arXiv research

We study triangulations $\cal T$ defined on a closed disc $X$ satisfying the following condition: In the interior of $X$, the valence of all vertices of $\cal T$ except one of them (the irregular vertex) is $6$. By using a flat singular Riemannian metric adapted to $\cal T$, we prove a uniqueness theorem when the valen…

We discuss the existence of Killing tensors for certain (physically motivated) stationary and axially symmetric vacuum space-times. We show nonexistence of a nontrivial Killing tensor for a Tomimatsu-Sato metric (up to valence 7), for a C-metric (up to valence 9) and for a Zipoy-Voorhees metric (up to valence 11). The …

The study counts triangulations of a projective plane with specific vertex valencies.

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.

Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the Schwarzschild space-time as its most prominent example. This paper is going to stu…

We consider the task of multimodal music mood prediction based on the audio signal and the lyrics of a track. We reproduce the implementation of traditional feature engineering based approaches and propose a new model based on deep learning. We compare the performance of both approaches on a database containing 18,000 …

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.

StarGAN model generates and recognizes emotions from facial expressions.

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 $R \subseteq \mathbb{C}$. Let $S$ denote the critical set of $f$ and $C(f)$ the global cluster set of $f$. We show that $f(S) \cup C(f)$ partitions the com…

This paper describes the participation of Amobee in the shared sentiment analysis task at SemEval 2018. We participated in all the English sub-tasks and the Spanish valence tasks. Our system consists of three parts: training task-specific word embeddings, training a model consisting of gated-recurrent-units (GRU) with …

Project creates new dataset for 'in the wild' emotions recognition.

It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence trees. We provide some obstructions and an arithmetic criterion for existence. Th…

An embedding of a graph into $\mathbb{R}^3$ 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 $\mathbb{R}^3$ is free, if $π_1(\mathbb{R}^3-f(G))$ 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%.

Automated prediction of valence, one key feature of a person's emotional state, from individuals' personal narratives may provide crucial information for mental healthcare (e.g. early diagnosis of mental diseases, supervision of disease course, etc.). In the Interspeech 2018 ComParE Self-Assessed Affect challenge, the …

Study tight contact structures on specific 3-manifolds.

Using the construction of a nonorientable Curtis-Tits group of type $\tilde A_n$, we obtain new explicit families of expander graphs of valency five for unitary groups over finite fields.

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.

In this research, an emotion recognition system is developed based on valence/arousal model using electroencephalography (EEG) signals. EEG signals are decomposed into the gamma, beta, alpha and theta frequency bands using discrete wavelet transform (DWT), and spectral features are extracted from each frequency band. P…

Graphs on surfaces have limits for complete walks, impacting ergodicity.

We introduce the continuum self-similar tree (CSST) and characterize it topologically. We apply this to answer a question of Curien about the topology of the continuum random tree (CRT). We also give a topological characterization of other trees with branch points of finite or infinite valences.

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.

Project extends emotion recognition database and trains neural networks for categorical and dimensional emotions.

We study the gordian graph of all knots in $\R^3$: 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.

This short paper describes our solution to the 2018 IEEE World Congress on Computational Intelligence One-Minute Gradual-Emotional Behavior Challenge, whose goal was to estimate continuous arousal and valence values from short videos. We designed four base regression models using visual and audio features, and then use…

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.

In this paper we propose a fusion approach to continuous emotion recognition that combines visual and auditory modalities in their representation spaces to predict the arousal and valence levels. The proposed approach employs a pre-trained convolution neural network and transfer learning to extract features from video …

Automatic prediction of emotion promises to revolutionise human-computer interaction. Recent trends involve fusion of multiple data modalities - audio, visual, and physiological - to classify emotional state. However, in practice, collection of physiological data `in the wild' is currently limited to heartbeat time ser…

This paper describes audEERING's submissions as well as additional evaluations for the One-Minute-Gradual (OMG) emotion recognition challenge. We provide the results for audio and video processing on subject (in)dependent evaluations. On the provided Development set, we achieved 0.343 Concordance Correlation Coefficien…

Over the past few years many research efforts have been devoted to the field of affect analysis. Various approaches have been proposed for: i) discrete emotion recognition in terms of the primary facial expressions; ii) emotion analysis in terms of facial Action Units (AUs), assuming a fixed expression intensity; iii) …

New $\hat{Z}$ invariant for plumbed 3-manifolds with detailed computations and conjectures.

We show that fMRI analysis using machine learning tools are sufficient to distinguish valence (i.e., positive or negative) of freely retrieved autobiographical memories in a cross-participant setting. Our methodology uses feature selection (ReliefF) in combination with boosting methods, both applied directly to data re…

Automatically assessing emotional valence in human speech has historically been a difficult task for machine learning algorithms. The subtle changes in the voice of the speaker that are indicative of positive or negative emotional states are often "overshadowed" by voice characteristics relating to emotional intensity …

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…

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…

First ABAW 2020 Competition analyzes affective behavior tasks.

Groups acting on product trees are boundary rigid.

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…

Model improves emotion recognition using multiple physiological signals.

We study the existence and uniqueness of the heat kernel on infinite, locally finite, connected graphs. For general graphs, a uniqueness criterion, shown to be optimal, is given in terms of the maximal valence on spheres about a fixed vertex. A sufficient condition for non-uniqueness is also presented. Furthermore, we …

We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the Nijenhuis integrability conditions for a Killing tensor into purely algebraic integra…

The availability of data on digital traces is growing to unprecedented sizes, but inferring actionable knowledge from large-scale data is far from being trivial. This is especially important for computational finance, where digital traces of human behavior offer a great potential to drive trading strategies. We contrib…