Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Chromatin-contact atlas reveals disorder-mediated protein interactions and moonlighting chromatin-associated RBPs

RNA-binding proteins (RBPs) play diverse roles in regulating co-transcriptional RNA-processing and chromatin functions, but our knowledge of the repertoire of chromatin-associated RBPs (caRBPs) and their interactions with chromatin remains limited. Here, we developed SPACE (Silica Particle Assisted Chromatin Enrichment) to isolate global and regional chromatin components with high specificity and sensitivity, and SPACEmap to identify the chromatin-contact regions in proteins. Applied to mouse embryonic stem cells, SPACE identified 1459 chromatin-associated proteins, ∼48% of which are annotated as RBPs, indicating their dual roles in chromatin and RNA-binding. Additionally, SPACEmap stringently verified chromatin-binding of 403 RBPs and identified their chromatin-contact regions. Notably, SPACEmap showed that about 40% of the caRBPs bind chromatin by intrinsically disordered regions (IDRs). Studying SPACE and total proteome dynamics from mES cells grown in 2iL and serum medium indicates significant correlation (R = 0.62). One of the most dynamic caRBPs is Dazl, which we find co-localized with PRC2 at transcription start sites of genes that are distinct from Dazl mRNA binding. Dazl and other PRC2-colocalised caRBPs are rich in intrinsically disordered regions (IDRs), which could contribute to the formation and regulation of phase-separated PRC condensates. Together, our approach provides an unprecedented insight into IDR-mediated interactions and caRBPs with moonlighting functions in native chromatin

Electrostatic deposition of graphene in a gaseous environment: A deterministic route to synthesize rolled graphenes?

The synthesis of single-wall carbon nanotubes (SWCNTs) of desired diameters and chiralities is critical to the design of nanoscale electronic devices with desired properties.1-6 The existing methods are based on self-assembly, 7-16 therefore lacking the control over their diameters and chiralities. The present work reports a direct route to roll graphene. Specifically, we found that the electrostatic deposition of graphene yielded: (i) flat graphene layers under high vacuum (10-7 Torr), (ii) completely scrolled graphene under hydrogen atmosphere, (iii) partially scrolled graphene under nitrogen atmosphere, and (iv) no scrolling for helium atmospheres. Our study shows that the application of the electrostatic field facilitates the rolling of graphene sheets exposed to appropriate gases and allows the rolling of any size graphene. The technique proposed here, in conjunction with a technique that produces graphene nanoribbons (GNRs) of uniform widths, will have significant impact on the development of carbon nanotube based devices. Furthermore, the present technique may be applied to obtain tubes/scrolls of other layered materials

A Novel Dielectric Anomaly in Cuprates and Nickelates: Signature of an Electronic Glassy State

The low-frequency dielectric response of hole-doped insulators La_{2}Cu_{1-x}Li_{x}O_{4} and La_{2-x}Sr_{x}NiO_{4} shows a large dielectric constant \epsilon ^{'} at high temperature and a step-like drop by a factor of 100 at a material-dependent low temperature T_{f}. T_{f} increases with frequency and the dielectric response shows universal scaling in a Cole-Cole plot, suggesting that a charge glass state is realized both in the cuprates and in the nickelates.Comment: 5 pages, 4 figure

The multilevel trigger system of the DIRAC experiment

The multilevel trigger system of the DIRAC experiment at CERN is presented. It includes a fast first level trigger as well as various trigger processors to select events with a pair of pions having a low relative momentum typical of the physical process under study. One of these processors employs the drift chamber data, another one is based on a neural network algorithm and the others use various hit-map detector correlations. Two versions of the trigger system used at different stages of the experiment are described. The complete system reduces the event rate by a factor of 1000, with efficiency $\geq$95% of detecting the events in the relative momentum range of interest.Comment: 21 pages, 11 figure

High pressure investigation of the heavy-fermion antiferromagnet U_3Ni_5Al_19

Measurements of magnetic susceptibility, specific heat, and electrical resistivity at applied pressures up to 55 kbar have been carried out on single crystals of the heavy-fermion antiferromagnet U_3Ni_5Al_19, which crystallizes in the Gd_3Ni_5Al_19 orthorhombic structure with two inequivalent U sites. At ambient pressure, a logarithmic T-dependence of the specific heat and T-linear electrical resistivity below 5 K indicates non-Fermi liquid (NFL) behavior in the presence of bulk antiferromagnetic order at T_N=23 K. Electrical resistivity measurements reveal a crossover from non-Fermi liquid to Fermi liquid behavior at intermediate pressures between 46 kbar and 51 kbar, followed by a return to NFL T^{3/2} behavior at higher pressures. These results provide evidence for an ambient pressure quantum critical point and an additional antiferromagnetic instability at P_c=60 kbar.Comment: 12 pages, 5 figure

Next-to-next-to-leading order fits to CCFR'97 xF3xF_3 data and infrared renormalons

We briefly summarize the outcomes of our recent improved fits to the experimental data of CCFR collaboration for $xF_3$ structure function of $\nu N$ deep-inelastic scattering at the next-to-next-to-leading order. Special attention is paid to the extraction of $\alpha_s(M_Z)$ and the parameter of the infrared renormalon model for $1/Q^2$-correction at different orders of perturbation theory. The results can be of interest for planning similar studies using possible future data of Neutrino Factories.Comment: 3 pages, presented at WG3 of 4th NuFact'02 Workshop, London 1-6 July, 200

On the Role of Higher Twist in Polarized Deep Inelastic Scattering

The higher twist corrections $h^N(x)/Q^2$ to the spin dependent proton and neutron structure functions $g_1^N(x, Q^2)$ are extracted in a model independent way from experimental data on $g_1^N$ and found to be non-negligible. It is shown that the NLO QCD polarized parton densities determined from the data on g1, including higher twist effects, are in good agreement with those found earlier from our analysis of the data on g1/F1 and A1 where higher twist effects are negligible. On the contrary, the LO QCD polarized parton densities obtained from the data on g1, including higher twist, differ significantly from our previous results.Comment: 18 pages, latex, 6 figures, final version which will be published in Phys. Rev. D, fig. 5 is changed, misprints in Table 2 are remove