the Lada hardware on the ISS and falls under a cooperative agreement between National Aeronautics and Space Administration (NASA) and the Russian Federal Space Association (FSA). Research Summary: Validating Vegetable Production Unit (VPU) Plants, Protocols, Procedures and Requirements (P3R) Using Currently Existing Flight Resources (Lada-VPU-P3R) will optimize hardware an

Quasiparticle scattering and local density of states in the d-density wave phase

We study the effects of single-impurity scattering on the local density of states in the high-$T_c$ cuprates. We compare the quasiparticle interference patterns in three different ordered states: d-wave superconductor (DSC), d-density wave (DDW), and coexisting DSC and DDW (DSC-DDW). In the coexisting state, at energies below the DSC gap, the patterns are almost identical to those in the pure DSC state with the same DSC gap. However, they are significantly different for energies greater than or equal to the DSC gap. This transition at an energy around the DSC gap can be used to test the nature of the superconducting state of the underdoped cuprates by scanning tunneling microscopy. Furthermore, we note that in the DDW state the effect of the coherence factors is stronger than in the DSC state. The new features arising due to DDW ordering are discussed.Comment: 6 page, 5 figures (Higher resolution figures are available by request