We describe the asymptotic behavior of Palais-Smale sequences associated to certain Yamabe-type equations on manifolds with boundary. We prove that each of those sequences converges to a solution of the limit equation plus a finite number of "bubbles" which are obtained by rescaling fundamental solutions of the corresp…
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48 results for “sequence behavior”
Paper characterizes behavior of sequences of solutions to Vafa-Witten equations.
problem Characterizing sequences of solutions to Vafa-Witten equations without convergent subsequences.
method Proves renormalization of subsequence of self-dual 2-form components converges on a set with Hausdorff dimension ≤ 2.
result Renormalized subsequence of self-dual 2-form components converges to a harmonic 2-form with values in a real line bundle on the complement of a closed set.
Time-based model improves recommendation performance.
problem Efficiently handling sequences of varying lengths in recommendation systems.
method Embedding layer and TSL attention-like mechanism with inner products.
result Model outperforms complex models on Taobao User Behavior dataset.
In \cite{CM5}, Colding and Minicozzi describe a type of compactness property possessed by sequences of embedded minimal surfaces in $\Real^3$ with finite genus and with boundaries going to . They show that any such sequence either contains a sub-sequence with uniformly bounded curvature or the sub-sequence has …
This paper proposes a generative model, the latent Dirichlet hidden Markov models (LDHMM), for characterizing a database of sequential behaviors (sequences). LDHMMs posit that each sequence is generated by an underlying Markov chain process, which are controlled by the corresponding parameters (i.e., the initial state …
Paper tackles embedding attributed sequences in unsupervised learning.
problem Mining tasks over attributed sequences with dependencies between sequences and attributes.
method Proposes a deep multimodal learning framework, NAS, for unsupervised learning of attributed sequences.
result NAS produces task-independent embeddings for various mining tasks on real-world datasets.
We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifolds. Asymptotic behavior of end invariants in a convergent sequence predicts the parabolic locus of the algebraic limit as well as how the a…
We will study the blowup behavior of a surface sequence immersed in with bounded Willmore functional and fixed genus.
The paper examines sequences of solutions to Seiberg-Witten systems in 4D manifolds.
problem Analyzing sequences of solutions to Seiberg-Witten systems in 4D manifolds.
method Investigates the behavior of sequences of solutions to Seiberg-Witten-like equations for Hermitian connections and spinor sections.
result Provides insights into the behavior of sequences of solutions to Seiberg-Witten systems in 4D manifolds.
The paper studies sequences of solutions to Hitchin-Simpson equations on Kähler manifolds.
problem Behavior of sequences of solutions to Hitchin-Simpson equations on Kähler manifolds.
method Compactness result for connections and renormalized Higgs fields.
result Every harmonic 1-form can be deformed into a sequence of solutions.
Calendar graph neural networks model user behavior with location and time data.
problem Modeling user behavior with location and time information for demographic prediction.
method Graph neural networks with a tripartite network of items, sessions, and locations, and a hierarchical calendar network.
result User embeddings preserve spatial and temporal patterns of various periodicity.
Improved neural models for diverse user event sequences.
problem Challenges in modeling diverse user event sequences.
method Mixtures of latent embeddings with amortized variational inference.
result Systematic improvements over existing work for various predictive metrics.
Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds, Imath.DG
We study Yamabe metrics, and the moduli space of Yamabe metrics, on an arbitrary closed 3-manifold M. The main focus is on the boundary behavior of the moduli space, i.e. the behavior of degenerating sequences of unit volume Yamabe metrics on M. It is proved that such degenerations, when non-trivial in a certain sense,…
Paper predicts user interests from browsing history and event sequences.
problem Capturing subtle user interests and inter-personal influence.
method Deep prediction method based on two RNNs modeling temporal point process and attention mechanism.
result Model outperforms state-of-the-art methods in fine-grained user interest prediction.
Theory developed to understand limit behavior of embedded minimal disks.
problem Understanding the behavior of limit laminations of properly embedded minimal disks.
method Developed theory of minimal θ-graphs and used to prove existence of non-properly embedded minimal surfaces.
result Existence of a complete, simply connected, minimal surface in hyperbolic space that is not properly embedded.
Sequence-to-sequence models predict resource usage for co-scheduled jobs in data centers.
problem Challenges in co-scheduling jobs due to resource interference and inefficiencies.
method Sequence-to-sequence models based on recurrent neural networks for workload interference prediction.
result Models accurately forecast resource usage trends from job profiles, improving scheduling decisions.
We construct sequences of pseudo-Anosov mapping classes whose dilatations behave asymptotically like the inverse of the Euler characteristic of the surface they are defined on. These sequences are used to show that if the genus, g, and punctures, n, of a surface are related by a rational ray g=rn then the minimal dilat…
A comparison of SLDS and LSTM for pedestrian behavior prediction shows SLDS works better with shorter sequences.
problem Time-critical pedestrian behavior prediction in autonomous vehicles.
method Comparison of a switching linear dynamical system (SLDS) and a three-layered bi-directional LSTM neural network.
result SLDS achieves higher accuracy with shorter sequences (10 samples) compared to LSTM's 80% accuracy with 100 samples.
Introduces alternators for modeling sequences, outperforming baselines.
problem Modeling complex sequential data with stability and efficiency.
method Two neural networks (OTN and FTN) alternate between outputting samples in observation and feature spaces, learned via cross-entropy criterion.
result Alternators outperform strong baselines in various domains (Lorenz equations, Neuroscience, Climate Science).
Constructs self-expanders of positive genus for cones in R^3.
problem Creating self-expanders of positive genus for cones in R^3.
method Constructs self-expanders asymptotic to cones, uses mean curvature flow.
result Constructs self-expanders with unbounded genus asymptotic to a rotationally symmetric cone.
A new framework improves ASR alignment accuracy via optimal transport.
problem Peaky behavior and alignment inaccuracies in E2E ASR models.
method Differentiable alignment framework based on 1D optimal transport.
result Significant improvement in ASR alignment performance compared to CTC.
Study on large mass monopoles focusing on their limiting behavior and properties.
problem Analyzing the limiting behavior of sequences of monopoles with large Yang--Mills--Higgs energies.
method Bubbling analysis and finite cardinality bounds on the blow-up set and zero set.
result For large mass monopoles, the zero set and blow-up set coincide and are finite sets of points.
CompILE learns reusable segments from demonstrations for hierarchical task execution.
problem Learning reusable, variable-length segments of hierarchical behavior from demonstrations.
method Unsupervised, fully-differentiable sequence segmentation module for latent encoding and re-composition.
result Model generalizes to longer sequences and unseen environments, learns task boundaries and event encodings.
The paper studies sequences of solutions to Kapustin-Witten equations with Nahm pole asymptotics.
problem Behavior of sequences of solutions to Kapustin-Witten equations with Nahm pole asymptotics.
method Analyzes sequences of solutions to Kapustin-Witten equations with Nahm pole asymptotics on a product space.
result Sequences either converge to another solution after automorphism or to a harmonic 1-form after renormalization.
GGP models multivariate time series with latent sub-sequences for diverse behaviors.
problem Modeling multivariate time series with diverse behaviors and patterns.
method Graph Gamma Process (GGP) linear dynamical systems with latent sub-sequences.
result GGP models exhibit good predictive performance and reveal interpretable latent patterns.
Neural M3 model adapts to diverse user behaviors over short and long timeframes.
problem Adapting to diverse user behaviors over short and long timeframes.
method Neural Multi-temporal-range Mixture Model (M3) combining short-term and long-term models with a learned gating mechanism.
result M3 consistently outperforms state-of-the-art sequential recommendation methods.
Study trajectories on homothety surfaces, linking to square torus and revealing mixed behaviors.
problem Analyzing linear trajectories on homothety surfaces.
method Examined a 1-parameter family of genus-2 homothety surfaces, considering their linear trajectories and their relation to square torus.
result Trajectories on homothety surfaces can contain either a closed loop or a lamination with Cantor cross-section, and their cutting sequences are either periodic or Sturmian.
The paper studies heat kernel behavior in RCD spaces and initiates Weyl's law study.
problem Understanding heat kernel behavior in RCD spaces.
method Proved pointwise convergence of heat kernels for mGH-convergent sequences of RCD spaces.
result Initiated study of Weyl's law in RCD spaces.
Paper models market dynamics using bull and bear forces.
problem Complex market dynamics influenced by biases and narratives.
method Bias to Behavior from Bull-Bear Dynamics (B4) model.
result Model predicts market trends with superior performance and interpretable insights.
Weak convergence of branched conformal immersions with uniformly bounded areas and Willmore energiesmath.DG
The paper extends a theorem and studies the convergence of branched conformal immersions with bounded areas and Willmore energies.
problem Analyzing the convergence of branched conformal immersions with bounded areas and Willmore energies.
method Extending a local convergence theorem and studying blowup behavior.
result The integral identity of Gauss curvature is proven.
Paper studies fractional CR Yamabe equation on sphere, proving multiplicity of solutions.
problem Fractional CR Yamabe equation on sphere solutions.
method Analyzed Palais-Smale sequences to characterize bubbling phenomena and prove multiplicity of solutions.
result Existence of infinitely many solutions to the fractional CR Yamabe equation.
Study of immersions with Willmore energy leading to spherical and catenoid bubbles.
problem Classifying immersions with specific energy properties.
method Analyzing sequences of weak immersions with diverging conformal classes, applying Möbius transformations, and strong -limits.
result Obtaining spherical and catenoid bubbles as limits of immersions.
Cryptocurrency Bubble Detection: A New Stock Market Dataset, Financial Task & Hyperbolic Modelscs.CL
New dataset and models detect cryptocurrency bubbles using social media data.
problem Detecting anomalous market behavior in cryptocoins and meme stocks.
method Developed a novel multi-span identification task and sequence-to-sequence hyperbolic models.
result Models effectively detect cryptocoins and meme stocks bubbles in zero-shot settings.
New algorithm reduces regret in fatigue-aware online recommendation.
problem Fatigue leads to user abandonment in online recommendation systems.
method Thompson Sampling for combinatorial bandits with fatigue model.
result Polynomial regret bound in number of items, outperforming naive approaches.
Study on degeneration of spectral sequence in complex manifolds under deformations.
problem Behavior of spectral sequence degeneration in complex manifolds under small deformations.
method Deformation theory, pseudo-differential operators, Kodaira-Spencer techniques.
result Degeneration at second step is open under certain conditions but not without them.
New annular link invariants from spectral sequence filtration.
problem Defining invariants for links in annuli.
method Sarkar-Seed-Szabó spectral sequence filtration.
result Necessary and sufficient conditions for braid properties.
Bayesian model predicts sequences better than LSTMs by identifying underlying rules.
problem Current RNNs struggle to generalize from limited training data and identify underlying rules in sequences.
method Bayesian model that learns underlying concepts from sequences and generalizes to new data.
result Bayesian model predicts sequences better than traditional LSTMs.
Given a fibered link, consider the characteristic polynomial of the monodromy restricted to first homology. This generalizes the notion of the Alexander polynomial of a knot. We define a construction, called iterated plumbing, to create a sequence of fibered links from a given one. The resulting sequence of characteris…
The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the ~-~quantile price is shown. The large Black-Scholes model is carefully examined.
Study index bounds for harmonic maps sequences with bubbles.
problem Upper and lower bounds of index and nullity for harmonic maps.
method Study limiting behavior of eigenfunctions of linearized operator; diagonalize index form with bilinear form varying with sequence.
result Obtain index bounds and show convergence of eigenfunctions on weak limit, bubbles, and neck regions.
The paper contains a combinatorial theorem (the sequence of Newton polygons of a reccurent sequence of polynomials is quasi-linear) and two applications of it in classical and quantum topology, namely in the behavior of the -polynomial and a fixed quantum invariant (such as the Jones polynomial) under filling. Our c…
COHORTNEY groups web users based on activity patterns.
problem Lack of academic discussion on cohort analysis for user behavior.
method Unsupervised non-parametric machine learning approach.
result COHORTNEY outperforms traditional methods in cohort analysis.
SIM models user interests from long sequential behavior data, improving click-through rate prediction.
problem Challenges in capturing user interests with long user behavior sequences.
method SIM uses a cascaded search paradigm with two units: General Search Unit and Exact Search Unit.
result SIM achieves significant CTR and RPM lifts in Alibaba's display advertising system.
Paper models user behavior in online social media using HMMs.
problem Understanding user behavior in online social media platforms.
method Leveraging Hidden Markov Models (HMMs) to represent user behavior, deriving a model-based distance, and using spectral clustering.
result Clusters of users with similar behavioral trajectories identified.
Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that (Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m, 0)|}{c_m}= \infty). We will use our results to discuss and to point out some strong differences with…
Study boundary behavior of limit interfaces in Riemannian manifolds without convexity assumptions.
problem Boundary behavior of limit interfaces in Riemannian manifolds.
method Proves limit-interface is a free boundary varifold, integer rectifiable up to boundary.
result No convexity assumption required; valid even when limit-interface clusters near boundary.
Study shows twist tori equidistribute in moduli space, with other families having singular distributions.
problem Statistical behavior of twist tori in moduli space of hyperbolic surfaces.
method Analyzing expanding families of twist tori and their limiting distributions.
result Equidistribution of twist tori to a Lebesgue measure, with other families having singular distributions.
New insights into how encoder-decoder networks generate attention matrices.
problem Understanding how encoder-decoder networks use attention matrices.
method Decomposing hidden states into temporal and input-driven components.
result Attention matrices are formed based on task requirements, not architecture type.