Sharp Analysis of Power Iteration for Tensor PCA

We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is either limited to a constant number of iterations, or requires a non-trivial data-independent initialization. In this paper, we move beyond these limitations and analyze the dynamics of randomly initialized tensor power iteration up to polynomially many steps. Our contributions are threefold: First, we establish sharp bounds on the number of iterations required for power method to converge to the planted signal, for a broad range of the signal-to-noise ratios. Second, our analysis reveals that the actual algorithmic threshold for power iteration is smaller than the one conjectured in literature by a polylog(n) factor, where n is the ambient dimension. Finally, we propose a simple and effective stopping criterion for power iteration, which provably outputs a solution that is highly correlated with the true signal. Extensive numerical experiments verify our theoretical results.Comment: 40 pages, 8 figure

Lower Bounds for the Convergence of Tensor Power Iteration on Random Overcomplete Models

Tensor decomposition serves as a powerful primitive in statistics and machine learning. In this paper, we focus on using power iteration to decompose an overcomplete random tensor. Past work studying the properties of tensor power iteration either requires a non-trivial data-independent initialization, or is restricted to the undercomplete regime. Moreover, several papers implicitly suggest that logarithmically many iterations (in terms of the input dimension) are sufficient for the power method to recover one of the tensor components. In this paper, we analyze the dynamics of tensor power iteration from random initialization in the overcomplete regime. Surprisingly, we show that polynomially many steps are necessary for convergence of tensor power iteration to any of the true component, which refutes the previous conjecture. On the other hand, our numerical experiments suggest that tensor power iteration successfully recovers tensor components for a broad range of parameters, despite that it takes at least polynomially many steps to converge. To further complement our empirical evidence, we prove that a popular objective function for tensor decomposition is strictly increasing along the power iteration path. Our proof is based on the Gaussian conditioning technique, which has been applied to analyze the approximate message passing (AMP) algorithm. The major ingredient of our argument is a conditioning lemma that allows us to generalize AMP-type analysis to non-proportional limit and polynomially many iterations of the power method.Comment: 40 pages, 3 figure

CAMON: Cooperative Agents for Multi-Object Navigation with LLM-based Conversations

Visual navigation tasks are critical for household service robots. As these tasks become increasingly complex, effective communication and collaboration among multiple robots become imperative to ensure successful completion. In recent years, large language models (LLMs) have exhibited remarkable comprehension and planning abilities in the context of embodied agents. However, their application in household scenarios, specifically in the use of multiple agents collaborating to complete complex navigation tasks through communication, remains unexplored. Therefore, this paper proposes a framework for decentralized multi-agent navigation, leveraging LLM-enabled communication and collaboration. By designing the communication-triggered dynamic leadership organization structure, we achieve faster team consensus with fewer communication instances, leading to better navigation effectiveness and collaborative exploration efficiency. With the proposed novel communication scheme, our framework promises to be conflict-free and robust in multi-object navigation tasks, even when there is a surge in team size.Comment: Accepted to the RSS 2024 Workshop: GROUN

Optimal chartering decisions for vessel fleet to support offshore wind farm maintenance operations

Offshore wind energy is expected to be the most significant source of future electricity supply in Europe. Offshore wind farms are located far from the shores, requiring a fleet of various types of vessels to access sites when maintaining offshore wind turbines. The employment of the vessels is costly, accounting for the majority of the total O&M costs for offshore wind energy. Therefore, configuring the size and mix of the vessel fleet to support maintenance operations in a cost-effective manner is an issue of importance to enhance economics of offshore wind sector. In this paper, a discrete event simulation based model is proposed to present how a mixed vessel fleet with the specific configuration, including crew transfer vessels, field support vessels, and heavy lift vessels, performs maintenance for an offshore wind farm. The economic performance of the vessel fleet under a predetermined condition-based opportunistic maintenance strategy is investigated by using the model. A metaheuristic algorithm, simulated annealing, is employed to find the optimal fleet size and mix to make leasing decisions with the minimum costs. The performance of the developed approaches is evaluated by using a generic offshore wind farm in the North Sea. The sensitivity analysis is performed to investigate the most influential O&M factors

Identification of lipid metabolism related immune markers in atherosclerosis through machine learning and experimental analysis

BackgroundAtherosclerosis is a significant contributor to cardiovascular disease, and conventional diagnostic methods frequently fall short in the timely and accurate detection of early-stage atherosclerosis. Abnormal lipid metabolism plays a critical role in the development of atherosclerosis. Consequently, the identification of new diagnostic markers is essential for the precise diagnosis of this condition.MethodThe datasets related to atherosclerosis utilized in this research were obtained from the GEO database (GSE2470, GSE24495, GSE100927 and GSE43292). The ssGSEA technique was first utilized to assess lipid metabolism scores in samples affected by atherosclerosis, thereby aiding in the discovery of important regulatory genes linked to lipid metabolism via WGCNA. Following this, differential expression analysis and functional evaluations were carried out, after which various machine learning approaches were employed to determine significant diagnostic genes for atherosclerosis. A diagnostic model was then developed and validated through several machine learning algorithms. Furthermore, molecular docking studies were conducted to analyze the binding affinity of these key markers with therapeutic agents for atherosclerosis. The ssGSEA technique was also used to measure immune cell scores in atherosclerotic samples, aiding the exploration of the connection between key diagnostic markers and immune cells. Finally, the expression variations of the identified pivotal genes were confirmed through experimental validation.ResultWGCNA identified 302 lipid metabolism-related genes in atherosclerotic samples, and functional analysis revealed that these genes are associated with multiple immune pathways. Through further differential analysis and screening using machine learning algorithms, APLNR, PCDH12, PODXL, SLC40A1, TM4SF18, and TNFRSF25 were identified as key diagnostic genes for atherosclerosis. The diagnostic model we constructed was confirmed to predict the occurrence of atherosclerosis with high accuracy, and molecular docking studies indicated that these six key diagnostic genes have potential as drug targets. Additionally, the ssGSEA algorithm further validated the association of these diagnostic genes with various immune cells. Finally, the expression levels of these six genes were experimentally confirmed.ConclusionOur study introduces novel lipid metabolism-related diagnostic markers for atherosclerosis and emphasizes their potential as immune-related drug targets. This research provides a valuable approach for the predictive diagnosis and targeted therapy of atherosclerosis

MicroRNA-503 inhibits the G1/S transition by downregulating cyclin D3 and E2F3 in hepatocellular carcinoma

Abstract Background Increasing evidence indicates that deregulation of microRNAs (miRNAs) is involved in tumorigenesis. Downregulation of microRNA-503 has been observed in various types of diseases, including cancer. However, the biological function of miR-503 in hepatocellular carcinoma (HCC) is still largely unknown. In this study we aimed to elucidate the prognostic implications of miR-503 in HCC and its pathophysiologic role. Methods Quantitative reverse transcriptase polymerase chain reaction was used to evaluate miR-503 expression in HCC tissues and cell lines. Western blotting was performed to evaluate the expression of the miR-503 target genes. In vivo and in vitro assays were performed to evaluate the function of miR-503 in HCC. Luciferase reporter assay was employed to validate the miR-503 target genes. Results miR-503 was frequently downregulated in HCC cell lines and tissues. Low expression levels of miR-503 were associated with enhanced malignant potential such as portal vein tumor thrombi, histologic grade, TNM stage, AFP level and poor prognosis. Multivariate analysis indicated that miR-503 downregulation was significantly associated with worse overall survival of HCC patients. Functional studies showed miR-503 suppressed the proliferation of HCC cells by induction of G1 phase arrest through Rb-E2F signaling pathways, and thus may function as a tumor suppressor. Further investigation characterized two cell cycle-related molecules, cyclin D3 and E2F3, as the direct miR-503 targets. Conclusion Our data highlight an important role for miR-503 in cell cycle regulation and in the molecular etiology of HCC, and implicate the potential application of miR-503 in prognosis prediction and miRNA-based HCC therapy. </jats:sec

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals &lt;1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Optimization of vessel fleet size and mix for offshore wind farm maintenance based on a simulation method

The research on sustainable energy is growing, among which, wind energy catching growing attention and the potential has been supported by more and more countries. Compared with onshore wind farms, offshore wind farms have more advantages including the abundant wind resource at the offshore location and more possible construction areas. While for an offshore wind farm, the operation and maintenance cost is the most significant part and fleet management contributes a lot to it. In order to optimize the fleet size and mix problem for an offshore wind farm based on a simulation method, this thesis has performed a few research steps. Firstly, a literature view on the modeling methods of fleet size and mix problems for offshore wind farms is finished. Different modeling methods and different factors considered in the model are viewed. Then, two simulation models, the open-loop simulation model and the feedforward simulation model, are introduced, including the model inputs, model agent and process, and model outputs. Afterward, the simulation-optimization methodology is introduced and the optimization algorithm used in this research is introduced. Next, one case study using two models separately for a long-term optimization and a short-term optimization is executed and followed by the results of these two simulation models as well as the comparison of the results from them.This thesis aims to combine the optimization method with a simulation model for offshore wind farms, which can be regarded as a decision support tool for fleet size and mix problems and is expected to be a practical technology for the operator/researcher of the offshore wind farm in the future.Mechanical Engineering | Multi-Machine Engineerin