Improved SIR algorithm identifies effective factors more accurately.
problem Identifying significant factors with lower intrinsic dimensionality.
method Overlapping Sliced Inverse Regression (OSIR) algorithm.
result OSIR algorithm estimates effective dimension reduction space and number of effective factors more accurately.
A new covariance estimator reduces dimensionality in high-dimensional undersized samples.
problem Challenges in estimating covariance matrices for high-dimensional data with fewer samples.
method Maximum Entropy Covariance (MEC) estimator that combines covariance matrices from different response categories.
result MEC estimator improves efficiency in dimension reduction methods like SIR and SAVE.
Study on r−shake slice knots and proves 0-shake slice knots are slice.
problem Understanding and characterizing r−shake slice knots. method Exploring the relation to corks and proving slice properties.
result Proves 0-shake slice knots are slice.
Proves certain knots are slice without shaking.
problem Identifying slice knots without using traditional methods.
method Direct proof for 0−shake slice knots. result Proves 0−shake slice knots are slice. Proves a special knot type is slice.
problem Characterizing slice knots.
method Proof by contradiction and algebraic topology.
result 0-shake slice knots are indeed slice.
The Conway knot is not slice, resolving a knot classification problem.
problem Determining which knots are slice in 4-dimensional space.
method Demonstrated through a proof involving knot classification and properties of slice knots.
result The Conway knot is the first example of a non-slice knot that is topologically slice and a positive mutant of a slice knot.
New findings on knots that are both topologically and rationally slice.
problem Understanding knots that are both topologically and rationally slice.
method Analyzing the concordance group of knots in S3. result There are infinitely many topologically slice knots that are strongly rationally slice but not slice.
Regular sliceness implies once-stably decomposable sliceness in symplectizations.
problem Relationship between regular and decomposable Lagrangian cobordisms in symplectizations.
method Stabilization-free strategy and satellite operations.
result Regular sliceness implies once-stably decomposable sliceness.
The paper defines new knot genera and finds bounds for stabilization distances.
problem Finding bounds for stabilization distances of symmetric surfaces.
method Defining new knot genera and using them to find bounds.
result Constructs unknotted symmetric 2-spheres without symmetric 3-ball bounds.
We consider linear slices of the space of Kleinian once-punctured torus groups; a linear slice is obtained by fixing the value of the trace of one of the generators. The linear slice for trace 2 is called the Maskit slice. We will show that if traces converge `horocyclically' to 2 then associated linear slices converge…
Proposes a new framework for detecting overlapping and non-overlapping communities.
problem Lack of methods for both overlapping and non-overlapping community detection.
method Integrated framework based on primary node criteria of internal and external association degrees.
result Outperforms existing methods on evaluation criteria.
New knots found with tough, unsliceable discs.
problem Finding tough knots that can't be sliced smoothly.
method Constructed infinitely many knots with non-approximable slice discs.
result Smoothly sliceable knots have non-approximable slice discs.
A novel time series imputation technique using tSMOTE for handling missing data.
problem Handling missing observations in irregular time series data.
method Time Sliced Synthetic Minority Oversampling Technique (tSMOTE) generalizing SMOTE for time series imputation.
result Improvement in classification accuracy for imputed data compared to standard imputation methods.
Automated image segmentation distinguishes overlapping human chromosomes.
problem Distinguishing overlapping human chromosomes for medical diagnostics.
method Customized convolutional neural network for image segmentation.
result IOU scores of 94.7% for overlapping regions, 88-94% for non-overlapping regions.
Study shows vanishing correction terms for doubly slice knots.
problem Understanding doubly slice knots and their properties.
method Analyzing connected sums of knots with coprime Alexander polynomials and using Ozsváth-Szabó correction terms.
result Correction terms vanish for doubly slice knots, providing new insights.
The study examines obstructions to links being shake slice.
problem Understanding when links are not shake slice.
method Examined shake concordance and zero surgery manifolds, and provided obstructions based on Arf invariants and algebraic sliceness.
result Links that are shake concordant have homology cobordant zero surgery manifolds, and provided specific obstructions to shake sliceness.
A new slicing method speeds up sliced Wasserstein estimation.
problem Efficiently estimating sliced Wasserstein distance.
method Random-Path Projecting Direction (RPD) for fast sampling.
result RPSW and IWRPSW show favorable performance in training generative models.
Overlapping clustering problem is an important learning issue in which clusters are not mutually exclusive and each object may belongs simultaneously to several clusters. This paper presents a kernel based method that produces overlapping clusters on a high feature space using mercer kernel techniques to improve separa…
Deconfounding scores improve causal effect estimation with weak overlap.
problem Challenges in causal treatment effect estimation due to weak overlap in high-dimensional data.
method Propose deconfounding scores to preserve identification and target estimation while improving overlap.
result Prognostic scores are overlap-optimal under a broad family of generalized linear models with Gaussian features.
A new method speeds up overlapping group lasso computations.
problem Time-consuming optimization of overlapping group lasso on large-scale problems.
method Non-overlapping statistical approximation to overlapping group lasso.
result The proposed penalty is statistically equivalent to overlapping group lasso.
Khovanov homology fails to differentiate certain slice disks.
problem Differentiating roll-spun slice disks from trivial ones.
method Using Khovanov homology and Morse theory.
result Khovanov homology cannot distinguish roll-spun slice disks from trivial ones.
New method freely slices good boundary links with specific conditions.
problem Slicing good boundary links with multiple components.
method Using a Seifert surface and homotopically trivial plus assumption.
result Provides new freely slice links and subsumes previous methods.
Characterizes values of slice-torus invariants related to knot genus.
problem Understanding the values of slice-torus invariants for knots.
method Characterization based on stable smooth slice genus.
result Existence of slice torus invariants without explicit constructions.
Paper bounds double slice genus of knots.
problem Understanding knot genus complexities.
method Using Casson-Gordon invariants, the paper defines and bounds the double slice genus.
result Double slice genus can be much larger than slice genus.
The study classifies χ−slice pretzel links and Seifert fiber spaces.
problem Understanding χ−slice pretzel links and their properties. method Analyzing the sliceness of pretzel knots and extending results to pretzel links.
result Complete classifications of positive and negative pretzel links that are χ−slice, and partial classifications of 3-stranded and 4-stranded pretzel links. New method improves CATE estimation in low overlap regions.
problem Low overlap in CATE estimation leads to poor performance of meta-learners.
method Overlap-Adaptive Regularization (OAR) that regularizes models proportionally to overlap weights.
result OAR significantly improves CATE estimation in low-overlap settings.
Proposes a sensitivity framework to handle limited overlap in causal inference.
problem Limited overlap between treated and control groups in observational studies.
method Sensitivity framework based on worst-case confidence bounds on bias introduced by trimming.
result Protects against spurious findings by quantifying uncertainty in regions with limited overlap.
Study slice-regular polynomial functions via twistor space group actions.
problem Characterize slice-regular functions and their polynomial subclasses.
method Employ the twistor construction and group actions of PGL(2,H). result Characterize slice-regular functions with planar twistor lifts and normal classes of polynomials.
Study uses knot Floer homology to distinguish slice disks.
problem Classifying slice disks of knots up to isotopy and diffeomorphism.
method Invariants in knot Floer homology to compute and distinguish slice disks.
result Invariant can distinguish non-isotopic slice disks with diffeomorphic complements.
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
The paper shows some Montesinos links can't be doubly sliced strongly.
problem Understanding double sliceness for Montesinos links.
method Using branched double covers and Seifert fibered spaces.
result A large family of Montesinos links are not strongly doubly slice.
Study shows most knots in a family are not slice.
problem Determining which 3-stranded pretzel knots are slice.
method Analyzing a specific infinite family of knots and proving their non-slice properties.
result Four-fifths of the remaining knots in the family are not slice.
Study on slicing knots in 4-manifolds, focusing on CP^2-slicing numbers.
problem Understanding the slicing properties of knots in 4-manifolds.
method Lower and upper bounds on CP^2-slicing numbers using double branched covers and Seifert forms.
result Findings on the finite and distinct CP^2-slicing numbers for certain knots.
We use techniques of Freedman and Teichner to prove that, under certain circumstances, the multi-infection of a slice link is again slice (not necessarily smoothly slice). We provide a general context for proving links are slice that includes many of the previously known results.
The study simplifies assessing overlap in logistic regression models using empirical likelihood.
problem Assessing overlap in multidimensional logistic regression models.
method Translation of Silvapulle's condition to empirical likelihood maximization, mechanized with R code.
result Minimal overlapping structures are cataloged in dimensions less than four, providing rules for higher dimensions.
New invariants for link concordance defined using Whitehead doubles.
problem Defining and analyzing new concordance invariants for links.
method Extending slice-torus invariants to links, proving properties, and using Whitehead doubles.
result New strong concordance invariants for links, independent of slice-torus link invariants.
New invariant measures doubly slice links, disproving previous bounds.
problem Understanding doubly slice links and their invariants.
method Introduced new invariant gst to measure doubly slice links and disproved previous bounds. result Examples of links with large doubly slice genus but gst=1. Estimates overlap in observational studies for causal effect estimation.
problem Overlap between treatment groups is crucial for causal effect estimation.
method Formalizes overlap estimation as a binary classification problem with Boolean rule classifiers.
result Rules provide interpretable explanations for causal conclusions.
New knots show linear independence in slice concordance.
problem Understanding the structure of rationally slice knots.
method Provided an infinite family of knots that are linearly independent.
result Found knots that are linearly independent and infinite order.
Study shows certain knots can't be sliced using 2-fold branched covers.
problem Determining which algebraically slice knots are actually slice.
method Used d invariants of 2-fold branched covers to show nonsliceness.
result Shows nonsliceness of a set of algebraically slice knots.
Bing doubling is an operation which produces a 2-component boundary link B(K) from a knot K. If K is slice, then B(K) is easily seen to be boundary slice. In this paper, we investigate whether the converse holds. Our main result is that if B(K) is boundary slice, then K is algebraically slice. We also show that the Ras…
We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a combinatorial proof of the slice-Bennequin inequality. Finally, we compute the Rasmussen invariant for quasipositive knots and show that most…
New knots found that can be cut topologically but not smoothly.
problem Existence of (1,1)-knots that are topologically slice but not smoothly slice. method Proof of existence of infinitely many (1,1)-knots. result Infinitely many (1,1)-knots topologically slice but not smoothly slice. Paper explores properties of slice-matching operators for measure transfer.
problem Efficiently transferring measures in high dimensions.
method Examines an associated slice-matching operator with source, target measures and slicing directions.
result Establishes invariance, equivariance, Lipschitz continuity, and error bounds.
The paper calculates the slice genus for many virtual knots.
problem Determining which virtual knots are slice.
method Computing Turaev's graded genus and developing an algorithm for virtual unknotting operations.
result Many virtual knots with 6 or fewer crossings are slice.
A new approach simplifies Sliced-Wasserstein distances to improve learning performance.
problem The concentration of measure phenomenon makes random projections uninformative in high dimensions.
method Propose rescaling the 1D Wasserstein distance to make all slices equally informative.
result The classical Sliced-Wasserstein, properly configured, can match or surpass complex variants.
The paper calculates the slicing degree of knots using advanced homology theories.
problem Determining the minimum slicing degree of knots.
method Rasmussen's s-invariant, knot Floer homology, and singular instanton homology.
result Computed slicing degrees for many small knots and some families of torus knots.
New lower bound for doubly slice genus using knot signatures.
problem Finding a lower bound for the doubly slice genus of knots.
method Using the classical signature function to derive a new lower bound.
result Proved that for every nonnegative integer N, there exists a knot with exactly N difference between slice and doubly slice genus.