Paper proposes a visual tool for analyzing financial markets.
problem Rational negligence in financial markets during the 2008 crisis.
method Visual declarative language based on port-graph rewriting.
result Visual tool for analyzing asset-backed securities.
This work makes deep reinforcement learning more transparent by visualizing the decision-making process.
problem Making deep reinforcement learning models transparent and explaining their decisions.
method Proposes to visualize the evidence on which the agent bases its decision.
result Makes deep reinforcement learning more transparent and interpretable.
Simplified presentation of symplectic fillings of lens spaces.
problem Symplectic fillings of lens spaces.
method Visual presentation of rational blowdown algorithm using triangulations of convex polygons.
result Organization of symplectic fillings into a graph.
Sparse regularization reduces NLP model complexity without sacrificing accuracy.
problem Excessive parameter usage in neural models for NLP leads to high memory and runtime usage.
method Apply group lasso to rational RNNs to learn sparse, parameter-efficient models.
result Sparse rational RNNs can have significantly fewer parameters than non-sparse models without losing performance.
We study the representation theory of the smallest quantum group and its categorification. The first part of the paper contains an easy visualization of the 3j-symbols in terms of weighted signed line arrangements in a fixed triangle and new binomial expressions for the 3j-symbols. All these formulas are realized as gr…
Suppose X/Gamma is an arithmetic locally symmetric space of noncompact type (with the natural metric induced by the Killing form of the isometry group of X), and let p be a point on the visual boundary of X. It was shown by T.Hattori that if each horoball based at p intersects every Gamma-orbit in X, then p is not on t…
KnotMosaics package simplifies knot theory computations in SageMath.
problem Efficiently computing knot mosaic diagrams and their properties.
method Developed a SageMath package for knot mosaic diagrams, implementing validation, strand tracing, and computation algorithms.
result Enabled easy computation of knot mosaic diagrams and their properties.
The paper constructs new rational homology 3-spheres bounding rational homology 4-balls.
problem Constructing rational homology 3-spheres that bound rational homology 4-balls.
method Exploring plumbed 3-manifolds and using rational homology circles.
result Infinite families of rational homology 3-spheres that bound rational homology 4-balls.
regvis.net offers a visual survey of regulatory visualization.
problem Lack of a comprehensive resource for regulatory visualization.
method Collection and manual tagging of 80+ publications, creation of a searchable webpage.
result First publication set tailored for regulatory visualization.
Algorithm transfers visual concepts to answer out-of-vocabulary questions.
problem Leveraging off-the-shelf visual and linguistic data for out-of-vocabulary answers in visual question answering.
method Unsupervised task discovery for learning task conditional visual classifier, then transferring to visual question answering models.
result Algorithm generalizes to out-of-vocabulary answers successfully.
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of rational helices to obtain a simpler construction of these curves and apply this t…
Classifies real rational knots and curves in a specific quadric space.
problem Classifying real rational knots and curves in a quadric space of signature (3,2). method Classification through a study of real rational curves of low degree in the quadric.
result Provides representatives of all real rational knots of degree ≤5 in the quadric. New method for simplifying knots with specific properties.
problem Understanding knots with a specific unknotting number.
method Derive and apply the Montesinos trick for proper rational tangle replacement.
result Prove that knots with proper rational unknotting number one are prime and classify certain types.
The study calculates the average genus of rational knots and links.
problem Finding the average genus of rational knots and links.
method Enumerating and calculating the number of rational knots and links with a given crossing number.
result A precise formula for the average minimal genus of rational knots and links.
Net2Vis automates CNN visualization for publications.
problem Lack of consistent visual representations in deep learning papers.
method Proposes a visual grammar and automated system for generating publication-ready CNN visualizations.
result Reduces time and ambiguity in generating network visualizations.
We note that a rational 3-tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational 3-tangle diagrams up to isotopy. However, there is no perfect classification about rational 3-tangle diagrams such as the classification of rational 2-tangle diagrams cor…
New rational band moves simplify knot classification.
problem Classifying knots using rational moves.
method Introduced oriented rational band moves and proved their effectiveness.
result Knots that can be unlinkified by rational moves are rationally slice.
Classifies surgeries on torus knots and cables that bound rational homology balls.
problem Which surgeries on torus knots and cables bound rational homology balls?
method Classification based on integral surgeries and rational numbers q/p for cables.
result Set of rational numbers q/p for cables of a given knot K is bounded.
Jones polynomial coincidences explored for rational knots.
problem Identifying coincidences in Jones polynomial of rational knots.
method Moves on continued fraction expansion of rational knots, conjectured to generate all coincidences.
result Conjectured moves are sufficient to generate all Jones rational coincidences.
Lower bounds on rational slice genus using Heegaard Floer invariants.
problem Measuring complexity of homology classes in 4-manifolds.
method Introducing rational slice genus, bounding Heegaard Floer τ invariants, using satellite links and closed braids.
result Lower bounds on rational slice genus in terms of Heegaard Floer τ invariants.
This paper gives two new combinatorial topological proofs of the classification of rational tangles. Each proof rests on an elegant lemma showing that rational tangles are isotopic to canonical alternating rational tangles. The first proof defines the tangle fraction from the canonical form and uses flyping to prove in…
Study connects taffy pulling, fractions, and rational tangles.
problem Understanding the relationship between taffy pulling, fractions, and rational tangles.
method Developed a taffy analogue for Conway's characterization of rational tangles and gave a geometric connection.
result Direct geometric connection between rational tangles and taffy pulls.
New knots show linear independence in slice concordance.
problem Understanding the structure of rationally slice knots.
method Provided an infinite family of knots that are linearly independent.
result Found knots that are linearly independent and infinite order.
The paper proves that rational concordance of double twist knots is reciprocal.
problem Determining when double twist knots are rationally slice.
method Using Donaldson's diagonalization theorem, the paper constructs rational ball obstructions for non-rational sliceness.
result Infinitely many prime power-fold cyclic branched covers do not bound a rational ball, proving the converse of rational concordance.
The study explores pinwheels in symplectic surfaces and non-squeezing of rational homology balls.
problem Understanding when Lagrangian pinwheels embed in symplectic rational and ruled surfaces.
method Almost toric fibrations and symplectic rational blow-up.
result A rational homology ball embeds into a rational homology cylinder if and only if the parameter is greater than or equal to 1.
Proposes a spectral method to assess and combine multiple data visualizations.
problem Evaluating and combining the strengths of different data visualization algorithms.
method Spectral method for assessing and combining multiple visualizations.
result Proposes a visualization eigenscore to quantify relative performance and a consensus visualization.
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.
This paper is an introduction to rational tangles, rational knots and links and their applications to DNA. The paper can be read as an introduction to our more technical papers on rational tangles (math.GT/0311499) and on rational knots (math.GT/0212011). The present paper includes a self-contained account of the tangl…
In this paper, we introduce a rational τ invariant for rationally null-homologous knots in contact 3-manifolds with nontrivial Ozsváth-Szabó contact invariants. Such an invariant is an upper bound for the sum of rational Thurston-Bennequin invariant and the rational rotation number of the Legendrian representatives o…
Classifies torus bundles bounding 4-manifolds with rational homology.
problem Classifying torus bundles over the circle that bound 4-manifolds with rational homology.
method Completely classified torus bundles over the circle that bound 4-manifolds with rational homology.
result Completely classified torus bundles over the circle that bound 4-manifolds with rational homology.
Study shows conditions for rational ellipticity of manifolds with symmetries.
problem Conditions for rational ellipticity of manifolds with symmetries.
method Analyzes conditions on compact simply connected manifolds with G-actions. result Proves rational ellipticity of M/G if M satisfies certain conditions. In this paper, We introduce an invariant of rational n-tangles which is obtained from the Kauffman bracket. It forms a vector with Laurent polynomial entries. We prove that the invariant classifies the rational 2-tangles and the reduced alternating rational 3-tangles. We conjecture that it classifies the rational 3-tan…
We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings. We classify rational, real and complex homotopy types of closed, simply connected, rationally elliptic 7-manifolds. We give par…
New 3-manifolds bound rational 4-balls through specific operations.
problem Finding rational homology 3-spheres that bound rational homology 4-balls.
method Two operations that preserve lattice embedding obstruction to bounding rational homology balls.
result Explicit examples of rational surgeries on torus knots that bound rational homology balls.
Convolutional neural networks (CNNs) have recently emerged as a popular building block for natural language processing (NLP). Despite their success, most existing CNN models employed in NLP share the same learned (and static) set of filters for all input sentences. In this paper, we consider an approach of using a smal…
Study rational homology cobordisms of 3-spheres and lens spaces.
problem When rational homology 3-spheres are cobordant to connected sums of lens spaces.
method Knot Floer homology combined with rational homology cobordism theory.
result Every rational homology cobordism class in the subgroup generated by lens spaces is uniquely represented by a connected sum of lens spaces.
AV-CPL uses continuous pseudo-labels for AVSR combining labeled and unlabeled data.
problem Improving AVSR performance with labeled and unlabeled data.
method Semi-supervised method using continuous pseudo-labels generated by the same AVSR model.
result Significant improvements in VSR performance on LRS3 dataset.
Researchers found all simply connected rational 5-spheres with Sasaki-Einstein metrics.
problem Identifying rational homology 5-spheres with Sasaki-Einstein metrics.
method Comprehensive analysis of simply connected rational homology 5-spheres.
result Determination of which simply connected rational homology 5-spheres admit Sasaki-Einstein metrics.
New knot invariant λ bounds rational unknotting.
problem Bounding rational unknotting number.
method Extracted invariant λ from Khovanov homology.
result Invariant λ is lower bound for proper rational unknotting number.
New proof for curved 3-cohom manifold rational ellipticity.
problem Rational ellipticity of curved manifolds with specific cohomogeneity.
method Proved rationally elliptic for cohomogeneity-three manifolds with positive curvature and no boundary quotient.
result Closed, simply connected, positively curved, cohomogeneity-three manifolds without boundary are rationally elliptic.
New 4-manifold accounts for rationally slice knots.
problem Characterize rationally slice knots.
method Show independence of construction of rational homology ball VK. result Single 4-manifold accounts for all known rationally slice knots.
We give a complete classification of the spherical 3-manifolds that bound smooth rational homology 4-balls. Furthermore, we determine the order of spherical 3-manifolds in the rational homology cobordism group of rational homology 3-spheres. To this end, we use constraints for 3-manifolds to bound rational homology bal…
Proves unicity of q-rational numbers up to conjugacy with new deformations.
problem Proving unicity of q-rational numbers up to conjugacy.
method Using character varieties to prove unicity, and characterizing new deformations.
result Exactly two deformations of q-integers, one new and one old, with new positivity properties.
We introduce the notion of rational links in the solid torus. We show that rational links in the solid torus are fully characterized by rational tangles, and hence by the continued fraction of the rational tangle. Furthermore, we generalize this by giving an infinite family of ambient isotopy invariants of colored diag…
We formulate the equivalence problem, in the sense of E. Cartan, for families of minimal rational curves on uniruled projective manifolds. An important invariant of this equivalence problem is the variety of minimal rational tangents. We study the case when varieties of minimal rational tangents at general points form …
Homological stability fails for Cremona groups, rational varieties, and function fields.
problem Homological stability in Cremona groups fails in both possible ways.
method Explained the failure of homological stability for Cremona groups.
result Homological stability fails for Cremona groups in both possible ways.
Visualizes futures markets using particle physics tools.
problem Understanding high-velocity data in futures markets.
method Uses ROOT, an open-source data-analysis tool, to reconstruct and visualize message-based data.
result Allows stakeholders to gain a better understanding of markets and monitor effectively.
We construct normal rationally connected varieties (of arbitrarily large dimension) not containing any smooth rational curves.