Relaxation time of LL-reversal chains and other chromosome shuffles

We prove tight bounds on the relaxation time of the so-called $L$-reversal chain, which was introduced by R. Durrett as a stochastic model for the evolution of chromosome chains. The process is described as follows. We have $n$ distinct letters on the vertices of the ${n}$-cycle (${{\mathbb{Z}}}$ mod $n$); at each step, a connected subset of the graph is chosen uniformly at random among all those of length at most $L$, and the current permutation is shuffled by reversing the order of the letters over that subset. We show that the relaxation time $\tau (n,L)$, defined as the inverse of the spectral gap of the associated Markov generator, satisfies $\tau (n,L)=O(n\vee \frac{n^3}{L^3})$. Our results can be interpreted as strong evidence for a conjecture of R. Durrett predicting a similar behavior for the mixing time of the chain.Comment: Published at http://dx.doi.org/10.1214/105051606000000295 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Two tone response of radiofrequency signals using the voltage output of a Superconducting Quantum Interference Filter

In the presence of weak time harmonic electromagnetic fields, Superconducting Quantum Interference Filters (SQIFs) show the typical behavior of non linear mixers. The SQIFs are manufactured from high-T_c grain boundary Josephson junctions and operated in active microcooler. The dependence of dc voltage output V_dc vs. static external magnetic field B is non-periodic and consists of a well pronounced unique dip at zero field, with marginal side modulations at higher fields. We have successfully exploited the parabolic shape of the voltage dip around B=0 to mix quadratically two external time harmonic rf-signals, at frequencies f_1 and f_2 below the Josephson frequency f_J, and detect the corresponding mixing signal at f_1-f_2. When the mixing takes place on the SQIF current-voltage characteristics the component at 2f_2 - f_1 is present. The experiments suggest potential applications of a SQIF as a non-linear mixing device, capable to operate at frequencies from dc to few GHz with a large dynamic range.Comment: 10 pages, 3 Figures, submitted to J. Supercond. (as proceeding of the HTSHFF Symposium, June 2006, Cardiff

Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains

We analyze the 1D focusing nonlinear Schr\"{o}dinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally these equations elucidate the unique role of the zero mode for the Neumann boundary conditions

Quadratic Mixing of Radio Frequency Signals using Superconducting Quantum Interference Filters

The authors demonstrate quadratic mixing of weak time harmonic electromagnetic fields applied to Superconducting Quantum Interference Filters, manufactured from high-$T_{\mathrm{c}}$ grain boundary Josephson junctions and operated in active microcooler. The authors use the parabolic shape of the dip in the dc-voltage output around B=0 to mix \emph{quadratically} two external rf-signals, at frequencies $f_{\mathrm{1}}$ and $f_{\mathrm{2}}$ well below the Josephson frequency $f_{\mathrm{J}}$, and detect the corresponding mixing signal at $| {f_{1}-f_{2}}|$. Quadratic mixing takes also place when the SQIF is operated without magnetic shield. The experimental results are well described by a simple analytical model based on the adiabatic approximation.Comment: 3 pages, 3 figure

High performance magnetic field sensor based on Superconducting Quantum Interference Filters

We have developed an absolute magnetic field sensor using Superconducting Quantum Interference Filter (SQIF) made of high-T_c grain boundary Josephson junctions. The device shows the typical magnetic field dependent voltage response V(B), which is sharp delta-like dip in the vicinity of zero magnetic field. When the SQIF is cooled with magnetic shield, and then the shield is removed, the presence of the ambient magnetic field induces a shift of the dip position from B_0 ~ 0 to a value B ~ B_1, which is about the average value of the earth magnetic field, at our latitude. When the SQIF is cooled in the ambient field without shielding, the dip is first found at B ~ B_1, and the further shielding of the SQIF results in a shift of the dip towards B_0 ~ 0. The low hysteresis observed in the sequence of experiments (less than 5% of B_1) makes SQIFs suitable for high precision measurements of the absolute magnetic field. The experimental results are discussed in view of potential applications of high-T_c SQIFs in magnetometry.Comment: 4 pages, 2 figure

Stability analysis of static solutions in a Josephson junction

We present all the possible solutions of a Josephson junction with bias current and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results, in terms of elliptic functions in the case of inline geometry, are in agreement with the numerical calculations and explain the strong hysteretic phenomena typically seen in the calculation of the maximum tunneling current. This suggests a different experimental approach based on the use, instead of the external magnetic field the modulus of the elliptic function or the related quantity the total magnetic flux to avoid hysteretic behavior and unfold the overlapping $I_{max}(H)$ curves.Comment: 36 pages with 17 figure

Which affects affect the use of new technologies? Italian adaptation of the Internet Motive Questionnaire for Adolescents (IMQ-A) and criterion validity with problematic use and body dissatisfaction

Given the negative role of problematic use of new technological devices (NTD) in behavioral and psychological domains, the aim of the study is the Italian adaptation and validation of the Internet Motive Questionnaire for Adolescents (IMQ-A) in order to understand the motivation for the use of NTD. A total of 769 students 10-19 aged (M = 13.22, SD = 1.56) completed the IMQ-A, the Collins Figures Rating Scale, and two measures regarding the problematic NTD use, focused on overuse during the night and during meals. The IMQ-A showed adequate internal consistency with regard to its four subscales: Coping (α = .84), Social (α = .80), Enhancement (α = .80), and Conformity (α = .68) motives. However, with regard to factorial structure, a threefactor model (excluding Conformity subscale) showed slightly better fit indices than the original model. Coping motive was correlated with problematic NTD use and succeeded in predicting higher scores in body dissatisfaction as evidence of criterion-related and external validity. The Italian adaptation of the IMQ-A can be useful in both research and clinical fields, in order to propose alternative strategies for coping to users and to improve emotion regulation facets

In silico karyotyping of chromosomally polymorphic malaria mosquitoes in the Anopheles gambiae complex

Chromosomal inversion polymorphisms play an important role in adaptation to environmental heterogeneities. For mosquito species in the Anopheles gambiae complex that are significant vectors of human malaria, paracentric inversion polymorphisms are abundant and are associated with ecologically and epidemiologically important phenotypes. Improved understanding of these traits relies on determining mosquito karyotype, which currently depends upon laborious cytogenetic methods whose application is limited both by the requirement for specialized expertise and for properly preserved adult females at specific gonotrophic stages. To overcome this limitation, we developed sets of tag single nucleotide polymorphisms (SNPs) inside inversions whose biallelic genotype is strongly correlated with inversion genotype. We leveraged 1,347 fully sequenced An. gambiae and Anopheles coluzzii genomes in the Ag1000G database of natural variation. Beginning with principal components analysis (PCA) of population samples, applied to windows of the genome containing individual chromosomal rearrangements, we classified samples into three inversion genotypes, distinguishing homozygous inverted and homozygous uninverted groups by inclusion of the small subset of specimens in Ag1000G that are associated with cytogenetic metadata. We then assessed the correlation between candidate tag SNP genotypes and PCA-based inversion genotypes in our training sets, selecting those candidates with >80% agreement. Our initial tests both in held-back validation samples from Ag1000G and in data independent of Ag1000G suggest that when used for in silico inversion genotyping of sequenced mosquitoes, these tags perform better than traditional cytogenetics, even for specimens where only a small subset of the tag SNPs can be successfully ascertained