The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

The changing UK careers landscape : tidal waves, turbulence and transformation

This article explores how the UK careers landscape in each of the four home nations is changing in response to neo-liberal policies. In this context, careers services are increasingly under pressure to demonstrate their added value, impact and returns on investment. As fiscal arrangements tighten and governments state their preferences and priorities for national careers services, differing strategic responses are beginning to emerge. A quasi-market, experimental approach is now the dominant discourse in England, in contrast to differing and complementary arrangements in Northern Ireland, Scotland and Wales. The article suggests that insofar as these developments are transforming national careers services, they are also creating significant challenges which require new forms of policy imagery and imagination for high-impact, all-age careers services

Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called ``Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.Comment: 59+1 pages, 7 Figure

Anthocyanins, phenols, and antioxidant activity in blackberry juice with plant extracts addition during heating

In this work the influence of addition of different plant extracts (olive leaf, green tea, pine bark PE 95%, pine bark PE 5:1, red wine PE 30%, red wine PE 4:1, and bioflavonoids) to blackberry juice during heating (at 30, 50, 70 and 90 °C) on the anthocyanin and phenol contents, polymeric colour, and antioxidant activity was investigated. Also, reaction rate constant, half-lives of degradation, and activation energy were calculated. Control sample was juice without addition of extracts. The highest anthocyanin content at 30 °C was in samples with the addition of olive leaf and green tea. At 90 °C the highest anthocyanin content was measured in samples with the addition of extract of red wine and bioflavonoides. Samples supplemented with the extracts had much higher antioxidant activity in comparison to the control sample. Results showed that at 90 °C the sample with green tea supplementation had the lowest reaction rate constant and the highest half-life. Activation energy ranged from 29 to 44 kJ mol−1

In vitro anti-HIV activity of some Indian medicinal plant extracts

Background Human Immunodeficiency Virus (HIV) persists to be a significant public health issue worldwide. The current strategy for the treatment of HIV infection, Highly Active Antiretroviral Therapy (HAART), has reduced deaths from AIDS related disease, but it can be an expensive regime for the underdeveloped and developing countries where the supply of drugs is scarce and often not well tolerated, especially in persons undergoing long term treatment. The present therapy also has limitations of development of multidrug resistance, thus there is a need for the discovery of novel anti-HIV compounds from plants as a potential alternative in combating HIV disease. Methods Ten Indian medicinal plants were tested for entry and replication inhibition against laboratory adapted strains HIV-1IIIB, HIV-1Ada5 and primary isolates HIV-1UG070, HIV-1VB59 in TZM-bl cell lines and primary isolates HIV-1UG070, HIV-1VB59 in PM1 cell lines. The plant extracts were further evaluated for toxicity in HEC-1A epithelial cell lines by transwell epithelial model. Results The methanolic extracts of Achyranthes aspera, Rosa centifolia and aqueous extract of Ficus benghalensis inhibited laboratory adapted HIV-1 strains (IC80 3.6–118 μg/ml) and primary isolates (IC80 4.8–156 μg/ml) in TZM-bl cells. Methanolic extract of Strychnos potatorum, aqueous extract of Ficus infectoria and hydroalcoholic extract of Annona squamosa inhibited laboratory adapted HIV-1 strains (IC80 4.24–125 μg/ml) and primary isolates (IC80 18–156 μg/ml) in TZM-bl cells. Methanolic extracts of Achyranthes aspera and Rosa centifolia, (IC801-9 μg/ml) further significantly inhibited HIV-1 primary isolates in PM1cells. Methanolic extracts of Tridax procumbens, Mallotus philippinensis, Annona reticulate, aqueous extract of Ficus benghalensis and hydroalcoholic extract of Albizzia lebbeck did not exhibit anti-HIV activity in all the tested strains. Methanolic extract of Rosa centifolia also demonstrated to be non-toxic to HEC-1A epithelial cells and maintained epithelial integrity (at 500 μg/ml) when tested in transwell dual-chamber. Conclusion These active methanolic extracts of Achyranthes aspera and Rosa centifolia, could be further subjected to chemical analysis to investigate the active moiety responsible for the anti-HIV activity. Methanolic extract of Rosa centifolia was found to be well tolerated maintaining the epithelial integrity of HEC-1A cells in vitro and thus has potential for investigating it further as candidate microbicide

Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

Contains fulltext : 50308.pdf (publisher's version ) (Closed access)In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control