On the Quantum Density of States and Partitioning an Integer

This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For $N$ bosons in a one dimensional harmonic oscillator potential, it is well known that the asymptotic (N -> infinity) density of states is identical to the Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of integers. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p^s(n), the latter being the number of partitions of n into a sum of s-th powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d^s(n) for distinct partitions. We find that the distinct square partitions d^2(n) show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. After deriving the Erdos-Lehner formula for restricted partitions for the $s=1$ case by our method, we generalize it to obtain a new formula for distinct restricted partitions.Comment: 17 pages including figure captions. 6 figures. To be submitted to J. Phys. A: Math. Ge

Synaptic MAGUK multimer formation is mediated by PDZ domains and promoted by ligand binding

To examine the scaffolding properties of PSD-95, we have taken advantage of established ligand/PDZ domain interactions and developed a cell-based assay for investigating protein complex formation. This assay enables quantitative analysis of PDZ domain-mediated protein clustering using bimolecular fluorescence complementation (BiFC). Two nonfluorescent halves of EYFP were fused to C-terminal PDZ ligand sequences to generate probes that sense for PDZ domain binding grooves of adjacent (interacting) molecules. When these probes are brought into proximity by the PDZ domains of a multiprotein scaffold, a functional fluorescent EYFP molecule can be detected. We have used this system to examine the properties of selected PSD-95 variants and thereby delineated regions of importance for PSD-95 complex formation. Further analysis led to the finding that PSD-95 multimerization is PDZ domain-mediated and promoted by ligand binding

The Lyapunov exponent in the Sinai billiard in the small scatterer limit

We show that Lyapunov exponent for the Sinai billiard is $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho

Nanoparticle electrical impedance tomography

We have developed a new approach to imaging with electrical impedance tomography (EIT) using gold nanoparticles (AuNPs) to enhance impedance changes at targeted tissue sites. This is achieved using radio frequency (RF) to heat nanoparticles while applying EIT imaging. The initial results using 5-nm citrate coated AuNPs show that heating can enhance the impedance in a solution containing AuNPs due to the application of an RF field at 2.60 GHz

Thermal Aspects in Deep Hole Drilling of Aluminium Cast Alloy Using Twist Drills and MQL

AbstractThe deep hole drilling process with solid carbide twist drills is an efficient alternative to the classic single-lip deep hole drilling, due to the generally higher feed rates possible and the consequently higher productivity. Furthermore the minimum quantity lubrication (MQL) can be applied, in order to reduce the production costs and implement an environmentally friendly process. Because of the significantly reduced cooling performance when using MQL, a higher heat loading results for the tool and the workpiece. This paper presents the investigations of the temperature distribution in the workpiece and the heat balance of the deep hole drilling process

J. Cell. Sci.

Electrophysiological studies demonstrate that transient receptor potential vanilloid subtype 1 (TRPV1) is involved in neuronal transmission. Although it is expressed in the peripheral as well as the central nervous system, the questions remain whether TRPV1 is present in synaptic structures and whether it is involved in synaptic processes. In the present study we gathered evidence that TRPV1 can be detected in spines of cortical neurons, that it colocalizes with both pre- and postsynaptic proteins, and that it regulates spine morphology. Moreover, TRPV1 is also present in biochemically prepared synaptosomes endogenously. In F11 cells, a cell line derived from dorsal-root-ganglion neurons, TRPV1 is enriched in the tips of elongated filopodia and also at sites of cell-cell contact. In addition, we also detected TRPV1 in synaptic transport vesicles, and in transport packets within filopodia and neurites. Using FM4-64 dye, we demonstrate that recycling and/or fusion of these vesicles can be rapidly modulated by TRPV1 activation, leading to rapid reorganization of filopodial structure. These data suggest that TRPV1 is involved in processes such as neuronal network formation, synapse modulation and release of synaptic transmitters

Locating functionalized gold nanoparticles using electrical impedance tomography

Objective: An imaging device to locate functionalised nanoparticles, whereby therapeutic agents are transported from the site of administration specifically to diseased tissues, remains a challenge for pharmaceutical research. Here, we show a new method based on electrical impedance tomography (EIT) to provide images of the location of gold nanoparticles (GNPs) and the excitation of GNPs with radio frequencies (RF) to change impedance permitting an estimation of their location in cell models Methods: We have created an imaging system using quantum cluster GNPs as contrast agent, activated with RF fields to heat the functionalized GNPs, which causes a change in impedance in the surrounding region. This change is then identified with EIT. Results: Images of impedance changes of around 80±4% are obtained for a sample of citrate stabilized GNPs in a solution of phosphate-buffered saline. A second quantification was carried out using colorectal cancer cells incubated with culture media, and the internalization of GNPs into the colorectal cancer cells was undertaken to compare them with the EIT images. When the cells were incubated with functionalised GNPs, the change was more apparent, approximately 40±2%. This change was reflected in the EIT image as the cell area was more clearly identifiable from the rest of the area. Significance: EIT can be used as a new method to locate functionalized GNPs in human cells and help in the development of GNP-based drugs in humans to improve their efficacy in the future

Fermi-Dirac statistics and the number theory

We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of the probability distribution of the number of different partitions.Comment: 7pages, 2 figures, epl.cls, revised versio

Locating Functionalized Gold Nanoparticles Using Electrical Impedance Tomography

Abstract Objective: An imaging device to locate functionalized nanoparticles, whereby therapeutic agents are transported from the site of administration specifically to diseased tissues, remains a challenge for pharmaceutical research. Here, we show a new method based on electrical impedance tomography (EIT) to provide images of the location of gold nanoparticles (GNPs) and the excitation of GNPs with radio frequencies (RF) to change impedance permitting an estimation of their location in cell models Methods: We have created an imaging system using quantum cluster GNPs as a contrast agent, activated with RF fields to heat the functionalized GNPs, which causes a change in impedance in the surrounding region. This change is then identified with EIT. Results: Images of impedance changes of around 804% are obtained for a sample of citrate stabilized GNPs in a solution of phosphate-buffered saline. A second quantification was carried out using colorectal cancer cells incubated with culture media, and the internalization of GNPs into the colorectal cancer cells was undertaken to compare them with the EIT images. When the cells were incubated with functionalized GNPs, the change was more apparent, approximately 402%. This change was reflected in the EIT image as the cell area was more clearly identifiable from the rest of the area. Significance: EIT can be used as a new method to locate functionalized GNPs in human cells and help in the development of GNP-based drugs in humans to improve their efficacy in the future