Weak Allee effect in a predator–prey model involving memory with a hump

In this paper we consider a predator–prey system which has a factor that allows for a reduction in fitness due to declining population sizes, often termed an Allee effect. We study the influence of the weak Allee effect which is included in the prey equation and we determine conditions for the occurrence of Hopf bifurcation. The prey population is limited by the carrying capacity of the environment, and the predator growth rate depends on past quantities of the prey which is represented by a weight function that specifies a moment in the past when the quantity of food is the most important from the point of view of the present growth of the predator. The stability properties of the system and the biological issues of the memory and Allee effect on the coexistence of the two species are studied. Finally we present some simulations to verify the veracity of the analytical conclusions.     

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Re _λ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.     

A cryptosystem based on cellular automata

Cryptosystems for binary information are based on two primitives: an indexed family of permutations of binary words and a generator of pseudorandom sequences of indices. A very efficient implementation of the primitives is constructed using the phenomenon of synchronization in cellular automata. (c) 1998 American Institute of Physics.     

Synchronization of cellular automaton pairs

The phenomenon of synchronization in pairs of cellular automata coupled in a driver-replica mode is studied. Necessary and sufficient conditions for synchronization in linear cellular automaton pairs are given. The couplings that make a pair synchronize are determined for all linear elementary cellular automata. (c) 1998 American Institute of Physics.     

Monitoring Tyrosinase Expression in Non‐metastatic and Metastatic Melanoma Tissues by Scanning Electrochemical Microscopy

Although tremendous progress has been made in the diagnosis of melanoma, the identification of different stages of malignancy in a reliable way remains challenging. Current strategies rely on optical monitoring of the concentration and spatial distribution of specific biomarkers. State‐of‐the‐art optical methods can be affected by background‐color interference and autofluorescence. We overcame these shortcomings by employing scanning electrochemical microscopy (SECM) to map the prognostic indicator tyrosinase (TyR) in non‐metastatic and metastatic melanoma tissues by using soft‐stylus microelectrodes. Electrochemical readout of the TyR distribution was enabled by adapting an immunochemical method. SECM can overcome the limitations of optical methods and opens unprecedented possibilities for improved diagnosis and understanding of the spatial distribution of TyR in different melanoma stages.     

Cavity-Directed Synthesis of Labile Polyoxometalates for Catalysis in Confined Spaces

The artificial microenvironments inside coordination cages have gained significant attention for performing enzyme-like catalytic reactions by facilitating the formation of labile and complex molecules through a “ship-in-a-bottle” approach. Despite many fascinating examples, this approach remains scarcely explored in the context of synthesizing metallic clusters such as polyoxometalates (POMs). The development of innovative approaches to control and influence the speciation of POMs in aqueous solutions would greatly advance their applicability and could ultimately lead to the formation of elusive clusters that cannot be synthesized by using traditional methods. In this study, we employ host–guest stabilization within a coordination cage to enable a novel cavity-directed synthesis of labile POMs in aqueous solutions under mild conditions. The elusive Lindqvist [M₆O₁₉]²⁻ (M=Mo or W) POMs were successfully synthesized at room temperature via the condensation of molybdate or tungstate building blocks within the confined cavity of a robust and water-soluble Pt₆L₄(NO₃)₁₂ coordination cage. Importantly, the encapsulation of these POMs enhances their stability in water, rendering them efficient catalysts for environmentally friendly and selective sulfoxidation reactions using H₂O₂ as a green oxidant in a pure aqueous medium. The approach developed in this paper offers a means to synthesize and stabilize the otherwise unstable metal-oxo clusters in water, which can broaden the scope of their applications.     

Comparative study of pattern correlation using Mexican hat and Coiflet wavelet-based filtering

In this work, a numerical study on the pattern correlation using wavelet filters is reported. A comparative study of the correlation using the Mexican hat and Coiflets filters is presented. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. Therefore, unlike the Mexican hat-based filter which acts only as a pass-band filter, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of the original image. Each one of the original images can be discomposed in an average image and several detail images at different levels of multiresolution. We study the numerical correlation between binary patterns using the Mexican hat filter and the first and second multiresolution level obtained by Coiflet filtering. Additionally, an analysis about the noise immunity for the Mexican hat and Coiflet filters is realized. The results show that Coiflet filters are better to identify special characteristics but perform the worst when they are used with noisy images. On the other side, the Mexican filter presents a better noise immunity but performs the worst when is used to compare special characteristics.     

Diffraction aperture non-ideal behaviour of air coupled transducers array elements designed for NDT

Air coupled piezoelectric ultrasonic array transducers are a novel tool that could lead to interesting advances in the area of non-contact laminar material testing using Lamb wave's propagation techniques. A key issue on the development of such transducers is their efficient coupling to air media (impedance mismatch between the piezoelectric material and air is 90 dB or more). Adaptation layers are used in order to attain good matching and avoid possible serious signal degradation. However, the introduction of these matching layers modify the transducer surface behaviour and, consequently, radiation characteristics are altered, making the usual idealization criteria (of uniform surface movement) adopted for field simulation purposes inaccurate. In our system, we have a concave linear-array transducer of 64 elements (electrically coupled by pairs) working at 0.8 MHz made of PZ27 rectangular piezoceramics (15 mm x 0.3 mm) with two matching layers made of polyurethane and porous cellulose bonded on them. Experimental measurements of the acoustic aperture of single excited array elements have shown an increment on the geometrical dimensions of its active surface. A sub-millimeter vibrometer laser scan has revealed an extension of the aperture beyond the supposed physical single array element dimensions. Non-uniform symmetric apodized velocity surface vibration amplitude profile with a concave delay contour indicates the presumed existence of travelling wave phenomena over the surface of the outer array matching layer. Also, asymptotic propagation velocities around 2500 m/s and attenuation coefficient between 15 and 20 dB/mm has been determined for the travelling waves showing clear tendencies. Further comparisons between the experimental measurements of single array element field radiation diagram and simulated equivalent aperture counterpart reveal good agreement versus the ideal (uniform displaced) rectangular aperture. For this purpose an Impulse Response Method (IRM) has been used.     

Mechanical, chemical and acoustic properties of new hybrid ceramic-polymer varnishes for musical instruments

Novel ceramic-polymer hybrid varnishes were designed to protect the wood surface of musical instruments. These hybrid coatings consist of chemically functionalized silica nanoparticles and synthetic solvent-based acrylic- and alkyd-polyurethanes. The nanoparticles were added to increase the abrasion resistance. An alkoxide was used to increase the number and reactivity of OH’s groups on the wood surface improving the adhesion with the coating through a chemical link between them. The properties of the synthetic coatings were compared with those of a traditional varnish (based on alcohol and natural resins) to obtain a better performance. Two types of woods were used: maple and spruce. The samples were characterized by UV-Vis, mechanical and abrasion tests, water’s absorption, acoustic properties, chemical resistance and SEM.     

On ≤k-Edges, Crossings, and Halving Lines of Geometric Drawings of K n

Let P be a set of points in general position in the plane. Join all pairs of points in P with straight line segments. The number of segment-crossings in such a drawing, denoted by $\operatorname {cr}(P)$ , is the rectilinear crossing number of P. A halving line of P is a line passing through two points of P that divides the rest of the points of P in (almost) half. The number of halving lines of P is denoted by h(P). Similarly, a k-edge, 0??k??n/2?1, is a line passing through two points of P and leaving exactly k points of P on one side. The number of ??k-edges of P is denoted by E _??k (P). Let $\overline {\mathrm {cr}}(n)$ , h(n), and E _??k (n) denote the minimum of $\operatorname {cr}(P)$ , the maximum of h(P), and the minimum of E _??k (P), respectively, over all sets P of n points in general position in the plane. We show that the previously best known lower bound on E _??k (n) is tight for k<?(4n?2)/9? and improve it for all k???(4n?2)/9?. This in turn improves the lower bound on $\overline {\mathrm {cr}}(n)$ from $0.37968\binom{n}{4}+\varTheta (n^{3})$ to $\frac{277}{729}\binom{n}{4}+\varTheta (n^{3})\geq 0.37997\binom{n}{4}+\varTheta (n^{3})$ . We also give the exact values of $\overline {\mathrm {cr}}(n)$ and h(n) for all n??27. Exact values were known only for n??18 and odd n??21 for the crossing number, and for n??14 and odd n??21 for halving lines.