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Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of the data, weighted by proximity. However, traditional LPR is sensitive to outliers and high-leverage points, which can significantly affect estimation accuracy. This paper revisits the kernel function used to compute regression weights and proposes a novel framework that incorporates both predictor and response variables in the weighting mechanism. By introducing two positive definite kernels, the proposed method robustly estimates weights, mitigating the influence of outliers through localized density estimation. The method is implemented in Python and is publicly available at https://github.com/yaniv-shulman/rsklpr, demonstrating competitive performance in synthetic benchmark experiments. Compared to standard LPR, the proposed approach consistently improves robustness and accuracy, especially in heteroscedastic and noisy environments, without requiring multiple iterations. This advancement provides a promising extension to traditional LPR, opening new possibilities for robust regression applications.

This paper introduces an adaptive physics-guided neural network (APGNN) framework for predicting quality attributes from image data by integrating physical laws into deep learning models. The APGNN adaptively balances data-driven and physics-informed predictions, enhancing model accuracy and robustness across different environments. Our approach is evaluated on both synthetic and real-world datasets, with comparisons to conventional data-driven models such as ResNet. For the synthetic data, 2D domains were generated using three distinct governing equations: the diffusion equation, the advection-diffusion equation, and the Poisson equation. Non-linear transformations were applied to these domains to emulate complex physical processes in image form. In real-world experiments, the APGNN consistently demonstrated superior performance in the diverse thermal image dataset. On the cucumber dataset, characterized by low material diversity and controlled conditions, APGNN and PGNN showed similar performance, both outperforming the data-driven ResNet. However, in the more complex thermal dataset, particularly for outdoor materials with higher environmental variability, APGNN outperformed both PGNN and ResNet by dynamically adjusting its reliance on physics-based versus data-driven insights. This adaptability allowed APGNN to maintain robust performance across structured, low-variability settings and more heterogeneous scenarios. These findings underscore the potential of adaptive physics-guided learning to integrate physical constraints effectively, even in challenging real-world contexts with diverse environmental conditions.

We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo method with four pseudo-random number generators and five Quasi-Monte Carlo implementations using different low-discrepancy sequences and the Hammersley set. For the comparison, we study different test matter geometries and problems. We present comparison results for single scatterings of radiation from a point source, multiple scatterings of radiation from a point source, and single scatterings of radiation from a spherical star. In all cases, Quasi-Monte Carlo shows better convergence than Monte Carlo. In several test cases, the gain in computation time to achieve a fixed error value reached 40 times. We obtained ten times speed up in many of the considered tests., Comment: 57 pages, 10 figures, 3 tables; Submitted to Astronomy and Computing

"Reading for Life" seeks to provide a gateway to that research. Reviewing data on reading and literacy and their impact on the physical, mental, and social-emotional components of health, this paper will: (1) Review the current state of children's literacy and health, particularly in the wake of the COVID-19 pandemic; (2) Explore the importance of early-childhood education and literacy interventions in preschool, and their roles in health outcomes; (3) Summarize existing literature on the relationship between literacy rates and physical, mental, and social-emotional health; and (4) Study successful collaborations between the education and medical fields to implement literacy interventions in pediatric healthcare settings. [This paper was prepared by Scholastic Research & Validation as part of the Yale Child Study Center-Scholastic Collaborative for Child & Family Resilience.]

The (Local) Lifting Property ((L)LP) is introduced by Kirchberg and deals with lifting completely positive maps. We give a characterization of the (L)LP in terms of lifting $\ast$-homomorphisms. We use it to prove that if $A$ and $B$ have the LP and $F$ is their finite-dimensional C*-subalgebra, then $A\ast_F B$ has the LP. This answers a question of Ozawa. We prove that Exel's soft tori have the LP. As a consequence we obtain that $C^*(F_n\times F_n)$ is inductive limit of RFD C*-algebras with the LP. We prove that for a class of C*-algebras including $C^*(F_n\times F_n)$ and all contractible C*-algebras, the LLP is equivalent to Ext being a group. As byproduct of methods developed in the paper we generalize Kirchberg's theorem about extensions with the WEP, give short proofs of several, old and new, facts about soft tori, new unified proofs of Li and Shen's characterization of RFD property of free products amalgamated over a finite-dimensional subalgebra and Blackadar's characterization of semiprojectivity of them.

We present an innovative approach leveraging Physics-Guided Neural Networks (PGNNs) for enhancing agricultural quality assessments. Central to our methodology is the application of physics-guided inverse regression, a technique that significantly improves the model's ability to precisely predict quality metrics of crops. This approach directly addresses the challenges of scalability, speed, and practicality that traditional assessment methods face. By integrating physical principles, notably Fick`s second law of diffusion, into neural network architectures, our developed PGNN model achieves a notable advancement in enhancing both the interpretability and accuracy of assessments. Empirical validation conducted on cucumbers and mushrooms demonstrates the superior capability of our model in outperforming conventional computer vision techniques in postharvest quality evaluation. This underscores our contribution as a scalable and efficient solution to the pressing demands of global food supply challenges.

We introduce Displayed Type Theory (dTT), a multi-modal homotopy type theory with discrete and simplicial modes. In the intended semantics, the discrete mode is interpreted by a model for an arbitrary $\infty$-topos, while the simplicial mode is interpreted by Reedy fibrant augmented semi-simplicial diagrams in that model. This simplicial structure is represented inside the theory by a primitive notion of display or dependency, guarded by modalities, yielding a partially-internal form of unary parametricity. Using the display primitive, we then give a coinductive definition, at the simplicial mode, of a type $\mathsf{SST}$ of semi-simplicial types. Roughly speaking, a semi-simplicial type $X$ consists of a type $X_0$ together with, for each $x:X_0$, a displayed semi-simplicial type over $X$. This mimics how simplices can be generated geometrically through repeated cones, and is made possible by the display primitive at the simplicial mode. The discrete part of $\mathsf{SST}$ then yields the usual infinite indexed definition of semi-simplicial types, both semantically and syntactically. Thus, dTT enables working with semi-simplicial types in full semantic generality., Comment: 106 pages, v2: new section on the correctness of SSTs and various improvements throughout

Parametricity is a property of the syntax of type theory implying, e.g., that there is only one function having the type of the polymorphic identity function. Parametricity is usually proven externally, and does not hold internally. Internalising it is difficult because once there is a term witnessing parametricity, it also has to be parametric itself and this results in the appearance of higher dimensional cubes. In previous theories with internal parametricity, either an explicit syntax for higher cubes is present or the theory is extended with a new sort for the interval. In this paper we present a type theory with internal parametricity which is a simple extension of Martin-L\"of type theory: there are a few new type formers, term formers and equations. Geometry is not explicit in this syntax, but emergent: the new operations and equations only refer to objects up to dimension 3. We show that this theory is modelled by presheaves over the BCH cube category. Fibrancy conditions are not needed because we use span-based rather than relational parametricity. We define a gluing model for this theory implying that external parametricity and canonicity hold. The theory can be seen as a special case of a new kind of modal type theory, and it is the simplest setting in which the computational properties of higher observational type theory can be demonstrated.

By Bekka's theorem the group C*-algebra of an amenable group $G$ is residually finite dimensional (RFD) if and only if $G$ is maximally almost periodic (MAP). We generalize this result in two directions of dynamical flavour. Firstly, we provide a sufficient condition for the RFD property of the C*-algebra of an amenable \'etale groupoid. Secondly, we characterize RFD property for crossed products by amenable actions of discrete groups on C*-algebras. The characterisation can be formulated in various terms, such as primitive ideals, (pure) states and approximations of representations, and can be viewed as a dynamical version of Exel-Loring characterization of RFD C*-algebras. As byproduct of our methods we also characterize the property FD of Lubotzky and Shalom for semidirect products by amenable groups and obtain characterizations of the properties MAP and RF for general semidirect products of groups. The latter descriptions allow us to obtain the properties MAP, RF, RFD and FD for various examples., Comment: 40 pages, v2 contains a modified introduction and several new examples in Section 5

IP prefix hijacks allow adversaries to redirect and intercept traffic, posing a threat to the stability and security of the Internet. To prevent prefix hijacks, networks should deploy RPKI and filter bogus BGP announcements with invalid routes. In this work we evaluate the impact of RPKI deployments on the security and resilience of the Internet. We aim to understand which networks filter invalid routes and how effective that filtering is in blocking prefix hijacks. We extend previous data acquisition and analysis methodologies to obtain more accurate identification of networks that filter invalid routes with RPKI. We find that more than 27% of networks enforce RPKI filtering and show for the first time that deployments follow the business incentives of inter-domain routing: providers have an increased motivation to filter in order to avoid losing customers' traffic. Analyzing the effectiveness of RPKI, we find that the current trend to deploy RPKI on routeservers of Internet Exchange Points (IXPs) only provides a localized protection against hijacks but has negligible impact on preventing their spread globally. In contrast, we show that RPKI filtering in Tier-1 providers greatly benefits the security of the Internet as it limits the spread of hijacks to a localized scope. Based on our observations, we provide recommendations on the future roadmap of RPKI deployment. We make our datasets available for public use [https://sit4.me/rpki]., Comment: Accepted for USENIX Security '23

We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This is achieved by a construction called "co-dextrification" that co-freely adds left adjoints to any such diagram, which can then be used to interpret the "context lock" functors of MTT. Furthermore, if any of the functors in the diagram have right adjoints, these can also be internalized in type theory as negative modalities in the style of FitchTT. We introduce the name Multimodal Adjoint Type Theory (MATT) for the resulting combined general modal type theory. In particular, we can interpret MATT in any finite diagram of toposes and geometric morphisms, with positive modalities for inverse image functors and negative modalities for direct image functors., Comment: 19 pages. v2: Improved notation; extended pre-proceedings version for MFPS 2023. v3: correct some mis-wordings, final. v4: condensed version for conference postproceedings

In this study, we present a novel method for measuring the magnetic susceptibility of liquids using a Mach-Zehnder interferometer. The proposed technique employs a ring magnet to deform the liquid, while a laser beam passes through the liquid to measure the resulting interference pattern. The deformation of the liquid, caused by the known magnetic field of the ring magnet, is used to calculate the magnetic susceptibility. We provide a comprehensive theoretical framework, including the relevant equations and models, for analyzing the data obtained using this method. We compare the Mach-Zehnder interferometer method with other established techniques, highlighting its advantages and disadvantages. Our findings indicate that the Mach-Zehnder interferometer technique offers high accuracy, sensitivity, and potential applications in characterizing magnetic properties of various liquid systems.

Measuring the magnetic field of permanent magnets can be challenging, but recent research has demonstrated the potential of using deformed diamagnetic liquids to estimate the magnetic field. In this paper, we explore two methods for measuring the magnetic field from the response of the diamagnetic liquid. The first method involves measuring the profile of the deformed liquid with a laser and then calculating the square of the magnetic field using an appropriate equation. The second method involves measuring the maximum slope of the liquid and numerically calculating the magnetic field distribution using the model of an ideal solenoid. We present experimental results using these methods and compare them with other established methods for measuring magnetic fields. The results show that the proposed methods are effective and have potential for use in a variety of applications. The proposed methods can help address the challenge of measuring magnetic fields in situations where other methods are not suitable or practical.

In recent years, deep learning has achieved remarkable success in various fields such as image recognition, natural language processing, and speech recognition. The effectiveness of deep learning largely depends on the optimization methods used to train deep neural networks. In this paper, we provide an overview of first-order optimization methods such as Stochastic Gradient Descent, Adagrad, Adadelta, and RMSprop, as well as recent momentum-based and adaptive gradient methods such as Nesterov accelerated gradient, Adam, Nadam, AdaMax, and AMSGrad. We also discuss the challenges associated with optimization in deep learning and explore techniques for addressing these challenges, including weight initialization, batch normalization, and layer normalization. Finally, we provide recommendations for selecting optimization methods for different deep learning tasks and datasets. This paper serves as a comprehensive guide to optimization methods in deep learning and can be used as a reference for researchers and practitioners in the field., Comment: We have decided to withdraw our manuscript 'Optimization Methods in Deep Learning: A Comprehensive Overview' from arXiv as we are now pursuing different research directions. We apologize for any inconvenience and appreciate your understanding

Measuring instruments are vital for obtaining accurate data in various fields, including scientific research, engineering, and manufacturing. However, data acquisition can be challenging, particularly when direct cable connections are not feasible or difficult to establish. In this paper, we propose a novel method for measuring instrument data acquisition utilizing a camera to capture the instrument display and image processing techniques to extract the measured values. Our method combines computer vision and machine learning techniques to recognize and extract numerical values from the instrument display. We demonstrate the effectiveness and accuracy of this approach by applying it to capture the magnetic field of a permanent magnet using a gauss meter and webcam. Our results indicate that the proposed method offers a practical and accurate solution for data acquisition in cases where direct cable connections are not possible. This method has potential applications in scientific research, engineering, and manufacturing industries.