A generic greedy algorithm, partially-ordered graphs and NP-completeness.

Let π be any fixed polynomial-time testable, non-trivial, hereditary property of graphs. Suppose that the vertices of a graph G are not necessarily linearly ordered but partially ordered, where we think of this partial order as a collection of (possibly exponentially many) linear orders in the natural way. We prove that the problem of deciding whether a lexicographically first maximal subgraph of G satisfying π, with respect to one of these linear orders, contains a specified vertex is NP-complete

Andreev scattering in the asymmetric ladder with preformed bosonic pairs

We discuss the phase coherence which emanates from the ladder-like proximity effect between a ``weak superconductor'' with preformed bosonic pairs (here, a single-chain Luther-Emery liquid with superconducting correlations that decay approximately as $x^{-1}$) and a Fermi gas with unpaired fermions. Carefully studying tunneling mechanism(s), we show that the boson-mediated Cooper pairing between remaining unpaired electrons results in a quasi long-range superconductivity: Superconducting correlations decay very slowly as $x^{-\eta}$ with $\eta\approx 1/2$. This process is reminiscent of the coupling of fermions to preformed bosonic pairs introduced in the context of high-Tc cuprates.Comment: 5 pages, final version (To appear in PRB Rapid Communication

Lymphomatoid granulomatosis A report of 4 cases

Only 1 case of lymphomatoid granulomatosis has previously been reported from South Africa. Experience with 4 such adult patients (2 blacks and 2 whites) is described. These patients were followed up for 15 - 48 months and none developed evidence of a lymphoma during this period. Fever, weight loss, cough and breathlessness were prominent symptoms in all patients. One patient, a black woman, with a diffuse interstitial paUern of lung involvement, had digital clubbing - a rare accompaniment that resolved after therapy. Dilated congestive cardiomyopathy was found in association with pulmonary nodules in a black male patient. All 4 patients were treated with cytotoxic regimens. The 2 patients treated with oral cyclophosphamide and prednisolone responded favourably. The possible explanation for paucity of reports of lymphomatoid granulomatosis from South Africa could be under-reporting, underdiagnosis or a true geographic/ethnic variation in the incidence of this condition

Optimization of the fixed-flexion knee radiograph

SummaryPurposeTo develop a user-friendly method of achieving optimal radiographs for measurement of joint space width of the knee with minimal radiation exposure. In order to accomplish this the X-ray technologist must (1) be able to identify the anterior and posterior rims of the tibial plateau at a variety of X-ray head angles and (2) be able to choose the direction to adjust the head angle to get a better view based on the criteria for acceptable radiographs.MethodsWe have developed a training manual and materials to instruct investigators and radiology technologists in a method that uses a commercially available Plexiglas positioning frame (Synaflexer™) and standard X-ray equipment to achieve optimal X-rays with regard to tibial plateau alignment of the knee. This should be accomplished with four or fewer radiographs.ResultsOptimized radiographs for joint space width measurements are achieved without the need for fluoroscopy or foot maps.ConclusionsThis method is readily understood and instituted by radiology technologists in the field

Complexity of Coloring Graphs without Paths and Cycles

Let $P_t$ and $C_\ell$ denote a path on $t$ vertices and a cycle on $\ell$ vertices, respectively. In this paper we study the $k$-coloring problem for $(P_t,C_\ell)$-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada, have proved that 3-colorability of $P_5$-free graphs has a finite forbidden induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and Vatshelle have shown that $k$-colorability of $P_5$-free graphs for $k \geq 4$ does not. These authors have also shown, aided by a computer search, that 4-colorability of $(P_5,C_5)$-free graphs does have a finite forbidden induced subgraph characterization. We prove that for any $k$, the $k$-colorability of $(P_6,C_4)$-free graphs has a finite forbidden induced subgraph characterization. We provide the full lists of forbidden induced subgraphs for $k=3$ and $k=4$. As an application, we obtain certifying polynomial time algorithms for 3-coloring and 4-coloring $(P_6,C_4)$-free graphs. (Polynomial time algorithms have been previously obtained by Golovach, Paulusma, and Song, but those algorithms are not certifying); To complement these results we show that in most other cases the $k$-coloring problem for $(P_t,C_\ell)$-free graphs is NP-complete. Specifically, for $\ell=5$ we show that $k$-coloring is NP-complete for $(P_t,C_5)$-free graphs when $k \ge 4$ and $t \ge 7$; for $\ell \ge 6$ we show that $k$-coloring is NP-complete for $(P_t,C_\ell)$-free graphs when $k \ge 5$, $t \ge 6$; and additionally, for $\ell=7$, we show that $k$-coloring is also NP-complete for $(P_t,C_7)$-free graphs if $k = 4$ and $t\ge 9$. This is the first systematic study of the complexity of the $k$-coloring problem for $(P_t,C_\ell)$-free graphs. We almost completely classify the complexity for the cases when $k \geq 4, \ell \geq 4$, and identify the last three open cases

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi

Field theory conjecture for loop-erased random walks

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion in epsilon=4-d. Up to two loop, the FRG agrees with rigorous bounds, correctly reproduces the leading logarithmic corrections at the upper critical dimension d=4, and compares well with numerical studies. We obtain the universal subleading logarithmic correction in d=4, which can be used as a further test of the conjecture.Comment: 5 page

Ferromagnetic properties of charged vector boson condensate

Bose-Einstein condensation of W bosons in the early universe is studied. It is shown that, in the broken phase of the standard electroweak theory, condensed W bosons form a ferromagnetic state with aligned spins. In this case the primeval plasma may be spontaneously magnetized inside macroscopically large domains and form magnetic fields which may be seeds for the observed today galactic and intergalactic fields. However, in a modified theory, e.g. in a theory without quartic self interactions of gauge bosons or for a smaller value of the weak mixing angle, antiferromagnetic condensation is possible. In the latter case W bosons form scalar condensate with macroscopically large electric charge density i.e. with a large average value of the bilinear product of W-vector fields but with microscopically small average value of the field itself.Comment: Some numerical estimates and discussions are added according to the referee's suggestions. This version is accepted for publication in JCA

List coloring in the absence of a linear forest.

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H

NEMO-ICB (v1.0): interactive icebergs in the NEMO ocean model globally configured at eddy-permitting resolution

An established iceberg module, ICB, is used interactively with the Nucleus for European Modelling of the Ocean (NEMO) ocean model in a new implementation, NEMO–ICB (v1.0). A 30-year hindcast (1976–2005) simulation with an eddy-permitting (0.25°) global configuration of NEMO–ICB is undertaken to evaluate the influence of icebergs on sea ice, hydrography, mixed layer depths (MLDs), and ocean currents, through comparison with a control simulation in which the equivalent iceberg mass flux is applied as coastal runoff, a common forcing in ocean models. In the Southern Hemisphere (SH), drift and melting of icebergs are in balance after around 5 years, whereas the equilibration timescale for the Northern Hemisphere (NH) is 15–20 years. Iceberg drift patterns, and Southern Ocean iceberg mass, compare favourably with available observations. Freshwater forcing due to iceberg melting is most pronounced very locally, in the coastal zone around much of Antarctica, where it often exceeds in magnitude and opposes the negative freshwater fluxes associated with sea ice freezing. However, at most locations in the polar Southern Ocean, the annual-mean freshwater flux due to icebergs, if present, is typically an order of magnitude smaller than the contribution of sea ice melting and precipitation. A notable exception is the southwest Atlantic sector of the Southern Ocean, where iceberg melting reaches around 50% of net precipitation over a large area. Including icebergs in place of coastal runoff, sea ice concentration and thickness are notably decreased at most locations around Antarctica, by up to ~ 20% in the eastern Weddell Sea, with more limited increases, of up to ~ 10% in the Bellingshausen Sea. Antarctic sea ice mass decreases by 2.9%, overall. As a consequence of changes in net freshwater forcing and sea ice, salinity and temperature distributions are also substantially altered. Surface salinity increases by ~ 0.1 psu around much of Antarctica, due to suppressed coastal runoff, with extensive freshening at depth, extending to the greatest depths in the polar Southern Ocean where discernible effects on both salinity and temperature reach 2500 m in the Weddell Sea by the last pentad of the simulation. Substantial physical and dynamical responses to icebergs, throughout the global ocean, are explained by rapid propagation of density anomalies from high-to-low latitudes. Complementary to the baseline model used here, three prototype modifications to NEMO–ICB are also introduced and discussed