Even knots with more than 30 crossings are not fertile.
problem Understanding fertility in knots with specific crossing numbers.
method Analyzing minimum crossing number diagrams and changing over-under information.
result Even knots with more than 30 crossings cannot be obtained from a minimum crossing number diagram by changing over-under information.
Discuss knots in SgimesS1, introducing rotating information and invariants.
problem Understanding knots in SgimesS1 and their invariants. method Introduce diagrams, moves, and rotating information to construct invariants.
result Construct invariants using the rotating information of knots in SgimesS1. Pseudodiagrams are diagrams of knots where some information about which strand goes over/under at certain crossings may be missing. Pseudoknots are equivalence classes of pseudodiagrams, with equivalence defined by a class of Reidemeister-type moves. In this paper, we introduce two natural extensions of classical knot …
A knot is fertile if it can generate all smaller knots through a specific diagram modification.
problem Understanding the conditions under which a knot can generate all smaller knots.
method Using obstructions and diagram modifications to analyze knot fertility.
result Finiteness of (c(K)+f,c(K)+p)-fertile knots for all f,p. The performance of most the clustering methods hinges on the used pairwise affinity, which is usually denoted by a similarity matrix. However, the pairwise similarity is notoriously known for its vulnerability of noise contamination or the imbalance in samples or features, and thus hinders accurate clustering. To tackl…
This paper studies knots in a thickened surface and introduces a new way to label crossings.
problem Analyzing knots in a thickened surface with a new labeling system.
method Introducing diagrams, moves, and a new labeling system for knots in SgimesS1. result Developed a new method to label crossings in knots in SgimesS1. We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact probabilities for knots in this model. As expected, most diagrams with 1…
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2-dimensional surface.) We prove that if a minimal genus …
It seems to be very unlikely that all relevant information in the stock market could be fully encoded in a geometrical shape. Still,the present paper will reveal the geometry behind the stock market transactions. The prices of market index (DJIA) stock components are arranged in ascending order from the smallest one in…
The paper extends knot theory to annular and toroidal pseudo knots.
problem Defining and classifying pseudo knots in annular and toroidal settings.
method Introducing pseudo knots as equivalence classes under moves, lifting to torus, and exploring inclusion relations.
result New invariants for classifying pseudo knots and links in solid and thickened torus.
Probabilistic pseudo knots model uncertain knot diagrams.
problem Modeling knots with unresolved crossings.
method Assign probabilities to undetermined crossings; define probabilistic equivalence and extend classical knot invariants.
result Capture uncertainty in physical, biological, and computational contexts.
Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
problem Unknottability of spatial graphs by region crossing changes.
method Region crossing changes to switch over/under relations within regions of spatial graph diagrams.
result Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
This paper tabulates prime knot projections up to eight double points.
problem Tabulating prime knot projections and their mirror images up to a certain number of double points.
method Systematic flypes and enumeration of tangles with at most four double points, using arrow diagrams.
result Complete table of prime knot projections with their mirror images up to eight double points.
Deep-learning model detects ASD from MRI data with high accuracy.
problem Challenges in diagnosing ASD due to subjective behavioral assessments and informant biases.
method Integrates deep-learning and SVM techniques to classify ASD brain scans.
result Highly accurate classification of ASD brain scans from neurotypical scans.
Study on random knot diagrams and their probability of forming specific knots.
problem Understanding the probability of forming specific knots from random knot diagrams.
method Analyzing free knot diagrams without over/under information and proving trefoil formation; making conjectures about unknot and trefoil probabilities.
result Every free knot diagram produces trefoil knots, and certain families of diagrams are completely worked out.
Develops a framework for stuck knots with rigid constraints and invariants.
problem Rigidity constraints on knot diagrams restrict allowable isotopies.
method Formalizes stuck crossings as rigid configurations, introduces unstick move, and constructs invariants.
result Rigidity contributes independent information even when knot type remains fixed.
Characterizes the OU matrix for up to 5 strands in braids.
problem Understanding the structure of braid diagrams through their matrices.
method Characterization of the OU matrix for up to 5 strands in braids.
result Standard form of the OU matrix for general braids of up to 5 strands is given and characterized.
We study the relationship between social media output and National Football League (NFL) games, using a dataset containing messages from Twitter and NFL game statistics. Specifically, we consider tweets pertaining to specific teams and games in the NFL season and use them alongside statistical game data to build predic…
We introduce a new numerical knot invariant, termed the \textit{segment number}, which is derived from partitioned knot diagrams subject to specific over/under-crossing constraints. We prove that a knot is non-trivial if and only if its segment number is at least 3. Furthermore, we investigate the structural properties…
Paper constructs a HOMFLYPT-type invariant for pseudo links.
problem Inability to construct polynomial invariants for pseudo links using Hecke algebra techniques.
method Using a resolution homomorphism and pseudo Hecke algebra of type \(A\), the paper constructs a HOMFLYPT-type invariant for oriented pseudo links.
result The constructed invariant satisfies a natural pseudo skein relation and admits a state-sum formulation.
Paper solves the minimal generating set problem for singular Reidemeister moves.
problem Determine minimal generating sets of oriented singular Reidemeister moves.
method Introduced new invariant for singular links to detect type IV moves and provide obstructions.
result Proved exactly 96 distinct inclusion-minimal generating sets for singular moves.
Both classical and virtual knots arise as formal Gauss diagrams modulo some abstract moves corresponding to Reidemeister moves. If we forget about both over/under crossings structure and writhe numbers of knots modulo the same Reidemeister moves, we get a dramatic simplification of virtual knots, which kills all classi…
The study proposes a framework to assess sustainability of firms using fund-level classifications and portfolio holdings.
problem To capture market-based sustainability assessments of firms.
method Exploiting fund-level sustainability classifications and granular portfolio holdings to construct Market-Implied Sustainability (MIS) scores.
result MIS scores capture sustainability dimensions different from conventional ESG ratings and improve portfolio performance.
Convolutional neural network based systems have largely failed to be adopted in many high-risk application areas, including healthcare, military, security, transportation, finance, and legal, due to their highly uninterpretable "black-box" nature. Towards solving this deficiency, we teach a novel multi-task capsule net…
COCOA can learn new tasks without forgetting previously learned ones in a distributed setting.
problem Continual learning with tasks arriving sequentially.
method Distributed optimization with COCOA algorithm.
result COCOA can perform continual learning without forgetting.
Quantized BNNs maintain uncertainty estimation quality despite reduced precision.
problem Reduced precision in BNNs due to quantization.
method Quantized BNNs with 32-bit weights and activations compressed to 16-bit integers.
result Uniform quantization does not significantly degrade uncertainty estimation quality.
Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models are rarely well-specified in practice. In this work, we study VB under model missp…
Chirality affects the curvature of molecular networks, influencing their shape and stability.
problem Understanding how chirality influences the curvature of molecular networks.
method Langevin dynamics simulations and constrained gradient optimization of square lattice networks.
result Linking chirality dictates the sign of Gaussian curvature in molecular chainmail networks.
This paper discusses a novel explanation for asymmetric volatility based on the anchoring behavioral pattern. Anchoring as a heuristic bias causes investors focusing on recent price changes and price levels, which two lead to a belief in continuing trend and mean-reversion respectively. The empirical results support ou…
Bayesian framework for semiparametric regression of discrete data.
problem Complex distributional features of discrete data.
method Semiparametric modeling with nonparametric marginal and latent linear regression.
result Posterior consistency and analytical/posterior predictive distributions.
Develops a new method to model overlapping asymmetric datasets effectively.
problem Handling overlapping asymmetric datasets in data science.
method Twice penalized P-Spline approximation method.
result Improves model fit by over 65% in a real-life dataset.
Study compares various ANN models for SPX and NDX options pricing.
problem Approximating complex multivariate functions for accurate option pricing.
method Hybrid RNN models (LSTM-GRU, TDNN, MLP, KAN) with attention mechanisms.
result LSTM-GRU hybrid RNN with attention outperforms other models.
A clinician desires to use a risk-stratification method that achieves confident risk-stratification - the risk estimates of the different patients reflect the true risks with a high probability. This allows him/her to use these risks to make accurate predictions about prognosis and decisions about screening, treatments…
We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
A new framework for information theory considers computational constraints.
problem Understanding information in complex systems with computational limitations.
method Variational extension of Shannon's information theory with computational constraints.
result Predictive V-information can be created through computation and reliably estimated from data. An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market participants have access t…
We study a simple model of an asset market with informed and non-informed agents. In the absence of non-informed agents, the market becomes information efficient when the number of traders with different private information is large enough. Upon introducing non-informed agents, we find that the latter contribute signif…
New method quantifies redundant information using information bottleneck.
problem Quantifying redundant information among multiple sources.
method Formulated as an information bottleneck problem, termed redundancy bottleneck.
result Extracts information that best predicts the target without revealing source identity.
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
Generalizes information theory to evolving belief.
problem Measuring change in belief over time.
method Derives a general theory of information from first principles.
result Recover all information measures and interprets entropy as expected gain.
Paper proposes a framework to identify and obfuscate sensitive features via information density estimation.
problem Identifying and protecting sensitive attributes from leakage in obfuscation mechanisms.
method Information density estimation to identify leaking features, followed by a targeted obfuscation mechanism.
result Proven leakage guarantee in terms of Eγ-divergence for the obfuscation mechanism. Review of information plane analyses in neural networks, highlighting mixed results and methodological challenges.
problem Understanding the relationship between information-theoretic compression and neural network performance.
method Literature review and detailed analysis of information quantity estimation methods.
result Information plane compression is not necessarily information-theoretic but compatible with geometric compression.
Information geometry offers new tools for statistical analysis.
problem Statistical analysis of probability distributions.
method Geometric perspective on statistical manifolds.
result New applications in radar sensing, signal processing, etc.
In this paper, we present a new approach to interpret deep learning models. By coupling mutual information with network science, we explore how information flows through feedforward networks. We show that efficiently approximating mutual information allows us to create an information measure that quantifies how much in…
Before the massive spread of computer technology, information was far from complex. The development of technology shifted the paradigm: from individuals who faced scarce and costly information to individuals who face massive amounts of information accessible at low costs. Nowadays we are living in the era of big data a…
In financial markets valuable information is rarely circulated homogeneously, because of time required for information to spread. However, advances in communication technology means that the 'lifetime' of important information is typically short. Hence, viewed as a tradable asset, information shares the characteristics…
Introduces relative information gain for improving Gaussian process regression rates.
problem Improving the sample complexity of estimating or maximizing unknown functions.
method Introduces relative information gain, interpolates between effective dimension and information gain, and proves PAC-Bayesian bounds.
result Obtains minimax-optimal rates of convergence through the relative information gain.
This paper uses information theory to improve risk modeling in big data.
problem Insufficient application of information theory in actuarial science.
method Explores information theory to uncover performance limits of insurance big data systems.
result Guidance for risk modeling and actuarial pricing systems.