Study characteristic classes for TC structures on principal G-bundles.
problem Classifying principal G-bundles with TC structures.
method Algebraic-geometric construction using power maps on BcomG. result Construction of characteristic classes for TC structures on SU(n), U(n), and Sp(n) bundles. Study new bounds on TC of spaces with subgroup inclusions.
problem Lower bounds on TC of spaces with subgroup inclusions.
method Generalizes TC results from aspherical spaces to spaces with subgroup inclusions.
result Establishes new lower bounds on sequential TCs of aspherical spaces.
AI helps forecasters understand TC convective evolution before intensification.
problem Challenges in extracting scientific insights from complex TC data.
method Combining AI prediction algorithms and classical statistical inference.
result Identifies patterns in TC convective structure leading to intensification.
Agent-based simulation assesses tradable credit schemes for congestion reduction.
problem Simplistic modeling of TCS impacts in transportation research.
method Agent- and activity-based simulation framework within SimMobility.
result TCS stabilizes network and market performance over time, reducing congestion.
We prove the formula TC(G∗H)=max{TC(G),TC(H),cd(G×H)} for the topological complexity of the free product of discrete groups with cohomological dimension >2.
Study numerical invariants for groups, computing for cyclic groups and surfaces.
problem Numerical invariants for groups and their computation.
method Computational and theoretical analysis of groups, including finite cyclic groups and nonorientable surfaces.
result Formula for the numerical invariant of free products of groups.
We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace(n). Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We show that the genus problem for these knots belongs to TC0 circuit complexity c…
We present some results supporting the Iwase-Sakai conjecture about coincidence of the topological complexity TC(X) and monoidal topological complexity TCM(X). Using these results we provide lower and upper bounds for the topological complexity of the wedge X∨Y. We use these bounds to give a counterexample t…
TC-VAE generates robust financial time series data with causal constraints.
problem Generating realistic financial time series data with causal relationships.
method TC-VAE with causality constraint, RealNVP prior, and Wasserstein distance.
result TC-VAE loss controls discrepancy between market and generated distributions.
The Lusternik-Schnirelmann category and topological complexity are important invariants of manifolds (and more generally, topological spaces). We study the behavior of these invariants under the operation of taking the connected sum of manifolds. We give a complete answer for the LS-categoryof orientable manifolds, $\c…
Study examines how twisting graphene nanoribbons affects their thermal conductivity.
problem Understanding how twisting affects thermal conductivity in graphene nanoribbons.
method Calculated geometric parameters of TGNRs, including twist and writhe, and used molecular dynamics simulations.
result Twisted graphene nanoribbons require at least two parameters to accurately describe their thermal conductivity.
New method detects TC imagery patterns for rapid intensity change.
problem Detecting upcoming rapid intensity changes in TC satellite imagery.
method Nonparametric test of association between images and event labels using neural networks and bootstrap.
result Identifies archetypes of infrared imagery associated with elevated rapid intensification risk.
The article applies Lusternik-Schnirelmann theory to establish lower bounds on critical points using sequential and parametrized topological complexity.
problem Establishing lower bounds on the number of critical points of functions using topological complexity.
method Applying Lusternik-Schnirelmann theory to sequential and parametrized topological complexity.
result Established various lower bounds on the number of critical points using sequential and parametrized topological complexity.
This study investigates self-organizing dynamics in a stochastic exponential DAM model using Temporal Complexity.
problem Understanding self-organizing behavior in artificial neural systems.
method Investigation of a stochastic exponential DAM model through Temporal Complexity analysis.
result The model exhibits regimes of complex intermittency with nontrivial temporal correlations and scale-free behavior.
Optimal order execution strategies for brokers under reference benchmarks.
problem Maximizing broker's utility of excess profit-and-loss subject to reference strategies.
method Formulated as a utility maximization problem, optimal strategies derived in closed form.
result General reference strategies can be approximated by piece-wise linear combinations of IS and TC orders.
We provide an upper bound on the topological complexity of twisted products. We use it to give an estimate TC(X)≤TC(π1(X))+dimX of the topological complexity of a space in terms of its dimension and the complexity of its fundamental group.
Defines new versions of distributional topological complexity for spaces.
problem Generalizing topological complexity to sequences.
method Introduces a sequence of higher versions of distributional topological complexity.
result The new versions are homotopy invariants and relate to distributional LS-category.
We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Per…
New TC variant dTC better fits motion planning for some systems.
problem Improving motion planning for autonomous systems.
method Defined and computed new homotopy invariant dTC.
result dTC and dcat provide better motion planning solutions.
Paper examines adversarial attacks on weather forecasting models, focusing on TC trajectory prediction.
problem Adversarial attacks can mislead downstream TC trajectory predictions in DLWF models.
method Proposes Cyc-Attack, a method using a surrogate model and skewness-aware loss function to generate adversarial TC paths.
result Cyc-Attack achieves higher true positive rates and lower false alarm rates compared to conventional methods.
EB-TCε identifies the best arm with ε confidence in stochastic bandits.
problem Identifying the best arm in stochastic bandits with a fixed level of confidence.
method EB-TCε is a novel sampling rule for ε-best arm identification in stochastic bandits.
result EB-TCε is the first anytime algorithm for fixed confidence or fixed budget identification.
As the size n of datasets become massive, many commonly-used clustering algorithms (for example, k-means or hierarchical agglomerative clustering (HAC) require prohibitive computational cost and memory. In this paper, we propose a solution to these clustering problems by extending threshold clustering (TC) to probl…
Develops a deep survival model for causal inference in longitudinal studies.
problem Estimating treatment effects on time-to-event outcomes in observational studies with time-dependent covariates.
method TCS model using potential outcomes framework and ensemble of recurrent subnetworks.
result Identifies conditional average treatment effects and individual treatment effect heterogeneity over time.
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space. The final goal is to construct an algorithm which will perform this task once th…
ReDi improves few-step generation for discrete data models.
problem Slow sampling speeds in discrete flow-based models.
method Rectified Discrete Flow (ReDi) reduces factorization error by rectifying coupling.
result Empirically, ReDi reduces Conditional Total Correlation and enables few-step generation.
Proposes UTC method for stock price prediction with uncertainty quantification.
problem Lack of uncertainty estimates in stock prediction methods.
method Combines TC method with probabilistic modeling for point and uncertainty predictions.
result UTC method achieves higher returns and lower risks than baselines.
New CSC model extracts EEG signals with low noise sensitivity.
problem Analyzing noisy EEG signals during anesthesia.
method Kruskal CSC model using Kruskal decomposition for low-rank tensor activations.
result TC-FISTA efficiently extracts robust, sparse, and interpretable EEG encodings.
New invariant connects virtual and classical linking numbers.
problem Linking numbers and virtual links.
method Introducing a quandle invariant Qtc(L) that preserves linking properties. result Invariant Qtc(L) is a quandle invariant that preserves linking properties. Modelling the real world complexity of music is a challenge for machine learning. We address the task of modeling melodic sequences from the same music genre. We perform a comparative analysis of two probabilistic models; a Dirichlet Variable Length Markov Model (Dirichlet-VMM) and a Time Convolutional Restricted Boltz…
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik-Schnirelmann category of X. Given a mechanical system with configuration space X, the invariant TC(X) measures the complexity of all possible mot…
We consider the non-perturbative superpotential for a class of four-dimensional N=1 vacua obtained from M-theory on seven-manifolds with holonomy G2. The class of G2-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S…
Study bounds VAR model's circuit complexity, showing it's limited to TC^0 circuits.
problem Understanding the limitations of the Visual AutoRegressive model.
method Established circuit complexity bounds for the VAR model.
result VAR model is equivalent to a TC^0 threshold circuit with hidden dimension ≤ O(n).
C2VAE learns disentangled and coupled representations without prior knowledge.
problem Learning disentangled and coupled representations in latent space.
method Introduces C2VAE, a self-supervised VAE that factorizes posterior and uses Gaussian copula for dependencies. result Demonstrates strong effect in enhancing disentangled representation learning.
We introduce the geodesic complexity of a metric space, inspired by the topological complexity of a topological space. Both of them are numerical invariants, but, while the TC only depends on the homotopy type, the GC is an invariant under isometries. We show that in many cases they coincide but we also develop tools t…
Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant −κ2. Using the cone total curvature TC(Γ) of a graph Γ which was introduced by Gulliver and Yamada Math. Z. 2006, we prove that the density at any point of a soap film-like…
We present a novel deep Recurrent Neural Network (RNN) model for acoustic modelling in Automatic Speech Recognition (ASR). We term our contribution as a TC-DNN-BLSTM-DNN model, the model combines a Deep Neural Network (DNN) with Time Convolution (TC), followed by a Bidirectional Long Short-Term Memory (BLSTM), and a fi…
Transformers learn chain-of-thought reasoning for longer problems, proving length generalization.
problem Challenging problems require deeper reasoning, but how do models generalize this to longer tasks?
method Theoretical analysis of transformers on synthetic state-tracking tasks, proving length generalization through attention concentration.
result Transformers can learn chain-of-thought reasoning for longer problems, proving length generalization.
New method adapts DLMs to intrinsic data dependence without prior knowledge.
problem Understanding how unmasking schedules affect DLM generation quality.
method Adapts unmasking schedule to target data distribution's dependence structure.
result Sampling convergence guarantees improve for low-complexity distributions.
Proposes LsrKD and MrKD to improve neural network training performance.
problem Improving neural network training performance, especially on deep networks.
method Extends Label Smoothing Regularization with Self-Knowledge Distillation, introducing LsrKD and MrKD.
result LsrKD and MrKD significantly improve training performance on deep neural networks.
The paper solves TIC LQ control problems using stochastic differential games.
problem Time-inconsistent linear-quadratic stochastic control problems.
method Stochastic differential games, spike variation approach.
result Achieves Nash equilibrium for TIC problems, demonstrating impact of ambiguity aversion.
Study shows peers' graduation improves residents' success in TCs.
problem Identifying peer influence in therapeutic communities adjusting for latent homophily.
method Used data on affirmations and exit dates to form peer networks, modeled latent homophily, and proposed bias correction methods.
result Positive effect of peers' graduation on residents' graduation, varying by gender, race, and role model definition.
In this study, we perform a novel analysis of the 2015 financial bubble in the Chinese stock market by calibrating the Log Periodic Power Law Singularity (LPPLS) model to two important Chinese stock indices, SSEC and SZSC, from early 2014 to June 2015. The back tests of the 2015 Chinese stock market bubbles indicates t…
You are a financial analyst. At the beginning of every week, you are able to rank every pair of stochastic processes starting from that week up to the horizon. Suppose that two processes are equal at the beginning of the week. Your ranking procedure is time consistent if the ranking does not change between this week an…
A new method selects robust features for ML models using causal discovery.
problem Challenges in feature selection for ML models with limited domain knowledge.
method Multidata causal feature selection using PC1 or PCMCI algorithms.
result The method improves model performance and provides interpretable drivers.
We propose a novel VAE-based deep auto-encoder model that can learn disentangled latent representations in a fully unsupervised manner, endowed with the ability to identify all meaningful sources of variation and their cardinality. Our model, dubbed Relevance-Factor-VAE, leverages the total correlation (TC) in the late…
M-theory compactified on G2-holonomy manifolds results in 4d N=1 supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle…
New algorithm improves tensor completion performance.
problem Tensor completion for partially observed data.
method Adaptive ADMM optimization framework for low-rank tensor completion.
result New method outperforms conventional techniques in NMSE.
Paper models and compresses wideband CSI feedback in FDD MIMO systems.
problem Fundamental limits of channel state information (CSI) feedback in FDD massive MIMO systems.
method Modeling CSI as a Gaussian-mixture source with latent geometry states, proposing Gaussian-mixture transform coding (GMTC).
result Near-optimal CSI compression achieved through state-adaptive transform coding without large neural encoders.