Layer-by-Layer electrostatic self-assembly of polyelectrolyte nanoshells on individual carbon nanotube templates

Carbon nanotubes have been featured prominently in the nanotechnology research for some time, yet robust strategies for noncovalent chemical modification of the nanotube surface are still missing. Such strategies are essential for the creation of functional device architectures. Here, we present a new general procedure for carbon nanotube modification based on polyelectrolyte layer-by-layer assembly. We have built multilayer structures around individual carbon nanotube bridges by first modifying the nanotube surface with a pyrene derivative followed by layer-by-layer deposition of polyelectrolyte macroions on the nanotube. Transmission electron microscopy and scanning confocal fluorescence microscopy images confirm the formation of nanometer-thick amorphous polymer nanoshells around the nanotubes. These multilayer polyelectrolyte shells on individual carbon nanotubes introduce nearly unlimited opportunities for the incorporation of various functionalities into nanotube devices, which, in turn, opens up the possibility of building more complex multicomponent structures.     

Inverse Sturm-Liouville problems with homogeneous delay

We study the inverse Sturm-Liouville problem with a delay $$- y''(x) + q(x)y(\alpha x), q \in L_2 [0,\pi ], \alpha \in (0,1],$$ and the boundary conditions y(0) = y(π) = 0.     

On smoothing,regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems

Traditionally, most stochastic approximation (SA) schemes for stochastic variational inequality (SVI) problems have required the underlying mapping to be either strongly monotone or monotone and Lipschitz continuous. In contrast, we consider SVIs with merely monotone and non-Lipschitzian maps. We develop a regularized smoothed SA (RSSA) scheme wherein the stepsize, smoothing, and regularization parameters are reduced after every iteration at a prescribed rate. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to the least norm solution in an almost sure sense, extending the results in Koshal et al. (IEEE Trans Autom Control 58(3):594–609, 2013) to the non-Lipschitzian regime. Additionally, we provide rate estimates that relate iterates to their counterparts derived from a smoothed Tikhonov trajectory associated with a deterministic problem. To derive non-asymptotic rate statements, we develop a variant of the RSSA scheme, denoted by aRSSA\(_r\), in which we employ a weighted iterate-averaging, parameterized by a scalar r where \(r = 1\) provides us with the standard averaging scheme. The main contributions are threefold: (i) when \(r<1\) and the parameter sequences are chosen appropriately, we show that the averaged sequence converges to the least norm solution almost surely and a suitably defined gap function diminishes at an approximate rate \(\mathcal{O}({1}\slash {\root 6 \of {k}})\) after k steps; (ii) when \(r<1\), and smoothing and regularization are suppressed, the gap function admits the rate \(\mathcal{O}({1}\slash {\sqrt{k}})\), thus improving the rate \(\mathcal{O}(\ln (k)/\sqrt{k})\) under standard averaging; and (iii) we develop a window-based variant of this scheme that also displays the optimal rate for \(r < 1\). Notably, we prove the superiority of the scheme with \(r < 1\) with its counterpart with \(r=1\) in terms of the constant factor of the error bound when the size of the averaging window is sufficiently large. We present the performance of the developed schemes on a stochastic Nash–Cournot game with merely monotone and non-Lipschitzian maps.     

Subgradient Methods for Saddle-Point Problems

We study subgradient methods for computing the saddle points of a convex-concave function. Our motivation comes from networking applications where dual and primal-dual subgradient methods have attracted much attention in the design of decentralized network protocols. We first present a subgradient algorithm for generating approximate saddle points and provide per-iteration convergence rate estimates on the constructed solutions. We then focus on Lagrangian duality, where we consider a convex primal optimization problem and its Lagrangian dual problem, and generate approximate primal-dual optimal solutions as approximate saddle points of the Lagrangian function. We present a variation of our subgradient method under the Slater constraint qualification and provide stronger estimates on the convergence rate of the generated primal sequences. In particular, we provide bounds on the amount of feasibility violation and on the primal objective function values at the approximate solutions. Our algorithm is particularly well-suited for problems where the subgradient of the dual function cannot be evaluated easily (equivalently, the minimum of the Lagrangian function at a dual solution cannot be computed efficiently), thus impeding the use of dual subgradient methods.     

Structural transformation of push-pull 5-substituted-4-oxothiazolidines during heating

The thermal stability of push-pull 5-substituted-4-oxothiazolidines was studied by DSC, IC and X-ray diffraction techniques. It was shown that the compounds are stable in the temperature range from room temperature to melting point. The melting is combined with breaking crystal structure and forming glass material as a new phase that forms crystals by cooling it very slowly. The rate constant, activation energy as well as activation parameters of process were determined.     

Preparation of silicate tungsten bronzes on aluminum by plasma electrolytic oxidation process in 12-tungstosilicic acid

The growth of silicate tungsten bronzes on aluminum by plasma electrolytic oxidation in 12-tungstosilicic acid is experimentally investigated and discussed. Real time imaging and optical emission spectroscopy characterization of plasma electrolytic oxidation show that spatial density of microdischarges is the highest in the early stage of the process, while the percentage of oxide coating area covered by active discharge sites decreases slowly with time. Emission spectrum of microdischarges has several intensive band peaks originating either from aluminum electrode or from the electrolyte. Surface roughness of obtained oxide coatings increases with prolonged time of plasma electrolytic oxidation, as their microhardness decreases. Raman spectroscopy and energy dispersive X-ray spectroscopy are employed to confirm that the outer layer of oxide coatings formed during the plasma electrolytic oxidation process is silicate tungsten bronzes.     

Minibatch stochastic subgradient-based projection algorithms for feasibility problems with convex inequalities

In this paper we consider convex feasibility problems where the feasible set is given as the intersection of a collection of closed convex sets. We assume that each set is specified algebraically as a convex inequality, where the associated convex function is general (possibly non-differentiable). For finding a point satisfying all the convex inequalities we design and analyze random projection algorithms using special subgradient iterations and extrapolated stepsizes. Moreover, the iterate updates are performed based on parallel random observations of several constraint components. For these minibatch stochastic subgradient-based projection methods we prove sublinear convergence results and, under some linear regularity condition for the functional constraints, we prove linear convergence rates. We also derive sufficient conditions under which these rates depend explicitly on the minibatch size. To the best of our knowledge, this work is the first deriving conditions that show theoretically when minibatch stochastic subgradient-based projection updates have a better complexity than their single-sample variants when parallel computing is used to implement the minibatch. Numerical results also show a better performance of our minibatch scheme over its non-minibatch counterpart.

     

Raman spectroscopic evidence for the most stable water/ethanol dimer and for the negative mixing energy in cold water/ethanol trimers

Spontaneous Raman scattering in supersonic jet expansions is used to prove that the mixed dimer of ethanol and water (corresponding to a volume fraction of 79% ethanol in the liquid) prefers ethanol in a gauche conformation as the hydrogen bond acceptor. This represents a particularly simple case of adaptive aggregation. Furthermore, it is shown experimentally that the isolated cold trimer built from one ethanol and two waters (corresponding to 64% ethanol in the liquid) has a significantly negative excess enthalpy, in line with the thermodynamic bulk observation at room temperature.     

Slow Unfolded-State Structuring in Acyl-CoA Binding Protein Folding Revealed by Simulation and Experiment

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ～10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (～100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.     

Structured sublinear compressive sensing via belief propagation

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with orthogonal matching pursuit (OMP) methods. For reduced-complexity greedy reconstruction schemes, we propose a new family of list-decoding belief propagation algorithms, as well as reinforced and multiple-basis belief propagation (BP) algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity–performance tradeoffs for very sparse signal vectors.