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.
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48 results for “digit sets”
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 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 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.
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.
New method for freezing sets in arbitrary dimensions.
problem Creating freezing sets for digital images in arbitrary dimensions.
method Using and adjacencies to obtain freezing sets in .
result Demonstrated freezing sets for digital images in arbitrary dimensions.
Study fixed points in digital images, introducing new invariants.
problem Understanding properties of digital images through fixed points.
method Introduce new invariants and freezing/cold sets to analyze fixed point sets.
result Existence of fixed point sets restricts maps on their complements.
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.
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 …
New tools for constructing fixed point sets in digital topology.
problem Constructing fixed point sets in digital topology.
method Defining excludable points and articulation points, and showing their exclusion from freezing sets.
result Excludable points and articulation points can be excluded from all freezing sets.
Digit Recognition From Wrist Movements and Security Concerns with Smart Wrist Wearable IOT Devicescs.CR
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.
3D self-affine tiles with specific digit sets have boundary homeomorphic to a 2-sphere.
problem Characterizing 3D self-affine tiles with collinear digit sets whose boundary is a sphere.
method Using lattice tiling combinatorics and topological properties of spheres, the paper characterizes such tiles.
result The boundary of these tiles is homeomorphic to a 2-sphere under certain conditions.
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.
Connectedness of planar self-affine sets associated with non-consecutive collinear digit setsmath.GN
In the paper, we focus on the connectedness of planar self-affine sets generated by an integer expanding matrix with and a collinear digit set , where and such that is linearly independent. We discuss the domain of…
Self-affine tiles homeomorphic to a ball proven for a specific digit set.
problem Topology of self-affine tiles with collinear digit sets.
method Proving homeomorphism to a ball using integral self-affine tiles with collinear digit sets.
result A large class of integral self-affine tiles with collinear digit sets is homeomorphic to a closed 3-dimensional ball.
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.
Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is known to hold for different types of financial data. The Illicit Financial Flow…
CRBM generates digital twins for MS patients, aiding in disease progression analysis.
problem Characterizing and analyzing disease progression in MS patients.
method Unsupervised machine learning with Conditional Restricted Boltzmann Machines (CRBMs).
result Generated digital twins are statistically indistinguishable from actual subjects.
Topology speeds up and improves CNNs for digit recognition.
problem Improving and speeding up deep learning models for digit recognition.
method Topological data analysis applied to CNNs to modify computations.
result Topology improves CNNs' performance and generalization.
New handwritten digits dataset for Kannada script.
problem Lack of datasets for Kannada numeral digits.
method Developed Kannada-MNIST and Dig-MNIST datasets.
result Initial CNN accuracy is lower than MNIST, indicating a challenge in generalization.
New method predicts political ideology from online activity.
problem Predicting political ideology from digital footprints.
method Statistical learning approaches applied to reddit data.
result Activity in non-political forums can predict political ideology with high accuracy.
Automates translating natural language to Verilog for digital design.
problem Manual translation of natural language specifications to Verilog is time-consuming and error-prone.
method Fine-tuned GPT-2 to derive Verilog from English, using a dataset of design tasks.
result GPT-2 achieved 94.8% correct translation across simple and abstract design tasks.
Study evaluates digital transformation impact on financial performance using LLMs.
problem Measuring and understanding the impact of digital transformation on financial performance.
method Constructed DT indicators from company reports; analyzed effects of different digital technologies.
result Digital transformation improves financial performance, but varies by technology.
Generative model calibrates 3D battery cathode morphologies from 2D images.
problem Calibrate 3D morphologies of all-solid-state battery cathodes from 2D microscopy images.
method Combining GANs with excursion sets of Gaussian random fields.
result Calibrated digital twins enable systematic exploration of morphological scenarios.
We study the connectedness of the planar self-affine sets generated by an integer expanding matrix with and a non-collinear digit set where and such that is linearly independent. By chec…
This paper explores IT governance for CBDC adoption in financial markets.
problem Adopting CBDC requires new IT governance models in financial markets.
method Systematic Literature Review (SLR) of 14 studies on IT resources and governance models.
result Many IT resources and preliminary IT designs for CBDC governance identified.
Study assesses impact of CBDC on financial stability in dual-currency economy.
problem Impact of CBDC on financial stability in dual-currency economy (Romania).
method Integrated analytical framework combining econometrics, machine learning, and behavioural modelling. CBDC adoption probabilities estimated using XGBoost and logistic regression models. Liquidity stress simulations and VAR, MSVAR, SVAR models capture macro-financial transmission.
result CBDC uptake would be moderate, primarily driven by digital readiness and trust in the central bank.
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.
Corrects a false claim about a digital sphere model's contractibility.
problem Incorrect claim about MSS_18's 18-contractibility.
method Analyzes digital image MSS_18 as a digital model of S^2.
result Shows MSS_18 is 18-contractible.
We describe a novel spiking neural network (SNN) for automated, real-time handwritten digit classification and its implementation on a GP-GPU platform. Information processing within the network, from feature extraction to classification is implemented by mimicking the basic aspects of neuronal spike initiation and prop…
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.
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.
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.
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.
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…
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.
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.
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.
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.
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.
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.
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
Optimal ANN pre-training with SDA reduces handwritten Bengali digit recognition error to 2.34%
problem Optimizing ANN architecture for Bengali handwritten digit recognition
method Pre-training ANN with stacked denoising autoencoder (SDA)
result Minimum validation error of 2.34% on handwritten Bengali dataset
Paper introduces a method to learn physics between digital twins using imperfect models.
problem Learning physics from imperfect data and low-fidelity models.
method Bayesian Hierarchical modeling with physics-informed Gaussian processes.
result Models learning between digital twins are less uncertain than independent models but not over-confident.
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.