Community detection in temporal multilayer networks, with an application to correlation networks

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the "modularity" quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a "null network"---is application-dependent. We differentiate between "null networks" and "null models" in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis only depends on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure \emph{persistence} of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular "Louvain" heuristic faces with temporal multilayer networks and suggest ways to mitigate them.Comment: 42 pages, many figures, final accepted version before typesettin

The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market

We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with larger numbers of opportunities with shorter mean durations occurring during more liquid hours. We demonstrate further that the number of arbitrage opportunities has decreased in recent years, implying a corresponding increase in pricing efficiency. Using trading simulations, we show that a trader would need to beat other market participants to an unfeasibly large proportion of arbitrage prices to profit from triangular arbitrage over a prolonged period of time. Our results suggest that the foreign exchange market is internally self-consistent and provide a limited verification of market efficiency

Temporal Evolution of Financial Market Correlations

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We then characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007--2008 credit and liquidity crisis.Comment: 15 pages, 10 figures, 1 table. Accepted for publication in Phys. Rev. E. v2 includes additional section

Self-organized global control of carbon emissions

There is much disagreement concerning how best to control global carbon emissions. We explore quantitatively how different control schemes affect the collective emission dynamics of a population of emitting entities. We uncover a complex trade-off which arises between average emissions (affecting the global climate), peak pollution levels (affecting citizens' everyday health), industrial efficiency (affecting the nation's economy), frequency of institutional intervention (affecting governmental costs), common information (affecting trading behavior) and market volatility (affecting financial stability). Our findings predict that a self-organized free-market approach at the level of a sector, state, country or continent, can provide better control than a top-down regulated scheme in terms of market volatility and monthly pollution peaks.Comment: 4 pages, 4 figure

Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007--2008 credit crisis

We study the cluster dynamics of multichannel (multivariate) time series by representing their correlations as time-dependent networks and investigating the evolution of network communities. We employ a node-centric approach that allows us to track the effects of the community evolution on the functional roles of individual nodes without having to track entire communities. As an example, we consider a foreign exchange market network in which each node represents an exchange rate and each edge represents a time-dependent correlation between the rates. We study the period 2005-2008, which includes the recent credit and liquidity crisis. Using dynamical community detection, we find that exchange rates that are strongly attached to their community are persistently grouped with the same set of rates, whereas exchange rates that are important for the transfer of information tend to be positioned on the edges of communities. Our analysis successfully uncovers major trading changes that occurred in the market during the credit crisis.Comment: 8 pages, 6 figures, accepted for publication in Chao

Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory

We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This happens for a finite-dimensional quasi-quantum group, whose definition involves a finite group $G$, and a 3-cocycle \om, which was first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more detail, and argue that in this case the invariants agree with the partition function of the topological field theory of Dijkgraaf and Witten depending on the same data G, \,\om.Comment: 30 page

High-Resolution Analysis of Zn^2+ Coordination in the Alkaline Phosphatase Superfamily by EXAFS and X-ray Crystallography

Comparisons among evolutionarily related enzymes offer opportunities to reveal how structural differences produce different catalytic activities. Two structurally related enzymes, Escherichia coli alkaline phosphatase (AP) and Xanthomonas axonopodis nucleotide pyrophosphatase/phosphodiesterase (NPP), have nearly identical binuclear Zn^2+ catalytic centers but show tremendous differential specificity for hydrolysis of phosphate monoesters or phosphate diesters. To determine if there are differences in Zn^2+ coordination in the two enzymes that might contribute to catalytic specificity, we analyzed both x-ray absorption spectroscopic and x-ray crystallographic data. We report a 1.29-Å crystal structure of AP with bound phosphate, allowing evaluation of interactions at the AP metal site with high resolution. To make systematic comparisons between AP and NPP, we measured zinc extended x-ray absorption fine structure for AP and NPP in the free-enzyme forms, with AMP and inorganic phosphate groundstate analogs and with vanadate transition-state analogs. These studies yielded average zinc–ligand distances in AP and NPP free-enzyme forms and ground-state analog forms that were identical within error, suggesting little difference in metal ion coordination among these forms. Upon binding of vanadate to both enzymes, small increases in average metal–ligand distances were observed, consistent with an increased coordination number. Slightly longer increases were observed in NPP relative to AP, which could arise from subtle rearrangements of the active site or differences in the geometry of the bound vanadyl species. Overall, the results suggest that the binuclear Zn^2+ catalytic site remains very similar between AP and NPP during the course of a reaction cycle

Large-scale ozone and aerosol distributions, air mass characteristics, and ozone fluxes over the western Pacific Ocean in late winter/early spring

Large‐scale measurements of ozone (O3) and aerosol distributions were made from the NASA DC‐8 aircraft during the Transport and Chemical Evolution over the Pacific (TRACE‐P) field experiment conducted in February–April 2001. Remote measurements were made with an airborne lidar to provide O3 and multiple‐wavelength aerosol backscatter profiles from near the surface to above the tropopause along the flight track. In situ measurements of O3, aerosols, and a wide range of trace gases were made onboard the DC‐8. Five‐day backward trajectories were used in conjunction with the O3 and aerosol distributions on each flight to indicate the possible origin of observed air masses, such as from biomass burning regions, continental pollution, desert regions, and oceanic regions. Average latitudinal O3 and aerosol scattering ratio distributions were derived from all flights west of 150°E, and these distributions showed the average latitude and altitude dependence of different dynamical and chemical processes in determining the atmospheric composition over the western Pacific. TRACE‐P (TP) showed an increase in the average latitudinal distributions of both O3 and aerosols compared to PEM‐West B (PWB), which was conducted in February–March 1994. O3, aerosol, and potential vorticity levels were used to identify nine air mass types and quantify their frequency of occurrence as a function of altitude. This paper discusses the characteristics of the different air mass types encountered during TP and compares them to PWB. These results confirmed that most of the O3 increase in TP was due to photochemistry. The average latitudinal eastward O3 flux in the western Pacific during TP was found to peak near 32°N with a total average O3 flux between 14 and 46°N of 5.2 Tg/day. The eastward total CO flux was calculated to be 2.2 Tg‐C/day with ∼6% estimated from Asia. The Asian flux of CO2 and CH4 was estimated at 4.9 and 0.06 Tg‐C/day