A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).Comment: 20 pages, 13 figure

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Distinct and Overlapping Effector Functions of Expanded Human CD4+, CD8α+ and CD4-CD8α- Invariant Natural Killer T Cells

CD1d-restricted invariant natural killer T (iNKT) cells have diverse immune stimulatory/regulatory activities through their ability to release cytokines and to kill or transactivate other cells. Activation of iNKT cells can protect against multiple diseases in mice but clinical trials in humans have had limited impact. Clinical studies to date have targeted polyclonal mixtures of iNKT cells and we proposed that their subset compositions will influence therapeutic outcomes. We sorted and expanded iNKT cells from healthy donors and compared the phenotypes, cytotoxic activities and cytokine profiles of the CD4+, CD8α+ and CD4−CD8α− double-negative (DN) subsets. CD4+ iNKT cells expanded more readily than CD8α+ and DN iNKT cells upon mitogen stimulation. CD8α+ and DN iNKT cells most frequently expressed CD56, CD161 and NKG2D and most potently killed CD1d+ cell lines and primary leukemia cells. All iNKT subsets released Th1 (IFN-γ and TNF-α) and Th2 (IL-4, IL-5 and IL-13) cytokines. Relative amounts followed a CD8α>DN>CD4 pattern for Th1 and CD4>DN>CD8α for Th2. All iNKT subsets could simultaneously produce IFN-γ and IL-4, but single-positivity for IFN-γ or IL-4 was strikingly rare in CD4+ and CD8α+ fractions, respectively. Only CD4+ iNKT cells produced IL-9 and IL-10; DN cells released IL-17; and none produced IL-22. All iNKT subsets upregulated CD40L upon glycolipid stimulation and induced IL-10 and IL-12 secretion by dendritic cells. Thus, subset composition of iNKT cells is a major determinant of function. Use of enriched CD8α+, DN or CD4+ iNKT cells may optimally harness the immunoregulatory properties of iNKT cells for treatment of disease

MAGE-A protein and MAGE-A10 gene expressions in liver metastasis in patients with stomach cancer

Tumour samples from 71 patients with stomach cancer, 41 patients with liver metastasis (group A) and 15 patients each in stages II–IV (group B) and stage I (group C) without liver metastasis were analysed. MAGE-A protein expression was evaluated by immunohistochemistry using a 6C1 monoclonal antibody and MAGE-A10 mRNA expression was detected by highly sensitive in situ hybridisation using a cRNA probe. Expressions of MAGE-A protein and MAGE-A10 mRNA in group A were detected in 65.9 and 80.5%, respectively. Both protein and gene showed significantly higher expression in group A than those in groups B (6.7, 26.7%) and C (0, 0%) (P=0.0003, P=<0.0001, respectively). MAGE-A10 mRNA expression in liver metastasis was found in eight (88.9%) out of nine patients. The concordant rate between MAGE-A family protein expression and MAGE-A10 mRNA expression in the primary sites was 81.7% (P<0.0001). MAGE-A10 gene expression was associated with reduced survival duration. The results of this study suggest that MAGE-A10 is a possible target in active immunotherapy for advanced stomach cancer

Pressure is not a state function for generic active fluids

Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties (density, temperature, etc.) through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state, their mechanical pressures exhibit anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle-wall and/or particle-particle interactions.Comment: 8 pages + 9 SI pages, Nature Physics (2015

Topological sound in active-liquid metamaterials

Liquids composed of self-propelled particles have been experimentally realized using molecular, colloidal, or macroscopic constituents. These active liquids can flow spontaneously even in the absence of an external drive. Unlike spontaneous active flow, the propagation of density waves in confined active liquids is not well explored. Here, we exploit a mapping between density waves on top of a chiral flow and electrons in a synthetic gauge field to lay out design principles for artificial structures termed topological active metamaterials. We design metamaterials that break time-reversal symmetry using lattices composed of annular channels filled with a spontaneously flowing active liquid. Such active metamaterials support topologically protected sound modes that propagate unidirectionally, without backscattering, along either sample edges or domain walls and despite overdamped particle dynamics. Our work illustrates how parity-symmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials

Adequate mathematical tools for superconductivity

This paper has for essential objective to point out the existence of, at least, two original mathematical techniques, particularly well adapted to the problems arised from the superconductors ; taking the interest and the complexity of the latter into account, it is really urgent to investigate a concrete cooperation between the concerned communities (Mathematicians, Physicists, Engineers) in order to improve their respective competences

Basic result on type II DM self-motions of planar Stewart Gough platforms

Abstract. In a recent publication [10] the author showed that self-motions of general planar Stewart Gough platforms can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, in [10] the author was able to compute the set of equations yielding a type II DM selfmotion explicitly. Based on these equations we present a basic result for this class of self-motions