TBIP uses texts to quantify lawmakers' political positions.
problem Quantifying lawmakers' political positions from speeches, tweets, etc.
method Unsupervised probabilistic topic model analyzing texts.
result TBIP separates lawmakers by party and infers ideal points close to vote-based.
We develop a model of issue-specific voting behavior. This model can be used to explore lawmakers' personal voting patterns of voting by issue area, providing an exploratory window into how the language of the law is correlated with political support. We derive approximate posterior inference algorithms based on variat…
Extends positive and almost positive links to successively almost positive ones.
problem Extending properties of positive and almost positive diagrams and links.
method Introducing successively almost positive diagrams and links, and analyzing their properties.
result Improves known results of positive and almost positive links.
The paper extends positivity results from vector bundles to Kobayashi positive ones.
problem Extending positivity results from vector bundles to Kobayashi positive ones.
method Using convexity of Kobayashi positive Finsler metrics and duality for convex Finsler metrics.
result The quotient and tensor product of Kobayashi positive vector bundles are also Kobayashi positive.
The study establishes conditions for positive and quasi-positive links.
problem Characterizing and testing positive and quasi-positive links.
method Proves necessary conditions for link concordance and positivity.
result Characterizes positive links with unlinking number 1 and 2, and tests positive links as closures of positive braids.
The paper defines new types of positivity and proves properties of Schur forms for vector bundles.
problem Defining and characterizing new types of positivity for vector bundles.
method Introducing and characterizing two types of strongly decomposable positivity, proving properties of Schur forms.
result Schur forms of strongly decomposable positive vector bundles are positive or weakly positive, answering a question of Griffiths.
New characterizations of partial positivity using Hörmander's L2-estimate.
problem Characterizing partial positivity in complex geometry.
method Using a twisted version of Hörmander's L2-estimate. result New characterizations of partial positivity, including uniform q-positivity and RC-positivity. Introduces Θ-positivity in Lie groups, generalizing Lusztig's positivity.
problem Generalizing Lusztig's total positivity to a broader class of Lie groups.
method Introduces and studies Θ-positivity in real simple Lie groups. result Four families of Lie groups admit Θ-positive structures. New bounds on Jones polynomial positivity for specific links.
problem Determining when Jones polynomial of positive links is non-negative.
method Developed new bounds and used them to obstruct positivity for infinitely many almost-positive diagrams.
result Infinitely many knots are classified as almost-positive.
Uniform RC-positivity results for direct image bundles.
problem Understanding the relation between rational connectedness and RC-positivity.
method Analyzing vector bundles and their direct images, using weak RC-positivity as a starting point.
result Uniform RC-positivity of direct image bundles under weak RC-positivity conditions.
We introduce the notion of a positive opetope and positive opetopic cardinals as certain finite combinatorial structures. The positive opetopic cardinals to positive-to-one polygraphs are like simple graphs to free omega-categories over omega-graphs, c.f. [MZ]. In particular, they allow us to give an explicit combinato…
Characterizes a subset of links using quasipositive and homogeneous properties.
problem Understanding the properties of T-positive links.
method Characterization through strongly quasipositive and T-homogeneous braids.
result T-positive links are precisely the strongly quasipositive links that are closures of T-homogeneous braids.
Positive braid knots have simple knot Floer homology.
problem Computing knot Floer homology for positive braids.
method Computed the next-to-top term of knot Floer homology.
result Rank is 1 for any prime positive braid knot.
Establishes geometric properties of elements in the positive semigroup of a general real semisimple Lie group.
problem Generalizing Lusztig's total positivity to the setting of general real semisimple Lie groups.
method Classifying Lie groups admitting a positive structure and establishing key properties of unipotent positive semigroups.
result Establishes key geometric properties of elements in the positive semigroup.
Extends Perelman's theorem to positive intermediate curvature conditions.
problem Positive intermediate curvature conditions and their implications.
method Generalization of Perelman's gluing theorem to positive intermediate curvature conditions.
result Observer moduli space can have non-trivial higher homotopy groups.
An oriented link is positive if it has a link diagram whose crossings are all positive. An oriented link is almost positive if it is not positive and has a link diagram with exactly one negative crossing. It is known that the Rasmussen invariant, 4-genus and 3-genus of a positive knot are equal. In this paper, we p…
Satellite links of fully positive braids are characterized.
problem Characterizing satellite links of fully positive braids.
method Analyzing fully positive braids and their satellites.
result Satellite links of fully positive braids are characterized by specific conditions.
New Θ-positive representations of surface groups discovered.
problem Generalizing Lusztig's total positivity to surface groups.
method Introducing Θ-positivity and proving properties of Θ-positive representations. result Discrete and faithful Θ-positive representations exist and form open sets in representation varieties. Workshop notes on positivity in Lie groups and its applications.
problem Understanding total and Θ-positivity in semisimple Lie groups. method Discussion and analysis of existing theories and recent developments.
result Progress in classifying higher Teichmüller spaces through Θ-positivity. Positive representations on surfaces have positive cross-ratios and satisfy a collar lemma.
problem Characterizing representations of surface groups with positive properties.
method Proving a collar lemma and showing positivity of cross-ratios for Θ-positive representations. result Closed subsets of representation varieties are characterized by Θ-positive representations. New upper bound on Jones polynomial for fibered positive links.
problem Classifying positive and non-positive knots of crossing number ≤ 12.
method Proved a new upper bound on the maximum degree of Jones polynomial for fibered positive knots.
result Maximum degree of Jones polynomial for fibered positive knots is at most four times the minimum degree.
We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots.
Proves positive Euler characteristic for certain manifolds with positive second intermediate Ricci curvature.
problem Hopf's conjecture on positive sectional curvature and its failure under relaxed conditions.
method Non-trivial extension of the Four Periodicity Theorem to higher degrees.
result Proves positive Euler characteristic for specific manifolds with positive second intermediate Ricci curvature.
Curvature of Bazaikin spaces fully characterized, with unique quasi-positive metric.
problem Characterizing sectional curvature of Bazaikin spaces.
method Completely characterized the sectional curvature of all 13-dimensional Bazaikin spaces.
result Unique quasi-positively curved Riemannian metric on Bazaikin spaces, with a unique almost positively curved but not positively curved space.
We prove new results about unknotting fibered positive knots and braids.
problem Proving the unknotting number equals genus for fibered positive knots and braids.
method Analyzing positive braid diagrams and fibered positive knots, proving new constraints and conjectures.
result We found fibered positive knots that cannot be unknotted optimally, contradicting Stoimenow's conjecture.
Positive Thompson links are proven for oriented subgroup elements.
problem Proving properties of Thompson links with positive elements.
method Analyzing elements of the oriented subgroup of the Thompson group.
result Positive oriented Thompson links are established.
The paper proves positivity of third Chern form for certain vector bundles.
problem Proving positivity of third Chern form for Griffiths positive vector bundles.
method Analyzing mixed discriminants and Schur forms.
result Positivity of third Chern form for Griffiths positive vector bundles.
Study on quantum sl3 invariant for positive links.
problem Characterizing and understanding the quantum sl3 invariant of positive links. method Skein theory of sl3-webs, explicit formulae, diagrammatic quantities, obstructions. result Positive links are fibered if and only if the second coefficient of the polynomial is 1.
We introduce Θ-positivity, a new notion of positivity in real semisimple Lie groups. The notion of Θ-positivity generalizes at the same time Lusztig's total positivity in split real Lie groups as well as well known concepts of positivity in Lie groups of Hermitian type. We show that there are two other families of …
Preserves positive intermediate curvature on manifolds.
problem Obstructs positive intermediate curvature on partial tori.
method Shows smooth interpolation of metrics with positive intermediate curvature.
result Proves non-existence of certain manifolds with positive intermediate curvature.
Study k-positive surface group representations and their degenerations.
problem Understanding the behavior of surface group representations under degenerations.
method Introduced k-positive representations and studied their degenerations using a limit theorem for positively ratioed representations.
result Degenerations of k-positive representations can lead to limits that are at least (k-3)-positive and irreducible limits are (k-1)-positive.
The paper explores criteria for positivity of forms and proves their strong positivity in specific cases.
problem Understanding positivity of exterior forms on complex vector spaces.
method Dimensionality reduction and criteria based on Hermitian matrices.
result Strong positivity of certain forms proven by duality.
Abstract reviews hyperbolic positive energy theorems.
problem Analyzing positive energy theorems for hyperbolic spaces.
method Review of existing literature on asymptotically hyperbolic manifolds.
result Summarizes positive energy theorems for hyperbolic spaces.
A complex disproves a curvature property.
problem Proving non-equivalence of curvature properties.
method Analyzing a specific 2-complex presentation.
result The contracting non-positive immersions property is not equivalent to positive maximal irreducible curvature.
Paper constructs infinitely many non-braid positive hyperbolic L-space knots.
problem Proving the non-braid positivity of hyperbolic L-space knots.
method Constructs infinitely many hyperbolic L-space knots that are not braid positive.
result Distinct examples from Baker and Kegel's constructions.
It was asked by J.Birman, Williams, and L.Rudolph whether nontrivial Lorentz knots have always positive signature. Lorentz knots are examples of positive braids (in our convention they have all crossings negative so they are negative links). It was shown by L.Rudolph that positive braids have positive signature (if the…
The paper examines positivity properties of singular Hermitian metrics.
problem Investigating positivity for singular Hermitian metrics.
method Exploring Griffiths, ω-trace, and RC positivity.
result These positivity notions imply cohomology vanishing and rational connectedness.
Proves metrics with positive intermediate Ricci curvature on complex manifolds.
problem Establishing metrics with positive intermediate Ricci curvature on complex manifolds.
method Canonical variation and surgery techniques.
result Existence of metrics with positive intermediate Ricci curvature on various examples.
The paper explores conditions for positive scalar curvature on manifolds with boundaries and their doubles.
problem Conditions for positive scalar curvature on manifolds with boundaries and their doubles.
method Analyzes the relationship between boundary conditions and positive scalar curvature metrics on manifolds and their doubles.
result Provides conditions for positive scalar curvature metrics on manifolds with boundaries and their doubles.
Ricci flow preserves positive sectional curvature on homogeneous spheres
problem Classification of positively curved metrics on homogeneous spaces
method Proving Ricci flow preserves positive sectional curvature on homogeneous spheres
result Completes classification of positively curved metrics on homogeneous spaces
New examples of knots with special bridge positions found.
problem Understanding special types of bridge positions for knots.
method Derived examples of knots with unperturbed weakly reducible non-minimal bridge positions.
result Connected sum of unperturbed bridge positions is unperturbed (a new conjecture).
We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen, Beliakova and Wehrli's s-invariant. We also study almost positive links, in particular, determine the s-invariants of almost positive links. This result suggests that all almost positive links might be strongl…
In this short note we discuss some recent results about two-positive Ricci curvature and their applications to positive Einstein curvature.
Positive-unlabeled (PU) learning trains a binary classifier using only positive and unlabeled data. A common simplifying assumption is that the positive data is representative of the target positive class. This assumption rarely holds in practice due to temporal drift, domain shift, and/or adversarial manipulation. Thi…
Study finds open manifolds without complete metrics with positive scalar curvature.
problem Topological obstruction to positive scalar curvature on open manifolds.
method Defined Schoen-Yau-Schick and weak Schoen-Yau-Schick manifolds to prove the absence of complete metrics with positive scalar curvature.
result Proved no complete metric with positive scalar curvature on open Schoen-Yau-Schick manifolds.
Researchers parametrize spaces of positive representations for Lie groups.
problem Tackling spaces of positive representations for Lie groups.
method Generalizing Lusztig's total positivity, they introduce spaces of positive framed representations and parametrize them.
result The number of connected components of the space of framed positive representations agrees with the number of positive representations.
We show that any closed incompressible surface in the complement of a positive knot is algebraically non-split from the knot, positive knots cannot bound non-free incompressible Seifert surfaces and that the splitability and the primeness of positive knots and links can be seen from their positive diagrams.
Abby Thompson proved that if a link K is in thin position but not in bridge position then the knot complement contains an essential meridional planar surface, and she asked whether some thin level surface must be essential. This note is to give a positive answer to this question, showing that the if a link is in thin…