Supporting Information: Fast, Copper-Free Click Chemistry, A Convenient Solid-Phase Approach to Oligonucleotide Conjugation

General experimental Analytical TLC was performed on precoated (250 μm) silica gel 60 F-254 plates from Merck. All plates were visualized by UV irradiation, and/or staining with 5% H2SO4 in ethanol followed by heating. Flash chromatography grade silica gel 60 (230-400 mesh) was obtained from Merck. Mass analysis was performed on an Ettan MALDI-TOF Pro from Amersham Biosciences or LASER-TOF LT3 from Scientific Analytical Instruments with 3- hydroxypicolinic acid or 2,’ 4’, 6’-trihydroxyacetophenone as matrix. The NMR spectra were obtained at 1H (300 MHz), 13C (75 MHz) and 31P (121 MHz) on a Bruker instrument at 25 ºC. Chemical shifts are reported in ppm downfield from TMS as standard. HPLC was carried out using a Gilson instrument equipped with a UV detector and a Nucleosil C18 column (4.0 × 250 mm) or Phenomenex Clarity. Fluorescence spectra were recorded on a Varian Cary Eclipse instrument. All other chemical agents were purchased from Aldrich Chemical Company unless otherwise noted

Data-driven Privacy-Preserving Communication

A communication system including a receiver to receive training data. An input interface to receive input data coupled to a hardware processor and a memory. The hardware processor is configured to initialize the privacy module using the training data. Generate a trained privacy module, by iteratively optimizing an objective function. Wherein for each iteration the objective function is computed by a combination of a distortion of the useful attributes in the transformed data and of a mutual information between the sensitive attributes and the transformed data. Such that the mutual information is estimated by the auxiliary module that maximizes a conditional likelihood of the sensitive attributes given the transformed data. Receive the input data via the input interface. Apply the trained privacy module on the input data to produce an application specific transformed data. A transmitter to transmit the application specific transformed data over a communication channel

An extended Falicov-Kimball model on a triangular lattice

The combined effect of frustration and correlation in electrons is a matter of considerable interest of late. In this context a Falicov-Kimball model on a triangular lattice with two localized states, relevant for certain correlated systems, is considered. Making use of the local symmetries of the model, our numerical study reveals a number of orbital ordered ground states, tuned by the small changes in parameters while quantum fluctuations between the localized and extended states produce homogeneous mixed valence. The inversion symmetry of the Hamiltonian is broken by most of these ordered states leading to orbitally driven ferroelectricity. We demonstrate that there is no spontaneous symmetry breaking when the ground state is inhomogeneous. The study could be relevant for frustrated systems like $GdI_2$, $NaTiO_2$ (in its low temperature C2/m phase) where two Mott localized states couple to a conduction band.Comment: 6 pages, 8 figure

Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fail