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Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…
We develop an axiomatic framework for fractal analysis and fractal number theory grounded in hierarchies of definability. Central to this approach is a sequence of formal systems F_n, each corresponding to a definability level S_n contained…
Quantitative finance is the use of mathematical models to analyse financial markets and securities. Typically requiring significant amounts of computation, an important question is the role that novel architectures can play in accelerating…
This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these…
3D occupancy prediction plays a pivotal role in the realm of autonomous driving, as it provides a comprehensive understanding of the driving environment. Most existing methods construct dense scene representations for occupancy prediction,…
We introduce a novel GARCH model that integrates two sources of uncertainty to better capture the rich, multi-component dynamics often observed in the volatility of financial assets. This model provides a quasi closed-form representation of…
Accurate and high-resolution precipitation nowcasting from radar echo sequences is crucial for disaster mitigation and economic planning, yet it remains a significant challenge. Key difficulties include modeling complex multi-scale…
This paper proposes a unified control framework based on Response-Aware Risk-Constrained Control Barrier Function for dynamic safety boundary control of vehicles. Addressing the problem of physical model parameter mismatch, the framework…
High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as…
Floating Car Observers (FCOs) extend traditional Floating Car Data (FCD) by integrating onboard sensors to detect and localize other traffic participants, providing richer and more detailed traffic data. In this work, we explore various…
This paper describes a flexible and tractable bottom-up dynamic correlation modelling framework with a consistent stochastic recovery specification. The stochastic recovery specification only models the first two moments of the spot…
Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
Traditional stochastic control methods in finance rely on simplifying assumptions that often fail in real world markets. While these methods work well in specific, well defined scenarios, they underperform when market conditions change. We…
Volatility forecasts play a central role among equity risk measures. Besides traditional statistical models, modern forecasting techniques based on machine learning can be employed when treating volatility as a univariate, daily…
The induction motor controlled by Indirect Field Oriented Control (IFOC) is known to have high performance and better stability. This paper reports the dynamical behavior of an indirect field oriented control (IFOC) induction motor drive in…
We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal…
Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…
This study proposes a unified forecasting framework for high-dimensional multi-task time series to meet the prediction demands of cloud native backend systems operating under highly dynamic loads, coupled metrics, and parallel tasks. The…
As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…