arXiv research

Paper generates personalized fonts from a few characters.

We present a probabilistic framework for studying adversarial attacks on discrete data. Based on this framework, we derive a perturbation-based method, Greedy Attack, and a scalable learning-based method, Gumbel Attack, that illustrate various tradeoffs in the design of attacks. We demonstrate the effectiveness of thes…

Amharic is the official language of the Federal Democratic Republic of Ethiopia. There are lots of historic Amharic and Ethiopic handwritten documents addressing various relevant issues including governance, science, religious, social rules, cultures and art works which are very reach indigenous knowledge. The Amharic …

FinMem enhances LLM trading agents with layered memory and character design.

Scene text magnifier aims to magnify text in natural scene images without recognition. It could help the special groups, who have myopia or dyslexia to better understand the scene. In this paper, we design the scene text magnifier through interacted four CNN-based networks: character erasing, character extraction, char…

In the last few years, many different methods have been focusing on using deep recurrent neural networks for natural language generation. The most widely used sequence-to-sequence neural methods are word-based: as such, they need a pre-processing step called delexicalization (conversely, relexicalization) to deal with …

We address the problem of synthetic gene design using Bayesian optimization. The main issue when designing a gene is that the design space is defined in terms of long strings of characters of different lengths, which renders the optimization intractable. We propose a three-step approach to deal with this issue. First, …

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.

Quantum character varieties unify four construction methods.

We show that for any knot there exist only finitely many irreducible metabelian characters in the $SL(2,\mathbb{C})$-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 $SL(2,\mathbb{C})$-character va…

Character varieties get a natural Poisson structure.

Study of orbifold Chern character using superconnections.

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.

Study SL(2,C) character schemes for finitely generated groups.

Background elimination for noisy character images or character images from real scene is still a challenging problem, due to the bewildering backgrounds, uneven illumination, low resolution and different distortions. We propose a stroke-based character reconstruction(SCR) method that use a weighted quadratic Bezier cur…

Character variety of Borromean link solved, Alexander polynomial formula found.

In this paper, we explore the ways to improve POS-tagging using various types of auxiliary losses and different word representations. As a baseline, we utilized a BiLSTM tagger, which is able to achieve state-of-the-art results on the sequence labelling tasks. We developed a new method for character-level word represen…

Computes dimensions of representation and character varieties for 2 and 3-dimensional orbifolds.

In this paper, we explore creative image generation constrained by small data. To partially automate the creation of cartoon sketches consistent with a specific designer's style, where acquiring a very large original image set is impossible or cost prohibitive, we exploit domain specific knowledge for a huge reduction …

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.

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.

Researchers describe character varieties for Hopf links, proving geometric properties.

Study of SU(2,1) character varieties on one-holed torus.

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.

This abstract explores an RNN-based approach to online handwritten recognition problem. Our method uses data from an accelerometer and a gyroscope mounted on a handheld pen-like device to train and run a character pre-diction model. We have built a dataset of timestamped gyroscope and accelerometer data gathered during…

A minimal RNN model learns to generate new characters from a single example.

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 …

We describe on any finitely generated group G the space of maps G->C which satisfy the parallelogram identity, f(xy)+f(xy^{-1})=2f(x)+2f(y). It is known (but not well-known) that these functions correspond to Zariski-tangent vectors at the trivial character of the character variety of G in SL_2(C). We study the obstruc…

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…

Study of pseudo-Anosov actions on $SU(2)$-character variety for genus 2 surfaces.

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…

Let $Γ$ be a finitely generated group and $G$ a real form of $\mathrm{SL}_n(\mathbb{C})$. We propose a definition for the $G$-character variety of $Γ$ as a subset of the $\mathrm{SL}_n(\mathbb{C})$-character variety of $Γ$. We consider two anti-holomorphic involutions of the $\mathrm{SL}_n(\mathbb{C})$ character variet…

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…

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.

Character varieties of knot groups into SU(3) are stratified and analyzed.

Develops equivariant Chern characters for coherent sheaves with 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.

New compactification for character varieties with good topological properties.

In the 80's, Quillen constructed a de Rham relative cohomology class associated to a smooth morphism between vector bundles, that we call the relative Quillen Chern character. In the first part of this paper we prove the multiplicativ property of the relative Quillen Chern character. Then we obtain a Riemann-Roch formu…

In this note we announce several results concerning the SL(2,C) character variety ${\mathcal X}$ of the one-holed torus. We give a description of the largest open subset ${\mathcal X}_{BQ}$ of ${\mathcal X}$ on which the mapping class group $Γ$ acts properly discontinuously, in terms of two very simple conditions, and …

Study character varieties of arborescent knots and hyperbolic knots.

Method determines SL(2,C) character variety for Montesinos knots.