arXiv research

Efficiently predicts optimal transport plans using sliced potentials.

Study shows inflation in 3+1D cosmologies with bounded scalar potential and specific symmetry.

Akbulut and Kirby conjectured that two knots with the same $0$-surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.

Alternative proof for links not smoothly slice in $S^2 imes S^2$.

Standardizes Dunfield-Gong's 4-sphere, solves knot sliceness problem.

We define an obstruction for a knot to be Z[Z]-homology ribbon, and use this to provide restrictions on the integers that can occur as the triple linking numbers of derivative links of knots that are either homotopy ribbon or doubly slice. Our main application finds new non-doubly slice knots. In particular this gives …

We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proofs we create a capped grope from a Casson towe…

We explore self-supervised models that can be potentially deployed on mobile devices to learn general purpose audio representations. Specifically, we propose methods that exploit the temporal context in the spectrogram domain. One method estimates the temporal gap between two short audio segments extracted at random fr…

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…

Generative model improved using Liouville PDE-based sliced-Wasserstein flow.

We explore the potential of a popular distributional semantics vector space model, word2vec, for capturing meaningful relationships in ecological (complex polyphonic) music. More precisely, the skip-gram version of word2vec is used to model slices of music from a large corpus spanning eight musical genres. In this newl…

We describe a robust calibration algorithm of a set of SSVI slices (i.e. a set of 3 SSVI parameters $θ, ρ, \varphi$ attached to each option maturity available on the market), which grants that these slices are free of Butterfly and Calendar-Spread arbitrage. Given such a set of consistent SSVI parameters, we show that …

We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2-knots. As an application, we produce infinite families…

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…

Paper explores using 0-surgery to find exotic 4-manifolds.

We propose an exact slice sampler for Hierarchical Dirichlet process (HDP) and its associated mixture models (Teh et al., 2006). Although there are existing MCMC algorithms for sampling from the HDP, a slice sampler has been missing from the literature. Slice sampling is well-known for its desirable properties includin…

FSIR extends SIR for federated learning with privacy and efficiency.

The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.

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…

Computer-Aided-Diagnosis (CADx) systems assist radiologists with identifying and classifying potentially malignant pulmonary nodules on chest CT scans using morphology and texture-based (radiomic) features. However, radiomic features are sensitive to differences in acquisitions due to variations in dose levels and slic…

We discuss how to apply work of L. Rudolph to braid conjugacy class invariants to obtain potentially effective obstructions to a slice knot being ribbon. We then apply these ideas to a family of braid conjugacy class invariants coming from Khovanov-Lee theory and explain why we do not obtain effective ribbon obstructio…

Gradient-guided nested sampling improves posterior inference efficiency.

If there are any 2-component counterexamples to the Generalized Property R Conjecture, a least genus component of all such counterexamples cannot be a fibered knot. Furthermore, the monodromy of a fibered component of any such counterexample has unexpected restrictions. The simplest plausible counterexample to the Gene…

Study on $r-$shake slice knots and proves 0-shake slice knots are slice.

Proves certain knots are slice without shaking.

A new method for distribution regression using sliced Wasserstein distance.

Proves a special knot type is slice.

New method constructs translationally equivariant hyperbolic affine spheres.

New findings on knots that are both topologically and rationally slice.

Regular sliceness implies once-stably decomposable sliceness in symplectizations.

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.

New knots found with tough, unsliceable discs.

The study examines obstructions to links being shake slice.

A new slicing method speeds up sliced Wasserstein estimation.

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…

sWk-means clusters multidimensional financial time series into distinct market regimes.

Khovanov homology fails to differentiate certain slice disks.

Characterizes values of slice-torus invariants related to knot genus.

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.

Computed tomography (CT) generates a stack of cross-sectional images covering a region of the body. The visual assessment of these images for the identification of potential abnormalities is a challenging and time consuming task due to the large amount of information that needs to be processed. In this article we propo…

Study slice-regular polynomial functions via twistor space group actions.

The paper shows some Montesinos links can't be doubly sliced strongly.

Study shows most knots in a family are not slice.

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.

Study on slicing knots in 4-manifolds, focusing on CP^2-slicing numbers.

New invariant measures doubly slice links, disproving previous bounds.