Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity

We introduce and study the problem Ordered Level Planarity which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y-monotone curve. This can be interpreted as a variant of Level Planarity in which the vertices on each level appear in a prescribed total order. We establish a complexity dichotomy with respect to both the maximum degree and the level-width, that is, the maximum number of vertices that share a level. Our study of Ordered Level Planarity is motivated by connections to several other graph drawing problems. Geodesic Planarity asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a polygonal path composed of line segments with two adjacent directions from a given set $S$ of directions symmetric with respect to the origin. Our results on Ordered Level Planarity imply $NP$-hardness for any $S$ with $|S|\ge 4$ even if the given graph is a matching. Katz, Krug, Rutter and Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where $S$ contains precisely the horizontal and vertical directions, can be solved in polynomial time [GD'09]. Our results imply that this is incorrect unless $P=NP$. Our reduction extends to settle the complexity of the Bi-Monotonicity problem, which was proposed by Fulek, Pelsmajer, Schaefer and \v{S}tefankovi\v{c}. Ordered Level Planarity turns out to be a special case of T-Level Planarity, Clustered Level Planarity and Constrained Level Planarity. Thus, our results strengthen previous hardness results. In particular, our reduction to Clustered Level Planarity generates instances with only two non-trivial clusters. This answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Rapid in vivo Taxotere quantitative chemosensitivity response by 4.23 Tesla sodium MRI and histo-immunostaining features in N-Methyl-N-Nitrosourea induced breast tumors in rats

BACKGROUND: Sodium weighted images can indicate sodium signal intensities from different features in the tumor before and 24 hours following administration of Taxotere. AIM: To evaluate the association of in vivo intracellular sodium magnetic resonance image intensities with immuno-biomarkers and histopathological features to monitor the early tumor response to Taxotere chemotherapy in Methyl-Nitroso-Urea induced rat xenograft breast tumors. METHODS AND MATERIALS: Methyl-Nitroso-Urea (MNU) induced rat xenograft breast tumors were imaged for sodium MRI and compared with tumor histology, immunostaining after 24 hours chemotherapy. RESULTS: Sodium MRI signal intensities represented sodium concentrations. Excised tumor histological sections showed different in vitro histological end points i.e. single strand DNA content of cell nuclei during cell cycle (G1/S-G2/M), distinct S or M histograms (Feulgen labeling to nuclear DNA content by CAS 200), mitotic figures and apoptosis at different locations of breast tumors. Necrosis and cystic fluid appeared gray on intracellular (IC) sodium images while apoptosis rich regions appeared brighter on IC sodium images. After 24 hours Taxotere-treated tumors showed lower 'IC/EC ratio' of viable cells (65–76%) with higher mitotic index; apoptotic tumor cells at high risk due to cytotoxicity (>70% with high apoptotic index); reduced proliferation index (270 vs 120 per high power field) associated with enhanced IC sodium in vivo MR image intensities and decreased tumor size (3%; p < 0.001; n = 16) than that of pre-treated tumors. IC-Na MR signal intensities possibly indicated Taxotere chemosensitivity response in vivo associated with apoptosis and different pre-malignant features within 24 hours of exposure of cancer cells to anti-neoplastic Taxotere drug. CONCLUSION: Sodium MRI imaging may be used as in vivo rapid drug monitoring method to evaluate Taxotere chemosensitivity response associated with neoplasia, apoptosis and tumor histology features

Methadone, Buprenorphine, and Street Drug Interactions with Antiretroviral Medications

While street drugs appear unlikely to alter the metabolism of antiretroviral (ARV) medications, several ARVs may induce or inhibit metabolism of various street drugs. However, research on these interactions is limited. Case reports have documented life-threatening overdoses of ecstasy and gamma-hydroxybutyrate after starting ritonavir, an ARV that inhibits several metabolic enzymes. For opioid addiction, methadone or buprenorphine are the treatments of choice. Because a number of ARVs decrease or increase methadone levels, patients should be monitored for methadone withdrawal or toxicity when they start or stop ARVs. Most ARVs do not cause buprenorphine withdrawal or toxicity, even if they alter buprenorphine levels, with rare exceptions to date including atazanavir/ritonavir associated with significant increases in buprenorphine and adverse events related to sedation and mental status changes in some cases. There are newer medications yet to be studied with methadone or buprenorphine. Further, there are many frequently used medications in treatment of complications of HIV disease that have not been studied. There is need for continuing research to define these drug interactions and their clinical significance

Domains growth and packing properties in driven granular media subject to gravity

We study the dynamical properties of recently introduced frustrated lattice gas models (IFLG and Tetris) for granular media under gentle shaking. We consider both the case where grains have inter-grain surface interactions and the case where they have not, corresponding, for instance, to the presence or absence of moisture in the packs. To characterise the grains packing structure, we discuss the properties of density distribution. In particular, we consider the phenomenon of grains domains formation under compaction. New results amenable of experimental check are discussed along with some important differences between the dynamics of the present models.Comment: 7 pages, 6 postscript files for figure

DREDed Anomaly Mediation

We offer a guide to dimensional reduction (DRED) in theories with anomaly mediated supersymmetry breaking. Evanescent operators proportional to epsilon arise in the bare Lagrangian when it is reduced from d=4 to d= (4-2 epsilon) dimensions. In the course of a detailed diagrammatic calculation, we show that inclusion of these operators is crucial. The evanescent operators conspire to drive the supersymmetry-breaking parameters along anomaly-mediation trajectories across heavy particle thresholds, guaranteeing the ultraviolet insensitivity.Comment: 24 pages. 10 figures. Uses Axodraw. Reference adde

The Gamma Ray Burst section of the White Paper on the Status and Future of Very High Energy Gamma Ray Astronomy: A Brief Preliminary Report

Original paper can be found at: http://proceedings.aip.org/proceedings/ Copyright American Institute of Physics DOI: 10.1063/1.2943545otherPeer reviewe

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $\chi^{(5)}$ and $\chi^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $SO(21, \mathbb{C})$.Comment: 33 page

Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics

We investigate the motion of a tagged spin in a ferromagnetic Ising chain evolving under Kawasaki dynamics. At equilibrium, the displacement is Gaussian, with a variance growing as $A t^{1/2}$. The temperature dependence of the prefactor $A$ is derived exactly. At low temperature, where the static correlation length $\xi$ is large, the mean square displacement grows as $(t/\xi^2)^{2/3}$ in the coarsening regime, i.e., as a finite fraction of the mean square domain length. The case of totally asymmetric dynamics, where $(+)$ (resp. $(-)$) spins move only to the right (resp. to the left), is also considered. In the steady state, the displacement variance grows as $B t^{2/3}$. The temperature dependence of the prefactor $B$ is derived exactly, using the Kardar-Parisi-Zhang theory. At low temperature, the displacement variance grows as $t/\xi^2$ in the coarsening regime, again proportionally to the mean square domain length.Comment: 22 pages, 8 figures. A few minor changes and update

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.Comment: 11 pages, 1 figure, Revte