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The R package trajmsm provides functions designed to simplify the estimation of the parameters of a model combining latent class growth analysis (LCGA), a trajectory analysis technique, and marginal structural models (MSMs) called LCGA-MSM. LCGA summarizes similar patterns of change over time into a few distinct categories called trajectory groups, which are then included as "treatments" in the MSM. MSMs are a class of causal models that correctly handle treatment-confounder feedback. The parameters of LCGA-MSMs can be consistently estimated using different estimators, such as inverse probability weighting (IPW), g-computation, and pooled longitudinal targeted maximum likelihood estimation (pooled LTMLE). These three estimators of the parameters of LCGA-MSMs are currently implemented in our package. In the context of a time-dependent outcome, we previously proposed a combination of LCGA and history-restricted MSMs (LCGA-HRMSMs). Our package provides additional functions to estimate the parameters of such models. Version 0.1.3 of the package is currently available on CRAN., Comment: 19 pages, 13 tables, 3 figures

Analyzing and effectively communicating the efficacy and toxicity of treatment is the basis of risk benefit analysis (RBA). More efficient and objective tools are needed. We apply Chauhan Weighted Trajectory Analysis (CWTA) to perform RBA with superior objectivity, power, and clarity. We used CWTA to perform 1000-fold simulations of RCTs using ordinal endpoints for both treatment efficacy and toxicity. RCTs were simulated with 1:1 allocation at defined sample sizes and hazard ratios. We studied the simplest case of 3 levels each of toxicity and efficacy and the general case of the advanced cancer trial, with efficacy graded by five RECIST 1.1 health statuses and toxicity by the six-point CTCAE scale (6 x 5 matrix). The latter model was applied to a real-world dose escalation phase I trial in advanced cancer. Simulations in both the 3 x 3 and the 6 x 5 advanced cancer matrix confirmed that drugs with both superior efficacy and toxicity profiles synergize for greater statistical power with CWTA-RBA. The CWTA-RBA 6 x 5 matrix reduced sample size requirements over CWTA efficacy-only analysis. Application to the dose finding phase I clinical trial provided objective, statistically significant validation for the selected dose. CWTA-RBA, by incorporating both drug efficacy and toxicity, provides a single test statistic and plot that analyzes and effectively communicates therapeutic risks and benefits. CWTA-RBA requires fewer patients than CWTA efficacy-only analysis when the experimental drug is both more effective and less toxic. CWTA-RBA facilitates the objective and efficient assessment of new therapies throughout the drug development pathway. Furthermore, several advantages over competing tests in communicating risk-benefit will assist regulatory review, clinical adoption, and understanding of therapeutic risks and benefits by clinicians and patients alike.

In this paper, we present ReeFRAME, a scalable Reeb graph-based framework designed to analyze vast volumes of GPS-enabled human trajectory data generated at 1Hz frequency. ReeFRAME models Patterns-of-life (PoL) at both the population and individual levels, utilizing Multi-Agent Reeb Graphs (MARGs) for population-level patterns and Temporal Reeb Graphs (TERGs) for individual trajectories. The framework's linear algorithmic complexity relative to the number of time points ensures scalability for anomaly detection. We validate ReeFRAME on six large-scale anomaly detection datasets, simulating real-time patterns with up to 500,000 agents over two months., Comment: GeoAnomalies Workshop @ ACM Sigspatial 2024

In many domains, such as healthcare, time-series data is often irregularly sampled with varying intervals between observations. This poses challenges for classical time-series models that require equally spaced data. To address this, we propose a novel time-series Transformer called Trajectory Generative Pre-trained Transformer (TrajGPT). TrajGPT employs a novel Selective Recurrent Attention (SRA) mechanism, which utilizes a data-dependent decay to adaptively filter out irrelevant past information based on contexts. By interpreting TrajGPT as discretized ordinary differential equations (ODEs), it effectively captures the underlying continuous dynamics and enables time-specific inference for forecasting arbitrary target timesteps. Experimental results demonstrate that TrajGPT excels in trajectory forecasting, drug usage prediction, and phenotype classification without requiring task-specific fine-tuning. By evolving the learned continuous dynamics, TrajGPT can interpolate and extrapolate disease risk trajectories from partially-observed time series. The visualization of predicted health trajectories shows that TrajGPT forecasts unseen diseases based on the history of clinically relevant phenotypes (i.e., contexts)., Comment: 9 pages

As Kaplan-Meier (KM) analysis is limited to single unidirectional endpoints, most advanced cancer randomized clinical trials (RCTs) are powered for either progression free survival (PFS) or overall survival (OS). This discards efficacy information carried by partial responses, complete responses, and stable disease that frequently precede progressive disease and death. Chauhan Weighted Trajectory Analysis (CWTA) is a generalization of KM that simultaneously assesses multiple rank-ordered endpoints. We hypothesized that CWTA could use this efficacy information to reduce sample size requirements and expedite efficacy signals in advanced cancer trials. We performed 100-fold and 1000-fold simulations of solid tumour systemic therapy RCTs with health statuses rank ordered from complete response (Stage 0) to death (Stage 4). At increments of sample size and hazard ratio, we compared KM PFS and OS with CWTA for (i) sample size requirements to achieve a power of 0.8 and (ii) time-to-first significant efficacy signal. CWTA consistently demonstrated greater power, and reduced sample size requirements by 18% to 35% compared to KM PFS and 14% to 20% compared to KM OS. CWTA also expedited time-to-efficacy signals 2- to 6-fold. CWTA, by incorporating all efficacy signals in the cancer treatment trajectory, provides clinically relevant reduction in required sample size and meaningfully expedites the efficacy signals of cancer treatments compared to KM PFS and KM OS. Using CWTA rather than KM as the primary trial outcome has the potential to meaningfully reduce the numbers of patients, trial duration, and costs to evaluate therapies in advanced cancer.

Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which can be estimated using already standard algorithms. However, characterizing a trajectory from an entropic perspective is far less developed. The search for such characterization leads us to use chain coding to discretize the description of a curve. Calculating the entropy density and entropy-related magnitudes from the resulting finite alphabet code becomes straightforward. In such a way, the entropy of a trajectory can be defined and used as an effective tool to assert creativity and pattern formation from a Shannon perspective. Applying the procedure to actual experimental physiological data and modelled trajectories of astronomical dynamics proved the robustness of the entropic characterization in a wealth of trajectories of different origins and the insight that can be gained from its use.

Model ensembles are effective tools for estimating prediction uncertainty in deep learning atomistic force fields. However, their widespread adoption is hindered by high computational costs and overconfident error estimates. In this work, we address these challenges by leveraging distributions of per-sample errors obtained during training and employing a distance-based similarity search in the model latent space. Our method, which we call LTAU, efficiently estimates the full probability distribution function (PDF) of errors for any test point using the logged training errors, achieving speeds that are 2--3 orders of magnitudes faster than typical ensemble methods and allowing it to be used for tasks where training or evaluating multiple models would be infeasible. We apply LTAU towards estimating parametric uncertainty in atomistic force fields (LTAU-FF), demonstrating that its improved ensemble diversity produces well-calibrated confidence intervals and predicts errors that correlate strongly with the true errors for data near the training domain. Furthermore, we show that the errors predicted by LTAU-FF can be used in practical applications for detecting out-of-domain data, tuning model performance, and predicting failure during simulations. We believe that LTAU will be a valuable tool for uncertainty quantification (UQ) in atomistic force fields and is a promising method that should be further explored in other domains of machine learning.

In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In order to investigate the effects generated by the truncation and hence the propagation properties displayed by the designed beams, here we resort to a new perspective based on a trajectory methodology, complementary to the density plots more commonly used to study the intensity distribution propagation. We consider three different aperture functions, which are convoluted with an ideal Airy beam. As it is shown, the corresponding trajectories reveals a deeper physical insight about the propagation dynamics exhibited by the beams analyzed due to their direct connection with the local phase variations undergone by the beams, which is in contrast with the global information provided by the usual standard tools. Furthermore, we introduce a new parameter, namely, the escape rate, which allow us to perform piecewise analyses of the intensity distribution without producing any change on it, e.g., determining unambiguously how much energy flux contributes to the leading maximum at each stage of the propagation, or for how long self-accelerating transverse propagation survives. The analysis presented in this work thus provides an insight into the behavior of finite-energy Airy beams, and therefore is expected to contribute to the design and applications exploiting this singular type of beams., Comment: 15 pages, 5 figures; very minor changes with respect to previous version

Virtual content instability caused by device pose tracking error remains a prevalent issue in markerless augmented reality (AR), especially on smartphones and tablets. However, when examining environments which will host AR experiences, it is challenging to determine where those instability artifacts will occur; we rarely have access to ground truth pose to measure pose error, and even if pose error is available, traditional visualizations do not connect that data with the real environment, limiting their usefulness. To address these issues we present SiTAR (Situated Trajectory Analysis for Augmented Reality), the first situated trajectory analysis system for AR that incorporates estimates of pose tracking error. We start by developing the first uncertainty-based pose error estimation method for visual-inertial simultaneous localization and mapping (VI-SLAM), which allows us to obtain pose error estimates without ground truth; we achieve an average accuracy of up to 96.1% and an average F1 score of up to 0.77 in our evaluations on four VI-SLAM datasets. Next we present our SiTAR system, implemented for ARCore devices, combining a backend that supplies uncertainty-based pose error estimates with a frontend that generates situated trajectory visualizations. Finally, we evaluate the efficacy of SiTAR in realistic conditions by testing three visualization techniques in an in-the-wild study with 15 users and 13 diverse environments; this study reveals the impact both environment scale and the properties of surfaces present can have on user experience and task performance., Comment: To appear in Proceedings of IEEE ISMAR 2023

Trajectories, sequentially measured quantities that form a path, are an important presence in many different fields, from hadronic beams in physics to electrocardiograms in medicine. Trajectory anal-ysis requires the quantification and classification of curves either using statistical descriptors or physics-based features. To date, there is no extensive and user-friendly package for trajectory anal-ysis available, despite its importance and potential application across domains. We developed a free open-source python package named TrajPy as a complementary tool to empower trajectory analysis. The package showcases a friendly graphic user interface and provides a set of physical descriptors that help characterizing these intricate structures. In combina-tion with image analysis, it was already successfully applied to the study of mitochondrial motility in neuroblastoma cell lines and to the analysis of in silico models for cell migration. The TrajPy package was developed in Python 3 and released under the GNU GPL-3 license. Easy installation is available through PyPi and the development source code can be found in the repository https://github.com/ocbe-uio/TrajPy/. The package release is automatically archived under the DOI 10.5281/zenodo.3656044., Comment: 4 pages, 1 figure

The Kaplan-Meier estimator (KM) is widely used in medical research to estimate the survival function from lifetime data. KM is a powerful tool to evaluate clinical trials due to simple computational requirements, a logrank hypothesis test, and the ability to censor patients. However, KM has several constraints and fails to generalize to ordinal variables of interest such as toxicity and ECOG performance. We devised Weighted Trajectory Analysis (WTA) to combine the advantages of KM with the ability to compare treatment groups for ordinal variables and fluctuating outcomes. To assess statistical significance, we developed a new hypothesis test analogous to the logrank test. We demonstrate the functionality of WTA through 1000-fold clinical trial simulations of unique stochastic models of chemotherapy toxicity and schizophrenia progression. At several increments of sample size and hazard ratio, we compare the performance of WTA to both KM and Generalized Estimating Equations (GEE). WTA generally required half the sample size to achieve comparable power to KM; advantages over GEE include its robust non-parametric approach and summary plot. We also apply WTA to real clinical data: the toxicity outcomes of melanoma patients receiving immunotherapy and the disease progression of patients with metastatic breast cancer receiving ramucirumab. The application of WTA demonstrates that using traditional methods such as percent incidence and KM can lead to both Type I and II errors by failing to model illness trajectory. This article outlines a novel method for clinical outcome assessment that extends the advantages of Kaplan-Meier estimates to ordinal outcome variables., Comment: 29 pages, 3 tables, 10 figures

In this paper, we lay out a vision for analysing semantic trajectory traces and generating synthetic semantic trajectory data (SSTs) using generative language model. Leveraging the advancements in deep learning, as evident by progress in the field of natural language processing (NLP), computer vision, etc. we intend to create intelligent models that can study the semantic trajectories in various contexts, predicting future trends, increasing machine understanding of the movement of animals, humans, goods, etc. enhancing human-computer interactions, and contributing to an array of applications ranging from urban-planning to personalized recommendation engines and business strategy., Comment: 8 pages, 1 figure, Submitted for peer review

Target tracking and trajectory modeling have important applications in surveillance video analysis and have received great attention in the fields of road safety and community security. In this work, we propose a lightweight real-time video analysis scheme that uses a model learned from motion patterns to monitor the behavior of objects, which can be used for applications such as real-time representation and prediction. The proposed sequence clustering algorithm based on discrete sequences makes the system have continuous online learning ability. The intrinsic repeatability of the target object trajectory is used to automatically construct the behavioral model in the three processes of feature extraction, cluster learning, and model application. In addition to the discretization of trajectory features and simple model applications, this paper focuses on online clustering algorithms and their incremental learning processes. Finally, through the learning of the trajectory model of the actual surveillance video image, the feasibility of the algorithm is verified. And the characteristics and performance of the clustering algorithm are discussed in the analysis. This scheme has real-time online learning and processing of motion models while avoiding a large number of arithmetic operations, which is more in line with the application scenarios of front-end intelligent perception.

Process mining can help acquire insightful knowledge and heighten the system's performance. In this study, we surveyed the trajectories of 1050 sepsis patients in a regional hospital in the Netherlands from the registration to the discharge phase. Based on this real-world case study, the event log comprises events and activities related to the emergency ward, admission to hospital wards, and discharge enriched with data from lab experiments and triage checklists. At first, we aim to discover this process through Heuristics Miner (HM) and Inductive Miner (IM) methods. Then, we analyze a systematic process model based on organizational information and knowledge. Besides, we address conformance checking given medical guidelines for these patients and monitor the related flows on the systematic process model. The results show that HM and IM are inadequate in identifying the relevant process. However, using a systematic process model based on expert knowledge and organizational information resulted in an average fitness of 97.8%, a simplicity of 77.7%, and a generalization of 80.2%. The analyses demonstrate that process mining can shed light on the patient flow in the hospital and inspect the day-to-day clinical performance versus medical guidelines. Also, the process models obtained by the HM and IM methods cannot provide a concrete comprehension of the process structure for stakeholders compared to the systematic process model. The implications of our findings include the potential for process mining to improve the quality of healthcare services, optimize resource allocation, and reduce costs. Our study also highlights the importance of considering expert knowledge and organizational information in developing effective process models., Comment: 22 pages, 6 figures, 1 table