Necessary conditions for optimality of decomposable entanglement witnesses

It is well known that the support of an optimal decomposable entanglement witness is completely entangled. We add two more necessary conditions for the optimality: The orthogonal complement of the support must have a nonzero product vector; another one will be given in terms of related faces of a convex cone. With these necessary conditions, we show that there exist examples of non-optimal decomposable entanglement witnesses which are the partial transposes of positive semi-definite matrices supported on completely entangled spaces, whenever both of the local dimensions are greater than or equal to three.Comment: Final form to be published in Rep. Math. Phys. The last example is corrected together with minor text

Sustainability performance measurement : a preliminary classification framework of models and indicators

In this position paper we focus on the diversity of sustainability measurements. Based on existing research on performance measurement, we propose a preliminary classification framework summarizing sustainability models and indicators. By describing illustrative examples, we claim that several models and indicators can be distinguished with their own peculiarities. Having such a framework is interesting for both academia and business to structure the range of models and indicators and to ultimately select the appropriate sustainability measurement approach. The proposed framework should be validated by further research

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, $\ell_e$, of a single, infinitely long charged polymer in the presence of screening. A Gaussian variational method is employed, taking $\ell_e$ as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, $\ell_e\sim\kappa^{-2}$, as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result $\ell_e\sim\kappa^{-1}$ found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.Comment: 11 pages, 6 figure

Vision-Based Autonomous Driving: A Model Learning Approach

We present an integrated approach for perception and control for an autonomous vehicle and demonstrate this approach in a high-fidelity urban driving simulator. Our approach first builds a model for the environment, then trains a policy exploiting the learned model to identify the action to take at each time-step. To build a model for the environment, we leverage several deep learning algorithms. To that end, first we train a variational autoencoder to encode the input image into an abstract latent representation. We then utilize a recurrent neural network to predict the latent representation of the next frame and handle temporal information. Finally, we utilize an evolutionary-based reinforcement learning algorithm to train a controller based on these latent representations to identify the action to take. We evaluate our approach in CARLA, a high-fidelity urban driving simulator, and conduct an extensive generalization study. Our results demonstrate that our approach outperforms several previously reported approaches in terms of the percentage of successfully completed episodes for a lane keeping task.Comment:

The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. This attraction results in a possible mechanical instability (collapse), alluding to the phenomenon of DNA condensation. In addition, we find that more counterions condense on slightly bent conformations of the chain than predicted by the Manning model for the case of an infinite cylinder. Finally, our results are compared with previous models and experiments.Comment: 13 pages, 2 ps figure

Conformational Instability of Rodlike Polyelectrolytes due to Counterion Fluctuations

The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length. It is also found that the onset of conformational instability is a re-entrant phenomenon as a function of polyelectrolyte length for the unscreened case, and the Debye length or salt concentration for the screened case. This may be relevant in understanding the experimentally observed re-entrant condensation of DNA.Comment: 8 pages, 4 figure

RNA–protein binding kinetics in an automated microfluidic reactor

Microfluidic chips can automate biochemical assays on the nanoliter scale, which is of considerable utility for RNA–protein binding reactions that would otherwise require large quantities of proteins. Unfortunately, complex reactions involving multiple reactants cannot be prepared in current microfluidic mixer designs, nor is investigation of long-time scale reactions possible. Here, a microfluidic ‘Riboreactor’ has been designed and constructed to facilitate the study of kinetics of RNA–protein complex formation over long time scales. With computer automation, the reactor can prepare binding reactions from any combination of eight reagents, and is optimized to monitor long reaction times. By integrating a two-photon microscope into the microfluidic platform, 5-nl reactions can be observed for longer than 1000 s with single-molecule sensitivity and negligible photobleaching. Using the Riboreactor, RNA–protein binding reactions with a fragment of the bacterial 30S ribosome were prepared in a fully automated fashion and binding rates were consistent with rates obtained from conventional assays. The microfluidic chip successfully combines automation, low sample consumption, ultra-sensitive fluorescence detection and a high degree of reproducibility. The chip should be able to probe complex reaction networks describing the assembly of large multicomponent RNPs such as the ribosome

Atomically dispersed Pt-N-4 sites as efficient and selective electrocatalysts for the chlorine evolution reaction

Chlorine evolution reaction (CER) is a critical anode reaction in chlor-alkali electrolysis. Although precious metal-based mixed metal oxides (MMOs) have been widely used as CER catalysts, they suffer from the concomitant generation of oxygen during the CER. Herein, we demonstrate that atomically dispersed Pt-N-4 sites doped on a carbon nanotube (Pt-1/CNT) can catalyse the CER with excellent activity and selectivity. The Pt-1/CNT catalyst shows superior CER activity to a Pt nanoparticle-based catalyst and a commercial Ru/Ir-based MMO catalyst. Notably, Pt-1/CNT exhibits near 100% CER selectivity even in acidic media, with low Cl- concentrations (0.1M), as well as in neutral media, whereas the MMO catalyst shows substantially lower CER selectivity. In situ electrochemical X-ray absorption spectroscopy reveals the direct adsorption of Cl- on Pt-N-4 sites during the CER. Density functional theory calculations suggest the PtN4C12 site as the most plausible active site structure for the CER

Binding of molecules to DNA and other semiflexible polymers

A theory is presented for the binding of small molecules such as surfactants to semiflexible polymers. The persistence length is assumed to be large compared to the monomer size but much smaller than the total chain length. Such polymers (e.g. DNA) represent an intermediate case between flexible polymers and stiff, rod-like ones, whose association with small molecules was previously studied. The chains are not flexible enough to actively participate in the self-assembly, yet their fluctuations induce long-range attractive interactions between bound molecules. In cases where the binding significantly affects the local chain stiffness, those interactions lead to a very sharp, cooperative association. This scenario is of relevance to the association of DNA with surfactants and compact proteins such as RecA. External tension exerted on the chain is found to significantly modify the binding by suppressing the fluctuation-induced interaction.Comment: 15 pages, 7 figures, RevTex, the published versio

Phase behaviour of a model of colloidal particles with a fluctuating internal state

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in a small region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure