Denote the free group on two letters by F2 and the SL(3,C)-representation variety of F2 by R = Hom(F2, SL(3, C)). There is a SL(3,C)-action on the coordinate ring of R, and the geometric points of the subring of invariants is an affine variety X. We determine explicit minimal generators and defining relations for the s…
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14 results for “F2”
The paper develops a new method to interpret deep neural networks using Cohen's f2.
problem Interpreting variable effects in deep neural networks is challenging due to their complexity and lack of statistical inferences.
method The paper adapts Fisher's variable permutation algorithm and applies statistical tests to Apley's accumulated local effect plots.
result The method provides a way to quantify and statistically assess the influence of variables in deep neural networks.
Given two maps f1 and f2 from the sphere Sm to an n-manifold N, when are they loose, i.e. when can they be deformed away from one another? We study the geometry of their (generic) coincidence locus and its Nielsen decomposition. On the one hand the resulting bordism class of coincidence data and the corresponding Niels…
Paper studies Landsberg curvature of a specific Finsler metric.
problem Analyzing Landsberg curvature of a particular Finsler metric.
method Derived Landsberg curvature and mean Landsberg curvature of the twisted product Finsler metric.
result Necessary and sufficient conditions for the metric to be Landsberg or weakly Landsberg are established.
We compute the rings for a closed -manifold and then determine the Borsuk-Ulam indices with in .
New argument for 3-manifold cohomology with coefficients.
problem Characterization of 3-manifold cohomology rings with coefficients.
method New argument based on Postnikov's 1948 characterization using intersection rings.
result A new proof for the characterization of 3-manifold cohomology rings.
On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of t…
A new stable similarity measure for time series using persistent homology.
problem Constructing a robust measure of time series similarity.
method Persistent homology for stability, bi-conditional periodicity score for similarity.
result Stability of the bi-conditional periodicity score under perturbations and dimension reduction.
Study on Ricci-Yamabe solitons on Walker manifolds.
problem Characterizing Walker manifolds for Ricci-Yamabe solitons.
method Explicit calculation of Ricci tensor, scalar curvature, and Hessian Perelman potential; solving partial differential equations.
result Identifying constraints on functions and vector field for soliton existence.
Profinite tensor powersmath.RA
Defines tensor product of profinitely many vector spaces over F2.
problem Defining tensor product of profinitely many copies of a vector space.
method Proposes a definition for finite-dimensional vector spaces over F2 with specific group actions.
result Organizes computations in Heegaard Floer homology.
Study reveals uniform difference in stretch factors between genus two handlebody group and outer automorphism group.
problem Analyzing the relationship between stretch factors in genus two handlebody group and outer automorphism group.
method Examined natural homomorphism from genus g handlebody group to outer automorphism group of free groups, focusing on pseudo-Anosov mapping classes and their stretch factors.
result Minimum stretch factor in genus two handlebody group is less than ten times the stretch factor of fully irreducible outer automorphism.
Balancing the Scales: A Comprehensive Study on Tackling Class Imbalance in Binary Classificationcs.LG
Study evaluates three class imbalance techniques across diverse datasets.
problem Class imbalance in binary classification tasks.
method Synthetic Minority Over-sampling Technique (SMOTE), Class Weights tuning, Decision Threshold Calibration.
result Decision Threshold Calibration is the most consistently effective technique.
New theorem removes uniform finite upper bound for shrinkability of null decompositions.
problem Shrinkability of null decompositions with non-singleton elements.
method Defining squeezable and squashable subsets, proving their equivalence, and applying these definitions to null decompositions.
result Any null decomposition of a compact metric space whose non-singleton elements are recursively squeezable is shrinkable.
The paper proposes a machine learning framework for detecting DeFi fraud across multiple blockchain chains.
problem Early detection of financial crimes in decentralized finance (DeFi) ecosystems.
method Extracting features from different blockchain chains, employing XGBoost and Neural Network for fraud detection.
result Introduction of novel DeFi-related features significantly improves fraud detection accuracy.