arXiv subjects

S. E. Ahnert

Publications and source records attributed to S. E. Ahnert.

11 recordsLinked to original sources

arXiv2018

The determinism and boundedness of self-assembling structures

Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems

cond-mat.soft↗

arXiv2016

Non-deterministic self-assembly with asymmetric interactions

We investigate general properties of non-deterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter can lead to self-limiting cluster growth. Furthermore, by adjusting the relative abundance of self-assembly particles in a two-particle mixture, we are able to tune the final sizes of these clusters. We show that this is a fundamental property of asymmetric interactions, which has potential applications in bioengineering, and provides new insights into the study of diseases caused by protein aggregation.

cond-mat.soft↗

arXiv2016

Non-deterministic self-assembly of two tile types on a lattice

Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of important functions in the cell, whereas protein aggregation is the hallmark of a number of diseases and represents a non-deterministic self-assembly process. Here we build on previous work on a lattice model of deterministic self-assembly to investigate non-deterministic self-assembly of single lattice tiles and mixtures of two tiles at varying relative concentrations. Despite limiting the simplicity of the model to two interface types, which results in 13 topologically distinct single tiles and 106 topologically distinct sets of two tiles, we observe a wide variety of concentration-dependent behaviours. Several two-tile sets display critical behaviours in form of a sharp transition from bound to unbound structures as the relative concentration of one tile to another increases. Other sets exhibit gradual monotonic changes in structural density, or non-monotonic changes, while again others show no concentration dependence at all. We catalogue this extensive range of behaviours and present a model that provides a reasonably good estimate of the critical concentrations for a subset of the critical transitions. In addition we show that the structures resulting from these tile sets are fractal, with one of two different fractal dimensions.

cs.ET↗

arXiv2010

Self-assembly, modularity and physical complexity

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favoured in biological self-assembly, for example of protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful distance measure between physical structures.

cond-mat.stat-mech↗

arXiv2008

Applying weighted network measures to microarray distance matrices

In recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted network into an ensemble of edges, and is particularly suited to the analysis of fully connected weighted networks. Here we apply our method to several such networks including distance matrices, and show that the clustering coefficient, constructed by using the ensemble approach, provides meaningful insights into the systems studied. In the particular case of two data sets from microarray experiments the clustering coefficient identifies a number of biologically significant genes, outperforming existing identification approaches.

physics.data-an↗

arXiv2007

An ensemble approach to the analysis of weighted networks

We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted networks, such as the average degree of the nearest neighbours, the clustering coefficient, the `betweenness', the distance between two nodes and the diameter of a network. All these measures are well established for unweighted networks but have hitherto proven difficult to define for weighted networks. Further to introducing this approach we demonstrate its advantages by applying the clustering coefficient constructed in this way to two real-world weighted networks.

cond-mat.stat-mech↗

arXiv2005

All possible bipartite positive-operator-value measurements of two-photon polarization states

Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State measurements and an entangled three-photon ancilla state, which can be prepared separately and in advance (or 'off-line'). As an example we give the detailed settings for a simultaneous measurement of all four Bell States for an arbitrary two-photon polarization state, which is impossible with linear optics alone.

quant-ph↗

arXiv2005

Reply to "Comment on 'A linear optics implementation of weak values in Hardy's paradox'"

The comment by Lundeen et al. contains two criticisms of our proposal. While we agree that the state-preparation procedure could be replaced by a simpler setup as proposed by the authors of the comment, we do not agree with the authors on their second, and more important point regarding two-particle weak measurements. We believe this to be the result of a misunderstanding of our original paper.

quant-ph↗

arXiv2004

General implementation of all possible positive-operator-value measurements of single photon polarization states

Positive Operator Value Measures (POVMs) are the most general class of quantum measurements. We propose a setup in which all possible POVMs of a single photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective non-orthogonal or non-projective sets of any number of POVM operators. Furthermore our implementation only requires vacuum ancillas, and is deterministic rather than probabilistic. Thus it realizes every POVM with the correct set of output states. We give the settings required to implement two different well-known non-orthogonal projective POVMs.

quant-ph↗

arXiv2004

Linear optics implementation of weak values in Hardy's paradox

We propose an experimental setup for the implementation of weak measurements in the context of the gedankenexperiment known as Hardy's Paradox. As Aharonov et al. showed, these weak values form a language with which the paradox can be resolved. Our analysis shows that this language is indeed consistent and experimentally testable. It also reveals exactly how a combination of weak values can give rise to an apparently paradoxical result.

quant-ph↗

arXiv2004

Weak Measurement of the Arrival Times of Single Photons and Pairs of Entangled Photons

In this paper we propose a setup for the weak measurement of photon arrival time. It is found that the weak values of this arrival time can lie far away from the expectation value, and in principle also in regions forbidden by special relativity. We discuss in brief the implications of these results as well as their reconciliation with the principle of causality. Furthermore, an analysis of the weak arrival times of a pair of photons in a Bell state shows that these weak arrival times are correlated.

quant-ph↗