Bounds on the number of real solutions to polynomial equations

We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the number of non-zero real solutions to a system of n polynomials in n variables having n+k+1 monomials whose exponent vectors generate a subgroup of Z^n of odd index. This bound exceeds the bound for positive solutions only by the constant factor (e^4+3)/(e^2+3) and it is asymptotically sharp for k fixed and n large.Comment: 5 page

Intermolecular correlations are necessary to explain diffuse scattering from protein crystals

Conformational changes drive protein function, including catalysis, allostery, and signaling. X-ray diffuse scattering from protein crystals has frequently been cited as a probe of these correlated motions, with significant potential to advance our understanding of biological dynamics. However, recent work challenged this prevailing view, suggesting instead that diffuse scattering primarily originates from rigid body motions and could therefore be applied to improve structure determination. To investigate the nature of the disorder giving rise to diffuse scattering, and thus the potential applications of this signal, a diverse repertoire of disorder models was assessed for its ability to reproduce the diffuse signal reconstructed from three protein crystals. This comparison revealed that multiple models of intramolecular conformational dynamics, including ensemble models inferred from the Bragg data, could not explain the signal. Models of rigid body or short-range liquid-like motions, in which dynamics are confined to the biological unit, showed modest agreement with the diffuse maps, but were unable to reproduce experimental features indicative of long-range correlations. Extending a model of liquid-like motions to include disorder across neighboring proteins in the crystal significantly improved agreement with all three systems and highlighted the contribution of intermolecular correlations to the observed signal. These findings anticipate a need to account for intermolecular disorder in order to advance the interpretation of diffuse scattering to either extract biological motions or aid structural inference.Comment: 12 pages, 5 figures (not including Supplementary Information

The Holographic Models of the scalar sector of QCD

We investigate the AdS/QCD duality for the two-point correlation functions of the lowest dimension scalar meson and scalar glueball operators, in the case of the Soft Wall holographic model of QCD. Masses and decay constants as well as gluon condensates are compared to their QCD estimates. In particular, the role of the boundary conditions for the bulk-to-boundary propagators is emphasized.Comment: Invited talk at the 5th International Conference on Quarks and Nuclear Physics QNP'09, Beijing, China, 21-26 September 2009. To be published in Chinese Physics

Ground state of a tightly bound composite dimer immersed in a Fermi Sea

In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.Comment: 11 pages; 3 figure

Differential leukocyte count method for bovine low somatic cell count milk

Whereas many differential leukocyte count methods for high somatic cell count (SCC) milk from mastitic cows are available, only a few have been developed for low SCC milk. We have developed a flow cytometric differential leukocyte count method for low SCC milk. The procedure consists of 1) 1.5 ml of diluted milk sample (30%, vol/vol dilution with PBS), 2) centrifugation, 3) leukocyte labeling with SYTO 13 and 4) flow cytometric analysis. Four major leukocyte populations can be clearly identified in the green fluorescence-side scatter dot plot: lymphocytes and monocytes (LM), polymorphonuclear neutrophils (PMN), mature macrophages (MO), and cells with apoptotic features based on chromatin condensation and nuclear fragmentation. The optimal processing temperature was 20degreesC. Significant differences among samples with similar differential leukocyte counts were found. Storage of milk samples during 2 d at 7degreesC had no effect on differential leukocyte count. Using the new method, differential leukocyte count was performed in low SCC milk samples from cows in early, mid, and late lactation. In accordance with previous studies, PMN and M P percentages were lower and LM percentages were higher in early lactation than in the other stages of lactation. The percentage of cells with apoptotic features was higher in early lactation than in mid and late lactation. In conclusion, a rapid, simple, accurate, and reproducible standard procedure was developed to determine the differential leukocyte count (MO, PMN, LM, and cells with apoptotic features) of bovine low SCC milk