Corrects incorrect assertions about fixed points in digital topology.
problem Incorrect or incorrectly proven assertions about fixed points in digital metric spaces.
method Analysis of existing assertions and proofs.
result Identifies and corrects errors in published assertions.
The paper highlights issues in fixed point claims in digital topology.
problem Flaws in published assertions about fixed points in digital metric spaces.
method Continues a series of studies examining these flaws.
result Identifies and discusses problems in fixed point claims.
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect or poorly stated fixed point assertions in digital topology.
method Discussion of problematic publications in digital metric spaces.
result Clarification of incorrect fixed point assertions.
Fixed point assertions in digital topology are often incorrect or poorly stated.
problem Fixed points in digital metric spaces
method Discussing publications with bad assertions
result Identifying and correcting errors in fixed point assertions
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect, incorrectly proven, or trivial fixed point assertions in digital topology.
method Continues earlier work on identifying and critiquing bad fixed point assertions.
result Clarifies the nature and extent of incorrect fixed point assertions in digital topology.
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited.
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases, researchers using these tools have derived conclusions that are incorrect or tr…
Proposes a method for modeling random objects in metric spaces using random effects.
problem Modeling random objects in non-Euclidean spaces with random effects.
method Nonlinear Fréchet-based algorithm for M-estimation.
result Consistent estimation of prediction target under random-effects formulation.
The paper introduces new geometric methods to analyze radar electromagnetic wave statistics.
problem Analyzing spatio-temporal and polarimetric fluctuations of radar electromagnetic waves.
method Using statistical mechanics and Information Geometry, the paper defines a Fréchet barycentre and maximum entropy density for radar measurements.
result New tools for describing radar electromagnetic wave fluctuations, including a distance on covariance matrices.
Study restrictions on digitally continuous functions and their effects.
problem Understanding effects of restrictions on digitally continuous functions.
method Analyzing digitally continuous functions and their modifications.
result Analogous result for topological spaces derived from digitally continuous functions.
Study of digital topology concepts like hyperspaces and function graphs.
problem Adapting classical topology concepts to digital topology.
method Define digital hyperspaces and function graphs, study their properties.
result Some relationships and graphical properties of digital hyperspaces and function graphs.
Novel framework for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models with metric responses.
method Developed algorithms for large datasets, agnostic to predictive models, with asymptotic and non-asymptotic guarantees.
result Asymptotic and non-asymptotic guarantees for special cases, demonstrated in clinical applications.
We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification acc…
It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1,⋯,xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. This data also applies to construct differe…
Paper proposes real-time risk metrics for stablecoin protocols.
problem Lack of risk management frameworks for stablecoins.
method Developed two risk metrics: capitalization and liquidity.
result Demonstrated practical benefits of real-time on-chain data.
In this paper, we show how to construct graph theoretical models of n-dimensional continuous objects and manifolds. These models retain topological properties of their continuous counterparts. An LCL collection of n-cells in Euclidean space is introduced and investigated. If an LCL collection of n-cells is a cover of a…
We give an answer to the question given by T.Y.Kong in his article "Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces?" In this article he asks the question, if so called "good pairs" of neighborhood relations can be found on the set Z^n such that the existence of digital manifolds of dimension …
Corrects errors in Hans' pseudocovering spaces paper.
problem Mathematical errors and citation issues in Hans' pseudocovering spaces paper.
method Identifies and corrects errors in Hans' previous work.
result Addresses mathematical and citation errors in Hans' pseudocovering spaces paper.
A novel approach for unsupervised domain adaptation for neural networks is proposed. It relies on metric-based regularization of the learning process. The metric-based regularization aims at domain-invariant latent feature representations by means of maximizing the similarity between domain-specific activation distribu…
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal mapping, or scaling, of power law distributed data. Power law distributed data are foun…
The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any…
Proposes a probabilistic digital twin for dynamical systems using sparse Bayesian learning.
problem Creating and updating accurate digital twins for complex dynamical systems.
method Sparse Bayesian machine learning, two approaches: input-output and output-only.
result Identifies correct perturbation terms and associated parameters in dynamical systems.
Enhanced multi-fidelity models improve digital twin accuracy and uncertainty quantification.
problem Lack of detailed application-specific data and inaccurate sensor data hinder surrogate model learning for digital twins.
method Proposes a multi-fidelity surrogate model framework integrating PCFE and GP, and deep-HPCFE with auto-regression schemes.
result Demonstrates improved accuracy and uncertainty quantification in digital twin systems.
Digital money could reduce germ spread during coronavirus.
problem Spreading of germs via paper money during coronavirus.
method Policy recommendations for mobile wallets, digital currencies, and data protection.
result Adopting digital money can help reduce germ spread.
The paper highlights issues with fixed point claims in digital images.
problem Flaws in published assertions about fixed points in digital images.
method Continues a series of studies examining digital topology.
result Identifies and discusses problems with fixed point claims.
Find limiting sets for digital cones and suspensions.
problem Digital topology cone and suspension constructions.
method Identify (m, n)-limiting sets, especially (0, 0)-freezing sets.
result Discover (0, 0)-limiting sets for digital cones and suspensions.
Study AFPP of unions of convex digital disks in 2D.
problem Conditions for AFPP of union of convex disks in digital plane.
method Use results from [6] to analyze AFPP.
result Conditions for AFPP of union of convex disks.
The paper addresses flaws in fixed point assertions for digital images.
problem Deficiencies in previously published works on fixed point assertions for digital images.
method Continues a series of studies to identify and rectify issues in fixed point assertions.
result Identifies and corrects flaws in fixed point assertions for digital images.
Study minimal freezing sets in convex digital disks.
problem Finding minimal freezing sets in convex digital disks.
method Showed how to find minimal freezing sets for convex disks in digital plane.
result Found minimal freezing sets for convex disks in digital plane.
Study on cold and freezing sets in digital images.
problem Properties of cold sets in digital images.
method Analysis of properties and relationships between cold and freezing sets.
result Examined relationships between cold and freezing sets.
Digital trees have approximate fixed point property, and conditions for products are explored.
problem Conditions for the approximate fixed point property in digital tree products.
method Analyzes digital trees and their products, explores conditions for the AFPP.
result Conditions are found for the AFPP in digital tree products.
Study convexity and AFPP in digital images.
problem Relationship between convexity and AFPP in digital images.
method Examined in Z^2 digital images.
result Relationship between convexity and AFPP in digital images.
We provide abelianizations of differentiable actions of finite groups on smooth real manifolds. De Concini-Procesi wonderful models for (local) subspace arrangements and a careful analysis of linear actions on real vector spaces are at the core of our construction. In fact, we show that our abelianizations have stabili…
Han discusses variants of digital covering maps and their equivalences.
problem Han's paper lacks thorough discussion on variants and their equivalences.
method Examined several variants of digital covering maps and compared their equivalences.
result Found several equivalences among the variants of digital covering maps.
Critiques incorrect fixed point assertions in digital topology.
problem Incorrect or incorrectly proven fixed point assertions in digital topology.
method Critical review of existing assertions.
result Identifies and critiques incorrect fixed point assertions.
Examines how irreducibility and rigidity affect digital images.
problem Understanding interactions between irreducibility and rigidity in digital images.
method Analyzes Cartesian products, wedges, and cold and freezing sets.
result Interactions between irreducibility and rigidity in digital images.
This study synthesizes stablecoin systems and develops a performance evaluation framework.
problem Fragmented academic research on stablecoins across economics, law, and computer science.
method Multi-method research design including literature synthesis, performance evaluation framework, and case study.
result Unified taxonomy and performance evaluation framework for stablecoin design.
Paper develops security model and pricing for stable digital currency in quantum blockchain network.
problem Securing and pricing stable digital currency in a quantum blockchain network.
method Developed a block-based quantum channel networking technology and a FinTech platform model with dynamic pricing.
result Established a generalized IoB security model using quantum channel networking and QKD.
A new method streamlines digital payment programming using smart contracts.
problem High costs and security challenges in programming smart contracts for digital payments.
method Transforming digital currencies into token streams and using configurable templates to generate specialized smart contracts.
result Reduces payment programming costs and enhances security, self-enforcement, adaptability, and controllability.
New framework explains leading digit patterns without probabilistic assumptions.
problem Explaining leading digit distributions without relying on probabilistic models.
method Shift-invariant functional equation and affine-plus-periodic formulas.
result Unified mathematical foundation for understanding digit distributions.
With the advent of smartphone indirect ophthalmoscopy, teleophthalmology - the use of specialist ophthalmology assets at a distance from the patient - has experienced a breakthrough, promising enormous benefits especially for healthcare in distant, inaccessible or opthalmologically underserved areas, where specialists …
Study freezing sets for digital images in a 2D grid.
problem Determine minimal freezing sets for digital images.
method Prove methods to obtain freezing sets for digital images (X, c_i) where X is a subset of Z^2.
result Examples show how methods can lead to the determination of minimal freezing sets.
This study redefines probability for finite outcomes using axioms and examples.
problem Defining probability for finite outcomes and preserving information.
method Developed three axioms for relative probability functions and provided examples and a system for their composition.
result Proved the topological closure of the relative probability space, preserving information under limits.
Pakistan examines digital mergers using traditional competition tools.
problem Regulating digital mergers in a developing country.
method Empirical comparative analysis of CCP's M&A decisions.
result CCP uses same decision factors for digital and traditional M&As.
Wrist movements can reveal digits, posing security risks.
problem Security vulnerabilities in wrist wearable devices.
method Machine learning model trained on wrist movement data.
result 100% accuracy in predicting digits via wrist movement.
Generative models create personalized patient health simulations.
problem Creating accurate digital twins for personalized medicine.
method Neural network architecture for conditional generative models of clinical trajectories.
result Same architecture generates accurate twins across 13 indications.
Model learns cancer tissue images onto a low-dimensional space revealing tissue characteristics.
problem Improving cancer diagnosis through high-fidelity digital pathology.
method Deep generative model using PathologyGAN to map real images onto a latent space.
result Latent space encodes morphological characteristics and reveals distinct tissue clusters.
ISOMORPH creates a digital twin for supply chain logistics, advancing time-series forecasting benchmarks.
problem Lack of public benchmarks for supply chain logistics time-series forecasting.
method Developed a digital twin simulator with interpretable parameters and modular topology, generating datasets and verifying conservation laws.
result Foundation models achieve MASE values exceeding public benchmarks at low-to-moderate horizons, supporting UQ.