Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a novel method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.Comment: 4 pages, 3 figure

A one-sided Prime Ideal Principle for noncommutative rings

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.Comment: 38 page

Are short-term variations in solar oscillation frequencies the signature of a second solar dynamo?

In addition to the well-known 11-year solar cycle, the Sun's magnetic activity also shows significant variation on shorter time scales, e.g. between one and two years. We observe a quasi-biennial (2-year) signal in the solar p-mode oscillation frequencies, which are sensitive probes of the solar interior. The signal is visible in Sun-as-a-star data observed by different instruments and here we describe the results obtained using BiSON, GOLF, and VIRGO data. Our results imply that the 2-year signal is susceptible to the influence of the main 11-year solar cycle. However, the source of the signal appears to be separate from that of the 11-year cycle. We speculate as to whether it might be the signature of a second dynamo, located in the region of near-surface rotational shear.Comment: 6 pages, 2 figures, proceedings for SOHO-24/GONG 2010 conference, to be published in JPC

Onset of Phase Synchronization in Neurons Conneted via Chemical Synapses

We study the onset of synchronous states in realistic chaotic neurons coupled by mutually inhibitory chemical synapses. For the realistic parameters, namely the synaptic strength and the intrinsic current, this synapse introduces non-coherences in the neuronal dynamics, yet allowing for chaotic phase synchronization in a large range of parameters. As we increase the synaptic strength, the neurons undergo to a periodic state, and no chaotic complete synchronization is found.Comment: to appear in Int. J. Bif. Chao

Spin dynamics and antiferromagnetic order in PrBa2Cu4O8 studied by Cu nuclear respnance

Results of the nuclear resonance experiments for the planar Cu sites in PrBa2Cu4O8 are presented. The NMR spectrum at 1.5 K in zero magnetic field revealed an internal field of 6.1 T, providing evidence for an antiferromagnetic order of the planar Cu spins. This confirms that the CuO2 planes are insulating, therefore, the metallic conduction in this material is entirely due to the one-dimensional zigzag Cu2O2 chains. The results of the spin-lattice relaxation rates measured by zero field NQR above 245 K in the paramagnetic state are explained by the theory for a Heisenberg model on a square lattice.Comment: 4 pages, 2 figure

One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.Comment: 10 pages, 1 figur

MAARS: a novel high-content acquisition software for the analysis of mitotic defects in fission yeast

Faithful segregation of chromosomes during cell division relies on multiple processes such as chromosome attachment and correct spindle positioning. Yet mitotic progression is defined by multiple parameters, which need to be quantitatively evaluated. To study the spatiotemporal control of mitotic progression, we developed a high-content analysis (HCA) approach that combines automated fluorescence microscopy with real-time quantitative image analysis and allows the unbiased acquisition of multiparametric data at the single-cell level for hundreds of cells simultaneously. The Mitotic Analysis and Recording System (MAARS) provides automatic and quantitative single-cell analysis of mitotic progression on an open-source platform. It can be used to analyze specific characteristics such as cell shape, cell size, metaphase/anaphase delays, and mitotic abnormalities including spindle mispositioning, spindle elongation defects, and chromosome segregation defects. Using this HCA approach, we were able to visualize rare and unexpected events of error correction during anaphase in wild-type or mutant cells. Our study illustrates that such an expert system of mitotic progression is able to highlight the complexity of the mechanisms required to prevent chromosome loss during cell division