BackgroundClinical researchers have often preferred to use a fixed effects model for the primary interpretation of a meta-analysis. Heterogeneity is usually assessed via the well known Q and I2 statistics, along with the random effects estimate they imply. In recent years, alternative methods for quantifying heterogeneity have been proposed, that are based on a 'generalised' Q statistic.MethodsWe review 18 IPD meta-analyses of RCTs into treatments for cancer, in order to quantify the amount of heterogeneity present and also to discuss practical methods for explaining heterogeneity.ResultsDiffering results were obtained when the standard Q and I2 statistics were used to test for the presence of heterogeneity. The two meta-analyses with the largest amount of heterogeneity were investigated further, and on inspection the straightforward application of a random effects model was not deemed appropriate. Compared to the standard Q statistic, the generalised Q statistic provided a more accurate platform for estimating the amount of heterogeneity in the 18 meta-analyses.ConclusionsExplaining heterogeneity via the pre-specification of trial subgroups, graphical diagnostic tools and sensitivity analyses produced a more desirable outcome than an automatic application of the random effects model. Generalised Q statistic methods for quantifying and adjusting for heterogeneity should be incorporated as standard into statistical software. Software is provided to help achieve this aim.
This study presents a detailed numerical analysis of a three-dimensional micro pin fin heat sink incorporating 55 fins arranged in a single channel in four distinct cross-sectional geometries: square, circular, triangular, and pentagonal. A conventional microchannel heat sink (MCHS) without pin fins serves as a baseline for comparison. Water is employed as the working fluid, and simulations are conducted over a laminar flow regime with Reynolds numbers ranging from 500 to 1500. To efficiently capture the thermo-hydrodynamic behavior and reduce computational cost, a representative single flow channel is simulated under symmetrical boundary conditions, and key pin fin parameters such as height and spacing are systematically varied. The cross-sectional hydraulic diameter and spacing are held constant for all cases, with step sizes and non-dimensional spacing ratios sp/hp adjusted to assess their effect on heat sink performance. Results indicate that among all geometries, circular fins exhibit the highest heat transfer enhancement, with the Nusselt number increasing by 60% at Re = 500 and by 90% at Re = 1500 compared to the baseline. However, this improved thermal performance is accompanied by a greater pressure drop relative to the other tested pin fin shapes. Following the circular fins, triangular and square configurations offer progressively lower heat transfer rates, while pentagonal pin fins demonstrate the minimum enhancement. Furthermore, for all fin geometries, increasing the Reynolds number leads to a consistent improvement in heat transfer. Overall, the study provides quantitative insights into the impact of pin fin geometry and arrangement on the thermal and fluid dynamic performance of micro pin fin heat sinks, offering valuable guidelines for the design of advanced cooling solutions in microelectronics.
Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well understood, hindering their real-world applicability. In this research, our aim is to offer actionable insights into the utility of deep PDE solvers for practical option pricing implementation. Through comparative experiments in both the Black--Scholes and the Heston model, we assess the empirical performance of two neural network algorithms to solve PDEs: the Deep Galerkin Method and the Time Deep Gradient Flow method (TDGF). We determine their empirical convergence rates and training time as functions of (i) the number of sampling stages, (ii) the number of samples, (iii) the number of layers, and (iv) the number of nodes per layer. For the TDGF, we also consider the order of the discretization scheme and the number of time steps.
This paper introduces StockGPT, an autoregressive ``number'' model trained and tested on 70 million daily U.S.\ stock returns over nearly 100 years. Treating each return series as a sequence of tokens, StockGPT automatically learns the hidden patterns predictive of future returns via its attention mechanism. On a held-out test sample from 2001 to 2023, daily and monthly rebalanced long-short portfolios formed from StockGPT predictions yield strong performance. The StockGPT-based portfolios span momentum and long-/short-term reversals, eliminating the need for manually crafted price-based strategies, and yield highly significant alphas against leading stock market factors, suggesting a novel AI pricing effect. This highlights the immense promise of generative AI in surpassing human in making complex financial investment decisions.
Commodity trading advisors (CTAs), who mainly trade commodity futures, showed good returns in the 2000s. However, since the 2010's, they have not performed very well. One possible reason of this phenomenon is the emergence of short-term reversal traders (STRTs) who prey on CTAs for profit. In this study, I built an artificial market model by adding a CTA agent (CTAA) and STRT agent (STRTA) to a prior model and investigated whether emerging STRTAs led to a decrease in CTAA revenue to determine whether STRTs prey on CTAs for profit. To the contrary, my results showed that a CTAA and STRTA are more likely to trade and earn more when both exist. Therefore, it is possible that they have a mutually beneficial relationship.
The current design space of derivatives in Decentralized Finance (DeFi) relies heavily on oracle systems. Replicating market makers (RMMs) provide a mechanism for converting specific payoff functions to an associated Constant Function Market Makers (CFMMs). We leverage RMMs to replicate the approximate payoff of a Black-Scholes covered call option. RMM-01 is the first implementation of an on-chain expiring option mechanism that relies on arbitrage rather than an external oracle for price. We provide frameworks for derivative instruments and structured products achievable on-chain without relying on oracles. We construct long and binary options and briefly discuss perpetual covered call strategies commonly referred to as "theta vaults." Moreover, we introduce a procedure to eliminate liquidation risk in lending markets. The results suggest that CFMMs are essential for structured product design with minimized trust dependencies.
In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy models; the calculations are in the dual space, and the Wiener-Hopf factorization is used. For wide regions in the parameter space, the precision of the order of $10^{-15}$ is achievable in seconds, and of the order of $10^{-9}-10^{-8}$ - in fractions of a second. The Wiener-Hopf factors and repeated integrals in the pricing formulas are calculated using sinh-deformations of the lines of integration, the corresponding changes of variables and the simplified trapezoid rule. If the Bromwich integral is calculated using the Gaver-Wynn Rho acceleration instead of the sinh-acceleration, the CPU time is typically smaller but the precision is of the order of $10^{-9}-10^{-6}$, at best. Explicit pricing algorithms and numerical examples are for no-touch options, digitals (equivalently, for the joint distribution function of a Lévy process and its supremum and infimum processes), and call options. Several graphs are produced to explain fundamental difficulties for accurate pricing of barrier options using time discretization and interpolation-based calculations in the state space.
We extract the e+e− → π+π− cross section in the energy range between 600 and 900 MeV, exploiting the method of initial state radiation. A data set with an integrated luminosity of 2.93 fb−1 taken at a centerof-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider is used. The cross section is measured with a systematic uncertainty of 0.9%. We extract the pion form factor |Fπ| as well as the contribution of the measured cross section to the leading-order hadronic vacuum polarization contribution to (g − 2)μ. We find this value to be a μ (600 − 900 MeV) = (368.2 ± 2.5stat ± 3.3sys) · 10−10, which is between the corresponding values using the BaBar or KLOE data.