arXiv subjects

Douglas P. Shepherd

Publications and source records attributed to Douglas P. Shepherd.

6 recordsLinked to original sources

arXiv2025

Mamba time series forecasting with uncertainty quantification

State space models, such as Mamba, have recently garnered attention in time series forecasting due to their ability to capture sequence patterns. However, in electricity consumption benchmarks, Mamba forecasts exhibit a mean error of approximately 8\%. Similarly, in traffic occupancy benchmarks, the mean error reaches 18\%. This discrepancy leaves us to wonder whether the prediction is simply inaccurate or falls within error given spread in historical data. To address this limitation, we propose a method to quantify the predictive uncertainty of Mamba forecasts. Here, we propose a dual-network framework based on the Mamba architecture for probabilistic forecasting, where one network generates point forecasts while the other estimates predictive uncertainty by modeling variance. We abbreviate our tool, Mamba with probabilistic time series forecasting, as Mamba-ProbTSF and the code for its implementation is available on GitHub (https://github.com/PessoaP/Mamba-ProbTSF). Evaluating this approach on synthetic and real-world benchmark datasets, we find Kullback-Leibler divergence between the learned distributions and the data--which, in the limit of infinite data, should converge to zero if the model correctly captures the underlying probability distribution--reduced to the order of $10^{-3}$ for synthetic data and $10^{-1}$ for real-world benchmark, demonstrating its effectiveness. We find that in both the electricity consumption and traffic occupancy benchmark, the true trajectory stays within the predicted uncertainty interval at the two-sigma level about 95\% of the time. We end with a consideration of potential limitations, adjustments to improve performance, and considerations for applying this framework to processes for purely or largely stochastic dynamics where the stochastic changes accumulate, as observed for example in pure Brownian motion or molecular dynamics trajectories.

stat.ML↗

arXiv2024

Re-thinking Richardson-Lucy without Iteration Cutoffs: Physically Motivated Bayesian Deconvolution

Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is achieved by iteratively maximizing a Poisson emission likelihood. However, the RL algorithm is known to prefer sparse solutions and overfit noise, leading to high-frequency artifacts. The structure of these artifacts is sensitive to the number of RL iterations, and this parameter is typically hand-tuned to achieve reasonable perceptual quality of the inferred object. Overfitting can be mitigated by introducing tunable regularizers or other ad hoc iteration cutoffs in the optimization as otherwise incorporating fully realistic models can introduce computational bottlenecks. To resolve these problems, we present Bayesian deconvolution, a rigorous deconvolution framework that combines a physically accurate image formation model avoiding the challenges inherent to the RL approach. Our approach achieves deconvolution while satisfying the following desiderata: I deconvolution is performed in the spatial domain (as opposed to the frequency domain) where all known noise sources are accurately modeled and integrated in the spirit of providing full probability distributions over the density of the putative object recovered; II the probability distribution is estimated without making assumptions on the sparsity or continuity of the underlying object; III unsupervised inference is performed and converges to a stable solution with no user-dependent parameter tuning or iteration cutoff; IV deconvolution produces strictly positive solutions; and V implementation is amenable to fast, parallelizable computation.

cs.CV↗

arXiv2024

Correcting for objective sample refractive index mismatch in extended field of view selective plane illumination microscopy

Selective plane illumination microscopy (SPIM) is an optical sectioning imaging approach based on orthogonal light pathways for excitation and detection. The excitation pathway has an inverse relation between the optical sectioning strength and the effective field of view (FOV). Multiple approaches exist to extend the effective FOV, and here we focus on remote focusing to axially scan the light sheet, synchronized with a CMOS camera's rolling shutter. A typical axially scanned SPIM configuration for imaging large samples utilizes a tunable optic for remote focusing, paired with air objectives focused into higher refractive index media. To quantitatively explore the effect of remote focus choices and sample space refractive index mismatch on light sheet intensity distributions, we developed a computational model integrating ray tracing and field propagation. We validate our model's performance against experimental light sheet profiles for various SPIM configurations. Our findings indicate that optimizing the position of the sample chamber relative to the excitation optics can enhance image quality by balancing aberrations induced by refractive index mismatch. We validate this prediction using a homebuilt, large sample axially scanned SPIM configuration and calibration samples.

physics.optics↗

arXiv2024

Fourier synthesis optical diffraction tomography for kilohertz rate volumetric imaging

Many biological and soft matter processes occur at high speeds in complex 3D environments, and developing imaging techniques capable of elucidating their dynamics is an outstanding experimental challenge. Here, we introduce Fourier Synthesis Optical Diffraction Tomography (FS-ODT), a novel approach for high-speed quantitative phase imaging capable of recording the 3D refractive index at kilohertz rates. FS-ODT introduces new pattern generation and inverse computational strategies that multiplex tens of illumination angles in a single tomogram, dramatically increasing the volumetric imaging rate. We validate FS-ODT performance by imaging samples of known composition and accurately recovering the refractive index for increasing pattern complexity. We further demonstrate the capabilities of FS-ODT for probing complex systems by studying the hindered diffusion of colloids in solution and the motility of single-cellular bacterial swimmers. We believe that FS-ODT is a promising approach for unlocking challenging imaging regimes in biophysics and soft matter that have been little explored, including understanding the physical interactions of colloids and microswimmers with their viscous 3D environment and the interplay between these stimuli and the molecular response of biological systems.

physics.optics↗

arXiv2023

Spatial wavefront shaping with a multipolar-resonant metasurface for structured illumination microscopy

Structured illumination microscopy (SIM) achieves superresolution in fluorescence imaging through patterned illumination and computational image reconstruction, yet current methods require bulky, costly modulation optics and high-precision optical alignment. This work demonstrates how nano-optical metasurfaces, rationally designed to tailor the optical wavefront at sub-wavelength dimensions, hold great potential as ultrathin, single-surface, all-optical wavefront modulators for SIM. We computationally demonstrate this principle with a multipolar-resonant metasurface composed of silicon nanostructures which generate versatile optical wavefronts in the far field upon variation of the polarization or angle of incident light. Algorithmic optimization is performed to identify the seven most suitable illumination patterns for SIM generated by the metasurface based on three key criteria. We find that multipolar-resonant metasurface SIM (mrm-SIM) achieves resolution comparable to conventional methods by applying the seven optimal metasurface-generated wavefronts to simulated fluorescent objects and reconstructing the objects using proximal gradient descent. The work presented here paves the way for a metasurface-enabled experimental simplification of structured illumination microscopy.

physics.optics↗

arXiv2022

Microscopic motility of isolated E. coli flagella

The fluctuation-dissipation theorem describes the intimate connection between the Brownian diffusion of thermal particles and their drag coefficients. In the simple case of spherical particles, it takes the form of the Stokes-Einstein relationship that links the particle geometry, fluid viscosity, and diffusive behavior. However, studying the fundamental properties of microscopic asymmetric particles, such as the helical-shaped propeller used by $\textit{E. coli}$, has remained out of reach for experimental approaches due to the need to quantify correlated translation and rotation simultaneously with sufficient spatial and temporal resolution. To solve this outstanding problem, we generated volumetric movies of fluorophore-labeled, freely diffusing, isolated $\textit{E. Coli}$ flagella using oblique plane microscopy. From these movies, we extracted trajectories and determined the hydrodynamic propulsion matrix directly from the diffusion of flagella via a generalized Einstein relation. Our results validate prior proposals, based on macroscopic wire helices and low Reynolds number scaling laws, that the average flagellum is a highly inefficient propeller. Specifically, we found the maximum propulsion efficiency of flagella is less than 5%. Beyond extending Brownian motion analysis to asymmetric 3D particles, our approach opens new avenues to study the propulsion matrix of particles in complex environments where direct hydrodynamic approaches are not feasible.

physics.bio-ph↗