Using data from a live trading experiment on the Binance Bitcoin perpetual, we examine the effects of (i) basic order book mechanics and (ii) the persistence of price changes from immediate to short timescales, revealing the interplay between returns, queue sizes, and orders' queue positions. We document a fundamental trade-off: a negative correlation between maker fill likelihood and post-fill returns. This dictates that viable maker strategies often require a contrarian approach, counter-trading the prevailing order book imbalance. These dynamics render commonly-cited strategies highly unprofitable, leading us to model `Reversals': situations where a contrarian maker strategy at the touch proves effective.

We augment the Heterogeneous Autoregressive Regression model for forecasting realized volatility, using various measurements for the daily, weekly, and monthly volatilities, in addition to other predictive features. The main focus is on novel methods for extracting volatility estimators using option price data. Firstly, we provide a dimensionality reduction method for implied volatility surfaces built under the Black-Scholes model, whereby we combine simple row-wise and column-wise decompositions of the implied volatility surface with principal component analysis. Secondly, we provide a method for extracting the implied volatility under the Heston and Bates models. This is achieved by a calibration of these models while assuming that some of the model parameters remain constant. We demonstrate that these augmentations result in improved daily forecasts for realized volatility in a selection of different stocks. These volatility forecasts can also be utilized to further increase predictive performance for the realized volatility of other instruments, and can be combined for forecasting VIX.

We present the findings of a large-scale live trading experiment involving the placement of millions of market orders sent at a high frequency on two cryptocurrency exchanges, Bybit and Binance. We analyze the execution outcomes of these orders in comparison to the expected outcome based on the most recent snapshot of the Limit Order Book (LOB) at the time of order submission for two execution modes: one using market orders and the second using marketable limit orders aiming at the best price. Discrepancies between the actual and expected outcomes are due to intermittent LOB updates during a time span resulting from delays on the exchange, delays on the trader's end, or communication delays between the trader and the exchange. We show these discrepancies are strongly correlated with market factors such as volatility, latency, and LOB liquidity. Notably, we find a consistent disadvantage to the trader, pointing to an adverse selection effect for taker orders: profitable orders (as measured by short-term future PnL returns) tend to achieve worse-than-expected outcomes, while unprofitable orders typically achieve their expected (adverse) outcomes. In the case of market orders, this translates to a worsening of fill prices, while marketable limit orders suffer from a substantial probability of failing-to-fill-immediately. Quantitative researchers who fail to take these effects into account face the familiar litany of underperforming in a live trading environment relative to stellar backtests. To address this concern, we propose parsimonious models to estimate an order's probability of failing-to-fill-immediately (in case of a marketable limit order) and the worsening of its fill price (in case of a market order), allowing for greater accuracy when carrying out backtests and minimizing the discrepancy between backtest and realized live PnL.

We study Kolmogorov forward equations (KFEs) and Zakai equations for diffusionprocesses with a fast mean-reverting stochastic volatility component. In the case of the KFE, aparabolic PDE in divergence form, we perform a matched asymptotic expansion up to first orderin the small mean-reversion time. The solutions are expressed in terms of suitable PDEs withcoefficients averaged over the ergodic distribution, in the spirit of extensive earlier work on thebackward equation (see [J.-P. Fouque et al.,Multiscale Stochastic Volatility for Equity, InterestRate, and Credit Derivatives, Cambridge, University Press, 2011]). We then construct a sequence ofapproximations to the Zakai equation, a parabolic stochastic PDE (SPDE), and verify numericallyfor the first two terms weak convergence order half and order one, respectively, in the mean-reversionparameter. To this end, we give a novel numerical scheme for the original two-dimensional SPDE,which is robust in the small parameter regime, and compare derived functionals of marginals againstthose approximated by the solution of a sequence of homogenized one-dimensional SPDEs.

In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectators? We study a terminal-boundary value problem for the nonlinear parabolic PDE $2\partial_te(t,x)=\log(-\partial_{xx}e(t,x))$ derived by Aldous and prove its wellposedness and regularity of its solution by combining PDE analysis and probabilistic tools, in particular the reformulation as a stochastic control problem with restricted control set, which allows us to deduce strict ellipticity. We establish key qualitative properties of the solution including concavity, monotonicity, convergence to a steady state for long remaining time and the asymptotic behaviour shortly before the terminal time. Moreover, we construct convergent numerical approximations. The analytical and numerical results allow us to highlight the behaviour of the win-probability process in the present case where the match may end early, in contrast to recent work by Backhoff-Veraguas and Beiglb\"ock where the match always runs the full length.

We propose a novel data-driven network framework for forecasting problems related to E-mini S\&P 500 and CBOE Volatility Index futures, in which products with different expirations act as distinct nodes. We provide visual demonstrations of the correlation structures of these products in terms of their returns, realized volatility, and trading volume. The resulting networks offer insights into the contemporaneous movements across the different products, illustrating how inherently connected the movements of the future products belonging to these two classes are. These networks are further utilized by a multi-channel Graph Convolutional Network to enhance the predictive power of a Long Short-Term Memory network, allowing for the propagation of forecasts of highly correlated quantities, combining the temporal with the spatial aspect of the term structure.

We introduce OFTER, a time series forecasting pipeline tailored for mid-sized multivariate time series. OFTER utilizes the non-parametric models of k-nearest neighbors and Generalized Regression Neural Networks, integrated with a dimensionality reduction component. To circumvent the curse of dimensionality, we employ a weighted norm based on a modified version of the maximal correlation coefficient. The pipeline we introduce is specifically designed for online tasks, has an interpretable output, and is able to outperform several state-of-the art baselines. The computational efficacy of the algorithm, its online nature, and its ability to operate in low signal-to-noise regimes, render OFTER an ideal approach for financial multivariate time series problems, such as daily equity forecasting. Our work demonstrates that while deep learning models hold significant promise for time series forecasting, traditional methods carefully integrating mainstream tools remain very competitive alternatives with the added benefits of scalability and interpretability.

Motivated by the modeling of customer mobility and congestion in supermarkets, we study queueing networks with a single source and a single sink. We assume that walkers traverse a network according to an unbiased random walk, and we analyze how network topology affects the total mean queue size Q, which we use to measure congestion. We examine network topologies that minimize Q and provide proofs of optimality for some cases and numerical evidence of optimality for others. Finally, we present greedy algorithms that add edges to and delete edges from a network to reduce Q, and we apply these algorithms to a network that we construct using a supermarket store layout. We find that these greedy algorithms, which typically tend to add edges to the sink node, are able to significantly reduce Q. Our work helps improve understanding of how to design networks with low congestion and how to amend networks to reduce congestion.

This corrects the article DOI: 10.1103/PhysRevE.100.062304.

Heat transport in granular and porous media occurs through conduction in the solid and radiation through the voids. By exploiting the separation of length scales between the small typical particles or voids and the large size of whole region, the method of multiple scales can be applied. For a purely diffusive system, this yields a problem on the macroscale with an effective conductivity, deduced by solving a 'cell problem' on the microscale. Here, we apply the method when radiation and conduction are both present; however, care must be taken to correctly handle the integral nature of the radiative boundary condition. Again, an effective conductivity is found by solving a 'cell problem' which, because of the non-linearity of radiative transfer, to be solved for each temperature value. We also incorporate modifications to the basic theory of multiple scales in order to deal with the non-local nature of the radiative boundary condition. We derive the multiple scales formulation of the problem and report on numerical comparisons between the homogenised problem and direct solution of the problem. We also compare the effective conductivity to that derived using Maxwell models and effective medium theory.

In light of micro-scale inefficiencies induced by the high degree of fragmentation of the Bitcoin trading landscape, we utilize a granular data set comprised of orderbook and trades data from the most liquid Bitcoin markets, in order to understand the price formation process at sub-1 second time scales. To achieve this goal, we construct a set of features that encapsulate relevant microstructural information over short lookback windows. These features are subsequently leveraged first to generate a leader-lagger network that quantifies how markets impact one another, and then to train linear models capable of explaining between 10% and 37% of total variation in $500$ms future returns (depending on which market is the prediction target). The results are then compared with those of various PnL calculations that take trading realities, such as transaction costs, into account. The PnL calculations are based on natural $\textit{taker}$ strategies (meaning they employ market orders) that we associate to each model. Our findings emphasize the role of a market's fee regime in determining its propensity to being a leader or a lagger, as well as the profitability of our taker strategy. Taking our analysis further, we also derive a natural $\textit{maker}$ strategy (i.e., one that uses only passive limit orders), which, due to the difficulties associated with backtesting maker strategies, we test in a real-world live trading experiment, in which we turned over 1.5 million USD in notional volume. Lending additional confidence to our models, and by extension to the features they are based on, the results indicate a significant improvement over a naive benchmark strategy, which we also deploy in a live trading environment with real capital, for the sake of comparison.

Whether enjoying the lucid prose of a favorite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar, but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvelously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in "stylometry", the quantitative analysis of written text. In this paper, we examine punctuation sequences in a corpus of literary documents and ask the following questions: Are the properties of such sequences a distinctive feature of different authors? Is it possible to distinguish literary genres based on their punctuation sequences? Do the punctuation styles of authors evolve over time? Are we on to something interesting in trying to do stylometry without words, or are we full of sound and fury (signifying nothing)?

The wet screen printing process can be modelled by paste being pushed through a mesh onto a substrate and conductors below. During the process defects, such as vias, voids, pinholes, craters and bubbles can form and evolve. The primary objective of the Study Group was to know how best to alter the properties of the paste (rather than the geometry of the screen printing process itself) in order to eliminate the defects. With these goals in mind this report describes a simple model for the closure of craters, a model for the partial closure of vias, a possible mechanism for the formation of pinholes and finally a more detailed consideration of the screen printing process.

Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such generative models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully-ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially-ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers.

A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyze how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market, which enables institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations.

Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent approach for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but potentially inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between the connectivity patterns in different layers. Finally, we explain how to use correlated models for edge "prediction" (i.e., inference) in multilayer networks. By incorporating edge correlations, we find that prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously purchased grocery products.

Characterizing large-scale organization in networks, including multilayer networks, is one of the most prominent topics in network science and is important for many applications. One type of mesoscale feature is community structure, in which sets of nodes are densely connected internally but sparsely connected to other dense sets of nodes. Two of the most popular approaches for community detection are to maximize an objective function called "modularity" and to perform statistical inference using stochastic block models. Generalizing work by Newman on monolayer networks (Physical Review E 94, 052315), we show in multilayer networks that maximizing modularity is equivalent, under certain conditions, to maximizing the posterior probability of community assignments under a suitably chosen stochastic block model. We derive versions of this equivalence for various types of multilayer structure, including temporal, multiplex, and multilevel networks. We consider cases in which the key parameters are constant, as well as ones in which they vary across layers; in the latter case, this yields a novel, layer-weighted version of the modularity function. Our results also help address a longstanding difficulty of multilayer modularity-maximization algorithms, which require the specification of two sets of tuning parameters that have been difficult to choose in practice. We show how to perform this parameter selection in a statistically-grounded way, and we demonstrate the effectiveness of our approach on both synthetic and empirical networks.

There are several models for the effective thermal conductivity of two-phase composite materials in terms of the conductivity of the solid and the disperse material. In this paper, we generalise three models of Maxwell type (namely, the classical Maxwell model and two generalisations of it obtained from effective medium theory and differential effective medium theory) so that the resulting effective thermal conductivity accounts for radiative heat transfer within gas voids. In the high-temperature regime, radiative transfer within voids strongly influences the thermal conductivity of the bulk material. Indeed, the utility of these models over classical Maxwell-type models is seen in the high-temperature regime, where they predict that the effective thermal conductivity of the composite material levels off to a constant value (as a function of temperature) at very high temperatures, provided that the material is not too porous, in agreement with experiments. This behaviour is in contrast to models which neglect radiative transfer within the pores, or lumped parameter models, as such models do not resolve the radiative transfer independently from other physical phenomena. Our results may be of particular use for industrial and scientific applications involving heat transfer within porous composite materials taking place in the high-temperature regime.

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intracity scales and intercountry scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65%-70% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than a supermarket's original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales.