Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Is the even distribution of insecticide-treated cattle essential for tsetse control? Modelling the impact of baits in heterogeneous environments

Background: Eliminating Rhodesian sleeping sickness, the zoonotic form of Human African Trypanosomiasis, can be achieved only through interventions against the vectors, species of tsetse (Glossina). The use of insecticide-treated cattle is the most cost-effective method of controlling tsetse but its impact might be compromised by the patchy distribution of livestock. A deterministic simulation model was used to analyse the effects of spatial heterogeneities in habitat and baits (insecticide-treated cattle and targets) on the distribution and abundance of tsetse. Methodology/Principal Findings: The simulated area comprised an operational block extending 32 km from an area of good habitat from which tsetse might invade. Within the operational block, habitat comprised good areas mixed with poor ones where survival probabilities and population densities were lower. In good habitat, the natural daily mortalities of adults averaged 6.14% for males and 3.07% for females; the population grew 8.46in a year following a 90% reduction in densities of adults and pupae, but expired when the population density of males was reduced to <0.1/km2; daily movement of adults averaged 249 m for males and 367 m for females. Baits were placed throughout the operational area, or patchily to simulate uneven distributions of cattle and targets. Gaps of 2–3 km between baits were inconsequential provided the average imposed mortality per km2 across the entire operational area was maintained. Leaving gaps 5–7 km wide inside an area where baits killed 10% per day delayed effective control by 4–11 years. Corrective measures that put a few baits within the gaps were more effective than deploying extra baits on the edges. Conclusions/Significance: The uneven distribution of cattle within settled areas is unlikely to compromise the impact of insecticide-treated cattle on tsetse. However, where areas of >3 km wide are cattle-free then insecticide-treated targets should be deployed to compensate for the lack of cattle

Tracking advanced persistent threats in critical infrastructures through opinion dynamics

Advanced persistent threats pose a serious issue for modern industrial environments, due to their targeted and complex attack vectors that are difficult to detect. This is especially severe in critical infrastructures that are accelerating the integration of IT technologies. It is then essential to further develop effective monitoring and response systems that ensure the continuity of business to face the arising set of cyber-security threats. In this paper, we study the practical applicability of a novel technique based on opinion dynamics, that permits to trace the attack throughout all its stages along the network by correlating different anomalies measured over time, thereby taking the persistence of threats and the criticality of resources into consideration. The resulting information is of essential importance to monitor the overall health of the control system and cor- respondingly deploy accurate response procedures. Advanced Persistent Threat Detection Traceability Opinion Dynamics.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening

Understanding the processes that underlie pollen release is a prime target for controlling fertility to enable selective breeding and the efficient production of hybrid crops. Pollen release requires anther opening, which involves changes in the biomechanical properties of the anther wall. In this research, we develop and use a mathematical model to understand how these biomechanical processes lead to anther opening

Towards a Soft Evaluation and Refinement of Tagging in Digital Humanities

In this paper we estimate the soundness of tagging in digital repositories within the field of Digital Humanities by studying the (semantic) conceptual structure behind the folksnonomy. The use of association rules associated to this conceptual structure (Stem and Luxenburger basis) allows to faithfully (from a semantic point of view) complete the tagging (or suggest such a completion).Ministerio de Economía y Competitividad TIN2013-41086-PJunta de Andalucía TIC-606

Sex chromosome positions in human interphase nuclei as studied by in situ hybridization with chromosome specific DNA probes

Two cloned repetitive DNA probes, pXBR and CY1, which bind preferentially to specific regions of the human X and Y chromosome, respectively, were used to study the distribution of the sex chromosomes in human lymphocyte nuclei by in situ hybridization experiments. Our data indicate a large variability of the distances between the sex chromosomes in male and female interphase nuclei. However, the mean distance observed between the X and Y chromosome was significantly smaller than the mean distance observed between the two X-chromosomes. The distribution of distances determined experimentally is compared with three model distributions of distances, and the question of a non-random distribution of sex chromosomes is discussed. Mathematical details of these model distributions are provided in an Appendix to this paper. In the case of a human translocation chromosome (XqterXp22.2::Yq11Y qter) contained in the Chinese hamster x human hybrid cell line 445 x 393, the binding sites of pXBR and CY1 were found close to each other in most interphase nuclei. These data demonstrate the potential use of chromosome-specific repetitive DNA probes to study the problem of interphase chromosome topography

Energy dependence of kaon production in central Pb+Pb collisions

Recent results from the NA49 experiment on the energy dependence of charged kaon production in central Pb+Pb collisions are presented. First results from the new data at 80 AGeV beam energy are compared with those from lower and higher energies. A difference in the energy dependence of the / and / ratios is observed. The / ratio shows a non-monotonic behaviour with a maximum near 40 AGeV.Comment: 8 pages, 7 figures, proceedings of talk at SQM2001, Frankfurt, Germany, to appear in J. Phys.

Principles of Stakes Fairness in Sport

Fairness in sport is not just about assigning the top prizes to the worthiest competitors. It is also about the way the prize structure itself is organised. For many sporting competitions, although it may be acceptable for winners to receive more than losers, it can seem unfair for winners to take everything and for losers to get nothing. Yet this insight leaves unanswered some difficult questions about what stakes fairness requires and which principles of stakes fairness are appropriate for particular competitions. In this article I specify a range of different principles of stakes fairness (ten in total) that could regulate sporting competitions. I also put forward a theoretical method for pairing up appropriate principles of stakes fairness with given sporting competitions. Specifically, I argue that the underlying rationales for holding sporting competitions can provide useful guides for identifying appropriate principles of stakes fairness. I then seek to clarify and work through some of the implications of this method for a sample of real world controversies over sporting prize structures. I also attempt to refine the method in response to two possible objections from indeterminacy and relativism. Finally, I compare and contrast my conclusions with more general philosophical debates about justice