Edge removal in random contact networks and the basic reproduction number

Understanding the effect of edge removal on the basic reproduction number ${\mathcal{R}_0}$ for disease spread on contact networks is important for disease management. The formula for the basic reproduction number ${\mathcal{R}_0}$ in random network SIR models of configuration type suggests that for degree distributions with large variance, a reduction of the average degree may actually increase ${\mathcal{R}_0}$ . To understand this phenomenon, we develop a dynamical model for the evolution of the degree distribution under random edge removal, and show that truly random removal always reduces ${\mathcal{R}_0}$ . The discrepancy implies that any increase in ${\mathcal{R}_0}$ must result from edge removal changing the network type, invalidating the use of the basic reproduction number formula for a random contact network. We further develop an epidemic model incorporating a contact network consisting of two groups of nodes with random intra- and inter-group connections, and derive its basic reproduction number. We then prove that random edge removal within either group, and between groups, always decreases the appropriately defined ${\mathcal{R}_0}$ . Our models also allow an estimation of the number of edges that need to be removed in order to curtail an epidemic.     

Analytic Calculation of Finite-Population Reproductive Numbers for Direct- and Vector-Transmitted Diseases with Homogeneous Mixing

The basic reproductive number, $\mathcal {R}_{0}$ , provides a foundation for evaluating how various factors affect the incidence of infectious diseases. Recently, it has been suggested that, particularly for vector-transmitted diseases, $\mathcal {R}_{0}$ should be modified to account for the effects of finite host population within a single disease transmission generation. Here, we use a transmission factor approach to calculate such “finite-population reproductive numbers,” under the assumption of homogeneous mixing, for both vector-borne and directly transmitted diseases. In the case of vector-borne diseases, we estimate finitepopulation reproductive numbers for both host-to-host and vector-to-vector generations, assuming that the vector population is effectively infinite. We find simple, interpretable formulas for all three of these quantities. In the direct case, we find that finite-population reproductive numbers diverge from $\mathcal {R}_{0}$ before $\mathcal {R}_{0}$ reaches half of the population size. In the vector-transmitted case, we find that the host-to-host number diverges at even lower values of $\mathcal {R}_{0}$ , while the vector-to-vector number diverges very little over realistic parameter ranges.     

Retention of Dissolved Inorganic Nitrogen by Foliage and Twigs of Four Temperate Tree Species

Nitrogen (N) retention by tree canopies is believed to be an important process for tree nutrient uptake, and its quantification is a key issue in determining the impact of atmospheric N deposition on forest ecosystems. Due to dry deposition and retention by other canopy elements, the actual uptake and assimilation by the tree canopy is often obscured in throughfall studies. In this study, ¹⁵N-labeled solutions ( $ ^{15} {\text{NH}}_{4}^{ + } $ and $ ^{15} {\text{NO}}_{3}^{ - } $ ) were used to assess dissolved inorganic N retention by leaves/needles and twigs of European beech, pedunculate oak, silver birch, and Scots pine saplings. The effects of N form, tree species, leaf phenology, and applied $ {\text{NO}}_{3}^{ - } $ to $ {\text{NH}}_{4}^{ + } $ ratio on the N retention were assessed. Retention patterns were mainly determined by foliar uptake, except for Scots pine. In twigs, a small but significant ¹⁵N enrichment was detected for $ {\text{NH}}_{4}^{ + } $ , which was found to be mainly due to physicochemical adsorption to the woody plant surface. The mean $ {{^{15} {\text{NH}}_{4}^{ + } } \mathord{\left/ {\vphantom {{^{15} {\text{NH}}_{4}^{ + } } {^{15} {\text{NO}}_{3}^{ - } }}} \right. \kern-0em} {^{15} {\text{NO}}_{3}^{ - } }} $ retention ratio varied considerably among species and phenological stadia, which indicates that the use of a fixed ratio in the canopy budget model could lead to an over- or underestimation of the total N retention. In addition, throughfall water under each branch was collected and analyzed for $ ^{15} {\text{NH}}_{4}^{ + } $ , $ ^{15} {\text{NO}}_{3}^{ - } $ , and all major ions. Net throughfall of $ ^{15} {\text{NH}}_{4}^{ + } $ was, on average, 20 times higher than the actual retention of $ ^{15} {\text{NH}}_{4}^{ + } $ by the plant material. This difference in $ ^{15} {\text{NH}}_{4}^{ + } $ retention could not be attributed to pools and fluxes measured in this study. The retention of $ ^{15} {\text{NH}}_{4}^{ + } $ was correlated with the net throughfall of K⁺, Mg²⁺, Ca²⁺, and weak acids during leaf development and the fully leafed period, while no significant relationships were found for $ ^{15} {\text{NO}}_{3}^{ - } $ retention. This suggests that the main driving factors for $ {\text{NH}}_{4}^{ + } $ retention might be ion exchange processes during the start and middle of the growing season and passive diffusion at leaf senescence. Actual assimilation or abiotic uptake of N through leaves and twigs was small in this study, for example, 1–5% of the applied dissolved ¹⁵N, indicating that the impact of canopy N retention from wet deposition on forest productivity and carbon sequestration is likely limited.     

Long-term analysis of Hubbard Brook stable oxygen isotope ratios of streamwater and precipitation sulfate

In response to decreasing atmospheric emissions of sulfur (S) since the 1970s there has been a concomitant decrease in S deposition to watersheds in the Northeastern U.S. Previous study at the Hubbard Brook Experimental Forest, NH (USA) using chemical and isotopic analyzes ( $ \delta^{34} {\text{S}}_{{{\text{SO}}_{4} }} $ ) combined with modeling has suggested that there is an internal source of S within these watersheds that results in a net loss of S via sulfate in drainage waters. The current study expands these previous investigations by the utilization of δ¹⁸O analyzes of precipitation sulfate and streamwater sulfate. Archived stream and bulk precipitation samples at the Hubbard Brook Experimental Forest from 1968–2004 were analyzed for stable oxygen isotope ratios of sulfate ( $ \delta^{18} {\text{O}}_{{{\text{SO}}_{4} }} $ ). Overall decreasing temporal trends and seasonally low winter values of $ \delta^{18} {\text{O}}_{{{\text{SO}}_{4} }} $ in bulk precipitation are most likely attributed to similar trends in precipitation $ \delta^{18} {\text{O}}_{{{\text{H}}_{2} {\text{O}}}} $ values. Regional climate trends and changes in temperature control precipitation $ \delta^{18} {\text{O}}_{{{\text{H}}_{2} {\text{O}}}} $ values that are reflected in the $ \delta^{18} {\text{O}}_{{{\text{SO}}_{4} }} $ values of precipitation. The significant relationship between ambient temperature and the $ \delta^{18} {\text{O}}_{{{\text{H}}_{2} {\text{O}}}} $ values of precipitation is shown from a nearby site in Ottawa, Ontario (Canada). Although streamwater $ \delta^{18} {\text{O}}_{{{\text{SO}}_{4} }} $ values did not reveal temporal trends, a large difference between precipitation and streamwater $ \delta^{18} {\text{O}}_{{{\text{SO}}_{4} }} $ values suggest the importance of internal cycling of S especially through the large organic S pool and the concomitant effect on the $ \delta^{18} {\text{O}}_{{{\text{SO}}_{4} }} $ values in drainage waters.     

On the page number of RNA secondary structures with pseudoknots

Let ${\mathcal {S}}$ denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. ${\{i, j\} \in \mathcal {S}}$ if there is a hydrogen bond between the ith and jth nucleotide. The page number of ${\mathcal {S}}$ , denoted ${\pi(\mathcal {S})}$ , is the minimum number k such that ${\mathcal {S}}$ can be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NP-complete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe an approximation algorithm from which it follows that ${\omega(\mathcal {S}) \leq \pi(\mathcal {S}) \leq \omega(\mathcal {S}) \cdot \log n}$ , where the clique number of ${\mathcal {S}, \omega(\mathcal {S})}$ , denotes the maximum number of base pairs that pairwise cross each other.     

Threshold dynamics of an infective disease model with a fixed latent period and non-local infections

In this paper, we derive and analyze an infectious disease model containing a fixed latency and non-local infection caused by the mobility of the latent individuals in a continuous bounded domain. The model is given by a spatially non-local reaction–diffusion system carrying a discrete delay associated with the zero-flux condition on the boundary. By applying some existing abstract results in dynamical systems theory, we prove the existence of a global attractor for the model system. By appealing to the theory of monotone dynamical systems and uniform persistence, we show that the model has the global threshold dynamics which can be described either by the principal eigenvalue of a linear non-local scalar reaction diffusion equation or equivalently by the basic reproduction number ${\mathcal{R}_0}$ for the model. Such threshold dynamics predicts whether the disease will die out or persist. We identify the next generation operator, the spectral radius of which defines basic reproduction number. When all model parameters are constants, we are able to find explicitly the principal eigenvalue and ${\mathcal{R}_0}$ . In addition to computing the spectral radius of the next generation operator, we also discuss an alternative way to compute ${\mathcal{R}_0}$ .     

Towards a conceptualization of ETL and physical storage of semantic data warehouses as a service

The data warehouse technology has become the incontestable tool for businesses and organizations to make strategic decisions to ensure their competitively. The construction of a data warehouse ( $\mathcal{D}\mathcal{W}$ ) passes by selecting relevant information sources, extracting relevant data and loading them into the $\mathcal{D}\mathcal{W}$ . These processes require a precise expertise from designers related to logical and physical implementations of information sources, which is not usually an easy task. The diversity and heterogeneity of information sources makes the construction process of the $\mathcal{D}\mathcal{W}$ complex and time consuming. Domain ontologies have been proposed to reduce heterogeneity between sources, platforms, services, etc. They resolve syntax and semantic conflicts. The phenomenon of adopting domain ontologies by organizations creates a new type of databases, called semantic databases ( $\mathcal{S}\mathcal{D}\mathcal{B}$ ). As a consequence, they become a candidate for building the semantic $\mathcal{D}\mathcal{W}$ ( $\mathcal{S}\mathcal{D}\mathcal{W}$ ). To handle the diversity of information sources and hide the implementations aspects of sources, proposing a generic framework for constructing $\mathcal{D}\mathcal{W}$ becomes a necessity. In this paper, we first proposed an ontology-based approach for designing $\mathcal{S}\mathcal {D}\mathcal{B}$ . Secondly, ETL phases are defined at ontological level to hide the implementation details. Thirdly, a storage service for ontologies and its associated data is given. Finally, our proposal is validated through a case study and a tool.     

Release of non-exchangeable {}^{{{\text{15}}}}{\text{NH}}^{{\text{ + }}}_{{\text{4}}} from subgrade, decomposed granite substrates and uptake by non-mycorrhizal and mycorrhizal California native annual grass, Vulpia microstachys

Release rates of recently fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ from non-exchangeable interlayer sites in 2:1 silicate minerals were determined for decomposed granite (DG) saprolites from three locations in California, USA. Recently-fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release from the DG substrate was quantified by extracting diffused $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ with H-resin, as well as a native, annual grass Vulpia microstachys. The $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release data varied with via the method of extraction, which included H-resin pre-treatments (Na⁺ or H⁺) and V. microstachys uptake (mycorrhizal inoculated or uninoculated). After 6 weeks (1008 h), more $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ was recovered from fixed interlayer positions by the H-resins as compared to uptake by V. microstachys. The H⁺ treated H-resins recovered more released $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ (≈94 mg ${\text{NH}}^{{\text{ + }}}_{{\text{4}}} - {\text{N}}\;{\text{kg}}^{1} $ or (12%) of total fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ ) in two of the three DG samples as compared to the Na⁺ treated resins, (which recovered ≈70–78 mg ${\text{NH}}^{{\text{ + }}}_{{\text{4}}} - {\text{N}}\;{\text{kg}}^{{{\text{ - 1}}}} $ (or 9–10%) of the total fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ ). The V. microstachys assimilated 8–9% of the total fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ with mycorrhizal inoculum as compared to only 2% without a mycorrhizal inoculum, over the same time period. The fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release kinetics from the H-resin experiments were most accurately described by first order and power function models, and can be characterized as biphasic using a heterogeneous diffusion model. Uptake of both the ¹⁵N and ambient, unlabelled N from the soils was closely related to plant biomass. There was no significant difference in percent of N per unit of biomass between the control and mycorrhizal treatments. The findings presented here indicate that observed, long-term $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release rates from DG in studies utilizing resins, may overestimate the levels of fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ made available to plants and microorganisms. Additionally, the study suggested that mycorrhizae facilitate the acquisition and plant uptake of fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ , resulting in markedly increased plant biomass production.     

A Bovine Babesiosis Model with Dispersion

Bovine Babesiosis (BB) is a tick borne parasitic disease with worldwide over 1.3 billion bovines at potential risk of being infected. The disease, also called tick fever, causes significant mortality from infection by the protozoa upon exposure to infected ticks. An important factor in the spread of the disease is the dispersion or migration of cattle as well as ticks. In this paper, we study the effect of this factor. We introduce a number, $\mathcal{P}$ , a “proliferation index,” which plays the same role as the basic reproduction number $\mathcal{R}_{0}$ with respect to the stability/instability of the disease-free equilibrium, and observe that $\mathcal{P}$ decreases as the dispersion coefficients increase. We prove, mathematically, that if $\mathcal{P}>1$ then the tick fever will remain endemic. We also consider the case where the birth rate of ticks undergoes seasonal oscillations. Based on data from Colombia, South Africa, and Brazil, we use the model to determine the effectiveness of several intervention schemes to control the progression of BB.     

Deriving fluorometer-specific values of relative PSI fluorescence intensity from quenching of F 0 fluorescence in leaves of Arabidopsis thaliana and Zea mays

The effect of stepwise increments of red light intensities on pulse-amplitude modulated (PAM) chlorophyll (Chl) fluorescence from leaves of A. thaliana and Z. mays was investigated. Minimum and maximum fluorescence were measured before illumination (F ₀ and F _M, respectively) and at the end of each light step ( $ F^{\prime}_{0} $ and $ F^{\prime}_{\text{M}} $ , respectively). Calculated $ F^{\prime}_{0} $ values derived from F ₀, F _M and $ F^{\prime}_{\text{M}} $ fluorescence according to Oxborough and Baker (1997) were lower than the corresponding measured $ F^{\prime}_{0} $ values. Based on the concept that calculated $ F^{\prime}_{0} $ values are under-estimated because the underlying theory ignores PSI fluorescence, a method was devised to gain relative PSI fluorescence intensities from differences between calculated and measured $ F^{\prime}_{0} $ . This method yields fluorometer-specific PSI data as its input data (F ₀, F _M, $ F^{\prime}_{0} $ and $ F^{\prime}_{\text{M}} $ ) depend solely on the spectral properties of the fluorometer used. Under the present conditions, the PSI contribution to F ₀ fluorescence was 0.24 in A. thaliana and it was independent on the light acclimation status; the corresponding value was 0.50 in Z. mays. Correction for PSI fluorescence affected Z. mays most: the linear relationship between PSI and PSII photochemical yields was clearly shifted toward the one-to-one proportionality line and maximum electron transport was increased by 50 %. Further, correction for PSI fluorescence increased the PSII reaction center-specific parameter, 1/F ₀ ? 1/F _M, up to 50 % in A. thaliana and up to 400 % in Z. mays.     

Longitudinal distribution of nitrate δ15N and δ18O in two contrasting tropical rivers: implications for instream nitrogen cycling

The longitudinal variations in the nitrogen (δ¹⁵N) and oxygen (δ¹⁸O) isotopic compositions of nitrate (NO₃ ^?), the carbon isotopic composition (δ¹³C) of dissolved inorganic carbon (DIC) and the δ¹³C and δ¹⁵N of particulate organic matter were determined in two Southeast Asian rivers contrasting in the watershed geology and land use to understand internal nitrogen cycling processes. The $ \delta^{15} {\text{N}}_{{{\text{NO}}_{3} }} $ became higher longitudinally in the freshwater reach of both rivers. The $ \delta^{18} {\text{O}}_{{{\text{NO}}_{3} }} $ also increased longitudinally in the river with a relatively steeper longitudinal gradient and a less cultivated watershed, while the $ \delta^{18} {\text{O}}_{{{\text{NO}}_{3} }} $ gradually decreased in the other river. A simple model for the $ \delta^{15} {\text{N}}_{{{\text{NO}}_{3} }} $ and the $ \delta^{18} {\text{O}}_{{{\text{NO}}_{3} }} $ that accounts for simultaneous input and removal of NO₃ ^? suggested that the dynamics of NO₃ ^? in the former river were controlled by the internal production by nitrification and the removal by denitrification, whereas that in the latter river was significantly affected by the anthropogenic NO₃ ^? loading in addition to the denitrification and/or assimilation. In the freshwater-brackish transition zone, heterotrophic activities in the river water were apparently elevated as indicated by minimal dissolved oxygen, minimal δ¹³C_DIC and maximal pCO₂. The δ¹⁵N of suspended particulate nitrogen (PN) varied in parallel to the $ \delta^{15} {\text{N}}_{{{\text{NO}}_{3} }} $ there, suggesting that the biochemical recycling processes (remineralization of PN coupled to nitrification, and assimilation of NO₃ ^?-N back to PN) played dominant roles in the instream nitrogen transformation. In the brackish zone of both rivers, the $ \delta^{15} {\text{N}}_{{{\text{NO}}_{3} }} $ displayed a declining trend while the $ \delta^{18} {\text{O}}_{{{\text{NO}}_{3} }} $ increased sharply. The redox cycling of NO₃ ^?/NO₂ ^? and/or deposition of atmospheric nitrogen oxides may have been the major controlling factor for the estuarine $ \delta^{15} {\text{N}}_{{{\text{NO}}_{3} }} $ and $ \delta^{18} {\text{O}}_{{{\text{NO}}_{3} }} $ , however, the exact mechanism behind the observed trends is currently unresolved.     

Studies on mass attenuation coefficient, effective atomic number and electron density of some vitamins

Mass attenuation coefficient, $ \mu_{m} $ , atomic cross-section, $ \sigma_{i} $ , electronic cross-section, $ \sigma_{e} $ , effective atomic number, $ Z_{\text{eff}} $ and effective electron density, $ N_{\text{el}} $ , were determined experimentally and theoretically for some vitamins (retinol, beta-carotene, thiamine, riboflavin, niacinamide, pantothenic acid, pyridoxine, biotin, folic acid, cyanocobalamin, ascorbic acid, cholecalciferol, alpha-tocopherol, ketamine, hesperidin) at 30.82, 59.54, 80.99, 356.61, 661.66 and 1,408.01?keV photon energies using a NaI(Tl) scintillation detector. The theoretical mass attenuation coefficients were estimated using mixture rules. The calculated values were compared with the experimental values for all vitamins.     

Quantifying the risk of mis-estimating correlation significance of climate–tree growth relationships

In dendroecology, sampling effort has a strong influence of both regional chronology properties and climate–tree growth relationships assessment. Recent studies evidenced that decreasing sample size leads to a weakening of the bootstrapped correlation coefficients ( ${\text{BCC}}$ BCC ). The present analysis focused on the risk of mis-estimating the significance of population ${\text{BCC}}\,\left( {{\text{BCC}}_{\text{POP}} } \right)$ BCC ( BCC POP ) from a sample of N trees, and then proposed an approach to detect and correct mis-estimations using the properties of the sample. The sample size effect and the limits of the correction were illustrated from 840 individual growth chronologies of Corsican pine (Pinus nigra Arnold ssp. laricio Poiret var. Corsicana) sampled in Western France. The 840 trees were used to assess the population characteristics, and the effect of sampling effort was investigated through a simulation approach based on a resampling procedure of N trees amongst 840 (N ? [5; 50]). Our results evidenced that the risk strongly varied amongst the climatic regressors. The highest risks were evidenced for significant ${\text{BCC}}_{\text{POP}}$ BCC POP , with a percentage of mis-estimation ranging from 25 to 80. On the contrary, small samples allowed providing an reliable estimation of the significance of non-significant ${\text{BCC}}_{\text{POP}}$ BCC POP . To a lesser extent, the risk slightly decreased with increasing N, according to a negative exponential trend. The detection and correction method was found relevant to detect mis-estimation only for significant ${\text{BCC}}_{\text{POP}}$ BCC POP ; otherwise, the ${\text{BCC}}_{\text{POP}}$ BCC POP significance was generally overestimated.     

Topological classification and enumeration of RNA structures by genus

To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer–Zagier, we compute the generating function $\mathbf{D}_{g,\sigma }(z)=\sum _{n}\mathbf{d}_{g,\sigma }(n)z^n$ for the number $\mathbf{d}_{g,\sigma }(n)$ of those structures of fixed genus $g$ and minimum stack size $\sigma $ with $n$ nucleotides so that no two consecutive nucleotides are basepaired and show that $\mathbf{D}_{g,\sigma }(z)$ is algebraic. In particular, we prove that $\mathbf{d}_{g,2}(n)\sim k_g\,n^{3(g-\frac{1}{2})} \gamma _2^n$ , where $\gamma _2\approx 1.9685$ . Thus, for stack size at least two, the genus only enters through the sub-exponential factor, and the slow growth rate compared to the number of RNA molecules implies the existence of neutral networks of distinct molecules with the same structure of any genus. Certain RNA structures called shapes are shown to be in natural one-to-one correspondence with the cells in the Penner–Strebel decomposition of Riemann’s moduli space of a surface of genus $g$ with one boundary component, thus providing a link between RNA enumerative problems and the geometry of Riemann’s moduli space.     

Provenance variation and genetic parameters of Eucalyptus viminalis in Argentina

Genetic parameters for growth, stem straightness, pilodyn penetration, relative bark thickness and survival were estimated in a base-population of five open-pollinated provenance/progeny trials of Eucalyptus viminalis. The trials, located in northern, central and southern Buenos Aires Province, Argentina, comprised 148 open-pollinated families from 13 Australian native provenances and eight local Argentinean seedlots. The Australian native provenances come from a limited range of the natural distribution. Overall survival, based on the latest assessment of each trial, was 62.4%. Single-site analyses showed that statistically significant provenances differences (p?<?0.05) for at least one of the studied traits in three out of the five trials analyzed. The local land race performed inconsistently in this study. The average narrow-sense individual-tree heritability estimate $ \left( {{{\hat{h}}^2}} \right) $ was 0.27 for diameter and 0.17 for total height. Values of $ {\hat{h}^2} $ also increased with age. Pilodyn penetration, assessed at only one site, was more heritable $ \left( {{{\hat{h}}^2} = 0.32} \right) $ than the average of growth traits. Estimated individual-tree heritabilities were moderate to low for stem straightness (average of 0.20) and relative bark thickness (0.16). The estimated additive genetic correlations $ \left( {{{{r}}_{{A}}}} \right) $ between diameter and height were consistently high and positive ( $ {{r}_{^A}} $ average of 0.90). High additive genetic correlations were observed between growth variables and pilodyn penetration ( $ {{r}_{^A}} $ average of 0.58). Relative bark thickness showed a negative correlation with diameter $ \left( {{{{r}}_{^A}} = - 0.39} \right) $ and height $ \left( {{{{r}}_{^A}} = - 0.51} \right) $ . The average estimated additive genetic correlation between sites was high for diameter (0.67). The implications of all these parameter estimates for genetic improvement of E. viminalis in Argentina are discussed.     

A Within-Host Virus Model with Periodic Multidrug Therapy

This paper is devoted to the investigation of the effects of periodic drug treatment on a standard within-host virus model. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable, and the disease eventually disappears if $\mathcal{R}_{0} < 1$ , while there exists at least one positive periodic state and the disease persists when $\mathcal{R}_{0}>1$ . We also consider an optimization problem by shifting the phase of these drug efficacy functions. It turns out that shifting the phase can certainly affect the stability of the infection free steady state. A numerical study is performed to illustrate our analytic results.     

Obtain Quadruple Intense Plasmonic Resonances from Multilayered Gold Nanoshells by Silver Coating: Application in Multiplex Sensing

Four intense and separate localized surface plasmon resonance (LSPR) absorption peaks have been obtained in the gold-dielectric–gold–silver multilayer nanoshells. The silver coating on the gold shell results in a new LSPR peak at about 400 nm corresponding to the $ {{\left| {\omega_{+}^{-}} \right\rangle}_{Ag }} $ mode. The intense local electric field concentrated in the silver shell at the wavelength of 400 nm indicates that this new plasmonic band is coming from the symmetric coupling between the antibonding silver shell plasmon mode and the inner sphere plasmon. Increasing the silver shell thickness also leads to the intensity increasing of the $ {{\left| {\omega_{+}^{-}} \right\rangle}_{Au }} $ mode and blue shift of $ \left| {\omega_{-}^{+}} \right\rangle $ and $ \left| {\omega_{-}^{-}} \right\rangle $ modes. Therefore, quadruple intense plasmonic resonances in the visible region could be achieved in gold-dielectric–gold–silver multilayer nanoshells by tuning the geometrical parameters. And the quadruple intense plasmonic resonances in the visible region provide well potential for multiplex biosensing based on LSPR.     

Cherry Picking: A Characterization of the Temporal Hybridization Number for a Set of Phylogenies

Recently, we have shown that calculating the minimum–temporal-hybridization number for a set ${\mathcal{P}}$ of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when ${\mathcal{P}}$ consists of exactly two trees. In this paper, we give the first characterization of the problem for ${\mathcal{P}}$ being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence. Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimum–temporal hybridization number for two trees is fixed-parameter tractable.     

Stress fermentation strategies for the production of hyperthermostable superoxide dismutase from Thermus thermophilus HB27: effects of ions

In this study, we explored how ammonium and metal ion stresses affected the production of recombinant hyperthermostable manganese superoxide dismutase (Mn-SOD). To improve Mn-SOD production, fed-batch culture in shake flasks and bioreactor fermentation were undertaken to examine the effects of $ {\text{NH}}_{ 4}^{{^{ + } }} $ and Mn²⁺ feeding. Under the optimized feeding time and concentrations of $ {\text{NH}}_{ 4}^{{^{ + } }} $ and Mn²⁺, the maximal SOD activity obtained from bioreactor fermentation reached some 480 U/ml, over 4 times higher than that in batch cultivation (113 U/ml), indicating a major enhancement of the concentration of Mn-SOD in the scale-up of hyperthermostable Mn-SOD production. In contrast, when the fed-batch culture with appropriate $ {\text{NH}}_{ 4}^{{^{ + } }} $ and Mn²⁺ feeding was carried out in the same 5-L stirred tank bioreactor, a maximal SOD concentration of some 450 U/ml was obtained, again indicating substantial increase in SOD activity as a result of $ {\text{NH}}_{ 4}^{{^{ + } }} $ and Mn²⁺ feeding. The isoelectric point (pI) of the sample was found to be 6.2. It was highly stable at 90 °C and circular dichroism measurements indicated a high α-helical content of 70 % as well, consistent with known SOD properties. This study indicates that $ {\text{NH}}_{ 4}^{{^{ + } }} $ and Mn²⁺ play important roles in Mn-SOD expression. Stress fermentation strategies established in this study are useful for large-scale efficient production of hyperthermostable Mn-SOD and may also be valuable for the scale-up of other extremozymes.     

When does pathogen evolution maximize the basic reproductive number in well-mixed host–pathogen systems?

Pathogen evolution towards the largest basic reproductive number, $\mathcal R _0$ , has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host–pathogen systems have defined general conditions under which $\mathcal R _0$ maximization occurs in terms of $\mathcal R _0$ itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host–pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes $\mathcal R _0$ . Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when $\mathcal R _0$ maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent $\mathcal R _0$ maximization.