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.
We propose an efficient lattice procedure which permits to obtain European and American option prices under the Black and Scholes model for digital options with barrier features. Numerical results show the accuracy of the proposed method.
A new method, tree-SNE, solves the scale problem in t-SNE.
problem Clustering and visualizing high-dimensional data, especially MNIST digits.
method Revisits t-SNE idea to create a 2+1 dimensional embedding with a scale parameter.
result The optimal embedding depends continuously on the scale parameter for all initial conditions.
We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall output is the average of all leaves weighted by the gating values on their path. …
dtControl uses decision trees to represent controllers efficiently and explainably.
problem Representing controllers concisely and explainably.
method dtControl uses decision tree learning algorithms to represent controllers. Novel techniques for determinizing controllers are introduced.
result Novel techniques for determinizing controllers during decision tree construction are extremely efficient, yielding small decision trees.
Classifier evasion consists in finding for a given instance x the nearest instance x′ such that the classifier predictions of x and x′ are different. We present two novel algorithms for systematically computing evasions for tree ensembles such as boosted trees and random forests. Our first algorithm uses a Mixe…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of correlation in MPS restricts its representation power heavily for modeling complex…
We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large datasets. While boundary trees use an Euclidean measure of similarity, the Differ…
We empirically investigate the (negative) expected accuracy as an alternative loss function to cross entropy (negative log likelihood) for classification tasks. Coupled with softmax activation, it has small derivatives over most of its domain, and is therefore hard to optimize. A modified, leaky version is evaluated on…
DOFEN improves DNN performance on tabular data benchmarks.
problem DOFEN tackles the performance gap between DNNs and tree-based models on tabular data.
method DOFEN uses a two-level rODT forest ensembling process inspired by oblivious decision trees.
result DOFEN achieves state-of-the-art results on the Tabular Benchmark.
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
Tree-SNE combines t-SNE and hierarchical clustering for data visualization.
problem Data visualization and clustering in complex datasets.
method Stacked one-dimensional t-SNE embeddings and alpha-clustering.
result Effective hierarchical clustering and visualization of various datasets.
Financial fraud detection in digital banking requires reasoning over multiple heterogeneous event streams.
problem Financial fraud detection in digital banking requires reasoning over multiple heterogeneous event streams.
method Multi-Stream Fraud Transformer (MSFT) architecture that encodes each event stream with independent Transformer encoders and fuses their representations through configurable mechanisms.
result Sequence models significantly outperform gradient-boosted trees operating on aggregated features.
The paper quantifies and attributes uncertainty in complex system simulations.
problem Uncertainty in complex system simulations due to unknown or approximated subprocesses.
method Developed a framework for quantifying and attributing submodel uncertainty using bootstrapping, Bayesian model averaging, and tree-based methods.
result Individual submodels contribute to overall uncertainty, and their importance can be quantified.
Paper introduces DNTs to clone black-box models efficiently.
problem Cloning functionality of black-box models.
method Deep Neural Trees (DNTs) trained with active learning.
result Trained DNT can clone task-specific behavior of black-box models.
New framework for regression trees with multivariate response and dynamic mean vectors.
problem Characterizing and implementing regression trees for multivariate responses.
method High dimensional model with dynamic mean vectors over multi-dimensional change axes.
result Optimal rate of convergence and asymptotic valid confidence intervals for change points.
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.
Study on cryptocurrency market correlations at various time scales.
problem Understanding the hierarchical structure of cryptocurrency market dynamics.
method Analysis of MST and TMFG for 25 liquid cryptocurrencies at different time horizons.
result Cryptocurrency market correlations decrease with finer time scales and show a growing hierarchical structure with coarser scales.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
The paper [10] incorrectly asserts that the digital image MSS_18, a digital model of the Euclidean 2-sphere S^2, is not 18-contractible. We show this assertion is false.
Study shows 'Belt and Road' node cities boost digital finance in China.
problem Impact of 'Belt and Road' node cities on digital inclusive finance.
method Descriptive analysis, literature review, theoretical model, differential differential method.
result Establishment of 'Belt and Road' node cities promotes digital inclusive finance in China, with Internet development as a mediating variable.
Surrogate models enhance digital twin technology for dynamic systems.
problem Lack of clarity and effective methods for digital twin applications.
method Exploration of Gaussian process (GP) emulators within digital twin framework.
result Surrogate models like GP emulators are effective for digital twin development.
SFC aims to protect the Amazon with a digital currency and smart contracts.
problem Protecting the Amazon's ecosystem and ensuring resource credibility.
method Blockchain, digital contracts, smart contracts with oracles.
result Ensures credibility and security for financial resources invested in Amazon projects.
Digital twin reduces costs in various fields.
problem High costs in decision-making processes.
method Use of digital twin model for cost reduction.
result Digital twin acts as a cost reduction method.
We study properties of shy maps in digital topology.