On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn--Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allows for the source terms to be dependent on the solution variables.Comment: 18 pages, changed proof from fixed point argument to Galerkin approximatio

Pseudo-Killing Spinors, Pseudo-supersymmetric p-branes, Bubbling and Less-bubbling AdS Spaces

We consider Einstein gravity coupled to an n-form field strength in D dimensions. Such a theory cannot be supersymmetrized in general, we nevertheless propose a pseudo-Killing spinor equation and show that the AdS X Sphere vacua have the maximum number of pseudo-Killing spinors, and hence are fully pseudo-supersymmetric. We show that extremal p-branes and their intersecting configurations preserve fractions of the pseudo-supersymmetry. We study the integrability condition for general (D,n) and obtain the additional constraints that are required so that the existence of the pseudo-Killing spinors implies the Einstein equations of motion. We obtain new pseudo-supersymmetric bubbling AdS_5 X S^5 spaces that are supported by a non-self-dual 5-form. This demonstrates that non-supersymmegtric conformal field theories may also have bubbling states of arbitrary droplets of free fermions in the phase space. We also obtain an example of less-bubbling AdS geometry in D=8, whose bubbling effects are severely restricted by the additional constraint arising from the integrability condition.Comment: typos corrected, extra comments and references added, version appeared in JHE

Approximating Nash Equilibria in Tree Polymatrix Games

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player

Rare B Decays with a HyperCP Particle of Spin One

In light of recent experimental information from the CLEO, BaBar, KTeV, and Belle collaborations, we investigate some consequences of the possibility that a light spin-one particle is responsible for the three Sigma^+ -> p mu^+ mu^- events observed by the HyperCP experiment. In particular, allowing the new particle to have both vector and axial-vector couplings to ordinary fermions, we systematically study its contributions to various processes involving b-flavored mesons, including B-Bbar mixing as well as leptonic, inclusive, and exclusive B decays. Using the latest experimental data, we extract bounds on its couplings and subsequently estimate upper limits for the branching ratios of a number of B decays with the new particle. This can serve to guide experimental searches for the particle in order to help confirm or refute its existence.Comment: 17 pages, 3 figures; discussion on spin-0 case modified, few errors corrected, main conclusions unchange

Experimental demonstration of a hyper-entangled ten-qubit Schr\"odinger cat state

Coherent manipulation of an increasing number of qubits for the generation of entangled states has been an important goal and benchmark in the emerging field of quantum information science. The multiparticle entangled states serve as physical resources for measurement-based quantum computing and high-precision quantum metrology. However, their experimental preparation has proved extremely challenging. To date, entangled states up to six, eight atoms, or six photonic qubits have been demonstrated. Here, by exploiting both the photons' polarization and momentum degrees of freedom, we report the creation of hyper-entangled six-, eight-, and ten-qubit Schr\"odinger cat states. We characterize the cat states by evaluating their fidelities and detecting the presence of genuine multi-partite entanglement. Small modifications of the experimental setup will allow the generation of various graph states up to ten qubits. Our method provides a shortcut to expand the effective Hilbert space, opening up interesting applications such as quantum-enhanced super-resolving phase measurement, graph-state generation for anyonic simulation and topological error correction, and novel tests of nonlocality with hyper-entanglement.Comment: 11 pages, 5 figures, comments welcom

In vitro induction and proliferation of protocorm-like bodies (PLBs) from leaf segments of Phalaenopsis bellina (Rchb.f.) Christenson

An in vitro culture procedure was established to induce protocorm-like bodies (PLBs) from leaf segments of the Phalaenopsis bellina (Rchb.f.) Christenson directly from epidermal cells without intervening callus on ½ strength modified Murashige and Skoog (MS) (in Physiol Plant 15:473–497, 1962) medium supplemented with 1-Naphthaleneacetic acid (NAA; 0, 0.1, 1 mg/l) and Thidiazuron (TDZ; 0, 0.1, 1, 3 mg/l). The best response was established at 3 mg/l TDZ which induced 78% of leaf segments to form a mean number of 14 PLBs per explant after 16 weeks of culture. No PLBs were found when leaf segments were cultured on ½ strength modified MS media supplemented with 0.1 and 1 mg/l NAA. The best induction percentage for auxin: cytokinin combination was at the combination of NAA and TDZ at 1.0 and 3.0 mg/l which gave 72% induction with 9 PLBs per explant. Semi-solid ½ strength MS and liquid Vacin and Went (VW) (in Bot Gaz 110:605–613, 1949) medium were used in order to find the highest survival and number of PLBs proliferation after 3 months in culture. Half strength MS showed an average of 9 PLBs in comparison with VW with an average of 5.3 PLBs per explants. Histological observations revealed that the regenerated PLBs were generally formed from the epidermal layers of the posterior regions of the leaf segments. Scanning electron micrograph of PLBs showed the origin of newly formed PLB from the peripheral region of leaf segments

Metamorphosis in the Cirripede Crustacean Balanus amphitrite

Stalked and acorn barnacles (Cirripedia Thoracica) have a complex life cycle that includes a free-swimming nauplius larva, a cypris larva and a permanently attached sessile juvenile and adult barnacle. The barnacle cyprid is among the most highly specialized of marine invertebrate larvae and its settlement biology has been intensively studied. By contrast, surprisingly few papers have dealt with the critical series of metamorphic events from cementation of the cyprid to the substratum until the appearance of a suspension feeding juvenile. This metamorphosis is both ontogenetically complex and critical to the survival of the barnacle. Here we use video microscopy to present a timeline and description of morphological events from settled cyprid to juvenile barnacle in the model species Balanus amphitrite, representing an important step towards both a broader understanding of the settlement ecology of this species and a platform for studying the factors that control its metamorphosis. Metamorphosis in B. amphitrite involves a complex sequence of events: cementation, epidermis separation from the cypris cuticle, degeneration of cypris musculature, rotation of the thorax inside the mantle cavity, building of the juvenile musculature, contraction of antennular muscles, raising of the body, shedding of the cypris cuticle, shell plate and basis formation and, possibly, a further moult to become a suspension feeding barnacle. We compare these events with developmental information from other barnacle species and discuss them in the framework of barnacle settlement ecology

In vivo testing of novel vaccine prototypes against Actinobacillus pleuropneumoniae

Actinobacillus pleuropneumoniae (A. pleuropneumoniae) is a Gram-negative bacterium that represents the main cause of porcine pleuropneumonia in pigs, causing significant economic losses to the livestock industry worldwide. A. pleuropneumoniae, as the majority of Gram-negative bacteria, excrete vesicles from its outer membrane (OM), accordingly defined as outer membrane vesicles (OMVs). Thanks to their antigenic similarity to the OM, OMVs have emerged as a promising tool in vaccinology. In this study we describe the in vivo testing of several vaccine prototypes for the prevention of infection by all known A. pleuropneumoniae serotypes. Previously identified vaccine candidates, the recombinant proteins ApfA and VacJ, administered individually or in various combinations with the OMVs, were employed as vaccination strategies. Our data show that the addition of the OMVs in the vaccine formulations significantly increased the specific IgG titer against both ApfA and VacJ in the immunized animals, confirming the previously postulated potential of the OMVs as adjuvant. Unfortunately, the antibody response raised did not translate into an effective protection against A. pleuropneumoniae infection, as none of the immunized groups following challenge showed a significantly lower degree of lesions than the controls. Interestingly, quite the opposite was true, as the animals with the highest IgG titers were also the ones bearing the most extensive lesions in their lungs. These results shed new light on A. pleuropneumoniae pathogenicity, suggesting that antibody-mediated cytotoxicity from the host immune response may play a central role in the development of the lesions typically associated with A. pleuropneumoniae infections

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8