Recommender systems build user profiles using concept analysis of usage matrices. The concepts are mined as spectra and form Galois connections. Descent is a general method for spectral decomposition in algebraic geometry and topology which also leads to generalized Galois connections. Both recommender systems and descent theory are vast research areas, separated by a technical gap so large that trying to establish a link would seem foolish. Yet a formal link emerged, all on its own, bottom-up, against authors' intentions and better judgment. Familiar problems of data analysis led to a novel solution in category theory. The present paper arose from a series of earlier efforts to provide a top-down account of these developments.
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The Segment Anything Model (SAM) has recently emerged as a significant breakthrough in foundation models, demonstrating remarkable zero-shot performance in object segmentation tasks. While SAM is designed for generalization, it exhibits limitations in handling specific medical imaging tasks that require fine-structure segmentation or precise boundaries. In this paper, we focus on the task of cardiac magnetic resonance imaging (cMRI) short-axis view segmentation using the SAM foundation model. We conduct a comprehensive investigation of the impact of different prompting strategies (including bounding boxes, positive points, negative points, and their combinations) on segmentation performance. We evaluate on two public datasets using the baseline model and models fine-tuned with varying amounts of annotated data, ranging from a limited number of volumes to a fully annotated dataset. Our findings indicate that prompting strategies significantly influence segmentation performance. Combining positive points with either bounding boxes or negative points shows substantial benefits, but little to no benefit when combined simultaneously. We further observe that fine-tuning SAM with a few annotated volumes improves segmentation performance when properly prompted. Specifically, fine-tuning with bounding boxes has a positive impact, while fine-tuning without bounding boxes leads to worse results compared to baseline.
The generalized additive Runge-Kutta (GARK) framework provides a powerful approach for solving additively partitioned ordinary differential equations. This work combines the ideas of symplectic GARK schemes and multirate GARK schemes to efficiently solve additively partitioned Hamiltonian systems with multiple time scales. Order conditions, as well as conditions for symplecticity and time-reversibility, are derived in the general setting of non-separable Hamiltonian systems. Investigations of the special case of separable Hamiltonian systems are also carried out. We show that particular partitions may introduce stability issues, and discuss partitions that enable an implicit-explicit integration leading to improved stability properties. Higher-order symplectic multirate GARK schemes based on advanced composition techniques are discussed. The performance of the schemes is demonstrated by means of the Fermi-Pasta-Ulam problem.
Modeling excess remains to be an important topic in insurance data modeling. Among the alternatives of modeling excess, the Peaks Over Threshold (POT) framework with Generalized Pareto distribution (GPD) is regarded as an efficient approach due to its flexibility. However, the selection of an appropriate threshold for such framework is a major difficulty. To address such difficulty, we applied several accumulation tests along with Anderson-Darling test to determine an optimal threshold. Based on the selected thresholds, the fitted GPD with the estimated quantiles can be found. We applied the procedure to the well-known Norwegian Fire Insurance data and constructed the confidence intervals for the Value-at-Risks (VaR). The accumulation test approach provides satisfactory performance in modeling the high quantiles of Norwegian Fire Insurance data compared to the previous graphical methods.
IoT devices trigger real-time applications by receiving data from their vicinity. Modeling these applications in the form of workflows enables automating their procedure, especially for the business and industry. Depending on the features of the applications, they can be modeled in different forms, including single workflow, multiple workflows, and workflow ensembles. Since the whole data must be sent to the cloud servers for processing and storage, cloud computing has many challenges for executing real-time applications, such as bandwidth limitation, delay, and privacy. Edge paradigms are introduced to address the challenges of cloud computing in executing IoT applications. Executing IoT applications using device-to-device communications in edge paradigms requiring direct communication between devices in a network with a graph topology. While there is no simulator supporting simulating workflow-based applications and device-to-device communication, this paper introduces a toolkit for simulating resource management of scientific workflows in distributed environments with graph topology called WIDESim.The graph topology of WIDESim enables D2D communications in edge paradigms. WIDESim can work with all three different structures of scientific workflows: single, multiple workflows, and workflow ensembles. It has no constraint on the topology of the distributed environment. Also, unlike most existing network simulators, this simulator enables dynamic resource management and scheduling. We have validated the performance of WIDESim in comparison to standard simulators and workflow management tools. Also, we have evaluated its performance in different scenarios of distributed computing systems using different types of workflow-based applications. The results indicate that WIDESim's performance is close to existing standard simulators besides its improvements.
In practice, preference learning from human feedback depends on incomplete data with hidden context. Hidden context refers to data that affects the feedback received, but which is not represented in the data used to train a preference model. This captures common issues of data collection, such as having human annotators with varied preferences, cognitive processes that result in seemingly irrational behavior, and combining data labeled according to different criteria. We prove that standard applications of preference learning, including reinforcement learning from human feedback (RLHF), implicitly aggregate over hidden contexts according to a well-known voting rule called Borda count. We show this can produce counter-intuitive results that are very different from other methods which implicitly aggregate via expected utility. Furthermore, our analysis formalizes the way that preference learning from users with diverse values tacitly implements a social choice function. A key implication of this result is that annotators have an incentive to misreport their preferences in order to influence the learned model, leading to vulnerabilities in the deployment of RLHF. As a step towards mitigating these problems, we introduce a class of methods called distributional preference learning (DPL). DPL methods estimate a distribution of possible score values for each alternative in order to better account for hidden context. Experimental results indicate that applying DPL to RLHF for LLM chatbots identifies hidden context in the data and significantly reduces subsequent jailbreak vulnerability. Our code and data are available at //github.com/cassidylaidlaw/hidden-context
Equivariant neural networks have considerably improved the accuracy and data-efficiency of predictions of molecular properties. Building on this success, we introduce EquiReact, an equivariant neural network to infer properties of chemical reactions, built from three-dimensional structures of reactants and products. We illustrate its competitive performance on the prediction of activation barriers on the GDB7-22-TS, Cyclo-23-TS and Proparg-21-TS datasets with different regimes according to the inclusion of atom-mapping information. We show that, compared to state-of-the-art models for reaction property prediction, EquiReact offers: (i) a flexible model with reduced sensitivity between atom-mapping regimes, (ii) better extrapolation capabilities to unseen chemistries, (iii) impressive prediction errors for datasets exhibiting subtle variations in three-dimensional geometries of reactants/products, (iv) reduced sensitivity to geometry quality and (iv) excellent data efficiency.
Robust Markov decision processes (MDPs) are used for applications of dynamic optimization in uncertain environments and have been studied extensively. Many of the main properties and algorithms of MDPs, such as value iteration and policy iteration, extend directly to RMDPs. Surprisingly, there is no known analog of the MDP convex optimization formulation for solving RMDPs. This work describes the first convex optimization formulation of RMDPs under the classical sa-rectangularity and s-rectangularity assumptions. By using entropic regularization and exponential change of variables, we derive a convex formulation with a number of variables and constraints polynomial in the number of states and actions, but with large coefficients in the constraints. We further simplify the formulation for RMDPs with polyhedral, ellipsoidal, or entropy-based uncertainty sets, showing that, in these cases, RMDPs can be reformulated as conic programs based on exponential cones, quadratic cones, and non-negative orthants. Our work opens a new research direction for RMDPs and can serve as a first step toward obtaining a tractable convex formulation of RMDPs.
Air-bearing platforms for simulating the rotational dynamics of satellites require highly precise ground truth systems. Unfortunately, commercial motion capture systems used for this scope are complex and expensive. This paper shows a novel and versatile method to compute the attitude of rotational air-bearing platforms using a monocular camera and sets of fiducial markers. The work proposes a geometry-based iterative algorithm that is significantly more accurate than other literature methods that involve the solution of the Perspective-n-Point problem. Additionally, auto-calibration procedures to perform a preliminary estimation of the system parameters are shown. The developed methodology is deployed onto a Raspberry Pi 4 micro-computer and tested with a set of LED markers. Data obtained with this setup are compared against computer simulations of the same system to understand and validate the attitude estimation performances. Simulation results show expected 1-sigma accuracies in the order of $\sim$ 12 arcsec and $\sim$ 37 arcsec for about- and cross-boresight rotations of the platform, and average latency times of 6 ms.
Smart meters are of the basic elements in the so-called Smart Grid. These devices, connected to the Internet, keep bidirectional communication with other devices in the Smart Grid structure to allow remote readings and maintenance. As any other device connected to a network, smart meters become vulnerable to attacks with different purposes, like stealing data or altering readings. Nowadays, it is becoming more and more popular to buy and plug-and-play smart meters, additionally to those installed by the energy providers, to directly monitor the energy consumption at home. This option inherently entails security risks that are under the responsibility of householders. In this paper, we focus on an open solution based on Smartpi 2.0 devices with two purposes. On the one hand, we propose a network configuration and different data flows to exchange data (energy readings) in the home. These flows are designed to support collaborative among the devices in order to prevent external attacks and attempts of corrupting the data. On the other hand, we check the vulnerability by performing two kind of attacks (denial of service and stealing and changing data by using a malware). We conclude that, as expected, these devices are vulnerable to these attacks, but we provide mechanisms to detect both of them and to solve, by applying cooperation techniques
Given any finite set equipped with a probability measure, one may compute its Shannon entropy or information content. The entropy becomes the logarithm of the cardinality of the set when the uniform probability is used. Leinster introduced a notion of Euler characteristic for certain finite categories, also known as magnitude, that can be seen as a categorical generalization of cardinality. This paper aims to connect the two ideas by considering the extension of Shannon entropy to finite categories endowed with probability, in such a way that the magnitude is recovered when a certain choice of "uniform" probability is made.
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