Expected distance based on random walks

By considering a graph as a network of resistances, Klein and Randi? (J Math Chem 12(1):81–95, 1993) proposed the definition of a distance measure. Indeed, if each edge of the graph represents a resistance of \(1 \varOmega \), the equivalent resistance of the graph between each pair of vertices may be used as a distance. Based upon random walks in graphs, Stephenson and Zelen (Soc Netw 11(1):1–37, 1989) built a computational model to find the probability that each edge is used. From a mathematical point of view, both articles are based upon exactly the same model and the link between random walks and the electrical representation was established by Newman (Soc Netw 27(1):39–54, 2005) when defining an alternative to Freeman’s (Sociometry 40:35–41, 1977, Soc Netw 1(3):215–239, 1979) betweenness centrality based upon random walks. In the present paper, the similitude between these two processes is exploited to propose a new random walks based distance measure that may be defined as the expected length of a walk between any pair of vertices. We call it the expected distance and we prove that it is actually a distance. From this new definition, the RW Index is proposed that sums the expected walks lengths between pairs of vertices exactly in the same way as the Wiener index sums the shortest paths distances or the Kirchhoff index sums the equivalent resistances. We compare the three indices and establish the vertex and the edge decompositions for both. We compute some value of the RW index for some families of graphs and conjecture the upper and lower bounds of the RW index.     

Non-Hermitian quantum mechanics: wave packet propagation on autoionizing potential energy surfaces

The correspondence between the time-dependent and time-independent molecular dynamic formalisms is shown for autoionizing processes. We demonstrate that the definition of the inner product in non-Hermitian quantum mechanics plays a key role in the proof. When the final state of the process is dissociative, it is technically favorable to introduce a complex absorbing potential into the calculations. The conditions which this potential should fulfill are briefly discussed. An illustrative numerical example is presented involving three potential energy surfaces.     

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.     

Luminescent chemosensors based on semiconductor quantum dots

Semiconductor quantum dots are inorganic nanoparticles with unique photophysical properties. In particular, their huge one- and two-photon absorption cross sections, tunable emission bands and excellent photobleaching resistances are stimulating the development of luminescent probes for biomedical imaging and sensing applications. Indeed, electron and energy transfer processes can be designed to switch the luminescence of semiconductor quantum dots in response to molecular recognition events. On the basis of these operating principles, the presence of target analytes can be transduced into detectable luminescence signals. In fact, luminescent chemosensors based on semiconductor quantum dots are starting to be developed to detect small molecules, monitor DNA hybridization, assess protein-ligand complementarities, test enzymatic activity and probe pH distributions. Although fundamental research is still very much needed to understand further the fundamental factors regulating the behavior of these systems and refine their performance, it is becoming apparent that sensitive probes based on semiconductor quantum dots will become invaluable analytical tools for a diversity of applications in biomedical research.     

Exact quantum master equation via the calculus on path integrals

An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. A novel truncation scheme is further proposed and compared with other approaches to close the resulting hierarchically coupled equations of motion. The interplay between system-bath interaction strength, non-Markovian property, and required level of hierarchy is also demonstrated with the aid of simple spin-boson systems.     

Structural characteristics of nanomaterials based on CdS quantum dots

CdS nanoparticles with sizes where a quantum-size effect is observed are structurally characterized in a detailed way. The following complex of structural methods is used to characterize the nanoparticles: electron diffraction; analytical, diffraction, and high-resolution transmission electron microscopy; and small-angle X-ray scattering.     

Immunoasssay based on the antibody-conjugated PAMAM-dendrimer-gold quantum dot complex

An immunoassay based upon photoluminescent gold quantum dots aimed at detecting human IgG in aqueous solution from micromolar to nanomolar concentrations is described.     

Visible light induced photoelectrochemical biosensing based on oxygen-sensitive quantum dots

A visible light induced photoelectrochemical biosensing platform based on oxygen-sensitive near-infrared quantum dots (NIR QDs) was developed for detection of glucose. The NIR QDs were synthesized in an aqueous solution, and characterized with scanning electron microscopy and X-ray photoelectron spectroscopy. The as-prepared NIR QDs were employed to construct oxygen-sensitive photoelectrochemical biosensor on a fluorine-doped tin oxide (FTO) electrode. The oxygen dependency of the photocurrent was investigated at as-prepared electrode, which demonstrated the signal of photocurrent is suppressed with the decreasing of oxygen. Coupling with the consumption of oxygen during enzymatic reaction, a photoelectrochemical strategy was proposed for the detection of substrate. Using glucose oxidase (GOx) as a model enzyme, that is, GOx was covalently attached to the surface of CdTe QDs, the resulting biosensor showed the sensitive response to glucose. Under the irradiation of visible light of a wavelength at 505 nm, the proposed photoelectrochemical method could detect glucose ranging from 0.1 mM to 11 mM with a detection limit of 0.04 mM. The photoelectrochemical biosensor showed a good performance with high upper detection limit, acceptable stability and accuracy, providing an alternative method for monitoring biomolecules and extending the application of near-infrared QDs.     

Multimodal imaging probes based on Gd-DOTA conjugated quantum dot nanomicelles

Recently, multimodal nanoparticles integrating dual- or tri-imaging modalities into a single hybrid nanosystem have attracted plenty of attention in biomedical research. Here, we report the fabrication of two types of multimodal micelle-encapsulated nanoparticles, which were systematically characterized and thoroughly evaluated in terms of their imaging potential and biocompatibility. Optical and magnetic resonance (MR) imaging probes were integrated by conjugating DOTA-gadolinium (Gd) derivative to quantum dot based nanomicelles. Two amphiphilic block copolymer micelles, amine-terminated mPEG-phospholipid and amine-modified Pluronic F127, were chosen as the capping agents because of their excellent biocompatibility and ability to prevent opsonization and prolong circulation time in vivo. Owing to their different hydrophobic-hydrophilic structure, the micellar aggregates exhibited different sizes and protection of core QDs. This work revealed the differences between these nanomicelles in terms of the stability over a wide range of pH, along with their cytotoxicity and the capacity for chelating gadolinium, thus providing a useful guideline for tailor-making multimodal nanoparticles for specific biomedical applications.     

A flow cytometric assay technology based on quantum dots-encoded beads

A flow cytometric detecting technology based on quantum dots (QDs)-encoded beads has been described. Using this technology, several QDs-encoded beads with different code were identified effectively, and the target molecule (DNA sequence) in solution was also detected accurately by coupling to its complementary sequence probed on QDs-encoded beads through DNA hybridization assay. The resolution of this technology for encoded beads is resulted from two longer wavelength fluorescence identification signals (yellow and red fluorescent signals of QDs), and the third shorter wavelength fluorescence signal (green reporting signal of fluorescein isothiocyanate (FITC)) for the determination of reaction between probe and target. In experiment, because of QDs’ unique optical character, only one excitation light source was needed to excite the QDs and probe dye FITC synchronously comparing with other flow cytometric assay technology. The results show that this technology has present excellent repeatability and good accuracy. It will become a promising multiple assay platform in various application fields after further improvement.     

Cell-penetrating quantum dots based on multivalent and endosome-disrupting surface coatings

We report the development of cell-penetrating quantum dots (QDs) based on the use of multivalent and endosome-disrupting (endosomolytic) surface coatings. Hyperbranched copolymer ligands such as polyethylene glycol (PEG) grafted polyethylenimine (PEI-g-PEG) are found to encapsulate and solubilize luminescent quantum dots through direct ligand-exchange reactions. Because of the positive charges and a "proton sponge effect" associated with multivalent amine groups, this class of ligand-exchanged QDs is able to penetrate cell membranes and is also able to disrupt endosomal organelles in living cells. The grafted PEG segment is essential for reducing the cytotoxicity of PEI as well as for improving the overall nanoparticle stability and biocompatibility. In comparison with previous QDs encapsulated with amphiphilic polymers, the cell-penetrating QDs are smaller in size and are considerably more stable in acidic environments. Cellular uptake and imaging studies reveal that the number of PEG grafts per PEI molecule has a pronounced effect on the intracellular pathways of internalized QDs. In particular, QDs coated with PEI-g-PEG2 are rapidly internalized by endocytosis, and are initially stored in vesicles, followed by slow endosomal escape and release into the cytoplasm. These insights are important toward the design and development of nanoparticle agents for intracellular imaging and therapeutic applications.     

Multiple homogeneous immunoassays based on a quantum dots-gold nanorods FRET nanoplatform

Multi-sized quantum dots (QDs) donors and tailor-made gold nanorods (GNRs) are employed to form a FRET nanoplatform for homogeneous immunoassays developed for analysis of multiple virus antigens. The single GNRs/multiple QDs nanocomposite based nanosensor offers a simple and sensitive approach for multiple analytes detection in a homogeneous format.     

Phase coherent electronics: a molecular switch based on quantum interference

The phenomenon of quantum mechanical interference may be used to control the conductivity of ballistic molecular wires. Using a simple model we demonstrate plausible effects and discuss its potential uses for constructing coherence-based molecular electronics.     

Accuracy of gates in a quantum computer based on vibrational eigenstates

A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.     

Supramolecular nanostructures based on bacterial reaction center proteins and quantum dots

Design of the nanostructures based on membrane proteins (the key functional elements of biomembranes) and colloid nanoparticles is a fascinating field at the interface of biochemistry and colloids, nanotechnology and biomedicine. The review discusses the main achievements in the field of ultrathin films prepared from bacterial reaction center proteins and light-harvesting complexes, as well as these complexes tagged with quantum dots. The principles of preparation of these thin films and their structure and properties at different interfaces are described; as well as their characteristics estimated using a combination of the modern interfacial techniques (absorption and fluorescence spectroscopy, atomic force and Brewster angle microscopy, etc.) are discussed. Further approaches to develop the nanostructures based on the membrane proteins and quantum dots are suggested. These supramolecular nanostructures are promising prototypes of the materials for photovoltaic, optoelectronic and biosensing applications.     

Determination of abscisic acid based on the fluorescent quenching of quantum dots

The quenching mechanism of the fluorescence of quantum dots by abscisic acid has been systematically investigated.The quenching constant KSV = 5.1 × 1011 / M was obtained under the optimized condition.On the basis of that,a very sensitive method for the determination of abscisic acid has been developed.The linear equation was F0/F = 0.9309 + 0.5072 C(pmol/L) and its linear range was 0.2-3.0 pmol/L with a correlation coefficient of 0.9939.The limit of detection was 0.09 pmol/L.     

Closed-form expressions of quantum electron transfer rate based on the stationary-phase approximation

Closed-form rate expressions are derived on the basis of the stationary-phase approximation for the Fermi golden rule expression of the quantum electron-transfer (ET) rate. First, on the basis of approximate solutions of the stationary-phase points near DeltaG = 0, -lambda, and lambda, where DeltaG is the reaction free energy and lambda is the reorganization energy, three closed-form rate expressions are derived, which are respectively valid near each value of DeltaG. Numerical tests for a model Ohmic spectral density with an exponential cutoff demonstrate good performance of the derived expressions in the respective regions of their validity. In particular, the expression near DeltaG = -lambda, which differs from the semiclassical approximation only by a prefactor quadratic in DeltaG, works substantially better than the latter. Then, a unified formula is suggested, which interpolates the three approximate expressions and serves as a good approximation in all three regions. We have also demonstrated that the interpolation formula can serve as a good quantitative means for understanding the temperature dependence of the quantum ET rate.