Putting time into proof outlines

A logic for reasoning about timing of concurrent programs is presented. The logic is based on proof outlines and can handle maximal parallelism as well as resource-constrained execution environments. The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action

Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation

The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology

Maps of complex motion selectivity in the superior temporal cortex of the alert macaque monkey: a double-label 2-deoxyglucose study

The superior temporal sulcus (STS) of the macaque monkey contains multiple visual areas. Many neurons within these regions respond selectively to motion direction and to more complex motion patterns, such as expansion, contraction and rotation. Single-unit recording and optical recording studies in MT/MST suggest that cells with similar tuning properties are clustered into columns extending through multiple cortical layers. In this study, we used a double-label 2-deoxyglucose technique in awake, behaving macaque monkeys to clarify this functional organization. This technique allowed us to label, in a single animal, two populations of neurons responding to two different visual stimuli. In one monkey we compared expansion with contraction; in a second monkey we compared expansion with clockwise rotation. Within the STS we found a patchy arrangement of cortical columns with alternating stimulus selectivity: columns of neurons preferring expansion versus contraction were more widely separated than those selective for expansion versus rotation. This mosaic of interdigitating columns on the floor and posterior bank of the STS included area MT and some neighboring regions of cortex, perhaps including area MST

Formation of antiwaves in gap-junction-coupled chains of neurons

Using network models consisting of gap junction coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and \pi. We call these phase shifts intermediate stable phaselocked states. These phase shifts can produce a large variety of wave-like activity patterns in one-dimensional chains and two-dimensional arrays of neurons, which can be studied by reducing the system of equations to a phase model. The 2\pi periodic coupling functions of these models are characterized by prominent higher order terms in their Fourier expansion, which can be varied by changing model parameters. We study how the relative contribution of the odd and even terms affect what solutions are possible, the basin of attraction of those solutions and their stability. These models may be applicable to the spinal central pattern generators of the dogfish and also to the developing neocortex of the neonatal rat

The regions of the sequence most exposed to the solvent within the amyloidogenic state of a protein initiate the aggregation process.

Formation of misfolded aggregates is an essential part of what proteins can do. The process of protein aggregation is central to many human diseases and any aggregating event needs to be prevented within a cell and in protein design. In order to aggregate, a protein needs to unfold its native state, at least partially. The conformational state that is prone to aggregate is difficult to study, due to its aggregating potential and heterogeneous nature. Here, we use a systematic approach of limited proteolysis, in combination with electrospray ionisation mass spectrometry, to investigate the regions that are most flexible and solvent-exposed within the native, ligand-bound and amyloidogenic states of muscle acylphosphatase (AcP), a protein previously shown to form amyloid fibrils in the presence of trifluoroethanol. Seven proteases with different degrees of specificity have been used for this purpose. Following exposure to the aggregating conditions, a number of sites along the sequence of AcP become susceptible to proteolytic digestion. The pattern of proteolytic cleavages obtained under these conditions is considerably different from that of the native and ligand-bound conformations and includes a portion within the N-terminal tail of the protein (residues 6-7), the region of the sequence 18-23 and the position 94 near the C terminus. There is a significant overlap between the regions of the sequence found to be solvent-exposed from the present study and those previously identified to be critical in the rate-determining steps of aggregation from protein engineering approaches. This indicates that a considerable degree of solvent exposure is a feature of the portions of a protein that initiate the process of aggregation

Phase Response Curves of Coupled Oscillators

Many real oscillators are coupled to other oscillators and the coupling can affect the response of the oscillators to stimuli. We investigate phase response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the system. Through simulation and analytic methods, the PRCs for globally coupled oscillators are also discussed.Comment: 5 pages 4 figur

Abundances in Stars from the Red Giant Branch Tip to the Near Main Sequence in M71: II. Iron Abundance

We present [Ffe/H] abundance results that involve a sample of stars with a wide range in luminosity from luminous giants to stars near the turnoff in a globular cluster. Our sample of 25 stars in M71 includes 10 giant stars more luminous than the RHB, 3 horizontal branch stars, 9 giant stars less luminous than the RHB, and 3 stars near the turnoff. We analyzed both Fe I and Fe II lines in high dispersion spectra observed with HIRES at the W. M. Keck Observatory. We find that the [Fe/H] abundances from both Fe I and Fe II lines agree with each other and with earlier determinations. Also the [Fe/H] obtained from Fe I and Fe II lines is constant within the rather small uncertainties for this group of stars over the full range in Teff and luminosity, suggesting that NLTE effects are negligible in our iron abundance determination. In this globular cluster, there is no difference among the mean [Fe/H] of giant stars located at or above the RHB, RHB stars, giant stars located below the RHB and stars near the turnoff.Comment: Minor changes to conform to version accepted for publication, with several new figures (Paper 2 of a pair

Abundances of Baade's Window Giants from Keck/HIRES Spectra: I. Stellar Parameters and [Fe/H] Values

We present the first results of a new abundance survey of the Milky Way bulge based on Keck/HIRES spectra of 27 K-giants in the Baade's Window ($l = 1$, $b = -4$) field. The spectral data used in this study are of much higher resolution and signal-to-noise than previous optical studies of Galactic bulge stars. The [Fe/H] values of our stars, which range between -1.29 and $+0.51$, were used to recalibrate large low resolution surveys of bulge stars. Our best value for the mean [Fe/H] of the bulge is $-0.10 \pm 0.04$. This mean value is similar to the mean metallicity of the local disk and indicates that there cannot be a strong metallicity gradient inside the solar circle. The metallicity distribution of stars confirms that the bulge does not suffer from the so-called ``G-dwarf'' problem. This paper also details the new abundance techniques necessary to analyze very metal-rich K-giants, including a new Fe line list and regions of low blanketing for continuum identification.Comment: Accepted for publication in January 2006 Astrophysical Journal. Long tables 3--6 withheld to save space (electronic tables in journal paper). 53 pages, 10 figures, 9 table