Demonstrating the Transferability and the Descriptive Power of Sketch-Map

Increasingly, it is recognized that new automated forms of analysis are required to understand the high-dimensional output obtained from atomistic simulations. Recently, we introduced a new dimensionality reduction algorithm, sketch-map, that was designed specifically to work with data from molecular dynamics trajectories. In what follows, we provide more details on how this algorithm works and on how to set its parameters. We also test it on two well-studied Lennard-Jones clusters and show that the coordinates we extract using this algorithm are extremely robust. In particular, we demonstrate that the coordinates constructed for one particular Lennard-Jones cluster can be used to describe the configurations adopted by a second, different cluster and even to tell apart different phases of bulk Lennard-Jonesium.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.

Simplifying the representation of complex free-energy landscapes using sketch-map

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible.

Invariant Information Local Sub-map Filter (IILSF) for Efficient Simultaneous Localisation and Mapping of Large Environments

This paper presents an Invariant Information Local Sub-map Filter (IILSF) as a technique for consistent Simultaneous Localisation and Mapping (SLAM) in a large environment. It harnesses the benefits of sub-map technique to improve the consistency and efficiency of Extended Kalman Filter (EKF) based SLAM. The IILSF makes use of invariant information obtained from estimated locations of features in independent sub-maps, instead of incorporating every observation directly into the global map. Then the global map is updated at regular intervals. Applying this technique to the EKF based SLAM algorithm: (a) reduces the computational complexity of maintaining the global map estimates and (b) simplifies transformation complexities and data association ambiguities usually experienced in fusing sub-maps together. Simulation results show that the method was able to accurately fuse local map observations to generate an efficient and consistent global map, in addition to significantly reducing computational cost and data association ambiguities.

The Map Defines the Territory: Remodelling NGO Partnerships for Knowledge Translation in Transition Contexts

The initial impetus for a theoretical exploration of organisational relationships is based on case study research on a Bulgarian NGO's implementation of values and goals into practices under a guiding relationship from a very experienced UK organisation in the same field. Findings diverged from conventional accounts of developing NGOs' dependence on more developed counterparts and that case study findings characterised the inter- dependency between the two organisations as more alike to a collaborative knowledge ...

The Map of Watchful Architecture

The international border between Northern Ireland and the South (the Republic of Ireland) came into being in 1922, but there are many important historical antecedents to the notion and expression of spatial separation in this borderland. The author identifies historical precedents and links them to recent defensive features in order to generate a 'map of watchful architecture' that includes recent and much older elements.

Fictional Ulster:A map of places created by writers

Ballybeg, the fictitious setting for Brian Friel’s plays, is more famous than most real villages in Ulster. Despite not existing, the village has a kind of cultural and geographic life. This is part of what this map is about. It locates and charts Ulster’s fictional places — places invented by writers down through the years. These places have meaning too, they are part of how Ulster pictures itself and how others picture Ulster.

The Map of Connections 3.1: Unofficial and previously unmapped Irish border crossings

I charted unofficial border-crossings along Ireland's border, those not found on any other map.

During many surveys of Ireland's border I discovered that it is often perforated. Gates are set in hedgerows for the convenience of farmers, stepping stones and community-built bridges span rivers, walkers’ routes and muddy by-ways go wherever they please. These kinds of connections have always been there, although I think it is fair to say that their numbers have increased during the Peace Process. Roads blocked or cratered during the Troubles are being re-connected at a rate too fast for the Ordnance Survey to keep up with. On the local level cross-border movement is quietly happening, unchecked and often unmapped, until now.

This map attempts to throw the borderline in perpendicular, showing it as a place of connection rather than division.