Stratigraphic correlation underpins all understanding of Earth’s history, yet few geoscientists have access to, or expertise in, numerical codes that can generate reproducible, optimal (in a least-squares framework) alignments between two stratigraphic time-series data sets. Here we introduce Align, a user-friendly computer app that makes accessible a published dynamic time warping (DTW) algorithm that, in a minute or less, catalogs a library of alignments between two time-series data sets by systematically exploring assumptions about the temporal overlap and relative sedimentation rates between the two stratigraphic sections. The Align app, written in the free, open-source R programming language, utilizes a graphical user interface (e.g., drop-down menus for data upload and sliding bars for parameter exploration) such that no coding is required. In addition to generating alignment libraries, a user can employ Align to visualize, explore, and cull each alignment library according to thresholds on Pearson’s correlation coefficient and/or temporal overlap. Here we demonstrate Align with time-series records of carbonate stable carbon isotope composition, though Align can, in principle, align any two quantitative stratigraphic time-series data sets.
more »
« less
Parameter-Free Ordered Partial Match Alignment with Hidden State Time Warping
This paper investigates an ordered partial matching alignment problem, in which the goal is to align two sequences in the presence of potentially non-matching regions. We propose a novel parameter-free dynamic programming alignment method called hidden state time warping that allows an alignment path to switch between two different planes: a “visible” plane corresponding to matching sections and a “hidden” plane corresponding to non-matching sections. By defining two distinct planes, we can allow different types of time warping in each plane (e.g., imposing a maximum warping factor in matching regions while allowing completely unconstrained movements in non-matching regions). The resulting algorithm can determine the optimal continuous alignment path via dynamic programming, and the visible plane induces a (possibly) discontinuous alignment path containing matching regions. We show that this approach outperforms existing parameter-free methods on two different partial matching alignment problems involving speech and music.
more »
« less
- Award ID(s):
- 1948531
- PAR ID:
- 10338591
- Date Published:
- Journal Name:
- Applied Sciences
- Volume:
- 12
- Issue:
- 8
- ISSN:
- 2076-3417
- Page Range / eLocation ID:
- 3783
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Dynamic time warping estimates the alignment between two sequences and is designed to handle a variable amount of time warping. In many contexts, it performs poorly when confronted with two sequences of different scale, in which the average slope of the true alignment path in the pairwise cost matrix deviates significantly from one. This paper investigates ways to improve the robustness of DTW to such global time warping conditions, using an audio–audio alignment task as a motivating scenario of interest. We modify a dataset commonly used for studying audio–audio synchronization in order to construct a benchmark in which the global time warping conditions are carefully controlled, and we evaluate the effectiveness of several strategies designed to handle global time warping. Among the strategies tested, there is a clear winner: performing sequence length normalization via downsampling before invoking DTW. This method achieves the best alignment accuracy across a wide range of global time warping conditions, and it maintains or reduces the runtime compared to standard usages of DTW. We present experiments and analyses to demonstrate its effectiveness in both controlled and realistic scenarios.more » « less
-
We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton-Jacobi-Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations.more » « less
-
A variety of supergravity and string models involve hidden sectors where the hidden sectors may couple feebly with the visible sectors via a variety of portals. While the coupling of the hidden sector to the visible sector is feeble its coupling to the inflaton is largely unknown. It could couple feebly or with the same strength as the visible sector which would result in either a cold or a hot hidden sector at the end of reheating. These two possibilities could lead to significantly different outcomes for observables. We investigate the thermal evolution of the two sectors in a cosmologically consistent hidden sector dark matter model where the hidden sector and the visible sector are thermally coupled. Within this framework we analyze several phenomena to illustrate their dependence on the initial conditions. These include the allowed parameter space of models, dark matter relic density, proton-dark matter cross section, effective massless neutrino species at BBN time, self-interacting dark matter cross-section, where self-interaction occurs via exchange of dark photon, and Sommerfeld enhancement. Finally fits to the velocity dependence of dark matter cross sections from galaxy scales to the scale of galaxy clusters is given. The analysis indicates significant effects of the initial conditions on the observables listed above. The analysis is carried out within the framework where dark matter is constituted of dark fermions and the mediation between the visible and the hidden sector occurs via the exchange of dark photons. The techniques discussed here may have applications for a wider class of hidden sector models using different mediations between the visible and the hidden sectors to explore the impact of Big Bang initial conditions on observable physics.more » « less
-
Abstract This work offers a new prospective on asymptotic perturbation theory for varying self‐adjoint extensions of symmetric operators. Employing symplectic formulation of self‐adjointness, we use a version of resolvent difference identity for two arbitrary self‐adjoint extensions that facilitates asymptotic analysis of resolvent operators via first‐order expansion for the family of Lagrangian planes associated with perturbed operators. Specifically, we derive a Riccati‐type differential equation and the first‐order asymptotic expansion for resolvents of self‐adjoint extensions determined by smooth one‐parameter families of Lagrangian planes. This asymptotic perturbation theory yields a symplectic version of the abstract Kato selection theorem and Hadamard–Rellich‐type variational formula for slopes of multiple eigenvalue curves bifurcating from an eigenvalue of the unperturbed operator. The latter, in turn, gives a general infinitesimal version of the celebrated formula equating the spectral flow of a path of self‐adjoint extensions and the Maslov index of the corresponding path of Lagrangian planes. Applications are given to quantum graphs, periodic Kronig–Penney model, elliptic second‐order partial differential operators with Robin boundary conditions, and physically relevant heat equations with thermal conductivity.more » « less
An official website of the United States government

