The Combined Effect of Connectivity and Dependency Links on Percolation of Networks

Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P <sub>∞</sub>, is given by P<sub>￥</sub>=p<sup>s-1</sup>[1-exp(-[`(k)]pP_￥) ]^sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks and find a formula for the size of the giant component in the percolation process: P _∞=p ^s−1(1−r ^k ) ^s where r is the solution of r=p ^s (r ^k−1−1)(1−r ^k )+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]<sub>min</sub>\bar{k}_{\min}, such that an ER network with [`(k)] ￡ [`(k)]_min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network.     

Beyond Equal-Power Sparse NOMA: Two User Classes and Closed-Form Bounds on the Achievable Region

Non-orthogonal multiple access (NOMA) is a promising technology for future beyond-5G wireless networks, whose fundamental information-theoretic limits are yet to be fully explored. Considering regular sparse code-domain NOMA (with a fixed and finite number of orthogonal resources allocated to any designated user and vice versa), this paper extends previous results by the authors to a setting comprising two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived and comparatively investigated in extreme-SNR regimes. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI. Valuable insights are provided into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge and cell-center users. The conditions for superior performance over dense code-domain NOMA (taking the form of randomly spread code-division multiple access), as well as a relatively small gap to the ultimate performance limits, are identified. The proposed bounds are also applicable for the analysis of interference networks, e.g., Wyner-type cellular models.     

A note on conjugate gradient convergence – Part II

Summary. Continuing our previous analysis, we derive the exact number of conjugate gradient iterations needed (to achieve a given tolerance) for the one-dimensional discrete Poisson equation on a uniform grid, and a particularly smooth solution vector. Received July 29, 1998 / Published online March 16, 2000     

Investigation of phase coupling phenomena in sustained portion of musical instruments sound

This work investigates aperiodicities that occur in the sustained portion of a sound of musical instrument played by a human player, due to synchronous versus asynchronous deviations of the partial phases. By using an additive sinusoidal analysis, phases of individual partials are precisely extracted and their correlation statistics and coupling effects are analyzed. It is shown that various musical instruments exhibit different phase coupling characteristics. The effect of phase coupling is compared to analysis by means of higher order statistics and it is shown that both methods are closely mathematically related. Following a detailed analysis of phase coupling for various musical instruments it is suggested that phase coupling is an important characteristic of a sustained portion of sound of individual musical instruments, and possibly even of instrumental families. Interesting differences in phase deviations where found for the flute, trumpet and cello. For the cello, the effect of vibrato is examined by comparing the analysis of a closed string sound played with a natural vibrato to analysis of an open string sound that contains no vibrato. Following, a possible model for phase deviations in the cello is presented and a simulation of phase fluctuations for this model is performed.     

Preparation and Characterization of Uniform Near IR Polystyrene Nanoparticles

Biomaterials for in vivo fluorescence imaging are required to be biocompatible, nontoxic, photostable and highly fluorescent. Fluorescence must be in the near infrared (NIR) region of the electromagnetic spectrum to avoid absorption and autofluorescence of endogenous tissues. NIR fluorescent polystyrene nanoparticles may be considered ideal biomaterials for in vivo imaging applications. These NIR nanoparticles were prepared by a swelling process of polystyrene template nanoparticles with a hydrophobic NIR dye dissolved in a water‐miscible swelling solvent, a method developed for preparation of nonbiodegradable nanoparticles, for NIR fluorescent bioimaging applications. This method overcomes common problems that occur with dye entrapment during nanoparticle formation such as loss of fluorescence and size polydispersity. Fluorescence intensity of the nanoparticles was found to be size dependent, and was optimized for differently sized nanoparticles. The resulting NIR nanoparticles were also found to be more fluorescent and highly photostable compared to the free dye in solution, showing their potential as biomaterials for in vivo fluorescence imaging.     

Engineering of superhydrophobic silica microparticles and thin coatings on polymeric films by ultrasound irradiation

Superhydrophobic coatings are one of the recent hot topics in industrial applications as well as academic studies. The mimicking lotus leaves' superhydrophobic properties have been successfully transferred to real-life applications. However, the current preparation methods used to obtain superhydrophobic coatings are still complex, commonly are not transparent and/or not durable.In the present study, a new relatively simple way to prepare superhydrophobic coatings on polymeric films is described. First, superhydrophobic silica microparticles (MPs) were synthesized by fluorination of SiO₂ MPs produced by a modified Stöber method. Briefly, tetraethyl orthosilicate was polymerized in an ethanol/water continuous phase under basic conditions, and the resultant SiO₂ MPs were dispersed in heptane as a continuous phase and reacted with 1H,1H,2H,2H-perfluorododecyltrichlorosilane (FTS) to yield FTS-SiO₂ MPs, which were dried and dispersed in decane. Superhydrophobic thin coatings were then produced by a ‘throwing stones’ sonication technique and deposited onto polycarbonate, polypropylene, polyethylene, and polyurethane films. The coatings are durable, may be transparent, and exhibit self-cleaning properties for the specific practical applications. The MPs and coated polymeric films were characterized by dynamic light scattering, high-resolution scanning electron microscopy, water contact and sliding angle measurements, and infrared and x-ray photoelectron spectroscopy. This ultrasound-assisted coating process may be upscaled and applied to many polymeric films, for instance polymethyl methacrylate, polystyrene, and polyvinyl chloride. Various applications are envisaged, including but not limited to self-cleaning windows, anti-sticking of snow to antennas and windows, solar panels, roof tiles, agricultural applications, corrosion resistance, and anti-biofouling.     

Photochromism of side-chain liquid crystal polymers containing spironaphthoxazines

Side-chain liquid crystal polyacrylates and polysiloxanes containing different photochromic spironaphthoxazine side groups were synthesized. Thermodynamic, spectral and kinetic properties of the polymers were investigated. The structure of the mesophase is discussed.     

Specific hemoperfusion through agarose acrobeads

Agarose acrobeads were produced by encapsulating polyacrolein microspheres (acrobeads) of 0.2 μm average diameter within an agarose matrix. Crosslinked agarose acrobeads of diameters ranging from 0.5 to 0.8 mm were found to be optimal spheres for specific hemoperfusion purposes. Agarose provides the biocompatibility and mechanical strength of the agarose acrobeads. Acrobeads contain a high aldehyde-group content through which various amino ligands, i.e., proteins, antigens, antibodies, enzymes, and so on, can be covalently bound in a single step under physiological pH (or other pH). Thus, antibodies, antigens, or toxic materials may be directly removed from whole blood by hemoperfusion. During in vitro and in vivo hemoperfusion trials, the content of erythrocytes, leukocytes, and thrombocytes was essentially unaltered. Likewise, a battery of the soluble blood components (Cl^-, K⁺, Na⁺, Ca²⁺, PO ₄ ^- ), total proteins, albumin, and C ₄ ^′ component of the complement cascade, as well as the enzymes SGOT, LDH, and alkaline phosphatase, remained constant within narrow limits during the hemoperfusion procedure. The chemical and physical structure of the beads is stable; neither acrolein nor bead fragments were detected in hemoperfusion trials. Similarly, leakage of antibody bound to the agarose acrobeads into the blood is insignificant. Thus far, we have demonstrated the efficacy of the crosslinked agarose acrobeads for extracorporeal removal of “unwanted” substances from whole blood in the following systems: (a) removal of specific antigens (digoxin or paraquat removal with antidigoxin or antiparaquat antibodies bound to the acrobeads, respectively), (b) removal of specific antibody (antiBSA) removal with BSA bound to the beads), (c) removal of immune complexes (BSA-antiBSA complex removal with C1q bound to acrobeads), and (d) removal of specific metals (removal of iron with deferoxamine bound to the agarose acrobeads).     

Controlled amine functionality in self-assembled monolayers via the hidden amine route: chemical and electronic tunability

A synthetic strategy for fabricating a dense amine functionalized self-assembled monolayer (SAM) on hydroxylated surfaces is presented. The assembly steps are monitored by X-ray photoelectron spectroscopy, Fourier transform infrared- attenuated total reflection, atomic force microscopy, variable angle spectroscopic ellipsometry, UV-vis surface spectroscopy, contact angle wettability, and contact potential difference measurements. The method applies alkylbromide-trichlorosilane for the fabrication of the SAM followed by surface transformation of the bromine moiety to amine by a two-step procedure: S(N)2 reaction that introduces the hidden amine, phthalimide, followed by the removal of the protecting group and exposing the free amine. The use of phthalimide moiety in the process enabled monitoring the substitution reaction rate on the surface (by absorption spectroscopy) and showed first-order kinetics. The simplicity of the process, nonharsh reagents, and short reaction time allow the use of such SAMs in molecular nanoelectronics applications, where complete control of the used SAM is needed. The different molecular dipole of each step of the process, which is verified by DFT calculations, supports the use of these SAMs as means to tune the electronic properties of semiconductors and for better synergism between SAMs and standard microelectronics processes and devices.