Self-assembly of two-dimensional binary quasicrystals: A possible route to a DNA quasicrystal

We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm `star' motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA

Coarse-grained simulations of DNA overstretching

We use a recently developed coarse-grained model to simulate the overstretching of duplex DNA. Overstretching at 23C occurs at 74 pN in the model, about 6-7 pN higher than the experimental value at equivalent salt conditions. Furthermore, the model reproduces the temperature dependence of the overstretching force well. The mechanism of overstretching is always force-induced melting by unpeeling from the free ends. That we never see S-DNA (overstretched duplex DNA), even though there is clear experimental evidence for this mode of overstretching under certain conditions, suggests that S-DNA is not simply an unstacked but hydrogen-bonded duplex, but instead probably has a more exotic structure.Comment: 11 pages, 11 figure

Extended shareholder liability for systematically important financial institutions

Regulators generally have tried to address the problems posed by the excessive risk-taking of Systemically Important Financial Institutions (SIFIs) by placing restrictions on the activities in which SIFIs engage. However, the complexity of these institutions makes such attempts necessarily imperfect. This Article proposes to address the problem at its very source, which is the incentives that SIFI owners have to push for excessive risk-taking by managers. Building on the traditional rule of “double liability,” we propose to modify the current (general) rule limiting the liability of SIFI shareholders to the amount of their initial investments in such companies. We propose replacing the extant limited liability regime with a new system that imposes additional liability over and above what SIFI shareholders already have invested in a preset amount that varies with a SIFI’s centrality in the financial network. Our liability regime has a number of advantages. First, by increasing shareholder exposure to downside risk, it discourages excessive risk-taking. At the same time, by placing a clearly defined ceiling on shareholders’ total liability exposure, it will not obliterate shareholders’ incentives to invest in the first place. Second, the liability to which shareholders are exposed is carefully tailored to the level of systemic risk that their institution creates. Thus, our rule induces shareholders to account for the negative externality SIFIs can impose without unduly stifling such financial institutions’ role within the financial system and in the wider economy. Third, as the amount of liability is clearly defined ex ante using the rigorous tools of network theory, our rule minimizes the influence of interest groups and the impact of idiosyncratic government decisions

Extended Shareholder Liability for Systematically Important Financial Institutions

Regulators generally have tried to address the problems posed by the excessive risk-taking of Systemically Important Financial Institutions (SIFIs) by placing restrictions on the activities in which SIFIs engage. However, the complexity of these institutions makes such attempts necessarily imperfect. This article proposes to address the problem at its very source, which is the incentives that SIFI owners have to push for excessive risk-taking by managers. Building on the traditional rule of “double liability,” we propose to modify the current (general) rule limiting the liability of SIFI shareholders to the amount of their initial investments in such companies. We propose replacing the extant limited liability regime with a new system that imposes additional liability over and above what SIFI shareholders already have invested in a pre-set amount that varies with a SIFI’s centrality in the financial network. Our liability regime has a number of advantages. First, by increasing shareholder exposure to downside risk, it discourages excessive risk-taking. At the same time, by placing a clearly defined ceiling on shareholders’ total liability exposure, it will not obliterate shareholders’ incentives to invest in the first place. Second, the liability to which shareholders are exposed is carefully tailored to the level of systemic risk that their institution creates. Thus, our rule induces shareholders to account for the negative externality SIFIs can impose without unduly stifling such financial institutions’ role within the financial system and in the wider economy. Third, as the amount of liability is clearly defined ex ante using the rigorous tools of network theory, our rule minimizes the influence of interest groups and the impact of idiosyncratic government decisions. Last, as markets know in advance the amount of liability to which shareholders are exposed, our rule favors the creation of a vibrant insurance and derivative market so that the risk of SIFIs defaults can be allocated to those who can better bear it

The effect of topology on the structure and free energy landscape of DNA kissing complexes

We use a recently developed coarse-grained model for DNA to study kissing complexes formed by hybridization of complementary hairpin loops. The binding of the loops is topologically constrained because their linking number must remain constant. By studying systems with linking numbers -1, 0 or 1 we show that the average number of interstrand base pairs is larger when the topology is more favourable for the right-handed wrapping of strands around each other. The thermodynamic stability of the kissing complex also decreases when the linking number changes from -1 to 0 to 1. The structures of the kissing complexes typically involve two intermolecular helices that coaxially stack with the hairpin stems at a parallel four-way junction

Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles

We study the performance of Monte Carlo simulations that sample a broad histogram in energy by determining the mean first-passage time to span the entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first show that flat-histogram Monte Carlo methods with single-spin flip updates such as the Wang-Landau algorithm or the multicanonical method perform sub-optimally in comparison to an unbiased Markovian random walk in energy space. For the d=1,2,3 Ising model, the mean first-passage time \tau scales with the number of spins N=L^d as \tau \propto N^2L^z. The critical exponent z is found to decrease as the dimensionality d is increased. In the mean-field limit of infinite dimensions we find that z vanishes up to logarithmic corrections. We then demonstrate how the slowdown characterized by z>0 for finite d can be overcome by two complementary approaches - cluster dynamics in connection with Wang-Landau sampling and the recently developed ensemble optimization technique. Both approaches are found to improve the random walk in energy space so that \tau \propto N^2 up to logarithmic corrections for the d=1 and d=2 Ising model

Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays

We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterize the polarization of the cosmic microwave background. In contrast to standard analyses, this approach makes no assumptions about the nature of the background and so has the potential to reveal much more about the physical processes that generated it. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction functions for the individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic, unpolarized and uncorrelated background can be accurately represented using only three modes, and so a search of this type will be only slightly more complicated than the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, by measuring the components of individual modes of the background and checking for consistency with isotropy, this approach has the potential to reveal much more information. Each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of the components that indicates the presence of correlations in the background on large angular scales would suggest startling new physics

Sequence-dependent thermodynamics of a coarse-grained DNA model

We introduce a sequence-dependent parametrization for a coarse-grained DNA model [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Chem. Phys. 134, 085101 (2011)] originally designed to reproduce the properties of DNA molecules with average sequences. The new parametrization introduces sequence-dependent stacking and base-pairing interaction strengths chosen to reproduce the melting temperatures of short duplexes. By developing a histogram reweighting technique, we are able to fit our parameters to the melting temperatures of thousands of sequences. To demonstrate the flexibility of the model, we study the effects of sequence on: (a) the heterogeneous stacking transition of single strands, (b) the tendency of a duplex to fray at its melting point, (c) the effects of stacking strength in the loop on the melting temperature of hairpins, (d) the force-extension properties of single strands and (e) the structure of a kissing-loop complex. Where possible we compare our results with experimental data and find a good agreement. A simulation code called oxDNA, implementing our model, is available as free software.Comment: 15 page