A stroke-based method reconstructs characters from noisy images.
problem Challenges in reconstructing characters from noisy images.
method Uses a weighted quadratic Bezier curve (WQBC) to represent strokes.
result Achieves excellent reconstruction in real scenes.
Shelstad's character identity is an equality between sums of characters of tempered representations in corresponding L-packets of two real, semisimple, linear, algebraic groups that are inner forms to each other. We reconstruct this character identity in the case of the discrete series, using index theory of elliptic…
Model disentangles font content and style.
problem Analyzing and reconstructing fonts.
method Variational inference and asymmetric transpose convolutional process.
result Model outperforms state-of-the-art models in font reconstruction.
Proposes categorification of Z-invariants for specific 3-manifolds.
problem Categorification of Z-invariants for negative definite plumbed 3-manifolds.
method Abelian categorification using 3d N=2 theory and log VOAs.
result Nested Weyl-type character formulas reconstruct Z^-invariants. AN2VEC disentangles feature and structural information in social networks.
problem Difficulty in separating feature and structural information in social networks.
method Graph Convolutional Networks (GCN) Variational Autoencoder for disentangled node embeddings.
result AN2VEC captures joint information of structure and features better than unshared information.
RTN generates realistic character transitions from context.
problem Manual transition animation creation is tedious and time-consuming.
method Recurrent Neural Network (RNN) with LSTM architecture trained on past context.
result RTN produces realistic transitions that rival motion capture.
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
Character scheme of small Seifert 3-manifolds is reduced if and only if no exceptional abelian character exists.
problem Character scheme of small Seifert 3-manifolds and its reduction condition.
method Complete description of the SL2(C)-character scheme of small Seifert 3-manifolds.
result Character scheme is reduced if and only if no exceptional abelian character exists, and exceptional abelian character has multiplicity 2.
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
We show that for any knot there exist only finitely many irreducible metabelian characters in the SL(2,C)-character variety of the knot group, and the number is given explicitly by using the determinant of the knot. Then it turns out that for any 2-bridge knot a section of the SL(2,C)-character va…
Study of orbifold Chern character using superconnections.
problem Chern character for orbifold settings.
method Use of flat antiholomorphic superconnections and Riemann-Roch-Grothendieck theorem.
result Uniqueness of orbifold Chern character proven.
Character varieties get a natural Poisson structure.
problem Character varieties of surfaces.
method Natural Poisson structure.
result Character varieties have a Poisson structure.
Study on deformations of trivial character in SL_2(C) for groups.
problem Deforming the trivial character in SL_2(C) for groups.
method Analyzing maps satisfying the parallelogram identity on groups and relating them to deformations of the trivial character.
result The trivial character is a smooth point if and only if H_1(G,C) has dimension less than 2.
In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by …
Study shows how certain knots and tori are detected by ideal points in character varieties.
problem Detecting essential twice-punctured tori in character varieties.
method Extending Tillmann's limiting character method to new families of knots and tori.
result Explicit determination of limiting characters at ideal points for specific knots and tori.
Study SL(2,C) character schemes for finitely generated groups.
problem Characterize SL(2,C) representations of finitely generated groups.
method Define coordinate rings and equations for SL(2,C) character schemes.
result Explicit equations for character schemes of finitely presented groups.
Character variety of Borromean link solved, Alexander polynomial formula found.
problem Character variety of Borromean link
method Determined irreducible SL(2,C) character variety, found Alexander polynomial formula
result Formula for twisted Alexander polynomial on character variety
Character varieties of 2-bridge knots and links explained using Farey recursion.
problem Understanding character varieties of 2-bridge knots and links.
method Using Farey recursion to define polynomials for character varieties.
result Character varieties described in terms of polynomials defined by Farey recursion.
Computes dimensions of representation and character varieties for 2 and 3-dimensional orbifolds.
problem Computing dimensions of representation and character varieties for orbifolds.
method Analyzes varieties of representations and characters of hyperbolic and non-hyperbolic orbifolds, provides tools for computation.
result Shows that the dimension of a specific component of characters equals half the dimension of the variety of characters of the boundary.
Paper generates personalized fonts from a few characters.
problem Creating personalized fonts from a limited set of characters.
method Designs a network framework to extract and recombine character content and style using various neural networks.
result Generated characters are structurally similar to real characters.
We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study t…
Study of quantum decorated character stacks and their quantizations.
problem Quantization of decorated character stacks and their compatibility with cutting and gluing.
method Using stratified factorization homology, extend Fock and Goncharov's construction to include stacky points.
result Construction of categorical charts and flips on quantum decorated character stacks.
Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of characters with trace free along meridians in the SL(2, C)-character variety of the knot exterior to the SL(2, C)-character variety of 2-fold…
Study character varieties of hyperbolic 3-manifolds using bundle methods.
problem Character varieties of hyperbolic 3-manifolds in once-punctured torus bundles.
method Restrict characters to the fibre and analyze branched covering maps.
result Infinite family of hyperbolic once-punctured bundles with unbounded genus.
Finite automorphisms of SL(2,C) character varieties identified.
problem Character varieties of surfaces with negative Euler characteristic.
method Algebraic automorphisms and mapping class groups studied.
result Finite extension of mapping class group identified.
Researchers describe character varieties for Hopf links, proving geometric properties.
problem Character variety geometry of Hopf links with n twists. method Geometric descriptions of irreducible and totally reducible representations.
result Complete geometric description of SU(2)-character variety for r=2. Study of SU(2,1) character varieties on one-holed torus.
problem Characterize representations of mapping class group on SU(2,1) character variety.
method Explicit description of SU(2,1) character variety, use of Farey graph adaptation, and mapping class group action analysis.
result Description of an open domain of discontinuity for mapping class group action.
RNN model predicts handwritten characters from accelerometer and gyroscope data.
problem Online handwritten character recognition using sensor data.
method RNN-based neural network trained on gyroscope and accelerometer data.
result High accuracy on test data, achieving character prediction.
We calculate the universal character ring of a class of two-generator, one-relator groups. As an application we give a less technical proof of a result in [LT] on the universal character ring of the (-2,3,2n+1)-pretzel knot. We also give an elementary proof of a result in [Ma] on the character variety of the (-2,3,2n+1…
Character variety of Whitehead link described in detail.
problem Character variety of Whitehead link.
method Nice description of a Zariski open subset.
result Zariski open subset of the character variety described.
Efficient method computes mSL(3,C)-character varieties for two-generator groups.
problem Computing mSL(3,C)-character varieties for two-generator groups. method Efficient method for two-generator groups.
result Efficient computation of mSL(3,C)-character varieties. Proves Torelli group action is ergodic on Lie group character varieties.
problem Ergodicity of Torelli group action on compact character varieties.
method Proof based on properties of connected, semi-simple Lie groups.
result Torelli group action on compact character varieties is ergodic.
A minimal RNN model learns to generate new characters from a single example.
problem Learning efficiency and compositional ability in AI.
method Minimal RNN model with one-shot inference mechanism.
result The model can recombine previously learned substructures to generate new characters.
Study SL2(F)-character varieties of knots over fields of odd characteristic.
problem Character varieties of knots over fields of odd characteristic exhibit ramification phenomena.
method Investigate sufficient conditions for ramification using double branched covers and Alexander polynomials.
result Character varieties of knots over fields of odd characteristic can present ramification phenomena.
Detecting essential surfaces in 3-manifolds and orbifolds using character varieties.
problem Detecting essential surfaces in 3-manifolds and orbifolds.
method Extending Culler and Shalen's construction to 3-orbifolds using SL2(C) character variety. result Any slope detected on a canonical component of the (P)SL2(C) character variety of a one-cusped hyperbolic 3-manifold with symmetries must be the slope of a symmetric surface. Quantum trace maps abelian character varieties to SL2 character varieties.
problem Classifying irreducible representations of Chekhov-Fock algebras.
method Non-commutative deformation of algebraic morphisms.
result Induces birational morphism between torus and SL2 character variety.
We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons …
Study of pseudo-Anosov actions on SU(2)-character variety for genus 2 surfaces.
problem Characterizing pseudo-Anosov actions on SU(2)-character variety. method Analysis of mapping class group subgroups and their pseudo-Anosov elements.
result Existence of a subgroup containing infinitely many pseudo-Anosov elements with invariant rational functions.
Let Γ be a finitely generated group and G a real form of SLn(C). We propose a definition for the G-character variety of Γ as a subset of the SLn(C)-character variety of Γ. We consider two anti-holomorphic involutions of the SLn(C) character variet…
The powerful character variety techniques of Culler and Shalen can be used to find essential surfaces in knot manifolds. We show that module structures on the coordinate ring of the character variety can be used to identify detected boundary slopes as well as when closed surfaces are detected. This approach also yields…
This note introduces and studies an open set of PSL(2,C) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact (i.e. Schottky) characters. This implies, in particular, that th…
End-to-end ASR model combines word and character representation for improved performance.
problem Difficulty in training with word-level supervision due to sparsity of examples.
method Multi-task learning framework combining word and character representations.
result Improved word-error rate (WER) by interpolating between word-level and character-level models.
Character varieties of knot groups into SU(3) are stratified and analyzed.
problem Characterizing representations of knot groups into SU(3).
method Stratification of character variety into reducible, 2D+1D, and irreducible representations.
result Homotopy equivalence between SU(3) and SL(3,C) character varieties.
Study character varieties of even pretzel knots, determining their mSL(2,C)-representations.
problem Determine character varieties of even classical pretzel knots.
method Compute irreducible mSL(2,C)-representations of even classical pretzel knots. result Clarify the steps to compute the A-polynomial of even classical pretzel knots.
In this paper we first prove that every differential character can be represented by differential form with singularities. Then we lift the Gauss-Bonnet-Chern theorem for vector bundles to differential characters.
Develops equivariant Chern characters for coherent sheaves with group actions.
problem Computing Chern characters for coherent sheaves on manifolds with group actions.
method Introduces equivariant Chern characters and proves Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology.
result Establishes a Riemann-Roch-Grothendieck theorem for coherent sheaves with finite group actions.
We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot,…
PFPN uses particle filtering to improve character control in physics-based simulations.
problem Premature commitment to suboptimal actions in high-dimensional continuous control problems for articulated characters.
method Proposes a particle-based action policy using particle filtering to dynamically explore and discretize the action space.
result Demonstrates better imitation performance and robustness to external perturbations compared to Gaussian policies.