Two Superconducting Phases in CeRh_1-xIr_xIn_5

Pressure studies of CeRh_1-xIr_xIn_5 indicate two superconducting phases as a function of x, one with T_c >= 2 K for x < 0.9 and the other with T_c < 1.2 K for x > 0.9. The higher T_c phase, phase-1, emerges in proximity to an antiferromagnetic quantum-critical point; whereas, Cooper pairing in the lower T_c phase-2 is inferred to arise from fluctuations of a yet to be found magnetic state. The T-x-P phase diagram of CeRh_1-xIr_xIn_5, though qualitatively similar, is distinctly different from that of CeCu_2(Si_1-xGe_x)_2.Comment: 5 pages, 3 figure

Superconductivity and Quantum Criticality in CeCoIn_5

Electrical resistivity measurements on a single crystal of the heavy-fermion superconductor CeCoIn_5 at pressures to 4.2 GPa reveal a strong crossover in transport properties near P^* \approx 1.6 GPa, where T_c is a maximum. The temperature-pressure phase diagram constructed from these data provides a natural connection to cuprate physics, including the possible existence of a pseudogap.Comment: 4 pages, 4 figure

Macrophage migration inhibitory factor downregulation: a novel mechanism of resistance to anti-angiogenic therapy.

Anti-angiogenic therapies for cancer such as VEGF neutralizing antibody bevacizumab have limited durability. While mechanisms of resistance remain undefined, it is likely that acquired resistance to anti-angiogenic therapy will involve alterations of the tumor microenvironment. We confirmed increased tumor-associated macrophages in bevacizumab-resistant glioblastoma patient specimens and two novel glioblastoma xenograft models of bevacizumab resistance. Microarray analysis suggested downregulated macrophage migration inhibitory factor (MIF) to be the most pertinent mediator of increased macrophages. Bevacizumab-resistant patient glioblastomas and both novel xenograft models of resistance had less MIF than bevacizumab-naive tumors, and harbored more M2/protumoral macrophages that specifically localized to the tumor edge. Xenografts expressing MIF-shRNA grew more rapidly with greater angiogenesis and had macrophages localizing to the tumor edge which were more prevalent and proliferative, and displayed M2 polarization, whereas bevacizumab-resistant xenografts transduced to upregulate MIF exhibited the opposite changes. Bone marrow-derived macrophage were polarized to an M2 phenotype in the presence of condition-media derived from bevacizumab-resistant xenograft-derived cells, while recombinant MIF drove M1 polarization. Media from macrophages exposed to bevacizumab-resistant tumor cell conditioned media increased glioma cell proliferation compared with media from macrophages exposed to bevacizumab-responsive tumor cell media, suggesting that macrophage polarization in bevacizumab-resistant xenografts is the source of their aggressive biology and results from a secreted factor. Two mechanisms of bevacizumab-induced MIF reduction were identified: (1) bevacizumab bound MIF and blocked MIF-induced M1 polarization of macrophages; and (2) VEGF increased glioma MIF production in a VEGFR2-dependent manner, suggesting that bevacizumab-induced VEGF depletion would downregulate MIF. Site-directed biopsies revealed enriched MIF and VEGF at the enhancing edge in bevacizumab-naive patients. This MIF enrichment was lost in bevacizumab-resistant glioblastomas, driving a tumor edge M1-to-M2 transition. Thus, bevacizumab resistance is driven by reduced MIF at the tumor edge causing proliferative expansion of M2 macrophages, which in turn promotes tumor growth

Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Cantor type functions in non-integer bases

Cantor's ternary function is generalized to arbitrary base-change functions in non-integer bases. Some of them share the curious properties of Cantor's function, while others behave quite differently

Reachability problems for PAMs

Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two intervals. As the main contribution of this paper we introduce new techniques for solving reachability problems based on p-adic norms and weights as well as showing decidability for two classes of maps. Then we show the connections between topological properties for PAM's orbits, reachability problems and representation of numbers in a rational base system. Finally we show a particular instance where the uniform distribution of the original orbit may not remain uniform or even dense after making regular shifts and taking a fractional part in that sequence.Comment: 16 page

Response of the Heavy-Fermion Superconductor CeCoIn5_5 to Pressure: Roles of Dimensionality and Proximity to a Quantum-Critical Point

We report measurements of the pressure-dependent superconducting transition temperature $T_c$ and electrical resistivity of the heavy-fermion compound CeCoIn$_5$. Pressure moves CeCoIn$_5$ away from its proximity to a quantum-critical point at atmospheric pressure. Experimental results are qualitatively consistent with theoretical predictions for strong-coupled, d-wave superconductivity in an anisotropic 3D superconductor.Comment: 9 pages, 5 figure