Eigenvector Synchronization, Graph Rigidity and the Molecule Problem

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend on previous work and propose the 3D-ASAP algorithm, for the graph realization problem in $\mathbb{R}^3$, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in $\mathbb{R}^3$, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms.Comment: 49 pages, 8 figure

Returns-Driven Macro Regimes and Characteristic Lead-Lag Behaviour between Asset Classes

We define data-driven macroeconomic regimes by clustering the relative performance in time of indices belonging to different asset classes. We then investigate lead-lag relationships within the regimes identified. Our study unravels market features characteristic of different windows in time and leverages on this knowledge to highlight market trends or risks that can be informative with respect to recurrent market developments. The framework developed also lays the foundations for multiple possible extensions.Comment: 9 pages, 8 figure

SEC Form 13F-HR: Statistical investigation of trading imbalances and profitability analysis

US Institutions with more than $100 million assets under management must disclose part of their long positions into the SEC Form 13F-HR on a quarterly basis. We consider the number of variations in holdings between consecutive reporting periods, and compute imbalances in buying versus selling behaviour for the assets under consideration. A significant opportunity for profit arises if an external investor is willing to trade contrarian to the 13F filings imbalances. Indeed, imbalances capture the amount of information already consumed in the market and the related trades tend to be inflated by crowding and herding. Betting on a relatively short-term movement of prices against the sign of imbalances results in a profitable strategy especially when using a time horizon between 21 and 42 trading days (corresponding to 1-2 calendar months) after each financial quarter ends.Comment: 23 pages, 18 figure