On the Iteration Complexity of Oblivious First-Order Optimization Algorithms

Abstract We consider a broad class of first-order optimization algorithms which are oblivious, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as smoothness or strong convexity parameters. With the knowledge of these two parameters, we show that any such algorithm attains an iteration complexity lower bound of Ω( L/ ) for L-smooth convex functions, andΩ( L/µ ln(1/ )) for Lsmooth µ-strongly convex functions. These lower bounds are stronger than those in the traditional oracle model, as they hold independently of the dimension. To attain these, we abandon the oracle model in favor of a structure-based approach which builds upon a framework recently proposed i

Synthesizing topological structures containing RNA

Though knotting and entanglement have been observed in DNA and proteins, their existence in RNA remains an enigma. Synthetic RNA topological structures are significant for understanding the physical and biological properties pertaining to RNA topology, and these properties in turn could facilitate identifying naturally occurring topologically nontrivial RNA molecules. Here we show that topological structures containing single-stranded RNA (ssRNA) free of strong base pairing interactions can be created either by configuring RNA?DNA hybrid four-way junctions or by template-directed synthesis with a single-stranded DNA (ssDNA) topological structure. By using a constructed ssRNA knot as a highly sensitive topological probe, we find that Escherichia coli DNA topoisomerase I has low RNA topoisomerase activity and that the R173A point mutation abolishes the unknotting activity for ssRNA, but not for ssDNA. Furthermore, we discover the topological inhibition of reverse transcription (RT) and obtain different RT?PCR patterns for an ssRNA knot and circle of the same sequence

Real-Time Detection of Telomerase Activity Using the Exponential Isothermal Amplification of Telomere Repeat Assay

As crucial pieces in the puzzle of cancer and human aging, telomeres and telomerase are indispensable in modern biology. Here we describe a novel exponential isothermal amplification of telomere repeat (EXPIATR) assaya sensitive, simple, and reliable <i>in vitro</i> method for measuring telomerase activity in cell extracts. Through a strategically designed path of nucleic acid isothermal amplifications, EXPIATR abandons the expensive thermal cycling protocol and achieves ultrafast detection: telomerase activity equivalent to a single HeLa cancer cell can be detected in ∼25 min

DNA-CNT Nanowire Networks for DNA Detection

The ability to detect biological analytes in a rapid, sensitive, operationally simple, and cost-effective manner will impact human health and safety. Hybrid biocatalyzed-carbon nanotube (CNT) nanowire-based detection methods offer a highly sensitive and specific platform for the fabrication of simple and effective conductometric devices. Here, we report a conductivity-based DNA detection method utilizing carbon nanotube−DNA nanowire devices and oligonucleotide-functionalized enzyme probes. Key to our sensor design is a DNA-linked-CNT wire motif, which forms a network of interrupted carbon nanotube wires connecting two electrodes. Sensing occurs at the DNA junctions linking CNTs, followed by amplification using enzymatic metalization leading to a conductimetric response. The DNA analyte detection limit is 10 fM with the ability to discriminate single, double, and triple base pair mismatches. DNA−CNT nanowires and device sensing gaps were characterized by scanning electron microscopy (SEM) and confocal Raman microscopy, supporting the enhanced conductometric response resulting from nanowire metallization.United States. Army Research Office (W911NF-07-D-0004)National Institute of General Medical Sciences (U.S.). Postdoctural Fellowship (1-F32-GM087028-01A1

Structures of Artificially Designed RNA Nanoarchitectures at Near-Atomic Resolution

Though advances in nanotechnology have enabled the construction of synthetic nucleic acid based nanoarchitectures with ever-increasing complexity for various applications, high-resolution structures are lacking due to the difficulty of obtaining good diffracting crystals. Here we report the design of RNA nanostructures based on homooligomerizable tiles from an RNA single-strand for X-ray determination. Three structures are solved to near-atomic resolution: a 2D parallelogram, an unexpectedly formed 3D nanobracelet, and a 3D nanocage. Structural details of their constituent motifs—such as kissing loops, branched kissing-loops and T-junctions—that resemble natural RNA motifs and resisted X-ray determination are revealed. This work unveils the largely unexplored potential of crystallography in gaining high-resolution feedback for nanostructure design and suggests a novel route to investigate RNA motif structures by configuring them into nanoarchitectures.</p

Structures of artificially designed discrete RNA nanoarchitectures at near-atomic resolution

Although advances in nanotechnology have enabled the construction of complex and functional synthetic nucleic acid-based nanoarchitectures, high-resolution discrete structures are lacking because of the difficulty in obtaining good diffracting crystals. Here, we report the design and construction of RNA nanostructures based on homooligomerizable one-stranded tiles for x-ray crystallographic determination. We solved three structures to near-atomic resolution: a 2D parallelogram, a 3D nanobracelet unexpectedly formed from an RNA designed for a nanocage, and, eventually, a bona fide 3D nanocage designed with the guidance of the two previous structures. Structural details of their constituent motifs, such as kissing loops, branched kissing loops, and T-junctions, that resemble natural RNA motifs and resisted x-ray determination are revealed, providing insights into those natural motifs. This work unveils the largely unexplored potential of crystallography in gaining high-resolution feedback for nanoarchitectural design and suggests a route to investigate RNA motif structures by configuring them into nanoarchitectures

Regiospecific Synthesis of Au-Nanorod/SWCNT/Au-Nanorod Heterojunctions

The synthesis of precisely defined nanoscale hybrid materials remains a challenge at the frontier of chemistry and material science. In particular, the assembly of diverse high-aspect ratio one-dimensional materials such as gold nanorods and carbon nanotubes into functional systems is of ever increasing interest due to their electronic and sensing applications. To meet these challenges, methods for interfacing gold nanorods with carbon materials such as single-walled carbon nanotubes (SWCNTs) in a regio-controlled manner are needed. Herein, we report a method for the regiospecific synthesis of terminally linked gold nanorod-SWCNTs based on a nanotube surface protection strategy. The key to our approach is a SWCNT surface protection procedure allowing for selective functionalization of the SWCNT termini.National Science Foundation (U.S.). (ECCS-0731100)United States. Army Research Office (W911NF-07-D-0004)National Institutes of Health (U.S.). National Institute of General Medical Sciences (U.S.) Postdoctural Fellowship (1-F32-GM087028-01A1

Supramolecular aptamer-thrombin linear and branched nanostructures

Alpha and beta conjugated bis-aptamers against thrombin act as bidentate "glue" for the self-assembly of thrombin nanowires; mixing the bidentate aptamer with a tripodal tridentate alpha aptamer construct yields branched thrombin nanowire structures