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…

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

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

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…

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…

Groups acting on product trees are boundary rigid.

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 …

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…

In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a sufficient condition for stochastic completeness is given in terms of the maximum vale…

New proof shows unique symplectic fillings for certain surface singularity links.

In this paper we show that if the minimal good resolution graph of a normal surface singularity contains at least two nodes (i.e. vertex with valency at least 3) then the singularity does not admit a smoothing with Milnor fiber having rational homology equal to the rational homology of the 4-disk $D^4$ (called a ration…

We define ruling invariants for even-valence Legendrian graphs in standard contact three-space. We prove that rulings exist if and only if the DGA of the graph, introduced by the first two authors, has an augmentation. We set up the usual ruling polynomials for various notions of gradedness and prove that if the graph …

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 …

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…

The paper explores new quandle systems for handlebody-links and spatial graphs.

We introduce a smooth quadratic conformal functional and its weighted version $W_2=\sum_e β^2(e)\quad W_{2,w}=\sum_e (n_i+n_j)β^2(e),$ where $β(e)$ is the extrinsic intersection angle of the circumcircles of the triangles of the mesh sharing the edge $e=(ij)$ and $n_i$ is the valence of vertex $i$. Besides minimizing…

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…

In this project, we created a database with two types of annotations used in the emotion recognition domain : Action Units and Valence Arousal to try to achieve better results than with only one model. The originality of the approach is also based on the type of architecture used to perform the prediction of the emotio…

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…

In this paper we develop the metric theory for the outer space of a free product of groups. This generalizes the theory of the outer space of a free group, and includes its relative versions. The outer space of a free product is made of $G$-trees with possibly non-trivial vertex stabilisers. The strategies are the same…

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…

In the context of HCI, building an automatic system to recognize affect of human facial expression in real-world condition is very crucial to make machine interact naturallisticaly with a man. However, existing facial emotion databases usually contain expression in the limited scenario under well-controlled condition. …

0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation or M can be shown to be one of the manifolds S^3, RP^3 or L(3,1). Similarly, any triangulation of a compact, orientable, …

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 …

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.…

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.

The main idea of this ISO is to use StarGAN (A type of GAN model) to perform training and testing on an emotion dataset resulting in a emotion recognition which can be generated by the valence arousal score of the 7 basic expressions. We have created an entirely new dataset consisting of 4K videos. This dataset consist…

Emotions recognition is the task of recognizing people's emotions. Usually it is achieved by analyzing expression of peoples faces. There are two ways for representing emotions: The categorical approach and the dimensional approach by using valence and arousal values. Valence shows how negative or positive an emotion i…

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.

Emotions play an important role in people's life. Understanding and recognising is not only important for interpersonal communication, but also has promising applications in Human-Computer Interaction, automobile safety and medical research. This project focuses on extending the emotion recognition database, and traini…

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…

Vertex distortion detects if a knot is unknot.

The study finds the bounds of vertex orbits in maps derived from specific lattices.

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.

Given a vertex of interest in a network $G_1$, the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network $G_2$. A vertex nomination scheme produces a list of the vertices in $G_2$, ranked according to how likely they are judged to be the corresponding vertex of …

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.

634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations of octonionic projective plane.

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 paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Defines formal vertex laws related to Lie conformal algebras.

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…

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$ (mod $6$), but there doesn't exist vertex-transitive map of such types. In particu…

The study examines vertices in curves with singular points in the Euclidean plane.