Method generates pseudo-features to balance imbalanced data.
problem Imbalanced data in deep learning problems.
method Generate pseudo-features from feature maps, augment minor-class data.
result Improves deep learning performance in imbalanced data problems.
NCC is inefficient in higher dimensions, NCDA improves performance.
problem Inefficiency of NCC in higher dimensions.
method Combining NCC with LDA to create NCDA.
result NCDA outperforms NCC and competes with LDA and QDA.
Statistical physics method analyzes minority game dynamics in financial markets.
problem Analyzing arbitrage dynamics in financial markets with noise.
method Cavity method from statistical physics for linear and time-dependent responses.
result Noise reduces arbitrage, and market dynamics exhibit non-Markovian behavior.
Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of q=2 groups. However, analytic calculations using the cavity method are challenging since they require us to understand p…
The paper uses belief propagation to analyze rankings and partial orders from partial information.
problem Analyzing rankings and partial orders from incomplete data.
method Continuous spin system and belief propagation algorithm.
result Computes marginal distribution and approximates number of linear extensions.
Statistical physics helps solve complex machine learning problems.
problem Large dimensional inference problems in machine learning.
method Replica symmetric level analysis and cavity methods.
result General framework for solving various problems with weak long-range interactions.
Paper introduces a framework for diagnosing Alzheimer's disease using higher-order topological features from fMRI.
problem Diagnosing Alzheimer's disease using brain network topology.
method Persistent homology to extract higher-order features (cycles, cavities) from fMRI data.
result Framework significantly outperforms existing methods in AD classification.
Predicts coherence from quantum heat engine noise using machine learning.
problem Predicting coherence in quantum heat engines from nonequilibrium fluctuations.
method Developed a machine learning protocol using K-Nearest Neighbor (KNN) model.
result Machine learning successfully predicts coherence from quantum heat engine noise.
AI detects oral pre-cancerous lesions with high accuracy.
problem Manual screening of oral cavity cancer is expensive and lacks specialists.
method Deep convolutional neural networks (DCNNs) using transfer learning.
result DCNN models achieve high accuracy in distinguishing between benign and pre-cancerous tongue lesions.
New method uses cohomology to quantify molecular similarity.
problem Quantifying structural dissimilarity in molecular data.
method Gromov-Hausdorff ultrametric based on simplicial complexes and cohomology.
result Demonstrates effectiveness in clustering organic-inorganic halide perovskite structures.
Study on limits of detecting a rank-one perturbation in Wigner matrices.
problem Detecting an additive rank-one perturbation in Wigner matrices.
method Gaussian interpolation methods and rigorous incarnation of the cavity method.
result Established the maximal region of contiguity between planted and null models, marking a phase transition for both estimation and detection.
Study investigates learning performance in inverse Ising problems with sparse teacher couplings.
problem Learning performance in inverse Ising problems with sparse teacher couplings.
method Pseudolikelihood maximization method, replica and cavity methods from statistical mechanics.
result Perfect inference of teacher's couplings is possible in the thermodynamic limit for certain conditions.
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
Proves upper bound on systolic ratio for circle fillings.
problem Bounding systolic ratio for circle fillings.
method Proved upper bound on systolic ratio depending on genus.
result Filling Area Conjecture holds for large genus.
A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.
problem Understanding what a discrete diffusion model learns in different coordinate systems.
method Rigorous derivation of continuous-time Markov chain ELBO, Oracle Distance theorem, and exact coordinates for optimizer.
result The negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one.
The paper constructs minimal coherent filling pairs on surfaces.
problem Finding minimal intersecting coherent filling pairs on surfaces.
method Geometric procedure starting from a torus filling pair.
result Construction of minimal intersecting coherent filling pairs on Sg for g≥3. Classifies symplectic fillings of specific torus bundles.
problem Classifying strong and exact symplectic fillings of virtually overtwisted torus bundles.
method Using Menke's JSJ-type decomposition theorem and round symplectic 1-handle attachment.
result Conditions for distinct tight lens space fillings to yield the same torus bundle filling.
The paper classifies symplectic fillings of lens spaces and constructs cobordisms.
problem Classifying symplectic fillings of lens spaces and constructing cobordisms.
method Analyzing tight and universally tight contact structures, using plumbing of disk bundles, and constructing cobordisms.
result Maximal second homology Stein fillings of lens spaces are given by specific plumbing.
Computes A-polynomials of knots from Whitehead sister link fillings.
problem Computing A-polynomials for knots from Whitehead sister link fillings.
method Using results on A-polynomials of Dehn fillings, formulas are derived for the A-polynomials of knots.
result Formulas to compute A-polynomials for knots from Whitehead sister link fillings.
If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.
We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and ∂-reducible. A manifold in the second family has boundary consi…
Study negative definite spin fillings of knot covers.
problem Existence of negative definite spin fillings in branched double covers.
method Derive obstructions and characterize special knots.
result Characterization of special alternating knots.
The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.
problem Cosmetic fillings on specific 3-manifolds.
method Analysis of Dehn fillings on compact, orientable 3-manifolds with incompressible torus boundaries.
result There are only finitely many pairs of purely cosmetic fillings.
Study generalizes Lebesgue curves to new space-filling and fractal sets.
problem Generating space-filling curves from planar substitutions.
method Generalized Lebesgue's construction to new curves and fractal sets.
result Some substitutions create relatively dense fractal-like sets.
Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of th…
If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperboli…
Affirmative proof that rank 3 3-manifolds have filling links.
problem Existence of filling links in rank 3 3-manifolds.
method Introduced and used the concept of filling links, proved for rank 3 manifolds.
result Every rank 3 closed orientable 3-manifold contains a filling link.
Study filling links in 3-manifolds to understand their topological properties.
problem Understanding the topological properties of 3-manifolds through filling links.
method Introduce and study filling links, prove their existence and injectivity properties.
result Existence of k-filling links in the 3-torus for each k>1.
New method fills cluster seeds with exact Lagrangian structures.
problem Surjectivity of map from Lagrangian fillings to cluster seeds.
method Construction of quiver with potential and Lagrangian disk surgeries.
result Trivial deformation space of quiver allows manipulation of fillings.
Study shows connectedness of Bowditch boundary persists in long Dehn fillings.
problem Persistence of Bowditch boundary connectedness in Dehn fillings.
method Analysis of relatively hyperbolic group pairs and peripheral subgroups.
result Connectedness of Bowditch boundary persists in sufficiently long Dehn fillings without needing restrictions.
This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.
problem Classifying and determining the length of the shortest filling pairs on a specific type of surface.
method Classifying and determining the length of the shortest filling pairs on a specific type of surface.
result The paper classifies and determines the length of the shortest minimal filling pairs on a genus two surface.
Let M be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if M is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If M has a non-boundary-paralle…
Positive braids have endless filling possibilities.
problem Understanding exact Lagrangian fillings of positive braid links.
method Analyzing positive braid Legendrian links and their fillings.
result Positive braid Legendrian links have infinitely many exact Lagrangian fillings.
Improved orderability in Dehn fillings without a hard condition.
problem Orderability of certain Dehn fillings
method Removed a condition from a recent result
result Improved results on orderability
ResNets converge to a limit model with improved error rates.
problem Understanding convergence of ResNets in the large-scale limit.
method Combining cavity method and propagation of chaos arguments on skeleton maps.
result Convergence rate of O(1/sqrt(D)) for ResNets in the large-scale limit.
Study on Legendrian knots and their non-orientable Lagrangian fillings.
problem Conditions for Legendrian knots to have non-orientable exact Lagrangian fillings.
method Developed combinatorial obstructions and classified fillability for various knot families.
result Completely determined decomposably non-orientable fillability for alternating and plus-adequate knots.
Four-dimensional Einstein Dehn filling is impossible.
problem Complex-hyperbolic Einstein Dehn filling in four dimensions.
method Proof of impossibility.
result Complex-hyperbolic Einstein Dehn filling cannot be performed in dimension four.
Unique symplectic fillings found for specific cotangent bundles.
problem Symplectic fillings of unit cotangent bundles.
method Proved uniqueness up to diffeomorphism.
result Unique symplectically aspherical fillings found.
Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.
problem Classify Stein fillings of planar contact 3-manifolds under constraints on their relative trisections.
method Partial classification of diffeomorphism types of fillings with relative trisections of genus at most 2.
result Partially classify the diffeomorphism types of Stein fillings with relative trisections of genus at most 2.
We extend Thurston's metric to projective filling currents, embedding Teichmüller space into the larger space.
problem Embedding Teichmüller space into the space of projectivized filling currents.
method Extending the symmetrized Thurston metric to PCfill(S) and studying its geometry. result There is no quasi-isometric projection back from PCfill(S) to T(S). Study shows no large mean curvature fill-ins for nonnegative scalar curvature.
problem Existence of fill-ins with nonnegative scalar curvature and large mean curvature.
method Analyzes closed Riemannian manifolds and scalar curvature properties.
result No closed Riemannian manifold admits a fill-in with nonnegative scalar curvature and large mean curvature.
The paper classifies minimal symplectic fillings of small Seifert 3-manifolds.
problem Classifying minimal symplectic fillings of small Seifert 3-manifolds.
method Using rational blowdowns and weighted homogeneous complex surface singularities.
result Every minimal symplectic filling of small Seifert 3-manifolds is obtained by a sequence of rational blowdowns.
We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…
The study lists all exceptional Dehn fillings on specific 3-manifolds.
problem Understanding exceptional Dehn fillings on hyperbolic 3-manifolds.
method Examined 1-cusped hyperbolic 3-manifolds with up to 9 ideal tetrahedra.
result Consistent with standard conjectures, suggests new ones.
Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.
problem Characterizing symplectic fillings of prequantization bundles with finite capacities.
method Analysis of symplectic capacities and diffeomorphisms.
result Symplectic fillings of prequantization bundles are diffeomorphic to disk bundles under finite capacity conditions.
Market makers face a trade-off between fill probability and post-fill returns, requiring contrarian strategies.
problem Navigating the trade-off between fill probability and post-fill returns in market making.
method Analysis of live trading data from Binance Bitcoin perpetual.
result A negative correlation between maker fill likelihood and post-fill returns, necessitating contrarian strategies.
Filling length measures the length of the contracting closed loops in a null-homotopy. The filling length function of Gromov for a finitely presented group measures the filling length as a function of length of edge-loops in the Cayley 2-complex. We give a bound on the filling length function in terms of the log of an …
Develops a diagrammatic method for symplectic filling classifications.
problem Classifying exact/weak symplectic fillings of 3D contact manifolds.
method Symplectic JSJ decomposition applied to contact surgery diagrams.
result Recover symplectic fillings for certain lens spaces and torus bundles, and classify fillings for a large class of plumbed 3-manifolds.