Spatiotemporal symmetries in the disynaptic canal-neck projection

The vestibular system in almost all vertebrates, and in particular in humans, controls balance by employing a set of six semicircular canals, three in each inner ear, to detect angular accelerations of the head in three mutually orthogonal coordinate planes. Signals from the canals are transmitted to eight (groups of) neck motoneurons, which activate the eight corresponding muscle groups. These signals may be either excitatory or inhibitory, depending on the direction of head acceleration. McCollum and Boyle have observed that in the cat the relevant network of neurons possesses octahedral symmetry, a structure that they deduce from the known innervation patterns (connections) from canals to muscles. We rederive the octahedral symmetry from mathematical features of the probable network architecture, and model the movement of the head in response to the activation patterns of the muscles concerned. We assume that connections between neck muscles can be modeled by a “coupled cell network,” a system of coupled ODEs whose variables correspond to the eight muscles, and that this network also has octahedral symmetry. The network and its symmetries imply that these ODEs must be equivariant under a suitable action of the octahedral group. It is observed that muscle motoneurons form natural “push-pull pairs” in which, for given movements of the head, one neuron produces an excitatory signal, whereas the other produces an inhibitory signal. By incorporating this feature into the mathematics in a natural way, we are led to a model in which the octahedral group acts by signed permutations on muscle motoneurons. We show that with the appropriate group actions, there are six possible spatiotemporal patterns of time-periodic states that can arise by Hopf bifurcation from an equilibrium representing an immobile head. Here we use results of Ashwin and Podvigina. Counting conjugate states, whose physiological interpretations can have significantly different features, there are 15 patterns of periodic oscillation, not counting left-right reflections or time-reversals as being different. We interpret these patterns as motions of the head, and note that all six types of pattern appear to correspond to natural head motions

Percolation on the average and spontaneous magnetization for q-states Potts model on graph

We prove that the q-states Potts model on graph is spontaneously magnetized at finite temperature if and only if the graph presents percolation on the average. Percolation on the average is a combinatorial problem defined by averaging over all the sites of the graph the probability of belonging to a cluster of a given size. In the paper we obtain an inequality between this average probability and the average magnetization, which is a typical extensive function describing the thermodynamic behaviour of the model

Recent X-ray measurements of the accretion-powered pulsar 4U 1907+09

X-ray observations of the accreting X-ray pulsar 4U~1907+09, obtained during February 1996 with the Proportional Counter Array on the Rossi X-ray Timing Experiment (RXTE), have enabled the first measurement of the intrinsic pulse period Ppulse since 1984: Ppulse=440.341[+0.012,-0.017] s. 4U 1907+09 is in a binary system with a blue supergiant. The orbital parameters were solved and this enabled the correction for orbital delay effects of a measurement of Ppulse obtained in 1990 with Ginga. Thus, three spin down rates could be extracted from four pulse periods obtained in 1983, 1984, 1990, and 1996. These are within 8% equal to a value of dPpulse/dt=+0.225 s/yr. This suggest that the pulsar is perhaps in a monotonous spin down mode since its discovery in 1983. Furthermore, the RXTE observations show transient ~18 s oscillations during a flare that lasted about 1 hour. The oscillations may be interpreted as Keplerian motion of an accretion disk near the magnetospheric radius. This, and the notion that the co-rotation radius is much larger than any conceivable value for the magnetospheric radius (because of the long spin period), renders it unlikely that this pulsar spins near equilibrium like is suspected for other slowing accreting X-ray pulsars. We suggest as an alternative that perhaps the frequent occurrence of a retrograde transient accretion disk may be consistently slowing the pulsar down. Further observations of flares can provide more evidence of this.Comment: 26 pages, 11 figures, to be published in Astrophysical Journal part I on March 20, 199

Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result

We give a rigorous proof of the existence of spontaneous magnetization at finite temperature for the Ising spin model defined on the Sierpinski carpet fractal. The theorem is inspired by the classical Peierls argument for the two dimensional lattice. Therefore, this exact result proves the existence of spontaneous magnetization for the Ising model in low dimensional structures, i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure

Measurement of forward photon production cross-section in proton-proton collisions at s\sqrt{s} = 13 TeV with the LHCf detector

In this paper, we report the production cross-section of forward photons in the pseudorapidity regions of $\eta\,>\,10.94$ and $8.99\,>\,\eta\,>\,8.81$, measured by the LHCf experiment with proton--proton collisions at $\sqrt{s}$ = 13 TeV. The results from the analysis of 0.191 $\mathrm{nb^{-1}}$ of data obtained in June 2015 are compared to the predictions of several hadronic interaction models that are used in air-shower simulations for ultra-high-energy cosmic rays. Although none of the models agree perfectly with the data, EPOS-LHC shows the best agreement with the experimental data among the models.Comment: 21 pages, 4 figure

Wet and dry deposition of mineral dust particles in Japan: factors related to temporal variation and spatial distribution

Recent ground networks and satellite remote-sensing observations have provided useful data related to spatial and vertical distributions of mineral dust particles in the atmosphere. However, measurements of temporal variations and spatial distributions of mineral dust deposition fluxes are limited in terms of their duration, location, and processes of deposition. To ascertain temporal variations and spatial distributions of mineral dust deposition using wet and dry processes, weekly deposition samples were obtained at Sapporo, Toyama, Nagoya, Tottori, Fukuoka, and Cape Hedo (Okinawa) in Japan during October 2008–December 2010 using automatic wet and dry separating samplers. Mineral dust weights in water-insoluble residue were estimated from Fe contents measured using an X-ray fluorescence analyser. Wet and dry deposition fluxes of mineral dusts were both high in spring and low in summer, showing similar seasonal variations to frequency of aeolian dust events (Kosa) in Japan. For wet deposition, highest and lowest annual dust fluxes were found at Toyama (9.6 g m⁻² yr⁻¹) and at Cape Hedo (1.7 g m⁻² yr⁻¹) as average values in 2009 and 2010. Higher wet deposition fluxes were observed at Toyama and Tottori, where frequent precipitation (> 60% days per month) was observed during dusty seasons. For dry deposition among Toyama, Tottori, Fukuoka, and Cape Hedo, the highest and lowest annual dust fluxes were found respectively at Fukuoka (5.2 g m⁻² yr⁻¹) and at Cape Hedo (2.0 g m⁻² yr⁻¹) as average values in 2009 and 2010. The average ratio of wet and dry deposition fluxes was the highest at Toyama (3.3) and the lowest at Hedo (0.82), showing a larger contribution of the dry process at western sites, probably because of the distance from desert source regions and because of the effectiveness of the wet process in the dusty season. <br><br> Size distributions of refractory dust particles were obtained using four-stage filtration: > 20, > 10, > 5, and > 1 μm diameter. Weight fractions of the sum of > 20 μm and 10–20 μm (giant fraction) were higher than 50% for most of the event samples. Irrespective of the deposition type, the giant dust fractions generally decreased with increasing distance from the source area, suggesting the selective depletion of larger giant particles during atmospheric transport. Based on temporal variations of PM_c (2.5 < <i>D</i> < 10 μm), ground-based lidar, backward air trajectories, and vertical profiles of potential temperatures, transport processes of dust particles are discussed for events with high-deposition and low-deposition flux with high PM_c. Low dry dust depositions with high PM_c concentrations were observed under stronger (5 K km⁻¹) stratification of potential temperature with thinner and lower (< 2 km) dust distributions because the PM_c fraction of dust particles only survived after depletion of giant dust particles by rapid gravitational settling at the time they reach Japan. In contrast, transport through a thicker (> 2 km) dust layer with weak vertical gradient of potential temperature carry more giant dust particles to Japan. Because giant dust particles are an important mass fraction of dust accumulation, especially in the North Pacific, which is known as a high-nutrient, low-chlorophyll (HNLC) region, the transport height and fraction of giant dust particles are important factors for studying dust budgets in the atmosphere and their role in biogeochemical cycles

The Optimal Exponent Base for emPAI Is 6.5

Exponentially Modified Protein Abundance Index (emPAI) is an established method of estimating protein abundances from peptide counts in a single LC-MS/MS experiment. EmPAI is defined as 10PAI minus one, where PAI (Protein Abundance Index) denotes the ratio of observed to observable peptides. EmPAI was first proposed by Ishihama et al [1] who found that PAI is approximately proportional to the logarithm of absolute protein concentration. I define emPAI65 = 6.5PAI-1 and show that it performs significantly better than emPAI, while it is equally easy to compute. The higher accuracy of emPAI65 is demonstrated by analyzing three data sets, including the one used in the original study [1]. I conclude that emPAI65 ought to be used instead of the original emPAI for protein quantitation

Measurement of the cosmic-ray antiproton spectrum at solar minimum with a long-duration balloon flight over Antarctica

The energy spectrum of cosmic-ray antiprotons from 0.17 to 3.5 GeV has been measured using 7886 antiprotons detected by BESS-Polar II during a long-duration flight over Antarctica near solar minimum in December 2007 and January 2008. This shows good consistency with secondary antiproton calculations. Cosmologically primary antiprotons have been investigated by comparing measured and calculated antiproton spectra. BESS-Polar II data show no evidence of primary antiprotons from evaporation of primordial black holes.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Constraints on Torque-Reversing Accretion-Powered X-ray Pulsars

The observed abrupt torque reversals in X-ray pulsars, 4U 1626-67, GX 1+4, and OAO 1657-415, can be explained by transition in accretion flow rotation from Keplerian to sub-Keplerian, which takes place at a critical accretion rate, $\sim 10^{16}-10^{17}g/s$. When a pulsar system spins up near equilibrium spin before the transition, the system goes into spin-down after transition to sub-Keplerian. If a system is well into the spin-up regime, the transition can cause a sharp decrease in spin-up rate but not a sudden spin-down. These observable types of abrupt torque change are distinguished from the smooth torque variation caused by change of ${\dot M}$ in the Keplerian flow. The observed abrupt torque reversal is expected when the pulsar magnetic field $B_*\sim 5\times 10^{11}b_p^{-1/2}L_{x,36}^{1/2}P_{*,10}^{1/2}G$ where the magnetic pitch parameter $b_p\sim$ a few, $L_{x,36}$ is the X-ray luminosity in $10^{36} erg/s$, and $P_{*,10}$ is the pulsar spin period in 10s. Observed quasi-periodic oscillation (QPO) periods tightly constrain the model. For 4U 1626-67, ${\dot M}\approx 2.7\times 10^{16}g/s$ with $b_p^{1/2} B_*\approx 2\times 10^{12}G$. We estimate ${\dot M}\sim 6\times 10^{16} g/s$ and $b_p^{1/2}B_*\sim 5\times 10^{13}G$ for GX 1+4, and ${\dot M} \sim 1\times 10^{17} g/s$ and $b_p^{1/2}B_*\sim 2\times 10^{13}G$ for OAO 1657-415. Reliable detection of QPOs before and after torque reversal could directly test the model.Comment: 11 pages, 2 figures, Ap