Study complex slices on real algebraic varieties and their properties.
problem Understanding the properties and bounds of complex slices on real algebraic varieties.
method Analyzing intersections and cohomology classes of complex subvarieties with real subvarieties.
result Proved an upper bound for the linking number of certain slices.
Study real slices of SL(r,C)-opers via Riemann surface involution.
problem Understanding geometric properties of real slices of SL(r,C)-opers.
method Action of anti-holomorphic involution σ on Riemann surface X, construction of involution for different descriptions of mSL(r,C)-opers. result Natural parametrization of fixed point locus via differentials on Riemann surface.
Proves a specific knot is not smoothly slice using real invariants.
problem Determining the smooth sliceness of (2n,1)-cables of the figure-eight knot. method Used real Seiberg-Witten Frøyshov invariant and developed an equivariant lattice homotopy type.
result Proves the (2n,1)-cable of the figure-eight knot is not smoothly slice when n is odd. Real slices of parabolic opers on Riemann surfaces are studied.
problem Understanding the fixed-point locus of involutions on parabolic opers.
method Investigated the space of parabolic SL(r,C)-opers and their involutions.
result Fixed-point loci of involutions on different descriptions of parabolic opers coincide.
In the present paper we introduce the class of slice-polynomial functions: slice regular functions {defined over the quaternions, outside the real axis,} whose restriction to any complex half-plane is a polynomial. These functions naturally emerge in the twistor interpretation of slice regularity introduced in \cite{ge…
Characterizes fractional Dehn twist coefficient and proves slice-Bennequin inequality.
problem Understanding the fractional Dehn twist coefficient and its relation to smooth slice genus.
method Characterization of FDTC and establishing the slice-Bennequin inequality.
result Affine linear lower bound for smooth slice genus in terms of FDTC.
In real-world machine learning applications, data subsets correspond to especially critical outcomes: vulnerable cyclist detections are safety-critical in an autonomous driving task, and "question" sentences might be important to a dialogue agent's language understanding for product purposes. While machine learning mod…
We describe a deep learning approach for automated brain hemorrhage detection from computed tomography (CT) scans. Our model emulates the procedure followed by radiologists to analyse a 3D CT scan in real-world. Similar to radiologists, the model sifts through 2D cross-sectional slices while paying close attention to p…
New method for triclustering with reduced arbitrariness.
problem Need for reduced arbitrariness in specifying cluster size.
method Spectral decomposition of tensor slices and intersection of clusters.
result Effective triclustering on synthetic and real-world data.
The paper explores statistical and topological properties of sliced probability divergences.
problem Understanding the topological, statistical, and computational consequences of slicing divergences.
method Deriving theoretical properties of sliced probability divergences, including metric axioms preservation and weak continuity.
result Sliced divergences share similar topological properties and have stable sample complexity.
Multiplayer Online Battle Arena (MOBA) is currently one of the most popular genres of digital games around the world. The domain of knowledge contained in these complicated games is large. It is hard for humans and algorithms to evaluate the real-time game situation or predict the game result. In this paper, we introdu…
The paper studies CMC foliations and their conformal aspects on Riemannian manifolds.
problem Understanding and normalizing CMC foliations on conformally compact manifolds.
method Non-linear PDEs and conformal transformations.
result Locally, any slicing can be made into a CMC foliation by conformal changes.
Sliced inverse regression (SIR) is a pioneer tool for supervised dimension reduction. It identifies the effective dimension reduction space, the subspace of significant factors with intrinsic lower dimensionality. In this paper, we propose to refine the SIR algorithm through an overlapping slicing scheme. The new algor…
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
Slice Tuner optimizes data acquisition for accurate and fair machine learning models.
problem Acquiring enough data for all slices of data to ensure accurate and fair models.
method Selective data acquisition using convex optimization and iterative learning curve updates.
result Significantly outperforms baselines in model accuracy and fairness.
Given a slice regular function f:Ω⊂H→H, with Ω∩R=∅, it is possible to lift it to a surface in the twistor space CP3 of S4≃H∪{∞} (see~\cite{gensalsto}). In this paper we show that the same result is true if one rem…
A new spherical Sliced-Wasserstein distance for data on spheres.
problem Defining Wasserstein distance on manifolds, especially spheres.
method Closed-form solutions of the Wasserstein distance on the circle and a new spherical Radon transform.
result A novel spherical Sliced-Wasserstein (SW) discrepancy for data on spheres.
We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical anal…
This paper improves normalizing flows by combining MLE and sliced-Wasserstein distance for better data fidelity.
problem Normalizing flows struggle with generating realistic data and detecting out-of-distribution data.
method Proposes a hybrid objective function combining MLE and sliced-Wasserstein distance.
result Shows better generative abilities and lower likelihood of out-of-distribution data.
Computes immersions of C2-projective spaces using K-theory.
problem Computing immersions of equivariant projective spaces.
method Geometric filtration and localized slice spectral sequence.
result Obtained equivariant analogue of James periodicity.
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. Study of a G2-equivariant octonionic operator and its right spectrum.
problem Understanding the spectrum of a G2-equivariant octonionic operator. method Computed the ordinary real spectrum and analyzed the octonionic right-eigenvalue problem using G2-decomposition and residual symmetry analysis. result Explicit spectral loci (quartic curve and circle) in each complex slice of the octonionic space.
After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the complex length l_V and the complex twist tau_V,W parameters define a holomorphic embedding of the quasifuchsian space QF of punctured tori into C^2. It is called the complex Fenchel-Nielsen coordinates of QF. For a complex number c, let Q_gam…
The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.
problem Privacy concerns in high-dimensional data analysis.
method Differentially private sliced inverse regression algorithms designed for privacy preservation.
result Achieves minimax lower bounds up to logarithmic factors.
The linear slice of quasi-Fuchsian once-punctured torus groups is defined by fixing the complex length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it always has one standard component containing Fuchsian groups. Komori and Yamashita proved t…
FSIR extends SIR for federated learning with privacy and efficiency.
problem Privacy-preserving dimension reduction in federated learning.
method FSIR employs sliced inverse regression with differential privacy and collaborative variable screening.
result FSIR achieves effective dimension reduction and privacy protection in federated learning.
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.
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.
In cardiac magnetic resonance imaging, fully-automatic segmentation of the heart enables precise structural and functional measurements to be taken, e.g. from short-axis MR images of the left-ventricle. In this work we propose a recurrent fully-convolutional network (RFCN) that learns image representations from the ful…
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.
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…
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.
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.
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.
A knot is said to be slice if it bounds a smooth properly embedded disk in the 4-ball. We demonstrate that the Conway knot, 11n34 in the Rolfsen tables, is not slice. This completes the classification of slice knots under 13 crossings, and gives the first example of a non-slice knot which is both topologically slice an…
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.
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.
New algorithm reduces dimensionality in federated learning.
problem Estimating central dimension reduction subspace and variable selection in federated learning.
method Federated sparse sliced inverse regression, convex optimization, linearized alternating direction method of multipliers.
result Upper bound of statistical error rate established under heterogeneous setting.
A new variational inference method using sliced Wasserstein distance is proposed.
problem The inefficiency and unreasonable properties of Kullback-Leibler divergence.
method Minimizing sliced Wasserstein distance, a valid metric from optimal transport.
result The proposed method approximates the unnormalized distribution efficiently and without requiring a tractable density function.
We show that if the connected sum of two knots with coprime Alexander polynomials is doubly slice, then the Ozsváth-Szabó correction terms as smooth double sliceness obstructions vanish for both knots. Recently, Jeffrey Meier gave smoothly slice knots that are topologically doubly slice, but not smoothly doubly slice. …
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. Let N be a smooth (n+l)-dimensional Riemannian manifold. We show that if V is an area-stationary union of three or more C1,μ n-dimensional submanifolds-with-boundary Mk⊂N with a common boundary Γ, then Γ is smooth and each Mk is smooth up to Γ (real-analytic in the case N is real-anal…
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.
New method for multiway clustering of 3rd order tensors.
problem Clustering of 3rd order tensors.
method MCAM method based on affinity matrix and clustering.
result Competitive results on synthetic and real datasets.
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.