Gradient Weighted Superpixels improve CNN interpretability without sacrificing speed.
problem Efficiency vs. interpretability trade-off in CNNs, especially for large input volumes.
method Gradient-based pixel scoring techniques applied to superpixels.
result Superpixels approximate LIME in a fraction of the time, improving interpretability.
Optimizes large stock order execution with LSTM neural networks.
problem Minimizing transaction costs in large stock order execution.
method Trained LSTM neural network to minimize transaction costs.
result LSTM strategy outperforms TWAP and VWAP strategies.
Models predict equities' daily trading volume using Bayesian methods.
problem Predicting equities' daily trading volume accurately.
method Bayesian econometric methods combining historical and current inputs.
result Unified approach for predicting total, remaining, intra-day, close auction, and seasonal volumes.
Novel method uses image descriptors to harmonize MRI brain volumes across centers.
problem Inconsistencies in MRI brain volume measurements across different centers and scanners.
method Trained a Relevance Vector Machine (RVM) model using image descriptors to harmonize brain volumes.
result Decreases scanner and center variability while preserving measurements for longitudinal studies.
Deep networks can interpolate noisy data without losing generalization.
problem Characterizing the relationship between interpolation and generalization in overparameterized deep networks.
method Analyzing the loss landscape of neural network functions over volumes around training data points, varying model parameters and training epochs.
result Loss sharpness in the input space follows a double descent, with large models predicting noisy targets over larger volumes around training data points.
CVAE improves stock volume forecasting with advanced input variables.
problem Improving accuracy of daily stock volume forecasts.
method Conditional Variational Auto-Encoder (CVAE) with advanced input variables.
result CVAE generates non-linear forecasts with better accuracy and correlation to actual data.
Infinite family of hyperbolic 3-manifolds with large volumes.
problem Finding large volume 3-manifolds.
method 2-fold branched covers of 3-manifolds M.
result Existence of hyperbolic 3-manifolds with arbitrarily large volume.
Law of large numbers for volumes of random 3-manifolds.
problem Understanding volumes of random 3-manifolds.
method Law of large numbers for random hyperbolic mapping tori and Heegaard splittings.
result Sharp answer to Dunfield and Thurston's conjecture.
The paper proposes a new order slicing strategy to reduce market impact in large-volume trading.
problem Significant market impact and slippage in large-volume trading.
method Volatility-volume-based order slicing strategy using Exponential Weighted Moving Average and Markov Chain Monte Carlo simulations.
result Improves trade execution efficiency and reduces market impact.
The study predicts large genus behavior of quadratic differential volumes and constants.
problem Predicting large genus behavior of quadratic differential volumes and constants.
method Analyzing conjectures on asymptotic behavior of Masur-Veech volumes and area Siegel-Veech constants.
result Conjectures on large genus asymptotics of quadratic differential volumes and constants.
Study Turaev-Viro invariants of Seifert fibered 3-manifolds, proving volume conjecture.
problem Understanding the asymptotic behavior of Turaev-Viro invariants for Seifert fibered 3-manifolds.
method Analysis of large r asymptotic behavior of Turaev-Viro invariants. result Proved the volume conjecture for Seifert fibered 3-manifolds with empty and non-empty boundaries.
The paper calculates super Weil-Petersson volumes for large genus.
problem Calculating super Weil-Petersson volumes for large genus.
method Analyzes super intersection numbers, proves coefficients are polynomials, and provides an algorithm to compute them.
result Proves existence of a complete asymptotic expansion of super Weil-Petersson volumes.
We describe a class of genus 2 closed hyperbolic 3-manifolds of arbitrarily large volume.
The study proves uniqueness of large isoperimetric sets in specific noncompact manifolds.
problem Proving uniqueness of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature.
method Analyzing properties of complete Riemannian manifolds with specific curvature conditions.
result There exists a set of volumes with density 1 at infinity where isoperimetric sets are unique and strictly volume preserving stable.
Paper investigates hardness of learning neural networks under manifold hypothesis.
problem Hardness of learning neural networks under the manifold hypothesis.
method Extending proofs of hardness in the SQ and cryptographic settings to the geometric setting.
result Learning is hard under input manifolds of bounded curvature but learnable with additional assumptions on manifold volume.
We find the asymptotic expansion of Masur-Veech volumes for large genus.
problem The asymptotic behavior of Masur-Veech volumes as genus increases.
method Combination of combinatorial and algebro-geometric approaches.
result Existence and computation of a complete asymptotic expansion.
To reduce the label complexity in Agnostic Active Learning (A^2 algorithm), volume-splitting splits the hypothesis edges to reduce the Vapnik-Chervonenkis (VC) dimension in version space. However, the effectiveness of volume-splitting critically depends on the initial hypothesis and this problem is also known as target…
We study the statistical properties of the recurrence intervals τ between successive trading volumes exceeding a certain threshold q. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2…
The paper presents unbiased estimators for random design regression.
problem Bias in least squares solutions for random design regression.
method Volume-rescaled sampling of input points to produce unbiased estimators.
result An unbiased estimator can be constructed with a sample size of O(dlogd + d/ε).
Study shows volume and genus unrelated for hyperbolic fibred knots.
problem Volume and genus of hyperbolic fibred knots are unrelated.
method Analyzes hyperbolic fibred knots in three-sphere.
result Volume and genus are unrelated for hyperbolic fibred knots.
We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may have arbitrarily large hyperbolic volume. Using this algorithm we concoct large v…
We prove that a reversible Berwaldian Finsler structure (M,F) with base-independent non-negative radial flag curvature and large volume growth does not have any closed geodesics.
In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume growth conditions. We also generize it to the manifolds with k-th asymptotica…
Study of limits of Einstein-Bogomol'nyi metrics on P^1 in two regimes.
problem Understanding limits of Einstein-Bogomol'nyi metrics on P^1.
method Analysis of two regimes: dissolving limit and large volume limit.
result Recovery of Einstein-Bogomol'nyi metrics on C with total string number N' for each N'.
By obtaining surgery descriptions of knots which lie on the genus one fiber of the trefoil or figure eight knot, we show that these include hyperbolic knots with arbitrarily large volume. These knots admit lens space surgeries and form two families of Berge knots. By way of tangle descriptions we also obtain surgery de…
Computes the contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes.
problem Calculating the contribution of specific geometric structures to volume calculations.
method Explicit computation and asymptotic analysis of square-tiled surfaces.
result The relative contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes is asymptotically 1/d, where d is the dimension of the stratum.
In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a conically bounded convex set, i.e., an unbounded convex body admitting an \emph{exterior} asymptotic cone. Results concerning existence of isoperimetric regions, the behavior of the isoperimetric pr…
Study on fibered knots in 3-manifolds, proving unrelated volume and genus.
problem Unrelated volume and genus in hyperbolic fibered knots.
method Proof of unrelated volume and genus for hyperbolic fibered knots in 3-manifolds.
result Proved that volume and genus are unrelated for hyperbolic fibered knots.
New metrics on 3D manifolds with large Steklov eigenvalues.
problem Finding metrics with large Steklov eigenvalues on compact manifolds.
method Expressed Steklov spectrum of warped products and applied to metrics with fixed volume.
result Examples of metrics on 3D manifolds with arbitrarily large first non-zero Steklov eigenvalue.
This paper proves that every oriented non-disk Seifert surface F for a knot K in S3 is smoothly concordant to a Seifert surface F′ for a hyperbolic knot K′ of arbitrarily large volume. This gives a new and simpler proof of the result of Friedl and of Kawauchi that every knot is S-equivalent…
As sound event classification moves towards larger datasets, issues of label noise become inevitable. Web sites can supply large volumes of user-contributed audio and metadata, but inferring labels from this metadata introduces errors due to unreliable inputs, and limitations in the mapping. There is, however, little r…
Upper bound for Laplacian eigenvalue via conformal volume.
problem Finding upper bounds for Laplacian eigenvalues.
method Using conformal volume to derive an upper bound.
result Effective upper bound for Laplacian eigenvalues on manifolds.
Study evaluates using multiple slices as input for CNNs in medical image segmentation.
problem Improving segmentation performance in medical images with limited computational resources.
method Compared pseudo-3D and 2D approaches using different CNN architectures and datasets.
result Multi-slice inputs did not significantly improve segmentation performance over 2D or 3D CNNs.
Chung-Grigor'yan-Yau's inequality describes upper bounds of eigenvalues of Laplacian in terms of subsets ("input") and their volumes. In this paper we will show that we can reduce "input" in Chung-Grigor'yan-Yau's inequality in the setting of Alexandrov spaces satisfying CD(0,∞). We will also discuss a related c…
Study Turaev-Viro invariants of 3-manifolds with toroidal boundary.
problem Volume conjecture for Seifert fibered and graph 3-manifolds.
method Large r asymptotic behavior of Turaev-Viro invariants under gluing operation. result Volume conjecture proven for Seifert fibered and graph 3-manifolds.
The paper calculates large genus limits for quadratic differential volumes and constants.
problem Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials.
method Combining recursive relations (Virasoro constraints) and asymmetric simple random walk jump probabilities.
result Confirm predictions about Masur-Veech volumes and area Siegel-Veech constants.
This work certifies non-uniform bounds against adversarial attacks for neural networks.
problem Certifying robust regions around data points against non-uniform adversarial attacks.
method Formulated as an optimization problem with nonlinear constraints, using the augmented Lagrangian method for general feedforward neural networks.
result Non-uniform bounds have larger volumes and better interpretability compared to uniform bounds.
We consider the rate of volume growth of large Carnot-Carathéodory metric balls on a class of unbounded model hypersurfaces in C2. When the hypersurface has a uniform global structure, we show that a metric ball of radius δ≫1 either has volume on the order of δ3 or δ4. We also give necessary and …
We obtain an estimate for the volume of neighbourhoods of sets of large curvature in three-dimensional Kähler-Einstein manifolds.
Uses news sentiment scores for direct reinforcement trading in financial markets.
problem Incorporating news data into quantitative trading remains challenging.
method Directly uses news sentiment scores and raw data as inputs for reinforcement learning, processed by sequence models.
result Achieves superior performance compared to market benchmarks.
Formulae for Masur-Veech volumes derived from intersection numbers of curves.
problem Computing volumes and densities of geodesics and surfaces.
method Intersection numbers of psi-classes and lattice point count.
result Formulae for Masur-Veech volumes as polynomials in intersection numbers.
Paper uses Transformers to predict intraday volume ratio with high accuracy.
problem Accurate prediction of intraday volume ratio for VWAP strategies.
method Transformer architecture with log-normal transformation and external features.
result Probabilistic forecasting captures mean and standard deviation of volume ratios.
We use a large census of hyperbolic 3-manifolds to experimentally investigate a conjecture of Neumann regarding the Bloch Group. We present an augmented census including, for feasible invariant trace fields, explicit manifolds (associated to that field) that appear to generate the Bloch group of that field. We also mak…
Study of large-n asymptotics for Weil-Petersson volumes of hyperbolic surfaces with cusps.
problem Understanding the geometry and spectral properties of random hyperbolic surfaces with many cusps.
method Large-n asymptotic analysis, spectral theory, and moduli space volumes. result Linear number of small Laplacian eigenvalues and relative frequency of simple vs. non-simple closed geodesics.
We show that the renormalized volume of a quasifuchsian hyperbolic 3-manifold is equal, up to an additive constant, to the volume of its convex core. We also provide a precise upper bound on the renormalized volume in terms of the Weil-Petersson distance between the conformal structures at infinity. As a consequence we…
If (M^n, g) is a complete Riemannian manifold with filling radius at least R, then we prove that it contains a ball of radius R and volume at least c(n)R^n. If (M^n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume at most c(n)Volume(M,hyp), then we prove that the universal cover of (M,g…
Linear bound on Betti numbers of negatively curved orbifolds.
problem Bounding Betti numbers of negatively curved orbifolds.
method Quantitative bound on the homology of spherical quotients.
result Linear growth of Betti numbers with volume, arbitrary field coefficients.
We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all suffi…