We extend Relative Robust Portfolio Optimization models to allow portfolios to optimize their performance when considered relative to a set of benchmarks. We do this in a minimum volatility setting, where we model regret directly as the maximum difference between our volatility and that of a given benchmark. Portfolio managers are also given the option of computing regret as a proportion of the benchmark’s performance, which is more in line with market practice than other approaches suggested in the literature. Furthermore, we propose using regret as an extra constraint rather than as a brand new objective function, so practitioners can maintain their current framework. We also look into how such a triple optimization problem can be solved or at least approximated for a general class of objective functions and uncertainty and benchmark sets. Finally, we illustrate the benefits of this approach by examining its performance against other common methods in the literature in several equity markets.

We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market practices than other approaches suggested in the literature. In addition, they are given the choice of simply adding an extra constraint to their optimisation problem instead of outright changing the objective function, as is commonly suggested in the literature. We illustrate the benefits of this approach by applying it to equity portfolios in a variety of regions.

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 depends only on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure 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.

The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the deviations in the waiting-time distribution away from one generated by a random process, may help unravel the feedback mechanisms that drive the underlying dynamics. We analyze the waiting-time distributions of high frequency foreign exchange data for the best executable bid-ask prices across all major currencies. We find that the lognormal distribution yields a good overall fit for the waiting-time distribution between currency rate changes if both short and long waiting times are included. If we restrict our study to long waiting-times, each currency pair's distribution is consistent with a power law tail with exponent near to 3.5. However for short waiting times, the overall distribution resembles one generated by an archetypal complex systems model in which boundedly rational agents compete for limited resources. Our findings suggest a gradual transition arises in trading behavior between a fast regime in which traders act in a boundedly rational way, and a slower one in which traders' decisions are driven by generic feedback mechanisms across multiple timescales and hence produce similar power-law tails irrespective of currency type.

Gad-1 and Gad-2 are antimicrobial peptide (AMP) sequences encoded by paralogous genes. They are rich in histidine, which suggests that their activity might be pH-dependent. We examined their structure–function relationships with a view to learning how to improve AMP therapeutic ratios. Activity assays with Gram-negative bacteria and cancer cell lines demonstrate that Gad-2 is substantially more active at slightly acidic pH than it is at neutral pH. By contrast, the activity of Gad-1 at lower pH is similar to its activity at pH 7. Circular dichroism spectra indicate that the greater functional plasticity of Gad-2 correlates with a greater structural plasticity; Gad-2's percent helicity varies dramatically with altered pH and lipid environment. Interestingly, Gad-2's highest levels of helicity do not correspond to the conditions where it is most active. High resolution solution NMR structures were determined in SDS micelles at pH 5, conditions that induce an intermediate level of helicity in the peptides. Gad-1 is more helical than Gad-2, with both peptides exhibiting the greatest helical tendencies in their central region and lowest helicity in their N-termini. The high resolution structures suggest that maximum activity relies on the appropriate balance between an N-terminal region with mixed hydrophobic/hydrophilic structure features and an amphipathic central and C-terminal region. Taken together with previous studies, our results suggest that to improve the therapeutic ratio of AMPs, consideration should be given to including sequential histidine-pairs, keeping the overall charge of the peptide modest, and retaining a degree of structural plasticity and imperfect amphipathicity.

Limit order books (LOBs) match buyers and sellers in more than half of the world's financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into certain aspects of the mechanism. We also illustrate that many such models poorly resemble real LOBs and that several well-established empirical facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved questions about LOBs.

Martin D. Gould,1, 2, 3, ∗ Mason A. Porter,1, 3 Nikolaus Hautsch,4 Stacy Williams,5 Mark McDonald,5 Daniel J. Fenn,5 and Sam D. Howison1, 2 1Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK 2Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford, OX2 6ED, UK 3CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, UK 4Chair of Econometrics, Humboldt-Universit ät zu Berlin, Berlin, 10178, Germany 5FX Quantitative Research, HSBC Bank, London E14 5HQ, UK

We use techniques from network science to study correlations in the foreign exchange (FX) market over the period 1991--2008. We consider an FX market network in which each node represents an exchange rate and each weighted edge represents a time-dependent correlation between the rates. To provide insights into the clustering of the exchange rate time series, we investigate dynamic communities in the network. We show that there is a relationship between an exchange rate's functional role within the market and its position within its community and use a node-centric community analysis to track the time dynamics of this role. This reveals which exchange rates dominate the market at particular times and also identifies exchange rates that experienced significant changes in market role. We also use the community dynamics to uncover major structural changes that occurred in the FX market. Our techniques are general and will be similarly useful for investigating correlations in other markets.

Deuterium NMR spectroscopy was used to study how the positioning of a dimerization motif within a transbilayer polypeptide influences its orientation and dynamics in bilayers. Three polypeptide variants comprising glycophorin A transmembrane (GpATM) dimerization motifs incorporated into lysine-terminated poly-leucine-alanine helices were mixed into 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine multilamellar vesicles. The variants differed in orientation of the motif segment around the helix axis with respect to the peptide ends. Polypeptides were labeled with methyl-deuterated alanines at positions that were identically situated relative to the peptide ends (Ala-20 and Ala-22) and at two positions within the motif. An analysis of quadrupole splittings revealed similar tilts and orientations of the peptide ends for all three variants, suggesting that average orientations were dominated by interactions at the bilayer surface. For one variant, however, fast orientational fluctuations about the helix axis were significantly smaller. This may indicate some perturbation of peptide dynamics and conformation by interactions that are sensitive to the motif orientation relative to the peptide ends. For the variant that displayed distinct dynamics, one orientation consistent with observed splittings corresponded to the motif being situated such that its two glycines were particularly accessible to adjacent peptides.

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 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.

Martin D. Gould, 2, ∗ Mason A. Porter, 2 Stacy Williams, Mark McDonald, Daniel J. Fenn, 2, 3 and Sam D. Howison Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, UK FX Quantitative Research, HSBC Bank, 8 Canada Square, London E14 5HQ, UK Mathematical and Computational Finance Group, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK

These studies detail the altered structure-function relationships caused by oxidation of surfactant protein B (SP-B), a mode of damage thought to be important in acute respiratory distress syndrome (ARDS), a common and frequently fatal condition. An 18-residue fragment comprising the N-terminal helix of SP-B was investigated in oxidized and unmodified forms by solution and solid-state nuclear magnetic resonance (NMR), circular dichroism (CD), and molecular dynamics (MD) simulation. Taken together, the results indicate that tryptophan oxidation causes substantial disruptions in helical structure and lipid interactions. The structural modifications induced by tryptophan oxidation were severe, with a reduction in helical extent from approximately three helical turns to, at most, one turn, and were observed in a variety of solvent environments, including sodium dodecyl sulfate (SDS) micelles, dodecyl phosphocholine (DPC) micelles, and a 40% hexafluoro-2-propanol (HFIP) aqueous solution. The unmodified peptide takes on an orientation within lipid bilayers that is tilted approximately 30° away from an in-plane position. Tryptophan oxidation causes significant modifications to the peptide-lipid interactions, and the peptide likely shifts to a more in-plane orientation within the lipids. Interestingly, the character of the disruptions to peptide-lipid interactions caused by tryptophan oxidation was highly dependent on the charge of the lipid headgroup.

As the pricing mechanism in more than half the world's financial markets, the limit order book has recently been the focus of a great deal of published literature in a wide range of disciplines. In this survey, we present a mathematical description of the price matching algorithm at the heart of limit order trading, and highlight some of the key publications - both empirical and theoretical - that have advanced understanding of the process to date. By examining existing models of limit order markets, we identify some of the key unresolved questions and difficulties facing researchers of limit order trading today.

The lung surfactant protein B (SP-B) is essential for life and plays a critical role in reducing surface tension in the lungs during breathing. An amphipathic helical fragment of SP-B composed of the 16 C-terminal residues, termed SP-BCTERM or SP-B63-78, has a charge of +3 and retains significant bioactivity compared to native SP-B. We have used 31P-, 2H-, 13C-, and 15N- solid state NMR to investigate the insertion of SP-BCTERM into lipid bilayers composed of model lipids, as well as bovine lung extracted surfactant (BLES). When the external magnetic field is parallel to the normal of the oriented lipid bilayers, the 15N chemical shift of the peptide backbone is at ∼ 98 ppm, which corresponds to a helical axis alignment of approximately 70° relative to the lipid bilayer normal. The depth of peptide insertion in vesicles was investigated by 13C{31P} REDOR, as well as by measuring the 13C relaxation time in the absence and presence of the paramagnetic probe Mn2+.

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 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.

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.

We investigate the clustering dynamics of multichannel (multivariate) time series by first representing their correlations as time-dependent networks and then examining the evolution of network communities. To do this, we employ a node-centric approach that allows us to to track the functional roles of individual nodes in time 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. Using dynamical community detection, we find that exchange rates with strong intra-community connections are persistently assigned to communities with the same set of nodes.

The dynamical response of a population of interconnected objects, when exposed to external perturbations, is of great interest to physicists working on complex systems. Here we focus on human systems, by analyzing the dynamical response of the world's financial community to various types of unexpected events-including the 9/11 terrorist attacks as they unfolded on a minute-by-minute basis. For the unfolding events of 9/11, our results show that there was a gradual collective understanding of what was happening, rather than an immediate realization. More generally, we find that for news items which are not simple economic statements-and hence whose implications for the market are not immediately obvious-there are periods of collective discovery during which opinions seem to vary in a remarkably synchronized way.

Dexamethasone, betamethasone and prednisolone are synthetic glucocorticosteroids authorised for therapeutic use in bovine animals within the European Union. Dexamethasone and betamethasone are used mainly for the treatment of metabolic and inflammatory diseases. Prednisolone is used to treat bovine mastitis. Maximum residue limits (MRLs) of 0.3 μg kg−1 for both dexamethasone and betamethasone and 6.0 μg kg−1 for prednisolone in bovine milk have been established. 6α-Methylprednisolone and flumethasone are not authorised for use in bovine animals and are completely banned in bovine milk. The proposed method is based on deprotenisation of milk using 20% (w/v) trichloroacetic acid. Samples are filtered using glass microfibre filters and subject to clean-up using OASIS HLB solid phase extraction. Separation was achieved on a Hypercarb 100 mm × 2.1 mm × 5 μm column. Mobile phase was: 90/10 acetonitrile/0.1% formic acid in water; flow rate was 600 μL min−1. The method allowed the rapid identification and confirmation of the five glucocorticosteroids according to the criteria laid down in Commission Decision 2002/657/EC. Matrix calibration curves for all compounds were linear in the interval 0.0 MRL to 2.0 MRL with a correlation coefficient (r2) higher than 0.96. Relative recoveries ranged from 97% for betamethasone to 111% for prednisolone. Precision at the MRL ranged from 3.8% for prednisolone to 13.8% for betamethasone. Decision limits, CCα, and detection capability, CCβ have been calculated for all compounds.