New examples show certain knots can't be obtained via specific surgeries.
problem Demonstrating certain knots cannot be obtained via Dehn surgery.
method Combining combinatorial arguments with chainmail links.
result Additional examples showing the impossibility of certain surgeries.
From Furuta's 810 theorem, we derive a smooth slicing obstruction for knots in S3 using a spin 4-manifold whose boundary is 0-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly sl…
New examples of 3-manifolds not obtained by surgery on knots.
problem Identifying 3-manifolds not obtained by Dehn surgery.
method Combining Furuta's 10/8-theorem with combinatorial arguments.
result Found new 3-manifolds with weight one fundamental group not obtained by surgery.
Study on constraints for topological and smooth realizations of line arrangements and configurations.
problem Investigating constraints on topological and smooth realizations of combinatorial line arrangements and (nk)-configurations. method Exploring constraints via locally-flatly or smoothly embedded 2-spheres, using Furuta's 10/8-Theorem, and G-signature theorem.
result Established a new lower bound for (nk)-configurations, showing n≥k2−5 for topological realizations. Using Seiberg-Witten Floer spectrum and Pin(2)-equivariant KO-theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology 3-spheres. As an application, we give explicit constrains on the intersection forms of spin 4-manifolds bounded by Brieskorn spheres $\pmΣ(2,3,6k\…
We obtain constraints on the topology of families of smooth 4-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation of Donaldson's diagonalisation theorem and Furuta's 10/8 theorem. As an appli…
Formula for renormalized area of hypersurfaces in hyperbolic spaces.
problem Calculating the renormalized area of asymptotically minimal hypersurfaces in hyperbolic spaces.
method Combining Chen's conformal invariant quantity and Chern-Gauss-Bonnet formulas.
result Extension of renormalized area formulas to higher dimensions and non-minimal cases.
The study proves all prime knots up to 10 crossings have superbridge index ≤ 5.
problem Determining the maximum superbridge index for prime knots up to 10 crossings.
method New upper bounds on stick numbers and equilateral stick numbers for specific knots, leading to conclusions about superbridge index.
result All prime knots through 10 crossings have a superbridge index ≤ 5.
Singularities of area minimizing hypersurfaces can be smoothed in dimensions 9 and 10.
problem Singularities of area minimizing hypersurfaces.
method Perturbation of singularities.
result Singularities can be perturbed away in dimensions 9 and 10.
Curved 10-manifolds with torus symmetry are spheres or complex projective spaces.
problem Characterizing positively curved manifolds with torus symmetry.
method Analyzing actions of 3-dimensional tori on closed, simply connected 10-manifolds. result Closed, simply connected, positively curved 10-manifolds with T3-symmetry are homotopy spheres or complex projective spaces. In this brief technical report we introduce the CINIC-10 dataset as a plug-in extended alternative for CIFAR-10. It was compiled by combining CIFAR-10 with images selected and downsampled from the ImageNet database. We present the approach to compiling the dataset, illustrate the example images for different classes, g…
Deep neural networks predict earthquake locations with high accuracy.
problem Predicting the location of earthquakes with high precision.
method Recurrent Convolutional Neural Networks (R-CNN) model that accounts for spatio-temporal dependencies.
result Neural networks model outperforms baseline models in predicting earthquakes with ROC AUC 0.975 and PR AUC 0.0890.
System segments Form 10-K documents into Item sections for financial analysis.
problem Segmenting Form 10-K documents into Item sections for efficient financial analysis.
method Developed an automatic Form 10-K Itemization system using NLP techniques.
result System achieves a retrieval rate of 93% for segmenting Item sections.
Expanded Legendrian knot atlas for 10-arc index knots.
problem Lack of Legendrian knot data for knots with high arc index.
method Created an atlas of Legendrian knots up to arc index 10.
result Legendrian knots of arc index 10 have been cataloged.
We give a complete enumeration of all combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product S2×S1 and 615 triangulations of the twisted sphere product $S^2_\times_S^1$. All the 3-spheres…
Solves the challenge of retrieving item-specific financial information from Form 10-Q filings.
problem Retrieving item-specific information from Form 10-Q filings with varying formats and machine-readable hierarchy.
method Complements a rule-based algorithm with a Convolutional Neural Network (CNN) image classifier to itemize 10-Q files.
result Demonstrates a generalized pipeline for rapid data retrieval from a large volume of textual data.
We use Heegaard Floer homology to obtain bounds on unknotting numbers. This is a generalisation of Ozsvath and Szabo's obstruction to unknotting number one. We determine the unknotting numbers of 9_10, 9_13, 9_35, 9_38, 10_53, 10_101 and 10_120; this completes the table of unknotting numbers for prime knots with crossi…
Table of symmetric diagrams for knots up to 10 crossings.
problem Finding symmetric diagrams for strongly invertible knots.
method Compilation of symmetric diagrams for knots up to 10 crossings.
result Similarity of transversal diagrams to symmetric union diagrams for strongly invertible knots.
New Einstein metrics found on a 10-dimensional sphere.
problem Finding non-round Einstein metrics on spheres.
method Proving existence of three new metrics on S10. result Existence of three non-round, non-isometric Einstein metrics with positive scalar curvature on S10. Analyzes spinor groups in specific dimensions.
problem Understanding spinor groups in low dimensions.
method Examined Spin(p,q) groups for specific (p,q) values.
result Determined orbit structures of Spin(p,q) groups.
Reducing ICD-10 code granularity improves cost model accuracy and stability.
problem High-dimensional regression with ICD-10 codes leads to unstable coefficient estimates.
method Log-linear analytics approach to cost model regularization through diagnostic code merging.
result Reducing ICD-10 code granularity from 7 characters to 6 or fewer improves model interpretability and consistency.
We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image classification. We demonstrate greatly improved image classification performance compared …
Paper finds at least 6 fixed points for a specific circle action on a 10D manifold.
problem Finding the minimum number of fixed points for a circle action on a 10D almost complex manifold.
method Established a lower bound by showing the non-existence of a circle action with 4 fixed points.
result There are at least 6 fixed points for a circle action on a 10D compact almost complex manifold.
Two methods improve 10-K item segmentation using large language models.
problem Challenges in extracting specific items from 10-K reports due to variations in document formats and item presentation.
method Two advanced item segmentation methods: GPT4ItemSeg and BERT4ItemSeg.
result BERT4ItemSeg achieves a macro-F1 of 0.9825, surpassing other methods.
Narrative disclosures in 10-K filings improve bankruptcy prediction beyond accounting ratios.
problem Traditional bankruptcy prediction models rely on accounting ratios, which may not capture early warning signals.
method Developed a PB Stress Score based on distress-specific language in 10-K narratives, evaluated against accounting and dictionary benchmarks.
result Adding the PB Stress Score increases AUC from 0.8323 to 0.9019 and improves top-decile bankruptcy capture from 44.12% to 64.71%.
The paper proves formulas for capillary surfaces and applies them to inequalities and area estimates.
problem Understanding capillary surfaces and their properties.
method Established monotonicity formulas for capillary surfaces in half-space and unit ball.
result Extended Li-Yau-type inequalities and optimal area estimates for capillary surfaces.
In this paper we investigate the unlinking numbers of 10-crossing links. We make use of various link invariants and explore their behaviour when crossings are changed. The methods we describe have been used previously to compute unlinking numbers of links with crossing number at most 9. Ultimately, we find the unlinkin…
We prove that the knots 13n592 and 15n41,127 both have stick number 10. These are the first non-torus prime knots with more than 9 crossings for which the exact stick number is known.
This paper calculates the non-orientable 4-genus for knots with 10 crossings.
problem Determining the non-orientable 4-genus for knots with a specific number of crossings.
method Calculating the minimal first Betti number of non-orientable surfaces smoothly embedded in a 4-ball with boundary the knot.
result The non-orientable 4-genus for knots with 10 crossings has been calculated.
Notes based on lessons given at {\sc Escuela " Fico González Acuña" de Nudos y 3-variedades}, Mérida Yucatán, México, 7--10 (2015) and {\sc Encuentro de nudos, trenzas y álgebras}, Oaxaca--México, 3--10 October (2018).
The list of knots with up to 10 crossings is commonly referred to as the Rolfsen Table. This paper presents a way to generate the Rolfsen table in a simple, clear, and reproducible manner. The methods we use are similar to those used by J. Hoste, M. Thistlethwaite, and J. Weeks in [1]. The difference between our method…
New proof shows no negative curvature Einstein metrics in specific dimensions.
problem Proving nonexistence of certain Einstein metrics in 9 and 10 dimensions.
method Cohomogeneity-one approach to show nonexistence of negative curvature Einstein metrics.
result Noncompact homogeneous spaces not diffeomorphic to Euclidean space of dimension 9 or 10 admit no homogeneous Einstein metrics of negative Ricci curvature, with only three potential exceptions.
In this paper, we introduce a new model for leveraging unlabeled data to improve generalization performances of image classifiers: a two-branch encoder-decoder architecture called HybridNet. The first branch receives supervision signal and is dedicated to the extraction of invariant class-related representations. The s…
Census of 10-tetrahedra hyperbolic 3-manifolds with 150,730 new examples.
problem Census of orientable cusped hyperbolic 3-manifolds up to 10 tetrahedra.
method Complete enumeration of minimal ideal triangulations.
result 439,898 new exceptional Dehn fillings and simplest knot exteriors.
Study automorphism groups of quandles up to order 10.
problem Understanding automorphism groups of quandles of various orders.
method Enumerated and computed automorphism groups and displacement groups of quandles up to order 10.
result Computed automorphism groups and displacement groups for all quandles up to order 10.
This paper explores normalization in neural ODEs, achieving high accuracy in CIFAR-10.
problem Understanding the role of normalization in neural ODEs.
method Investigated different normalization techniques and their impact on neural ODEs performance.
result Achieved 93% accuracy in CIFAR-10 classification task.
Newly characterizes the Standard Model gauge group using spinors and geometry.
problem Characterize the Standard Model gauge group GSM within Spin(10).
method Characterizes GSM as a subgroup of Spin(10) using the geometry of pure spinors and Clifford algebras.
result GSM is the intersection of Georgi-Glashow SU(5) and Pati-Salam Spin(6) x Spin(4).
Flapan--Naimi--Pommersheim showed that every spatial embedding of K10, the complete graph on ten vertices, contains a non-split three-component link; that is, K10 is intrinsically triple-linked in R3. The work of Bowlin--Foisy and Flapan--Foisy--Naimi--Pommersheim extended the list of known intrin…
We show 10/8-type inequalities for some end-periodic 4-manifolds which have positive scalar curvature metrics on the ends. As an application, we construct a new family of closed 4-manifolds which do not admit positive scalar curvature metrics.
Machine learning is currently dominated by largely experimental work focused on improvements in a few key tasks. However, the impressive accuracy numbers of the best performing models are questionable because the same test sets have been used to select these models for multiple years now. To understand the danger of ov…
Improved image classification accuracy on CIFAR-10 dataset.
problem Classifying images from the CIFAR-10 dataset with high accuracy.
method Combining features from manual and deep learning approaches, including VGG16, Inception ResNet v2, HOG, and pixel intensities.
result Achieved 94.6% testing accuracy by combining top 1000 principal components.
This note fills a hole in the author's previous paper ``Ricci-Flat Holonomy: a Classification'', by dealing with irreducible holonomy algebras that are subalgebras or real forms of $\mbb{C} \oplus \mf{spin}(10,\mbb{C})$. These all turn out to be of Ricci-type.
The paper develops a new theory for knots and 3-manifolds with involutions.
problem Developing a new theory for knots and 3-manifolds with involutions.
method Establishing a version of Seiberg-Witten Floer K-theory for knots and 3-manifolds with involutions.
result 10/8-type inequalities for knots and involutions, yielding lower bounds on stabilizing numbers and relative genera.
Paper shows minimum 10 vertices for hyperbolic origami 2-torus.
problem Finding minimum vertices for hyperbolic origami 2-torus.
method Geodesic triangulation and isometric polyhedral embedding.
result 10 vertices are the minimum required for a hyperbolic origami 2-torus.
This paper classifies semi-equivelar gems on a double torus.
problem Classifying semi-equivelar gems on surfaces with negative Euler characteristic.
method Regular colored graphs representing the double torus, with identical cyclic face degree sequences around each vertex.
result 31 types of semi-equivelar gems on the double torus.
Class I CR manifolds have initial G-structure a certain 4-dimensional subgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_5(C). Class III-2 CR manifolds have initial G-…
CSP improves time-series forecasting without training, outperforming DeepNPTS in speed and accuracy.
problem Improving probabilistic time-series forecasting without training.
method Mixing empirical and residual draws around a seasonal naive forecast.
result CSP significantly outperforms DeepNPTS on CRPS, normalized mean quantile loss, and coverage metrics.
Withdrawn and replaced by two related manuscripts: (1) "Stabilization in the braid groups I:MTWS", published in Geometry and Topology Volume 10 (2006), 413-540, arXiv:math.GT/0310279, and (2) "Stabilization in the braid groups II: Transversal simplicity of knots", Geometry and Topology Volume 10 (2006), to appear, arXi…