The Betti numbers of forests

This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs

The Betti numbers of forests

This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs

Ripples in Tapped or Blown Powder

We observe ripples forming on the surface of a granular powder in a container submitted from below to a series of brief and distinct shocks. After a few taps, the pattern turns out to be stable against any further shock of the same amplitude. We find experimentally that the characteristic wavelength of the pattern is proportional to the amplitude of the shocks. Starting from consideration involving Darcy's law for air flow through the porous granulate and avalanche properties, we build up a semi-quantitative model which fits satisfactorily the set of experimental observations as well as a couple of additional experiments.Comment: 7 pages, four postscript figures, submitted PRL 11/19/9

Reflective Scattering and Unitarity

Interpretation of unitarity saturation as reflective scattering is discussed. Analogies with optics and Berry phase alongside with the experimental consequences of the proposed interpretation at the LHC energies are considered.Comment: 4 pages, 1 figure, talk given by S. Troshin at Diffraction 2008, September 9-14, La Londe-les-Maures, Franc

Effects of cluster diffusion on the island density and size distribution in submonolayer island growth

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model, we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island-size with exponent mu. Results are presented for mu = 1/2, 1, and 3/2 corresponding to cluster diffusion via Brownian motion, correlated evaporation-condensation, and edge-diffusion respectively, as well as for higher values including mu = 2,3, and 6. We also compare our results with those obtained in the limit of no cluster mobility corresponding to mu = infinity. In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for mu < 1, for mu = 1/2 we find Ns({\theta}) ~ s^{-\tau} (where Ns({\theta}) is the number of islands of size s at coverage {\theta}) up to a cross-over island-size S_c. However, the value of {\tau} obtained in our simulations is higher than the mean-field (MF) prediction {\tau} = (3 - mu)/2. Similarly, the value of the exponent {\zeta} corresponding to the dependence of S_c on the average island-size S (e.g. S_c ~ S^{\zeta}) is also significantly higher than the MF prediction {\zeta} = 2/(mu+1). A generalized scaling form for the ISD is also proposed for mu < 1, and using this form excellent scaling is found for mu = 1/2. However, for finite mu >= 1 neither the generalized scaling form nor the standard scaling form Ns({\theta}) = {\theta} /S^2 f(s/S) lead to scaling of the entire ISD for finite values of the ratio R of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing R and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.Comment: 12 pages, submitted to Physical Review

Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies

We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian oscillator and inspired our work. Linear stability analysis of the Fokker-Planck equation for an infinite population is amenable to exact solution and we show that the incoherent state is unstable passed a critical coupling strength K_c(\ga, \sigf), where \ga is the inverse characteristic drifting time and \sigf the asymptotic frequency dispersion. Expectedly $K_c$ agrees with the noisy Kuramoto model in the large \ga (Schmolukowski) limit but increases slower as \ga decreases. Asymptotic expansion of the solution for \ga\to 0 shows that the noiseless Kuramoto model with Gaussian frequency distribution is recovered in that limit. Thus varying a single parameter allows to interpolate smoothly between two regimes: one dominated by the frequency dispersion and the other by phase diffusion.Comment: 5 pages, 5 figures, accepted in Phys. Rev.

Maxwell-Chern-Simons Q-balls

We examine the energetics of $Q$-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged $Q$-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the $Q$-ball. Similar to the case of gauged $Q$-balls, Maxwell-Chern-Simons $Q$-balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical technique known as relaxation. The results are compared to expectations based on qualitative arguments.Comment: 6 pages. Talk given at Theory CANADA 2, Perimeter Institut

Magnetic imaging with an ensemble of Nitrogen Vacancy centers in diamond

The nitrogen-vacancy (NV) color center in diamond is an atom-like system in the solid-state which specific spin properties can be efficiently used as a sensitive magnetic sensor. An external magnetic field induces Zeeman shifts of the NV center levels which can be measured using Optically Detected Magnetic Resonance (ODMR). In this work, we exploit the ODMR signal of an ensemble of NV centers in order to quantitatively map the vectorial structure of a magnetic field produced by a sample close to the surface of a CVD diamond hosting a thin layer of NV centers. The reconstruction of the magnetic field is based on a maximum-likelihood technique which exploits the response of the four intrinsic orientations of the NV center inside the diamond lattice. The sensitivity associated to a 1 {\mu}m^2 area of the doped layer, equivalent to a sensor consisting of approximately 10^4 NV centers, is of the order of 2 {\mu}T/sqrt{Hz}. The spatial resolution of the imaging device is 400 nm, limited by the numerical aperture of the optical microscope which is used to collect the photoluminescence of the NV layer. The versatility of the sensor is illustrated by the accurate reconstruction of the magnetic field created by a DC current inside a copper wire deposited on the diamond sample.Comment: 11 pages, 5 figures, figure 4 added, results unchange

DNA-encoded nucleosome occupancy is associated with transcription levels in the human malaria parasite Plasmodium falciparum.

BackgroundIn eukaryotic organisms, packaging of DNA into nucleosomes controls gene expression by regulating access of the promoter to transcription factors. The human malaria parasite Plasmodium falciparum encodes relatively few transcription factors, while extensive nucleosome remodeling occurs during its replicative cycle in red blood cells. These observations point towards an important role of the nucleosome landscape in regulating gene expression. However, the relation between nucleosome positioning and transcriptional activity has thus far not been explored in detail in the parasite.ResultsHere, we analyzed nucleosome positioning in the asexual and sexual stages of the parasite's erythrocytic cycle using chromatin immunoprecipitation of MNase-digested chromatin, followed by next-generation sequencing. We observed a relatively open chromatin structure at the trophozoite and gametocyte stages, consistent with high levels of transcriptional activity in these stages. Nucleosome occupancy of genes and promoter regions were subsequently compared to steady-state mRNA expression levels. Transcript abundance showed a strong inverse correlation with nucleosome occupancy levels in promoter regions. In addition, AT-repeat sequences were strongly unfavorable for nucleosome binding in P. falciparum, and were overrepresented in promoters of highly expressed genes.ConclusionsThe connection between chromatin structure and gene expression in P. falciparum shares similarities with other eukaryotes. However, the remarkable nucleosome dynamics during the erythrocytic stages and the absence of a large variety of transcription factors may indicate that nucleosome binding and remodeling are critical regulators of transcript levels. Moreover, the strong dependency between chromatin structure and DNA sequence suggests that the P. falciparum genome may have been shaped by nucleosome binding preferences. Nucleosome remodeling mechanisms in this deadly parasite could thus provide potent novel anti-malarial targets