Localization of compact invariant sets and global stability in analysis of one tumor growth model

In this paper, we study some features of global behavior of the four‐dimensional superficial bladder cancer model with Bacillus Calmette‐Guérin (BCG) immunotherapy described by Bunimovich‐Mendrazitsky et al. in 2007 with the help of localization analysis of its compact invariant sets. Its dynamics is defined by the BCG treatment and by densities of three cells populations: effector cells, tumor infected cells by BCG, and tumor uninfected cells. We find upper bounds for ultimate dynamics of the whole state vector in the positive orthant and also under condition that there are no uninfected tumor cells. Further, we prove the existence of the bounded positively invariant domain in both of these two situations. Finally, by using these assertions, we derive our main result: sufficient conditions of global asymptotic stability of the tumor‐free equilibrium point in the positive orthant. Copyright © 2013 John Wiley & Sons, Ltd.     

FRET detection of Octamer-4 on a protein nanoarray made by size-dependent self-assembly

An alternative approach for fabricating a protein array at nanoscale is suggested with a capability of characterization and/or localization of multiple components on a nanoarray. Fluorescent micro- and nanobeads each conjugated with different antibodies are assembled by size-dependent self-assembly (SDSA) onto nanometer wells that were created on a polymethyl methacrylate (PMMA) substrate by electron beam lithography (EBL). Antibody-conjugated beads of different diameters are added serially and electrostatically attached to corresponding wells through electrostatic attraction between the charged beads (confirmed by zeta potential analysis) and exposed p-doped silicon substrate underneath the PMMA layer. This SDSA method is enhanced by vibrated-wire-guide manipulation of droplets on the PMMA surface containing nanometer wells. Saturation rates of antibody-conjugated beads to the nanometer patterns are up to 97% under one component and 58–70% under two components nanoarrays. High-density arrays (up to 40,000 wells) could be fabricated, which can also be multi-component. Target detection utilizes fluorescence resonance energy transfer (FRET) from fluorescent beads to fluorescent-tagged secondary antibodies to Octamer-4 (Oct4), which eliminates the need for multiple steps of rinsing. The 100 nm green beads are covalently conjugated with anti-Oct4 to capture Oct4 peptides (39 kDa); where the secondary anti-Oct4 and F(ab)₂ fragment of anti-gIgG tagged with phycoerythrin are then added to function as an indicator of Oct4 detection. FRET signals are detected through confocal microscopes, and further confirmed by Fluorolog3 spectrofluorometer. The success rates of detecting Oct4 are 32% and 14% of the beads in right place under one and two component nanoarrays, respectively. Ratiometric FRET is used to quantify the amount of Oct4 peptides per each bead, which is estimated about 2 molecules per bead.     

Polynomial and regular images of ℝ n

We obtain new necessary conditions for ann-dimensional semialgebraic subset of ℝ ⁿ to be a polynomial image of ℝ ⁿ . Moreover, we prove that a large family of planar bidimensional semialgebraic sets with piecewise linear boundary are images of polynomial or regular maps, and we estimate in both cases the dimension of their generic fibers. Supported by Spanish GAAR BFM2002-04797 and European RAAG HPRN-CT-2001-00271.     

An algorithm to compute odd orders and ramification indices of cyclic actions on compact surfaces

In this paper we get an effective algorithm to compute all odd orders and ramification indices of homeomorphisms acting on compact surfaces, orientable or not. E. Bujalance and A. F. Costa were partially supported by DGICYT PB 89-201 and Science Plan N SC1-CT91-0716, J. M. Gamboa was partially supported by DGICYT PB 89-379 and Science Plan N SC1-CT91-0716, and J. Lafuente was partially supported by Science Plan N SC1-CT91-0716.     

A Simple,High‐Yield Synthesis of DNA Duplexes Containing a Covalent,Thermally Cleavable Interstrand Cross‐Link at a Defined Location

Interstrand DNA–DNA cross‐links are highly toxic to cells because these lesions block the extraction of information from the genetic material. The pathways by which cells repair cross‐links are important, but not well understood. The preparation of chemically well‐defined cross‐linked DNA substrates represents a significant challenge in the study of cross‐link repair. Here a simple method is reported that employs “post‐synthetic” modifications of commercially available 2′‐deoxyoligonucleotides to install a single cross‐link in high yield at a specified location within a DNA duplex. The cross‐linking process exploits the formation of a hydrazone between a non‐natural N⁴‐amino‐2′‐deoxycytidine nucleobase and the aldehyde residue of an abasic site in duplex DNA. The resulting cross‐link is stable under physiological conditions, but can be readily dissociated and re‐formed through heating–cooling cycles.     

Vacuum behavior in two-dimensional scalar electrodynamics

The vacuum properties in two-dimensional scalar electrodynamics are investigated by calculating the one-loop contribution to the effective lagrangian for a constant electric field.     

Acoustic voice analysis in patients with essential tremor

To quantify several acoustic features of the voice in patients with essentialtremor (ET), 28 patients and 28 age- and sex-matched controls were studied. ET severity was assessed with the rating scale for tremor of Fahn, Tolosa, and Marín. The Computerized Speech Lab 4300 program (Kay Elemetrics) was used. Two-second samples of a sustained /a/ and a sentence were captured with a microphone and laryngograph equipment. Measures included fundamental frequency (F₀), frequency perturbation (fitter, Koike algorithm), intensity perturbation (shimmer, Horii algorithm), and harmonic-to-noise ratio (H/N, Yumoto algorithm) of the vowel /a/, and the frequency and intensity variability of the sentence, phonational range, and dynamic range at the natural frequency, maximum phonational time, and s/z ratio. All subjects underwent indirect laryngoscopy and/or laryngeal fibroscopy. When compared with controls, ET patients showed higher jitter, lower H/N ratio (the last one only with laryngographic signal), of the vowel /a/, lower frequency variability in the microphonc signal, lower intensity variability in the laryngographic signal of the sentence, and significantly lower dynamic range at natural frequency of phonation. ET patients reported higher frequency of the presence of high voice intensity, tremor, and struggle. Several acoustic parameters were influenced by the severity of the disease, including shimmer, jitter, H/N ratio, frequency variability of the sentence, and s/z ratio, although neither of the acoustic analysis values or the phonetometric measurements were affected by the presence of voice tremor or by a successful pharmacological treatment of ET.     

Electrical conductivity of cationic polyelectrolytes in aqueous solution

Four different fluoride, chloride, bromide, and nitrate cationic polyelectrolytes were prepared. Their electrolytic conductivity in aqueous dilute solution was investigated. The results show a remarkable increase, with dilution being practically constant down to limiting concentration. The limiting equivalent conductivity Λ° follows the order The distances between neighboring charges calculated from experimental data are in good agreement with those calculated geometrically according to Manning's definition. The results are mainly dependent on the assumption that Br^? and NO₃^? interact in a similar manner with the cationic charges on the polyion. This phenomenon also has been observed in cationic micelles.     

Fundamental considerations on the mechanisms of silver cementation onto zinc particles in the Merril-Crowe process

Studies on the Merrill-Crowe process as applied to silver recovery have shown that one half of the used zinc powder is wasted in water reduction at high cyanide concentrations, while the other half reduces silver ions from the cyanide solution. However, the cementation mechanisms as an electrochemical process taking place on the zinc surface do not explain the split of the electric current resulting from the anodic dissolution of zinc into two equal values. This study demonstrates that the mechanism for silver precipitation at high and low cyanide concentrations differs considerably. At low cyanide concentrations cementation is essentially an electrochemically-controlled process following a shrinking-core behavior. At high cyanide concentrations, the process seems not to be electrochemically controlled. The areas for zinc dissolution and silver deposition are not connected by an electrical-conducting medium and reduction of silver-cyano complex ions takes place by hydrogen adsorbed onto silver growing outward from the cementing zinc particles. The results are based on scanning electron microscopy of solids recovered from cementations in stirred reactors and in situ observations by optical microscopy of the cementation process on the edge of thin zinc disks in cyanide solutions.     

Radiative processes as a condensation phenomenon and the physical meaning of deformed canonical structures

We study the radiative corrections of QED₃ from the dual point of view and show that this process is the exact dual to the Julia–Toulouse mechanism introduced by Quevedo and Trugenberger [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143] some years ago. We discuss the physics behind this mechanism that involves condensation of topological defects. It is shown that the dual Stuckelberg mechanism is responsible for the “rank-jump” phenomenon that transforms the scalar field (dual to Maxwell in this dimensionality) into the vectorial self-dual field. This phenomenon is studied using the ideas of noncommutative fields theory that examines possible deformations of the canonical structure of some well-known models in (2+1)D$(2+1)\mathrm{D}$. A deformation is constructed linking the massless scalar field theory with the self-dual theory. This is the exact dual of the known deformation connecting the Maxwell theory with the Maxwell–Chern–Simons theory. Duality, radiative corrections, the Julia–Toulouse mechanism and canonical deformations are then used to establish a web of relations between the mentioned theories and to propose a physical picture of the deformation procedure adopted.