More Like this

1. Path Properties of a Generalized Fractional Brownian Motion

   https://doi.org/10.1007/s10959-020-01066-1  

   Ichiba, Tomoyuki; Pang, Guodong; Taqqu, Murad S. (January 2021, Journal of Theoretical Probability)

   null (Ed.)

   The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power-law shape function and non-stationary noises with a power-law variance function. In this paper, we study sample path properties of the generalized fractional Brownian motion, including Hölder continuity, path differentiability/non-differentiability, and functional and local law of the iterated logarithms. 

   more » « less
2. THE EASE OF FITTING BUT FUTILITY OF TESTING A NONSTATIONARY POISSON PROCESSES FROM ONE SAMPLE PATH

   Nelson, B L; Leemis, L M (December 2020, Proceedings of the Winter Simulation Conference)

   Bae, K-H; Feng, B; Kim, S; Lazarova-Molnar, S; Zheng, Z; Roeder, T; Thiesing, R (Ed.)

   The nonstationary Poisson process (NSPP) is a workhorse tool for modeling and simulating arrival processes with time-dependent rates. In many applications only a single sequence of arrival times are observed. While one sample path is sufficient for estimating the arrival rate or integrated rate function of the process—as we illustrate in this paper—we show that testing for Poissonness, in the general case, is futile. In other words, when only a single sequence of arrival data are observed then one can fit an NSPP to it, but the choice of “NSPP” can only be justified by an understanding of the underlying process physics, or a leap of faith, not by testing the data. This result suggests the need for sensitivity analysis when such a model is used to generate arrivals in a simulation. 

   more » « less
3. Frequency Modulation Based Long‐Wave Infrared Detection and Imaging at Room Temperature

   https://doi.org/10.1002/adfm.202309298  

   Guo, Tianyi; Dasgupta, Arindam; Chandra, Sayan; Ballav, Swastik; Cencillo‐Abad, Pablo; Mukherjee, Souptik; Biswas, Aritra; Shabbir, Muhammad_Waqas; Chanda, Debashis (October 2023, Advanced Functional Materials)

   Abstract Detection of long wave infrared (LWIR) light at room temperature is a long‐standing challenge due to the low energy of photons. A low‐cost, high‐performance LWIR detector or camera that operates under such conditions is pursued for decades. Currently, all available detectors operate based on amplitude modulation (AM) and are limited in performance by AM noises, including Johnson noise, shot noise, and background fluctuation noise. To address this challenge, a frequency modulation (FM)‐based detection technique is introduced, which offers inherent robustness against different types of AM noises. The FM‐based approach yields an outstanding room temperature noise equivalent power (NEP), response time, and detectivity (D*). This result promises a novel uncooled LWIR detection scheme that is highly sensitive, low‐cost, and can be easily integrated with electronic readout circuitry, without the need for complex hybridization. 

   more » « less
4. Functional Bayesian Networks for Discovering Causality from Multivariate Functional Data

   https://doi.org/10.1111/biom.13922  

   Zhou, Fangting; He, Kejun; Wang, Kunbo; Xu, Yanxun; Ni, Yang (August 2023, Biometrics)

   Abstract Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest. In this paper, we develop a novel Bayesian network (BN) model for multivariate functional data where conditional independencies and causal structure are encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian processes, which is the key to unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional BN model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples demonstrate the practical utility of the proposed model. 

   more » « less
5. Entanglement-enhanced dual-comb spectroscopy

   https://doi.org/10.1038/s41534-023-00758-w  

   Shi, Haowei; Chen, Zaijun; Fraser, Scott E.; Yu, Mengjie; Zhang, Zheshen; Zhuang, Quntao (September 2023, npj Quantum Information)

   Abstract Dual-comb interferometry harnesses the interference of two laser frequency combs to provide unprecedented capability in spectroscopy applications. In the past decade, the state-of-the-art systems have reached a point where the signal-to-noise ratio per unit acquisition time is fundamentally limited by shot noise from vacuum fluctuations. To address the issue, we propose an entanglement-enhanced dual-comb spectroscopy protocol that leverages quantum resources to significantly improve the signal-to-noise ratio performance. To analyze the performance of real systems, we develop a quantum model of dual-comb spectroscopy that takes practical noises into consideration. Based on this model, we propose quantum combs with side-band entanglement around each comb lines to suppress the shot noise in heterodyne detection. Our results show significant quantum advantages in the uW to mW power range, making this technique particularly attractive for biological and chemical sensing applications. Furthermore, the quantum comb can be engineered using nonlinear optics and promises near-term experimentation. 

   more » « less