Development of designed site-directed pseudopeptide-peptido-mimetic immunogens as novel minimal subunit-vaccine candidates for malaria

Synthetic vaccines constitute the most promising tools for controlling and preventing infectious diseases. When synthetic immunogens are designed from the pathogen native sequences, these are normally poorly immunogenic and do not induce protection, as demonstrated in our research. After attempting many synthetic strategies for improving the immunogenicity properties of these sequences, the approach consisting of identifying high binding motifs present in those, and then performing specific changes on amino-acids belonging to such motifs, has proven to be a workable strategy. In addition, other strategies consisting of chemically introducing non-natural constraints to the backbone topology of the molecule and modifying the α-carbon asymmetry are becoming valuable tools to be considered in this pursuit. Non-natural structural constraints to the peptide backbone can be achieved by introducing peptide bond isosters such as reduced amides, partially retro or retro-inverso modifications or even including urea motifs. The second can be obtained by strategically replacing L-amino-acids with their enantiomeric forms for obtaining both structurally site-directed designed immunogens as potential vaccine candidates and their Ig structural molecular images, both having immuno-therapeutic effects for preventing and controlling malaria.     

Tomographic Representation of Electrocardiogram Signals

We consider signals of an arbitrary nature in the tomographic representation and compare their tomographic representation and the fractional Fourier transform. Also we illustrate how to apply the tomograms and the identical Radon transform for processing medical electrocardiogram (ECG) signals. The first results obtained show that, in contrast to routine Fourier analysis, the Radon transform revealed additional information for patients with early signs of ischemic heart disease (IHD) compared to healthy persons.     

Modeling of vertical external cavity semiconductor laser with MQW resonant structure

Numerical model is developed for modeling pulsed operation of a vertical external cavity semiconductor laser (VECSEL) with a resonant gain structure. Properties of optical modes for compound resonator formed by Bragg reflector, chip boundary and external spherical mirror were studied. For above threshold operation carrier density in each of quantum wells (QW) obeys non-linear diffusion equation with a source supplied by electron-hole pairs generated in barrier layers by pump radiation or fast electron beam. A new iteration procedure for round-trip operator evaluation was developed, which provides linear growth of computation time with the number of QWs. Results of numerical simulations are reported for a VECSEL comprising 25 QW in resonant configuration and the output spherical mirror with curvature radius 3 cm. Variation of distance to the external mirror is found to result in notable changes in power and optical quality of the output beam. The decisive role of gain and index non-linearity in these changes is identified. A range of values of distance to external mirror is found where iterative procedure does not converge. In another range, the resulting solution depends on the initial conditions for the iteration procedure.     

Spanning Connectivity of the Power of a Graph and Hamilton-Connected Index of a Graph

Let G = (V, E) be a connected graph. The hamiltonian index h(G) (Hamilton-connected index hc(G)) of G is the least nonnegative integer k for which the iterated line graph L ^k (G) is hamiltonian (Hamilton-connected). In this paper we show the following. (a) If |V(G)| ≥ k + 1 ≥ 4, then in G ^k , for any pair of distinct vertices {u, v}, there exists k internally disjoint (u, v)-paths that contains all vertices of G; (b) for a tree T,  h(T) ≤ hc(T) ≤ h(T) + 1, and for a unicyclic graph G,  h(G) ≤ hc(G) ≤ max{h(G) + 1, k′ + 1}, where k′ is the length of a longest path with all vertices on the cycle such that the two ends of it are of degree at least 3 and all internal vertices are of degree 2; (c) we also characterize the trees and unicyclic graphs G for which hc(G) = h(G) + 1.     

Neighborhood Union Conditions for Hamiltonicity of P 3-Dominated Graphs

As an extension of quasi claw-free graphs, the class of P ₃-dominated graphs has been introduced by Broersma and Vumar (Math Methods Oper Res 69:297–306, 2009). For a noncomplete graph G, the number NC and NC ₂ are defined as \({NC=\min\{|N(x)\cup N(y)|: x,y\in V(G) {\rm and} xy\notin E(G)\}\, {\rm and} NC_2=\min\{|N(x)\cup N(y)|: x,y\in V(G)\, {\rm and}\, d(x,y)=2 \}}\) , respectively. For a complete graph G, set \({NC=NC_{2}=|V(G)|-1}\) . In this paper, we prove that a 2-connected P ₃-dominated graph of order n is traceable if \({NC\geq (n-2)/2}\) . Moreover, we prove that a 3-connected P ₃-dominated graph of order n is hamiltonian if \({NC_2\geq (2n-6)/3}\) . Our results extend some previous results on claw-free graphs.     

Time Reversal and Tomographic Representation for Signal Processing in Living Systems

The tomographic representation for signal processing opens new opportunities for studies of living system signals. Some signals can be described by functions of time f(t), which are approximately connected with each other by reversing of time. In this case, there is a possibility to observe transformation of tomograms for such functions. We obtain the correspondence of tomograms for functions f(t) and f(?t) in the vicinity of the frequency scale and illustrate by the examples of electric impedance of rat femoral artery pulsing in two different modes. We show that the use of a reference signal for signal processing of living systems provides new opportunities for employing both – their standard Fourier transforms and tomograms – to obtain new additional and useful information.

     

Hyperelliptic jacobians with real multiplication

Let K be a field of characteristic p≠2, and let f(x) be a sextic polynomial irreducible over K with no repeated roots, whose Galois group is isomorphic to A₅. If the jacobian J(C) of the hyperelliptic curve C:y²=f(x) admits real multiplication over the ground field from an order of a real quadratic field D, then either its endomorphism algebra is isomorphic to D, or p>0 and J(C) is a supersingular abelian variety. The supersingular outcome cannot occur when p splits in D.     

Degree bounds for the circumference of 3‐connected graphs

Let C be a longest cycle in the 3‐connected graph G and let H be a component of G ? V(C) such that |V(H)| ≥ 3. We supply estimates of the form |C| ≥ 2d(u) + 2d(v) ? α(4 ≤ α ≤ 8), where u,v are suitably chosen non‐adjacent vertices in G. Also the exceptional classes for α = 6,7,8 are characterized. © 2005 Wiley Periodicals, Inc. J Graph Theory