The paper shows non-aspherical path components in G2-moduli spaces.
problem Characterizing non-aspherical path components in G2-moduli spaces.
method Using generalised Kummer construction and resolving singularities with Eguchi-Hanson spaces, the authors establish a fibration over each path component with Eilenberg Mac Lane spaces as fibres.
result The comparison map is a fibration over each path component with Eilenberg Mac Lane spaces as fibres, indicating non-trivial families of G2-manifolds.
Let X be a subcomplex of the standard CW-decomposition of the n-dimensional torus. We exhibit an explicit optimal motion planning algorithm for X. This construction is used to calculate the topological complexity of complements of general position arrangements and Eilenberg-Mac Lane spaces associated to right-angled Ar…
An almost-direct product of free groups is an iterated semidirect product of finitely generated free groups in which the action of the constituent free groups on the homology of one another is trivial. We determine the structure of the cohomology ring of such a group. This is used to analyze the topological complexity …
Integrally splits L-spectra of integers into simpler components.
problem Understanding the homotopy type of L-spectra of integers.
method Using Anderson duality and splitting into simpler spectra.
result Splits L-spectra of integers into simpler components.
We show that for closed orientable manifolds the k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate cohomology in top-degree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles…
Abstract sketches historical development of Lie brackets, crossed modules, and Lie-Rinehart algebras.
problem Characterizing and understanding the relationships between Lie brackets, crossed modules, and Lie-Rinehart algebras.
method Historical review and combinatorial group theory considerations.
result The mutual relationship between Lie-Rinehart algebras and Lie brackets, and the historical development of these concepts.
The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples S//p for prime numbers p. These can be realized as Thom spectra, and therefore relate to other Thom spectra such as the unoriented bordism spectrum MO. We compute the Hochschild and André-Quillen …
New probabilistic invariants bound classical topological complexity and category.
problem Bounding classical topological complexity and category.
method Developed probabilistic variants of one-category and diagonal topological complexity.
result Identified new invariants with distributional category and complexity on Eilenberg-Mac Lane spaces.
Describes the relationship between two spectral sequences and their joint refinement.
problem Computing the cohomology of a group or space using spectral sequences.
method Joint tri-graded refinement of the Leray--Serre and Eilenberg--Moore spectral sequences.
result One of the spectral sequences always degenerates from its second page, and the other satisfies a local-to-global property.
Study on statistical estimation over Gaussian MAC, comparing analog and digital schemes.
problem Distributed minimax statistical estimation over a Gaussian MAC.
method Developed analog joint estimation-communication schemes and derived information-theoretic lower bounds.
result Achieved risk within a logarithmic factor of information-theoretic lower bounds.
Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We consider problems of estim…
MAC Net is a compositional attention network designed for Visual Question Answering. We propose a modified MAC net architecture for Natural Language Question Answering. Question Answering typically requires Language Understanding and multi-step Reasoning. MAC net's unique architecture - the separation between memory an…
A new machine learning framework called machine collaboration improves prediction accuracy.
problem Improving prediction accuracy in machine learning.
method Machine Collaboration (MaC) framework, which uses a circular and interactive learning approach.
result Machine Collaboration framework significantly outperforms other state-of-the-art methods in most cases.
Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.
problem Existence and non-existence of positive solutions for the Lane-Emden equation on Riemannian models.
method Analysis of the subcritical Lane-Emden equation on various Riemannian manifolds with polynomial volume growth.
result Subcritical regime divides into three ranges with distinct existence and non-existence phenomena.
Lane change is a challenging task which requires delicate actions to ensure safety and comfort. Some recent studies have attempted to solve the lane-change control problem with Reinforcement Learning (RL), yet the action is confined to discrete action space. To overcome this limitation, we formulate the lane change beh…
In this paper we adopted state-of-the-art machine learning algorithms, namely: random forest (RF) and least squares boosting, to model crash data and identify the optimum model to study the impact of narrow lanes on the safety of arterial roads. Using a ten-year crash dataset in four cities in Nebraska, two machine lea…
Paper presents a self-supervised method to infer road lane networks.
problem Difficult and costly to create lane maps for autonomous vehicles.
method Self-supervised learning using neural and search-based model.
result Model can generalize to new road layouts, unlike previous approaches.
In this paper, we consider the joint design of data compression and 802.15.4-based medium access control (MAC) protocol for smartgrids with renewable energy. We study the setting where a number of nodes, each of which comprises electricity load and/or renewable sources, report periodically their injected powers to a da…
New theorem bounds group quotient size to subgroups index.
problem Understanding subgroup structure in hyperbolic groups.
method Proved quotient size bounds on Eilenberg-MacLane spaces.
result One-ended hyperbolic groups cannot have isomorphic finite-index subgroups.
We propose a new algorithm, Mean Actor-Critic (MAC), for discrete-action continuous-state reinforcement learning. MAC is a policy gradient algorithm that uses the agent's explicit representation of all action values to estimate the gradient of the policy, rather than using only the actions that were actually executed. …
We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation −Δgu=∣u∣p−1u in a class of Riemannian models (M,g) of dimension n≥3 which includes the classical hyperbolic space Hn as well as manifolds with sectional curvatures unbounded below. Sign properties…
This paper compares machine learning methods for recognizing lane change intentions from vehicle trajectories.
problem Accurately detecting and predicting lane change processes in autonomous vehicles.
method Comparison of different machine learning methods on high-dimensional time series data.
result Ensemble methods reduce Type II and Type III classification errors, while LightGBM outperforms XGBoost in training efficiency.
This paper improves anomaly detection in lane rendering images for safer navigation.
problem Anomalies in lane rendering images can mislead drivers, posing safety risks.
method Proposes a four-phase pipeline using Transformer models, self-supervised pre-training, and fine-tuning.
result The pipeline enhances detection accuracy and reduces training time.
Paper addresses FL over MAC with DP constraints, proposing a novel consensus scheme.
problem Federated learning over a multiple access channel with differential privacy constraints.
method Proposes a novel consensus scheme using digital distributed stochastic gradient descent (D-DSGD) with artificial noise to preserve DP.
result Demonstrates improved convergence rate and DP level for a given MAC capacity.
Traffic speed prediction is a critically important component of intelligent transportation systems (ITS). Recently, with the rapid development of deep learning and transportation data science, a growing body of new traffic speed prediction models have been designed, which achieved high accuracy and large-scale predicti…
Study on radial solutions of Lane-Emden system on Cartan-Hadamard manifolds.
problem Existence and qualitative properties of radial solutions on Cartan-Hadamard manifolds.
method Analytical and asymptotic analysis of radial solutions, focusing on critical and supercritical exponents.
result Existence of one-parameter family of radial solutions for critical or supercritical exponents, with different dimensions of existence regions based on stochastic completeness.
Long-term lane change prediction model predicts maneuvers with 75% accuracy.
problem Predicting long-term lane changes for safer autonomous driving.
method Introduced three models: logistic regression, MLP, and RNN. Used NGSIM dataset with new labeling scheme.
result Developed model predicts 75% of lane changes with an average advanced time of 8.05 seconds.
This paper provides a systematic and comprehensive survey that reviews the latest research efforts focused on machine learning (ML) based performance improvement of wireless networks, while considering all layers of the protocol stack (PHY, MAC and network). First, the related work and paper contributions are discussed…
Characterizes Stein surfaces with finite homotopy rank-sum.
problem Finite homotopy rank-sum in Stein spaces.
method Rational homotopy theory, classification of Stein surfaces.
result Affine Stein surfaces with finite fundamental group are either simply connected or of order 2.
We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: \begin{equation}\nonumber (-Δ)^3 u=|u|^{p-1}u \hbox{ in } \mathbb{R}^n, \end{equation} where p is below the Joseph-Lundgren exponent. As a byproduct w…
New duality concept for vector spaces and groupoids.
problem Defining and studying duals for vector spaces and groupoids.
method Introducing and analyzing n-duals for simplicial vector spaces and n-groupoid objects. result Non-degenerate canonical pairing up to homotopy for homotopy n-types. A new model captures car-following and lane-changing behaviors in traffic.
problem Modeling stochastic microscopic traffic behaviors.
method Physics regularized Gaussian process (PRGP) approach.
result The proposed model outperforms previous methods in estimation precision.
Autonomous driving decision-making is a great challenge due to the complexity and uncertainty of the traffic environment. Combined with the rule-based constraints, a Deep Q-Network (DQN) based method is applied for autonomous driving lane change decision-making task in this study. Through the combination of high-level …
Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane space K(G,1).
We create a 3-skeleton for a symmetric group's classifying space.
problem Classifying space construction for symmetric groups.
method Combining rewriting systems and combinatorial methods.
result Correctness of the constructed 3-skeleton.
MAC combines models without locking them, improving ensemble performance.
problem Improving ensemble learning performance with flexibility.
method Model agnostic combination technique that dynamically combines models.
result MAC outperforms classical methods and competitive to boosting.
The vision of automated driving is to increase both road safety and efficiency, while offering passengers a convenient travel experience. This requires that autonomous systems correctly estimate the current traffic scene and its likely evolution. In highway scenarios early recognition of cut-in maneuvers is essential f…
Researchers calculate cohomological dimensions of manifold configuration spaces, proving arithmeticity and providing bounds.
problem Calculating the cohomological dimensions of configuration spaces of manifolds.
method Defined a reduced Chevalley Eilenberg complex and provided precise formulas and bounds.
result Arithmeticity of cohomological dimensions in configuration spaces of manifolds with non-trivial co-dimension one cohomology groups.
Study cohomology of hemistrict Lie 2-algebras, proving isomorphic results.
problem Understanding cohomology of hemistrict Lie 2-algebras.
method Functorial construction and isomorphism proof of cohomology.
result Cohomology of hemistrict Lie 2-algebras is isomorphic to Chevalley-Eilenberg cohomology.
A countable CW complex K is quasi-finite (as defined by A.Karasev) if for every finite subcomplex M of K there is a finite subcomplex e(M) such that any map f:A→M, where A is closed in a separable metric space X satisfying XτK, has an extension g:X→e(M). Levin's results imply that none of the Ei…
We show that the spectrum constructed by Everitt and Turner as a possible Khovanov homotopy type is a product of Eilenberg-MacLane spaces and is thus determined by Khovanov homology. By using the Dold-Thom functor it can therefore be obtained from the Khovanov homotopy type constructed by Lipshitz and Sarkar.
Intelligent motion planning is one of the core components in automated vehicles, which has received extensive interests. Traditional motion planning methods suffer from several drawbacks in terms of optimality, efficiency and generalization capability. Sampling based methods cannot guarantee the optimality of the gener…
Novel proof technique for Gelfand-Fuks cohomology.
problem Comparing sheaf-like data over manifold Cartesian powers.
method Local-to-global analysis through generalized good covers and factorization algebras.
result Unified approach to Gelfand-Fuks cohomology.
Study probabilistic category and complexity bounds, comparing with classical invariants.
problem Bounding classical category and complexity in probabilistic settings.
method Probabilistic Lusternik-Schnirelmann category and topological complexity computations.
result Established a universal upper bound in finite cases, contrasting with classical invariants.
Autonomous lane changing is a critical feature for advanced autonomous driving systems, that involves several challenges such as uncertainty in other driver's behaviors and the trade-off between safety and agility. In this work, we develop a novel simulation environment that emulates these challenges and train a deep r…
Inspired by the work of Chevalley and Eilenberg on the de Rham cohomology on compact Lie groups, we prove that, under certain algebraic and topological conditions, the cohomology associated to left-invariant elliptic, and even hypocomplex, involutive structures on compact Lie groups can be computed by using only Lie al…
DSGD with OAC-MAC scheme achieves better convergence in noisy wireless networks.
problem Performance of decentralized SGD in noisy wireless environments.
method Proposed OAC-MAC scheme for over-the-air computation in DSGD.
result OAC-MAC scheme converges faster with fewer communication rounds.
Adaptive framework generates challenging adversarial scenarios for autonomous vehicles.
problem Lack of efficient and adaptable evaluation methods for autonomous vehicles.
method Adaptive evaluation framework using ensemble models and nonparametric Bayesian clustering.
result Adversarial scenarios significantly degrade tested autonomous vehicles' performance.