Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

Simplified modelling of explosion propagation by dust lifting in coal mines

Dispersion of accumulated layers of combustible dust by turbulent flow or shock waves ahead of the propagating flame may sustain explosion propagation in coal mine galleries and other industrial facilities. The mechanisms involved in transforming dust layers into dust suspensions are rather complex, and detailed numerical modelling of this process is therefore practically impossible, at least on industrial scales. In the computational fluid dynamics code DESC (Dust Explosion Simulation Code), a simplified empirical relation describes the dust-lifting phenomenon. The relation originates from experimental work in a laboratory-scale shock tube, and a small wind tunnel, at Warsaw University of Technology. The present paper describes the modelling of dust lifting in the current version of DESC, and illustrates the performance of the code by simulating some large-scale dust explosion experiments conducted in a 100-m surface gallery at the Experimental Mine Barbara in Katowice, Poland. Although there are significant uncertainties associated with this type of calculations, the results suggest that a simplified approach to dust lifting may become a useful tool for risk assessments in the future.publishedVersio

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Modelling the impact of social protection on tuberculosis: the S-PROTECT project.

BACKGROUND: Tackling the social determinants of Tuberculosis (TB) through social protection is a key element of the post-2015 End TB Strategy. However, evidence informing policies are still scarce. Mathematical modelling has the potential to contribute to fill this knowledge gap, but existing models are inadequate. The S-PROTECT consortium aimed to develop an innovative mathematical modelling approach to better understand the role of social protection to improve TB care, prevention and control. METHODS: S-PROTECT used a three-steps approach: 1) the development of a conceptual framework; 2) the extraction from this framework of three high-priority mechanistic pathways amenable for modelling; 3) the development of a revised version of a standard TB transmission model able to capture the structure of these pathways. As a test case we used the Bolsa Familia Programme (BFP), the Brazilian conditional cash transfer scheme. RESULTS: Assessing one of these pathways, we estimated that BFP can reduce TB prevalence by 4% by improving households income and thus their nutritional status. When looking at the direct impact via malnutrition (not income mediated) the impact was 33%. This variation was due to limited data availability, uncertainties on data transformation and the pathway approach taken. These results are preliminary and only aim to serve as illustrative example of the methodological challenges encountered in this first modelling attempt, nonetheless they suggest the potential added value of integrating TB standard of care with social protection strategies. CONCLUSIONS: Results are to be confirmed with further analysis. However, by developing a generalizable modelling framework, S-PROTECT proved that the modelling of social protection is complex, but doable and allowed to draw the research road map for the future in this field

Angle-resolved photoemission study and first principles calculation of the electronic structure of GaTe

The electronic band structure of GaTe has been calculated by numerical atomic orbitals density-functional theory, in the local density approximation. In addition, the valence-band dispersion along various directions of the GaTe Brillouin zone has been determined experimentally by angle-resolved photoelectron spectroscopy. Along these directions, the calculated valence-band structure is in good concordance with the valence-band dispersion obtained by these measurements. It has been established that GaTe is a direct-gap semiconductor with the band gap located at the Z point, that is, at Brillouin zone border in the direction perpendicular to the layers. The valence-band maximum shows a marked \textit{p}-like behavior, with a pronounced anion contribution. The conduction band minimum arises from states with a comparable \textit{s}- \textit{p}-cation and \textit{p}-anion orbital contribution. Spin-orbit interaction appears to specially alter dispersion and binding energy of states of the topmost valence bands lying at $\Gamma$. By spin-orbit, it is favored hybridization of the topmost \textit{p}$_z$-valence band with deeper and flatter \textit{p$_x$}-\textit{p$_y$} bands and the valence-band minimum at $\Gamma$ is raised towards the Fermi level since it appears to be determined by the shifted up \textit{p$_x$}-\textit{p$_y$} bands.Comment: 7 text pages, 6 eps figures, submitted to PR

Eliminating Malaria Vectors.

Malaria vectors which predominantly feed indoors upon humans have been locally eliminated from several settings with insecticide treated nets (ITNs), indoor residual spraying or larval source management. Recent dramatic declines of An. gambiae in east Africa with imperfect ITN coverage suggest mosquito populations can rapidly collapse when forced below realistically achievable, non-zero thresholds of density and supporting resource availability. Here we explain why insecticide-based mosquito elimination strategies are feasible, desirable and can be extended to a wider variety of species by expanding the vector control arsenal to cover a broader spectrum of the resources they need to survive. The greatest advantage of eliminating mosquitoes, rather than merely controlling them, is that this precludes local selection for behavioural or physiological resistance traits. The greatest challenges are therefore to achieve high biological coverage of targeted resources rapidly enough to prevent local emergence of resistance and to then continually exclude, monitor for and respond to re-invasion from external populations

Astrocytes Do Not Forfeit Their Neuroprotective Roles After Surviving Intense Oxidative Stress

In order to fulfill their evolutionary role as support cells, astrocytes have to tolerate intense oxidative stress under conditions of brain injury and disease. It is well known that astrocytes exposed to mild oxidative stress are preconditioned against subsequent stress exposure in dual hit models. However, it is unclear whether severe oxidative stress leads to stress tolerance, stress exacerbation, or no change in stress resistance in astrocytes. Furthermore, it is not known whether reactive astrocytes surviving intense oxidative stress can still support nearby neurons. The data in this Brief Report suggest that primary cortical astrocytes surviving high concentrations of the oxidative toxicant paraquat are completely resistant against subsequent oxidative challenges of the same intensity. Inhibitors of multiple endogenous defenses (e.g., glutathione, heme oxygenase 1, ERK1/2, Akt) failed to abolish or even reduce their stress resistance. Stress-reactive cortical astrocytes surviving intense oxidative stress still managed to protect primary cortical neurons against subsequent oxidative injuries in neuron/astrocyte co-cultures, even at concentrations of paraquat that otherwise led to more than 80% neuron loss. Although our previous work demonstrated a lack of stress tolerance in primary neurons exposed to dual paraquat hits, here we show that intensely stressed primary neurons can resist a second hit of hydrogen peroxide. These collective findings suggest that stress-reactive astroglia are not necessarily neurotoxic, and that severe oxidative stress does not invariably lead to stress exacerbation in either glia or neurons. Therefore, interference with the natural functions of stress-reactive astrocytes might have the unintended consequence of accelerating neurodegeneration

Entomological Surveillance of Behavioural Resilience and Resistance in Residual Malaria Vector Populations.

The most potent malaria vectors rely heavily upon human blood so they are vulnerable to attack with insecticide-treated nets (ITNs) and indoor residual spraying (IRS) within houses. Mosquito taxa that can avoid feeding or resting indoors, or by obtaining blood from animals, mediate a growing proportion of the dwindling transmission that persists as ITNs and IRS are scaled up. Increasing frequency of behavioural evasion traits within persisting residual vector systems usually reflect the successful suppression of the most potent and vulnerable vector taxa by IRS or ITNs, rather than their failure. Many of the commonly observed changes in mosquito behavioural patterns following intervention scale-up may well be explained by modified taxonomic composition and expression of phenotypically plastic behavioural preferences, rather than altered innate preferences of individuals or populations. Detailed review of the contemporary evidence base does not yet provide any clear-cut example of true behavioural resistance and is, therefore, consistent with the hypothesis presented. Caution should be exercised before over-interpreting most existing reports of increased frequency of behavioural traits which enable mosquitoes to evade fatal contact with insecticides: this may simply be the result of suppressing the most behaviourally vulnerable of the vector taxa that constituted the original transmission system. Mosquito taxa which have always exhibited such evasive traits may be more accurately described as behaviourally resilient, rather than resistant. Ongoing national or regional entomological monitoring surveys of physiological susceptibility to insecticides should be supplemented with biologically and epidemiologically meaningfully estimates of malaria vector population dynamics and the behavioural phenotypes that determine intervention impact, in order to design, select, evaluate and optimize the implementation of vector control measures

Optimal Resource Allocation over Networks via Lottery-Based Mechanisms

We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called the system problem, to find the optimal lottery allocation. The system problem exhibits a two-layer structure comprised of a permutation profile and optimal allocations given the permutation profile. For any fixed permutation profile, we provide a market-based mechanism to find the optimal allocations and prove the existence of equilibrium prices. We show that the system problem has a duality gap, in general, and that the primal problem is NP-hard. We then consider a relaxation of the system problem and derive some qualitative features of the optimal lottery structure