Study triangulations with a unique irregular vertex of valence 6k.
problem Characterize triangulations with a specific valence for vertices.
method Use a flat singular Riemannian metric adapted to triangulations.
result Uniqueness theorem for triangulations with irregular vertex valence not a multiple of 6.
The study counts triangulations of a projective plane with specific vertex valencies.
problem Counting triangulations of a projective plane with unique vertex valencies.
method Analyzes the growth of triangulations with no more than n triangles, using complex mathematical functions and series.
result The number of triangulations grows as C·n^2 + O(n^3/2) with C ≈ 0.2087432125056015.
Deep learning model outperforms traditional methods in music mood prediction.
problem Predicting the emotional state of music from audio and lyrics.
method Implemented deep learning model alongside traditional feature engineering methods and compared their performance.
result Deep learning model outperforms traditional methods in arousal detection.
We introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. This pair of trees have their edges labeled by integers, they have no valence 2 vertices, and they have the same number of valence 1 vertices. The number of valence 1 vertices of the trees is called the girth of the kno…
Project uses GANs to recognize facial expressions and emotions from-the-wild with dual model approach.
problem Facial expression and emotion recognition in real-world scenarios.
method Created a dual GAN model architecture for Action Units and Valence Arousal annotations.
result Dual GAN model achieved better results than single model for emotion recognition.
The study of Killing tensor fields in Weyl's class of stationary and axially symmetric space-times.
problem Understanding the space of Killing tensor fields of valence 3 in Weyl's class.
method Analyzing the static vacuum sub-class of stationary and axially symmetric space-times, proving reducibility of valence-3 Killing tensors.
result The space of Killing tensor fields of valence 3 in Weyl's class is reducible to Killing vector fields and quadratic Killing tensor fields.
Study shows nonexistence of Killing tensors for specific axially symmetric vacuum space-times.
problem Existence of Killing tensors in stationary and axially symmetric space-times.
method Mathematically rigorous, computer algebra computations with complex equations.
result Nonexistence of nontrivial Killing tensors for certain metrics up to high valences.
The study examines surface groups' actions on trees of various valences.
problem Whether surface groups can act freely and properly on finite products of bounded valence trees.
method The approach involves studying character varieties of surface groups over fields of positive characteristic.
result Provides obstructions and an arithmetic criterion for existence of such actions.
For analytic functions in the unit disk, general bounds on the Schwarzian derivative in terms of Nehari functions are shown to imply uniform local univalence and in some cases finite and bounded valence. Similar results are obtained for the Weierstrass--Enneper lifts of planar harmonic mappings to their associated mini…
Aff-Wild database expands facial expression recognition to real-world conditions.
problem Lack of spontaneous facial expression databases in real-world conditions.
method Collects spontaneous facial expressions from YouTube, annotates with valence and arousal, uses deep learning techniques.
result Developed an end-to-end DNN model achieving 0.555 CCC for valence and 0.499 CCC for arousal.
fMRI analysis classifies autobiographical memory valence across individuals.
problem Classifying valence of autobiographical memories across different participants.
method Feature selection (ReliefF) combined with boosting methods applied to voxel space data.
result Classification accuracy of 62% in cross-participant setting, significantly higher than previous results.
StarGAN model generates and recognizes emotions from facial expressions.
problem Emotion recognition and generation from facial expressions.
method Used StarGAN model to train on a new emotion dataset of 4K videos.
result Trained StarGAN model can generate and recognize emotions based on valence arousal scores.
The valence of a function f at a point w is the number of distinct, finite solutions to f(z)=w. Let f be a complex-valued harmonic function in an open set R⊆C. Let S denote the critical set of f and C(f) the global cluster set of f. We show that f(S)∪C(f) partitions the com…
Project creates new dataset for 'in the wild' emotions recognition.
problem Recognition of emotions in real-life unpredictable situations.
method Design and implement a new dataset and deep learning model.
result Demonstrates effectiveness of the new deep learning model for real-life emotions recognition.
An embedding of a graph into R3 is said to be linear, if any edge of the graph is sent to be a line segment. And we say that an embedding f of a graph G into R3 is free, if π1(R3−f(G)) is a free group. It was known that for any complete graph its linear embedding is always free.…
This research improves emotion detection from speech, enhancing CCC by 30%.
problem Improving emotion detection from speech for categorical emotions.
method Used LSTM and TC-LSTM networks, trained with multiple datasets and robust features.
result Improved CCC for valence by 30% compared to baseline.
Amobee won 3rd and 1st place in SemEval 2018 sentiment classification tasks.
problem Sentiment classification in multiple languages.
method Training GRU-CNN model with word embeddings and stacking ensembles.
result 3rd and 1st place in valence ordinal classification sub-tasks in English and Spanish.
Study tight contact structures on specific 3-manifolds.
problem Counting and constructing tight contact structures on plumbed 3-manifolds.
method Algorithm to construct stein diagrams for tight structures without Giroux torsion.
result Explicit algorithm to construct tight contact structures.
Using the construction of a nonorientable Curtis-Tits group of type A~n, we obtain new explicit families of expander graphs of valency five for unitary groups over finite fields.
Models predict emotional valence from narratives, matching human raters.
problem Predicting emotional valence from multimodal time-series data.
method Adapted attention-based mechanisms (Transformer, Memory Fusion Network) to emotional narratives.
result Models perform well, matching human raters on emotional valence prediction.
Predicting emotional state from narratives using contextual information.
problem Predicting valence from personal narratives using contextual information.
method Investigated multiple machine learning techniques to model narratives, focusing on textual information.
result Models capture inter-individual differences, leading to more accurate predictions of emotional state.
We prove that an irreducible lattice in a semisimple algebraic group is virtually isomorphic to an arithmetic lattice if and only if it admits a faithful self-similar action on a rooted tree of finite valency.
Thanks to the recent work of Bhupal, Stipsicz, Szabo, and the author, one has a complete list of resolution graphs of weighted homogeneous complex surface singularities admitting a rational homology disk ("QHD") smoothing, i.e., one with Milnor number 0. They fall into several classes, the most interesting of which are…
Cannon, Floyd and Parry have studied the modulus of finite subdivision rules extensively. We investigate the properties of the modulus of subdivision rules with linear and exponential growth at every vertex, using barycentric subdivision and a subdivision rule for the Borromean rings as examples. We show that the subdi…
New model recognizes emotions with missing modalities, improving accuracy.
problem Handling missing modalities in emotion recognition.
method Transformer-based architecture with cross-attention and self-attention mechanisms.
result Improvement of 37% in predicting arousal values and 30% in valence values compared to baseline.
Graphs on surfaces have limits for complete walks, impacting ergodicity.
problem Graphs embedded in surfaces have limits for complete leftward walks.
method Analyzes graphs embedded in surfaces, proving limits on valence for complete walks.
result The valence of graphs embedded in surfaces is bounded for complete walks.
Project extends emotion recognition database and trains neural networks for categorical and dimensional emotions.
problem Understanding and recognizing emotions for human-computer interaction, safety, and medical research.
method Training CNN + RNN models with emotion category and valence/arousal representations, comparing three model types.
result Categorical emotion recognition performance improves with combined model training.
Emotion recognition system using EEG signals achieves high accuracy.
problem Developing an accurate emotion recognition system using EEG signals.
method EEG signals were decomposed into frequency bands using DWT, features were extracted, PCA was applied, and SVM, KNN, and ANN were used for classification.
result Cross-validated SVM with RBF kernel achieved 91.3% accuracy for arousal and 91.1% for valence in the beta frequency band.
To a finite, connected, unoriented graph of Betti-number g>=2 and valencies >=3 we associate a finitely summable, commutative spectral triple (in the sense of Connes), whose induced zeta functions encode the graph. This gives another example where non-commutative geometry provides a rigid framework for classification.
We study the gordian graph of all knots in R3: two knots are adjacent if they differ by a single crossing change. We prove that this graph contains isometrically an infinite countable tree with infinite valency, and that the complement of any finite subset is connected.
We show that every inner metric space X is the metric quotient of a complete R-tree via a free isometric action, which we call the covering R-tree of X. The quotient mapping is a weak submetry (hence, open) and light. In the case of compact 1-dimensional geodesic space X, the free isometric action is via a subgroup of …
The paper proves a combinatorial Ricci flow converges to hyperbolic structures on certain 3-manifolds.
problem Proving convergence of combinatorial Ricci flow to hyperbolic structures.
method Combinatorial Ricci flow on closed pseudo 3-manifolds with specific edge valences.
result Existence and uniqueness of a complete hyperbolic metric with totally geodesic boundary.
New Z^ invariant for plumbed 3-manifolds with detailed computations and conjectures.
problem Computing and understanding Z^ invariants for plumbed 3-manifolds. method Introducing a two-variable refinement Z^a(q,t), analytically computing limits, and proposing conjectures based on numerical data. result Proposed conjecture that the recovered Z^a(q) is an invariant for all tree plumbed 3-manifolds. Introduces CSST and characterizes its topology.
problem Characterize the topology of the continuum random tree.
method Introduce continuum self-similar tree (CSST) and apply it.
result Characterizes the topology of CSST and other trees.
In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing. New examples of surface singularities with rational homology disk smoothings are a…
Deep learning model predicts human emotions in real-world settings.
problem Automatic emotional state assessment in natural settings.
method End-to-end deep neural architecture (AffWildNet) combining convolutional and recurrent layers.
result AffWildNet achieved state-of-the-art results on Aff-Wild Challenge.
Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of determining partial differential equations for the group invariants and is entirely algebr…
Paper proposes methods to reduce affect estimation labeling costs.
problem High cost and time-consuming for labeling affective computing samples.
method Multi-task active learning for regression to select beneficial samples.
result Optimal sample selection leads to better estimation performance.
Paper tackles multi-task learning for emotion recognition and generation using Aff-Wild dataset.
problem Developing a multi-task learning approach for emotion recognition and generation using Aff-Wild dataset.
method Deep neural network with shared hidden layers and GAN for multi-task learning and image generation.
result Good performance of the proposed approach on Aff-Wild dataset.
A fusion approach combines audio and video features for emotion recognition.
problem Continuous emotion recognition using both visual and auditory modalities.
method Pre-trained CNN features from video frames and minimalistic auditory descriptors. Fusion at feature or prediction level. SVR for prediction.
result Improves CCCs of 0.749 and 0.565 for arousal and valence respectively.
Bayesian deep learning predicts emotion from heartbeat data.
problem Uncertainty in emotion prediction from physiological data.
method End-to-end deep learning model with Bayesian uncertainty estimation.
result Peak classification accuracy of 90% on benchmark datasets.
Improved video emotion estimation in one minute.
problem Estimating continuous emotional states from short videos.
method Used four base regression models and a spectral approach to fuse them.
result Improved performance in estimating arousal and valence values.
First ABAW 2020 Competition analyzes affective behavior tasks.
problem Automatic analysis of valence-arousal, basic expressions, and action units in real-world scenarios.
method Provided Aff-Wild2 database, described Challenges, evaluation metrics, and top-performing systems.
result Demonstrated the feasibility of automatic affective behavior analysis in real-world settings.
Improved emotional speech classification using deep learning.
problem Difficult to assess subtle emotional changes in speech.
method Deep Convolutional Generative Adversarial Networks (DCGAN) for unlabeled data, multitask learning.
result Speaker-independent classification performance improved to 43.88% on a 5-point scale and 49.80% on a 3-point scale.
audEERING improves emotion recognition in 1 minute.
problem Improving emotion recognition in short timeframes.
method Submissions and evaluations for the OMG emotion recognition challenge.
result Achieved high CCC scores for arousal and valence.
Groups acting on product trees are boundary rigid.
problem Understanding boundary rigidity of groups acting on product trees.
method Analyzing geometric actions and visual boundaries of groups.
result Visual boundaries of CAT(0) spaces are homeomorphic to a join of two Cantor sets.
Model improves emotion recognition using multiple physiological signals.
problem Single physiological signal is insufficient for accurate emotion recognition.
method Fused multiple modal physiological signals (EEG, EMG, EOG) for emotion classification.
result Best classification accuracy of 94.42% on arousal and 94.02% on valence in two-class tasks.
Motivated by his studies in knot theory V. Vassiliev introduced X-graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which X-graph can be embedded into a plane respecting the the X-structure at every vertex. The conjecture was proved by…