The study examines entropy and pressure at infinity in negatively curved manifolds, linking them to strong positive recurrence.
problem Investigating strong positive recurrence in negatively curved manifolds.
method Defining and comparing entropy and pressure at infinity through different measures.
result Strong positive recurrence potentials admit finite Gibbs measures.
New theorem on critical exponents for group actions.
problem Critical exponents of group actions.
method Proving critical exponents coincide under co-amenability condition.
result Generalizes previous results on critical exponents.
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.
Study identifies prime strongly positive amphicheiral knots with double symmetry.
problem Characterizing prime strongly positive amphicheiral knots with specific symmetries.
method Examined knots up to 16 crossings, identified prime knots with double symmetry, and presented almost doubly symmetric diagrams.
result Found the first prime strongly positive amphicheiral knot not slice.
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.
Strongly quasipositive links are those links which can be seen as closures of positive braids in terms of band generators. In this paper we give a necessary condition for a link with braid index 3 to be strongly quasipositive, by proving that in that case it has positive Conway polynomial (that is, all its coefficients…
The paper explores fibered and quasi-positive links, introducing new families and invariants.
problem Understanding the structure of L-space links and their properties. method Using the H-function as a concordance link invariant.
result Introduced a subfamily of fibered strongly quasi-positive L-space links and an infinite family of non-quasi-positive L-space links. Proves alternating quasipositive links are positive and strongly quasipositive.
problem Characterizing alternating quasipositive links.
method Analyzing alternating diagrams with specific crossing conditions.
result Alternating quasipositive links are positive and strongly quasipositive.
Proves almost positive links are strongly quasipositive, answering Stoimenow's question.
problem Proving links with a single negative crossing are strongly quasipositive.
method Analyzing diagrams with a single negative crossing and characterizing quasipositive canonical surfaces.
result Prime knots up to 13 crossings are identified as strongly quasipositive.
We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresho…
The study establishes a link between fibered links and their concordance invariants.
problem Determining the conditions for fibered strongly quasi-positive links.
method Proved that an n-component fibered link L is strongly quasi-positive if and only if τ(L)=g3(L)+n−1. result Explicitly determined fibered prime links with at most 9 crossings and their properties.
We begin a systematic study of a curvature condition (strongly positive curvature) which lies strictly between positive curvature operator and positive sectional curvature, and stems from the work of Thorpe in the 1970s. We prove that this condition is preserved under Riemannian submersions and Cheeger deformations, an…
We obtain a complete description of the moduli spaces of homogeneous metrics with strongly positive curvature on the Wallach flag manifolds W6, W12 and W24, which are respectively the manifolds of complete flags in C3, H3 and Ca3. Together with our earlier work, this concl…
Proves manifolds with positive scalar curvature have inessential covers.
problem Positive scalar curvature manifolds with abelian fundamental groups.
method Proves existence of finite covers with deformed classifying maps.
result Existence of strongly inessential covers for most manifolds.
This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.
problem Understanding how recurrence and non-linear dynamics in cortical networks contribute to their function.
method Transformed time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.
result Optimal time-series classifiers can be built from random reservoir networks, demonstrating significant performance gains.
Paper proves CLT for quantile SGD with constant learning rate.
problem Quantile estimation via SGD with non-smooth, non-strongly convex loss.
method Viewed as a Markov chain, derived stationary distribution, analyzed MGF, proved CLT.
result Centered and standardized stationary distribution converges to Gaussian as ηightarrow0. Holomorphic family of strongly pseudoconvex domains in Kähler manifolds are studied.
problem Characterize the Kähler-Einstein metrics on holomorphic families of strongly pseudoconvex domains.
method Analyzes the properties of Kähler-Einstein metrics on fibers and their extension across singular fibers.
result Proves the positive-definiteness of the induced (1,1)-form on strongly pseudoconvex domains. We use the Birman-Ko-Lee presentation of the braid group to show that all closures of strongly quasipositive braids whose normal form contains a positive power of the dual Garside element δ are fibered. We classify links which admit such a braid representative in geometric terms as boundaries of plumbings of positive…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections and estimate system parameters of a recurrent network, given a sequence of node …
LSTMs were introduced to combat vanishing gradients in simple RNNs by augmenting them with gated additive recurrent connections. We present an alternative view to explain the success of LSTMs: the gates themselves are versatile recurrent models that provide more representational power than previously appreciated. We do…
In this paper we examine the relationship between various types of positivity for knots and the concodance invariant tau discovered by Ozsvath and Szabo and independently by Rasmussen. The main result shows that, for fibered knots, tau characterizes strong quasipositivity. This is quantified by the statement that for K…
We find an infinite family of Seifert fibered surgeries on strongly invertible knots which do not have primitive/Seifert positions. Each member of the family is obtained from a trefoil knot after alternate twists along a pair of seiferters for a Seifert fibered surgery on a trefoil knot.
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key …
In answer to a question of Long, Flapan constructed an example of a prime strongly positive amphicheiral knot that is not slice. Long had proved that all such knots are algebraically slice. Here we show that the concordance group of algebraically slice knots contains an infinitely generated free subgroup that is genera…
The paper proves that a fiberwise Kähler-Ricci flow is positive for all time on a family of bounded strongly pseudoconvex domains.
problem Proving positivity of a fiberwise Kähler-Ricci flow on a family of bounded strongly pseudoconvex domains.
method By constructing a family of flows on fibers and showing that the induced form on the total space is positive.
result The fiberwise Kähler-Ricci flow is positive for all time on the total space.
Strongly polynomial algorithm for approximate Forster transforms and halfspace learning.
problem Computing approximate Forster transforms and halfspace learning.
method Strongly polynomial time algorithm for approximate Forster transforms and halfspace learning.
result First strongly polynomial time algorithm for distribution-free PAC learning of halfspaces.
A polynomial f(t) with rational coefficients is strongly irreducible if f(t^k) is irreducible for all positive integers k. Likewise, two polynomials f and g are strongly coprime if f(t^k) and g(t^l) are relatively prime for all positive integers k and l. We provide some sufficient conditions for strong irreducibility a…
Characterizes diagrams achieving Morton-Franks-Williams inequality for positive knots and links.
problem Understanding when the Morton-Franks-Williams inequality holds for positive knots and links.
method Combinatorial characterisation and generating examples.
result Examples of diagrams achieving crossing number, braid index, and maximal self-linking number.
Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.
problem Understanding when and why Transformers outperform other neural network architectures.
method Analyzing a sequence-to-sequence data generating model with dynamic sparsity, proving sample complexity differences between feedforward, recurrent, and Transformers.
result Transformers can learn dynamic sparsity models with lower sample complexity than feedforward and recurrent networks.
Classifies braids with positive Artin presentations and their fundamental groups.
problem Classifying braids with positive Artin presentations and understanding their fundamental groups.
method Analyzing framed, closed pure n-braids in the 3-sphere to determine if they represent positive Artin presentations.
result Closed, pure n-braids B' in the 3-sphere that represent positive Artin presentations are strongly invertible, and some 3-manifolds do not admit such presentations.
Regularizes RNNs to handle long-range dependencies and multiple time scales.
problem Identifying nonlinear dynamical systems with varying time scales and long-range dependencies.
method A simple regularization scheme for vanilla RNNs with ReLU activation.
result Regularized RNNs can solve long-range dependency problems and express slow time scales.
Constructs a convex Finsler metric on vector bundles under specific conditions.
problem Creating a convex Finsler metric on vector bundles with positive curvature.
method Uses the negativity of direct image bundles and Minkowski inequality for norms.
result Shows how to upgrade a Kobayashi positive Finsler metric to a convex one.
Paper uses RNNs for more accurate indoor WiFi localization.
problem Accurate indoor WiFi localization using RSSI measurements.
method Proposes recurrent neural networks (RNNs) for trajectory positioning of RSSI data.
result Achieves an average localization error of 0.75 m with 80% under 1 m, outperforming conventional algorithms.
Transformer models outperform recurrent ones in modeling hierarchical data.
problem Modeling hierarchical structure in data.
method Introducing Multiresolution Transformer Networks leveraging self-attention.
result Multiresolution Transformer Networks significantly outperform state-of-the-art models on query suggestion datasets.
The article enumerates doubly symmetric diagrams for knots up to 18 crossings.
problem Enumerating doubly symmetric diagrams for knots.
method Developed an enumeration strategy for prime knots given by doubly symmetric diagrams.
result Determined all cases of doubly symmetric diagrams up to 18 crossings.
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…
Two deep learning models improve indoor location prediction from WiFi fingerprints.
problem Indoor location prediction from WiFi fingerprints.
method Convolutional mixture density recurrent neural network and VAE-based semi-supervised learning model.
result Proposed models outperform existing methods in real-world datasets.
Study the smallest Laplace eigenvalue in special geometric spaces.
problem Finding the smallest positive eigenvalue of Laplace-Beltrami operator in strongly isotropy irreducible spaces.
method Explicit expression for simply connected cases, proving Einstein manifold properties and eigenvalue bounds.
result Proved E<λ1≤16E for all strongly isotropy irreducible spaces. Non-normal RNNs outperform orthogonal ones in sequential tasks.
problem Vanishing/exploding gradients in RNNs training.
method Investigate non-normal RNNs with non-normal recurrent connectivity matrix.
result Non-normal RNNs outperform orthogonal ones in various benchmarks.
Unified detection of isolated and overlapping audio events using CNN-RNN.
problem Detecting both isolated and overlapping audio events simultaneously.
method Multi-label multi-task framework based on CNN-RNN, with sequential losses.
result Good generalization on isolated and overlapping audio event detection datasets.
GIRNet tackles multi-tasking with mixed domain sequences, improving sentiment and tagging tasks.
problem Labeling sequences with mixed domain data and position-specific inference.
method Unified position-sensitive multi-task RNN architecture with gated state sequences from auxiliary data.
result GIRNet achieves new state-of-the-art performance in sentiment classification, POS tagging, and target position-sensitive annotation.
We prove that Kobayashi isometries between strongly convex domains are holomorphic or anti-holomorphic. More precisely, let n1,n2 be positive integers and let $Ω_i \subset \C^{n_i}, \ i=1,2$, be bounded C3 strongly convex domains. If φ:(Ω1,dΩ1K)→(Ω2,dΩ2K) is an isometry, i.e. $ d^K_…
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).
In this paper we study Kaehler manifolds that are strongly not relative to any projective Kaehler manifold, i.e. those Kaehler manifolds that do not share a Kaehler submanifold with any projective Kaehler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results whic…
Geodesic currents in strongly hyperbolic spaces are dense.
problem Characterizing geodesic currents with strongly hyperbolic dual pseudometrics.
method Combining finite-cover argument and boundary data characterization.
result Dense subset of geodesic currents with strongly hyperbolic dual pseudometrics.
This paper proposed a method for stock prediction. In terms of feature extraction, we extract the features of stock-related news besides stock prices. We first select some seed words based on experience which are the symbols of good news and bad news. Then we propose an optimization method and calculate the positive po…
This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.
problem Hexagonal grid firing patterns in grid cells.
method Learning a distance-preserving position embedding in neural space using a recurrent neural network.
result The conformal isometric embedding of 2D physical space into neural space explains hexagonal grid firing patterns.
We prove that all currently known examples of manifolds with nonnegative sectional curvature satisfy a stronger condition: their curvature operator can be modified with a 4-form to become positive-semidefinite.