Power allocation strategies for distributed space-time codes in two-way relay networks

We study a two-way relay network (TWRN), where distributed space-time codes are constructed across multiple relay terminals in an amplify-and-forward mode. Each relay transmits a scaled linear combination of its received symbols and their conjugates,with the scaling factor chosen based on automatic gain control. We consider equal power allocation (EPA) across the relays, as well as the optimal power allocation (OPA) strategy given access to instantaneous channel state information (CSI). For EPA, we derive an upper bound on the pairwise-error-probability (PEP), from which we prove that full diversity is achieved in TWRNs. This result is in contrast to one-way relay networks, in which case a maximum diversity order of only unity can be obtained. When instantaneous CSI is available at the relays, we show that the OPA which minimizes the conditional PEP of the worse link can be cast as a generalized linear fractional program, which can be solved efficiently using the Dinkelback-type procedure.We also prove that, if the sum-power of the relay terminals is constrained, then the OPA will activate at most two relays.

PDB-Explorer: a web-based interactive map of the protein data bank in shape space

Background The RCSB Protein Data Bank (PDB) provides public access to experimentally determined 3D-structures of biological macromolecules (proteins, peptides and nucleic acids). While various tools are available to explore the PDB, options to access the global structural diversity of the entire PDB and to perceive relationships between PDB structures remain very limited. Methods A 136-dimensional atom pair 3D-fingerprint for proteins (3DP) counting categorized atom pairs at increasing through-space distances was designed to represent the molecular shape of PDB-entries. Nearest neighbor searches examples were reported exemplifying the ability of 3DP-similarity to identify closely related biomolecules from small peptides to enzyme and large multiprotein complexes such as virus particles. The principle component analysis was used to obtain the visualization of PDB in 3DP-space. Results The 3DP property space groups proteins and protein assemblies according to their 3D-shape similarity, yet shows exquisite ability to distinguish between closely related structures. An interactive website called PDB-Explorer is presented featuring a color-coded interactive map of PDB in 3DP-space. Each pixel of the map contains one or more PDB-entries which are directly visualized as ribbon diagrams when the pixel is selected. The PDB-Explorer website allows performing 3DP-nearest neighbor searches of any PDB-entry or of any structure uploaded as protein-type PDB file. All functionalities on the website are implemented in JavaScript in a platform-independent manner and draw data from a server that is updated daily with the latest PDB additions, ensuring complete and up-to-date coverage. The essentially instantaneous 3DP-similarity search with the PDB-Explorer provides results comparable to those of much slower 3D-alignment algorithms, and automatically clusters proteins from the same superfamilies in tight groups. Conclusion A chemical space classification of PDB based on molecular shape was obtained using a new atom-pair 3D-fingerprint for proteins and implemented in a web-based database exploration tool comprising an interactive color-coded map of the PDB chemical space and a nearest neighbor search tool. The PDB-Explorer website is freely available at www.​cheminfo.​org/​pdbexplorer and represents an unprecedented opportunity to interactively visualize and explore the structural diversity of the PDB.

Generalized synchronization in relay systems with instantaneous coupling

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.