Simple Extensions Research Articles

Updated Cosmological Constraints in Extended Parameter Space with Planck PR4, DESI Baryon Acoustic Oscillations, and Supernovae: Dynamical Dark Energy, Neutrino Masses, Lensing Anomaly, and the Hubble Tension

We present updated constraints on cosmological parameters in a 12-parameter model, extending the standard six-parameter ΛCDM by including dynamical dark energy (DE; w 0, w a ), the sum of neutrino masses (∑m ν ), the effective number of non-photon radiation species (N eff), the lensing amplitude scaling (A lens), and the running of the scalar spectral index (α s ). For cosmic wave background (CMB) data, we use the Planck Public Release (PR) 4 (2020) HiLLiPoP and LoLLiPoP likelihoods, Planck PR4+Atacama Cosmology Telescope (ACT) DR6 lensing, and Planck 2018 low-ℓ TT likelihoods, along with DESI DR1 baryon acoustic oscillations (BAO) and Pantheon+ and DESY5 uncalibrated Type Ia supernovae (SNe) likelihoods. Key findings are the following: (i) Contrary to DESI results, CMB+BAO+Pantheon+ data include a cosmological constant within 2σ, while CMB+BAO+DESY5 excludes it at over 2σ, indicating the dynamical nature of DE is not yet robust. Potential systematics in the DESY5 sample may drive this exclusion. (ii) Some data combinations show a 1σ+ detection of nonzero ∑m ν , indicating possible future detection. We also provide a robust upper bound of ∑m ν ≲ 0.3 eV (95% confidence limit (CL)). (iii) With CMB+BAO+SNe, A lens = 1 is included at 2σ (albeit not at 1σ), indicating no significant lensing anomaly in this extended cosmology with Planck PR4 likelihoods. (iv) The Hubble tension persists at 3.2 to 3.9σ, suggesting these simple extensions do not resolve it. (v) The S 8 tension with Dark Energy Survey Year 3 weak lensing is reduced to 1.4σ, likely due to additional parameters and the Planck PR4 likelihoods.

A local encryption method for large-scale vector maps based on spatial hierarchical index and 4D hyperchaotic system

With the development of geographic information services, applications based on map data are increasing. Internet and mobile communication technologies have brought great convenience to the distribution, sharing, and acquisition of map data. Unfortunately, it also brings great challenges to protect the security and privacy of confidential map data. Although several encryption algorithms have been developed for map data, most of the existing methods are simple extensions of classical encryption algorithms for text data in cryptography, ignoring special structures and characteristics of geospatial data. Existing methods mainly take the entire map or layers as encryption units, which makes the encryption efficiency for large-scale map data low and limits the ability to perform local and incremental encryption for local areas, making it still challenging to meet the needs of map data in applications, such as autonomous driving. To solve the limitations, a local encryption approach for large-scale vector map data is proposed in this paper considering the structure characteristics of map data. Experiments on map data of different types (including points, lines, and polygons) demonstrate the effectiveness of the proposed method. With local and parallel encryption strategies, the proposed method has higher efficiency compared to available algorithms for large-scale map data.

Bayesian confidence in optimal decisions.

The optimal way to make decisions in many circumstances is to track the difference in evidence collected in favor of the options. The drift diffusion model (DDM) implements this approach and provides an excellent account of decisions and response times. However, existing DDM-based models of confidence exhibit certain deficits, and many theories of confidence have used alternative, nonoptimal models of decisions. Motivated by the historical success of the DDM, we ask whether simple extensions to this framework might allow it to better account for confidence. Motivated by the idea that the brain will not duplicate representations of evidence, in all model variants decisions and confidence are based on the same evidence accumulation process. We compare the models to benchmark results, and successfully apply four qualitative tests concerning the relationships between confidence, evidence, and time, in a new preregistered study. Using computationally cheap expressions to model confidence on a trial-by-trial basis, we find that a subset of model variants also provide a very good to excellent account of precise quantitative effects observed in confidence data. Specifically, our results favor the hypothesis that confidence reflects the strength of accumulated evidence penalized by the time taken to reach the decision (Bayesian readout), with the penalty applied not perfectly calibrated to the specific task context. These results suggest there is no need to abandon the DDM or single accumulator models to successfully account for confidence reports. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Differentiably simple rings and ring extensions defined by p-basis

We review the concept of differentiably simple ring and we give a new proof of Harper's Theorem on the characterization of Noetherian differentiably simple rings in positive characteristic. We then study flat families of differentiably simple rings, or equivalently, finite flat extensions of rings which locally admit p-basis. These extensions are called Galois extensions of exponent one. For such an extension A⊂C, we introduce an A-scheme, called the Yuan scheme, which parametrizes subextensions A⊂B⊂C such that B⊂C is Galois of a fixed rank. So, roughly, the Yuan scheme can be thought of as a kind of Grassmannian of Galois subextensions. We finally prove that the Yuan scheme is smooth and compute the dimension of the fibers.

Interactive and educational simulation tool for permanent magnet synchronous machines

PurposeThis paper aims to present an interactive design and simulation tool for permanent magnet synchronous machines based on the finite-element-method. The tool is intended for education and research on electrical machines.Design/methodology/approachA coupling between the software MATLAB and finite element method magnetics is used. Several functionalities are included as modular scripts and represented in the form of a graphical user interface. Included are fully parametrized motor models, automatic winding generations and the evaluation of torque waveforms, core losses and speed-torque-diagrams. A survey was conducted to determine how the motivation of students concerning the covered topics is influenced by using the tool.FindingsDue to its simplicity and the intuitive visualization of the results, the tool provides direct access to the topic of electrical machines without having to deal with separate scripts. The modular structure of the software allows simple extensions with new functions. Because students can directly contribute to the tool with their own work, their motivation for using and extending it increases.Originality/valueThe presented tool offers more functionalities compared to similar free software packages, e.g. the calculation of core losses and speed-torque diagrams. Also, it is designed in such a way that it can be easily understood and extended by students.

Testing for Equivalence of Pre-Trends in Difference-in-Differences Estimation

The plausibility of the “parallel trends assumption” in Difference-in-Differences estimation is usually assessed by a test of the null hypothesis that the difference between the average outcomes of both groups is constant over time before the treatment. However, failure to reject the null hypothesis does not imply the absence of differences in time trends between both groups. We provide equivalence tests that allow researchers to find evidence in favor of the parallel trends assumption and thus increase the credibility of their treatment effect estimates. While we motivate our tests in the standard two-way fixed effects model, we discuss simple extensions to settings in which treatment adoption is staggered over time.

Preservation of Loewy diagrams under exact functors

We derive sufficient conditions for exact functors on locally finite abelian categories to preserve Loewy diagrams of objects. We apply our results to determine sufficient conditions for induction functors associated to simple current extensions of vertex algebras to preserve Loewy diagrams.

Counting nearest faraway flats for Coxeter chambers

In a finite Coxeter group W and with two given conjugacy classes of parabolic subgroups [X] and [Y] , we count those parabolic subgroups of W in [Y] that are full support, while simultaneously being simple extensions (i.e., extensions by a single reflection) of some standard parabolic subgroup of W in [X] . The enumeration is given by a product formula that depends only on the two parabolic types. Our derivation is case-free and combines a geometric interpretation of the “full support” property with a double-counting argument involving Crapo's beta invariant. As a corollary, this approach gives the first case-free proof of Chapoton's formula for the number of reflections of full support in a real reflection group W .

Illustrative Multi‐Centennial Projections of Global Mean Sea‐Level Rise and Their Application

AbstractWe produce projections of global mean sea‐level rise to 2500 for low and medium emissions scenarios (Shared Socioeconomic Pathways SSP1‐2.6 and SSP2‐4.5) relative to 2020, based on extending and combining model ensemble data from current literature. We find that emissions have a large effect on sea‐level rise on these long timescales, with [5, 95]% intervals of [0.3, 4.3]m and [1.0, 7.6]m under SSP1‐2.6 and SSP2‐4.5 respectively, and a difference in the 95% quantile of 1.6 m at 2300 and 3.3 m at 2500 for the two scenarios. The largest and most uncertain component is the Antarctic ice sheet, projected to contribute 5%–95% intervals of [−0.1, 2.3]m by 2500 under SSP1‐2.6 and [0.0, 3.8]m under SSP2‐4.5. We discuss how the simple statistical extensions used here could be replaced with more physically based methods for more robust predictions. We show that, despite their uncertainties, current multi‐centennial projections combined into multi‐study projections as presented here can be used to avoid future “lock‐ins” in terms of risk and adaptation needs to sea‐level rise.

Multi-view dreaming: multi-view world model with contrastive learning

In this paper, we propose Multi-View Dreaming, a novel reinforcement learning agent for integrated recognition and control from multi-view observations by extending Dreaming. Most current reinforcement learning method assumes a single-view observation space, and this imposes limitations on the observed data, such as lack of spatial information and occlusions. This makes obtaining ideal observational information from the environment difficult and is a bottleneck for real-world robotics applications. In this paper, we use contrastive learning to train a shared latent space between different viewpoints and show how the Products of Experts approach can be used to integrate and control the probability distributions of latent states for multiple viewpoints. We also propose Multi-View DreamingV2, a variant of Multi-View Dreaming that uses a categorical distribution to model the latent state instead of the Gaussian distribution. Experiments show that the proposed method outperforms simple extensions of existing methods in a realistic robot control task.

Inferential Deflationism

Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. We implement the deflationist insight in a bilateral theory by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. We combine this account of the meaning of the truth predicate with a new diagnosis of the liar paradox: its derivation requires the truth rules to preserve evidence, but these rules only preserve commitment. The result is a novel inferential deflationist theory of truth, which solves the liar paradox in a principled manner. We end by showing that our theory and simple extensions thereof have the resources to axiomatize the internal logic of several supervaluational hierarchies, including Cantini’s. This solves open problems of Halbach (2011) and Horsten (2011).

Simple Extensions

Summary In this article we continue the formalization of field theory in Mizar. We introduce simple extensions: an extension E of F is simple if E is generated over F by a single element of E, that is E = F (a) for some a ∈ E. First, we prove that a finite extension E of F is simple if and only if there are only finitely many intermediate fields between E and F [7]. Second, we show that finite extensions of a field F with characteristic 0 are always simple [1]. For this we had to prove, that irreducible polynomials over F have single roots only, which required extending results on divisibility and gcds of polynomials [14], [13] and formal derivation of polynomials [15].

A Data-dependent Approach for High-dimensional (Robust) Wasserstein Alignment

Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of two-dimensional (2D) or 3D patterns in the field of computer vision. Recently, the alignment problem in high dimensions finds several novel applications in practice. However, the research is still rather limited in the algorithmic aspect. To the best of our knowledge, most existing approaches are just simple extensions of their counterparts for 2D and 3D cases and often suffer from the issues such as high computational complexities. In this article, we propose an effective framework to compress the high-dimensional geometric patterns. Any existing alignment method can be applied to the compressed geometric patterns and the time complexity can be significantly reduced. Our idea is inspired by the observation that high-dimensional data often has a low intrinsic dimension. Our framework is a “data-dependent” approach that has the complexity depending on the intrinsic dimension of the input data. Our experimental results reveal that running the alignment algorithm on compressed patterns can achieve similar qualities, comparing with the results on the original patterns, but the runtimes (including the times cost for compression) are substantially lower.

General Solutions of First-Order Algebraic ODEs in Simple Constant Extensions

General Solutions of First-Order Algebraic ODEs in Simple Constant Extensions

Undergraduate Tutorial for Simulating Flocking with the Vicsek Model

ABSTRACT There are many instances of collective behaviors in the natural world. For example, eukaryotic cells coordinate their motion to heal wounds; bacteria swarm during colony expansion; defects in alignment in growing bacterial populations lead to biofilm growth; and birds move within dynamic flocks. Although the details of how these groups behave vary across animals and species, they share the same qualitative feature: they exhibit collective behaviors that are not simple extensions of details associated with the motion of an individual. To learn more about these biological systems, we propose studying these systems through the lens of the foundational Vicsek model. Here, we present the process of building this computational model from scratch in a tutorial format that focuses on building the appropriate skills of an undergraduate student. In doing so, an undergraduate student should be able to work alongside this article, the corresponding tutorial, and the original manuscript of the Vicsek model to build their own model. We conclude by summarizing some of the current work involving computational modeling of flocking with Vicsek-type models.

A proof of concept for matchete: an automated tool for matching effective theories

Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at https://gitlab.com/matchete/matchete.

How robust are particle physics predictions in asymptotic safety?

The framework of trans-Planckian asymptotic safety has been shown to generate phenomenological predictions in the Standard Model and in some of its simple new physics extensions. A heuristic approach is often adopted, which bypasses the functional renormalization group by relying on a parametric description of quantum gravity with universal coefficients that are eventually obtained from low-energy observations. Within this approach a few simplifying approximations are typically introduced, including the computation of matter renormalization group equations at 1 loop, an arbitrary definition of the position of the Planck scale at 10^{19},textrm{GeV}, and an instantaneous decoupling of gravitational interactions below the Planck scale. In this work we systematically investigate, both analytically and numerically, the impact of dropping each of those approximations on the predictions for certain particle physics scenarios. In particular we study two extensions of the Standard Model, the gauged B-L model and the leptoquark S_3 model, for which we determine a set of irrelevant gauge and Yukawa couplings. In each model, we present numerical and analytical estimates of the uncertainties associated with the predictions from asymptotic safety.

Synthesis of water-soluble NIR macro-photocatalysts from polymerizable zinc phthalocyanine

To improve the solubility and recyclability of the NIR photocatalyst, two synthetic strategies, namely “living” polymers with permanent NIR photocatalyst by reversible addition-fragmentation chain transfer (RAFT) polymerization and “non-living” polymers with recyclable NIR macro-photocatalyst (macro-PC) by conventional radical polymerization, were developed by copolymerization of hydrophilic and polymerizable zinc phthalocyanine (ZnTAPc-MAm or ZnTAPc-Am) monomers. The resultant macro-PCs from RAFT polymerization were endowed with permanent NIR photocatalysis due to the attachment of zinc phthalocyanine moieties, and the features of both “living” and permanent NIR photocatalyst of the “living” macro-PCs were verified by much simple multiple chain extensions via RAFT polymerization in water (only involved in “living” polymers and fresh monomer) under irradiation with NIR LED light (λmax = 730 nm) at room temperature. In addition, the resultant water-soluble “non-living” macro-PCs from conventional radical polymerization were endowed with only NIR photocatalysis property but they could be easily recycled just by centrifugation, which facilitates to synthesize tailored polymers by recyclable PCs under NIR irradiation.

RGBD1K: A Large-Scale Dataset and Benchmark for RGB-D Object Tracking

RGB-D object tracking has attracted considerable attention recently, achieving promising performance thanks to the symbiosis between visual and depth channels. However, given a limited amount of annotated RGB-D tracking data, most state-of-the-art RGB-D trackers are simple extensions of high-performance RGB-only trackers, without fully exploiting the underlying potential of the depth channel in the offline training stage. To address the dataset deficiency issue, a new RGB-D dataset named RGBD1K is released in this paper. The RGBD1K contains 1,050 sequences with about 2.5M frames in total. To demonstrate the benefits of training on a larger RGB-D data set in general, and RGBD1K in particular, we develop a transformer-based RGB-D tracker, named SPT, as a baseline for future visual object tracking studies using the new dataset. The results, of extensive experiments using the SPT tracker demonstrate the potential of the RGBD1K dataset to improve the performance of RGB-D tracking, inspiring future developments of effective tracker designs. The dataset and codes will be available on the project homepage: https://github.com/xuefeng-zhu5/RGBD1K.

The defect formula

In this paper we present a characterization for the defect of simple algebraic extensions of valued fields. This characterization generalizes the known result for the henselian case, namely that the defect is the product of the relative degrees of limit augmentations. The main tool used here is the graded algebra associated to a valuation on a polynomial ring. Let Kh be a henselization of a valued field K. Another relevant result proved in this paper is that for every valuation μh on Kh[x], with restriction μ on K[x], the corresponding map Gμ↪Gμh of graded algebras is an isomorphism.