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MolecularWebXR is our new website for education, science communication and scientific peer discussion in chemistry and biology built on WebXR. It democratizes multi-user, inclusive virtual reality (VR) experiences that are deeply immersive for users wearing high-end headsets, yet allow participation by users with consumer devices such as smartphones, possibly inserted into cardboard goggles for immersivity, or even computers or tablets. With no installs as it is all web-served, MolecularWebXR enables multiple users to simultaneously explore, communicate and discuss chemistry and biology concepts in immersive 3D environments, manipulating objects with their bare hands, either present in the same real space or scattered throughout the globe thanks to built-in audio features. A series of preset rooms cover educational material on chemistry and structural biology, and an empty room can be populated with material prepared ad hoc using moleculARweb's VMD-based PDB2AR tool. We verified ease of use and versatility by users aged 12-80 in entirely virtual sessions or mixed real-virtual sessions at science outreach events, student instruction, scientific collaborations, and conference lectures. MolecularWebXR is available for free use without registration at https://molecularwebxr.org, and a blog post version of this preprint with embedded videos is available at https://go.epfl.ch/molecularwebxr-blog-post., Comment: 13 pages, 3 figures

Music listening preferences at a given time depend on a wide range of contextual factors, such as user emotional state, location and activity at listening time, the day of the week, the time of the day, etc. It is therefore of great importance to take them into account when recommending music. However, it is very difficult to develop context-aware recommender systems that consider these factors, both because of the difficulty of detecting some of them, such as emotional state, and because of the drawbacks derived from the inclusion of many factors, such as sparsity problems in contextual pre-filtering. This work involves the proposal of a method for the detection of the user contextual state when listening to music based on the social tags of music items. The intrinsic characteristics of social tagging that allow for the description of items in multiple dimensions can be exploited to capture many contextual dimensions in the user listening sessions. The embeddings of the tags of the first items played in each session are used to represent the context of that session. Recommendations are then generated based on both user preferences and the similarity of the items computed from tag embeddings. Social tags have been used extensively in many recommender systems, however, to our knowledge, they have been hardly used to dynamically infer contextual states., Comment: 15th ACM Conference on Recommender Systems-Workshop on Context-Aware Recommender Systems (RECSYS 2021-CARS)

A \emph{$[z, r; g]$-mixed cage} is a mixed graph $z$-regular by arcs, $r$-regular by edges, with girth $g$ and minimum order. %In this paper we study structural properties of mixed cages: Let $n[z,r;g]$ denote the order of a $[z,r;g]$-mixed cage. In this paper we prove that $n[z,r;g]$ is a monotonicity function, with respect of $g$, for $z\in \{1,2\}$, and we use it to prove that the underlying graph of a $[z,r;g]$-mixed cage is 2-connected, for $z\in \{1,2\}$. We also prove that $[z,r;g]$-mixed cages are strong connected. We present bounds of $n[z,r;g]$ and constructions of $[z,r;5]$-mixed graphs and show a $[10,3;5]$-mixed cage of order $50$., Comment: 13 pages, 13 figures

Online streaming services have become the most popular way of listening to music. The majority of these services are endowed with recommendation mechanisms that help users to discover songs and artists that may interest them from the vast amount of music available. However, many are not reliable as they may not take into account contextual aspects or the ever-evolving user behavior. Therefore, it is necessary to develop systems that consider these aspects. In the field of music, time is one of the most important factors influencing user preferences and managing its effects, and is the motivation behind the work presented in this paper. Here, the temporal information regarding when songs are played is examined. The purpose is to model both the evolution of user preferences in the form of evolving implicit ratings and user listening behavior. In the collaborative filtering method proposed in this work, daily listening habits are captured in order to characterize users and provide them with more reliable recommendations. The results of the validation prove that this approach outperforms other methods in generating both context-aware and context-free recommendations

In recent years, streaming music platforms have become very popular mainly due to the huge number of songs these systems make available to users. This enormous availability means that recommendation mechanisms that help users to select the music they like need to be incorporated. However, developing reliable recommender systems in the music field involves dealing with many problems, some of which are generic and widely studied in the literature, while others are specific to this application domain and are therefore less well-known. This work is focused on two important issues that have not received much attention: managing gray-sheep users and obtaining implicit ratings. The first one is usually addressed by resorting to content information that is often difficult to obtain. The other drawback is related to the sparsity problem that arises when there are obstacles to gather explicit ratings. In this work, the referred shortcomings are addressed by means of a recommendation approach based on the users' streaming sessions. The method is aimed at managing the well-known power-law probability distribution representing the listening behavior of users. This proposal improves the recommendation reliability of collaborative filtering methods while reducing the complexity of the procedures used so far to deal with the gray-sheep problem., Comment: Accepted in Complexity (ISSN: 1099-0526)

The \emph{packing chromatic number $\chi_\rho (G)$} of a graph $G$ is the smallest integer $k$ for which there exists a vertex coloring $\Gamma: V(G)\rightarrow \{1,2,\dots , k\}$ such that any two vertices of color $i$ are at distance at least $i + 1$. For $g\in \{6,8,12\}$, $(q+1,g)$-Moore graphs are $(q+1)$-regular graphs with girth $g$ which are the incidence graphs of a symmetric generalized $g/2$-gons of order $q$. In this paper we study the packing chromatic number of a $(q+1,g)$-Moore graph $G$. For $g=6$ we present the exact value of $\chi_\rho (G)$. For $g=8$, we determine $\chi_\rho (G)$ in terms of the intersection of certain structures in generalized quadrangles. For $g=12$, we present lower and upper bounds for this invariant when $q\ge 9$ an odd prime power., Comment: 14 pages, 2 figures

A vertex coloring of a strong digraph $D$ is a \emph{strong vertex-monochromatic connection coloring (SVMC-coloring)} if for every pair $u, v$ of vertices in $D$ there exists an $(u,v)$-path having all its internal vertices of the same color. Let $smc_v(D)$ denote the maximum number of colors used in an SVMC-coloring of a digraph $D$. In this paper we determine the value of $smc_v(D)$, whenever $D$ is the line digraph of a digraph. Also, if $T$ is a tournament, we give conditions to find the exact value of $smc_v(T)$., Comment: submitted to Discrete Mathematicas

We present a position operator that is compatible with periodic boundary conditions (PBC). It is a one-body operator that can be applied in calculations of correlated materials by simply replacing the traditional position vector by the new definition. We show that it satisfies important fundamental as well as practical constraints. To illustrate the usefulness of the PBC position operator we apply it to the localization tensor, a key quantity that is able to differentiate metallic from insulating states. In particular, we show that the localization tensor given in terms of the PBC position operator yields the correct expression in the thermodynamic limit. Moreover, we show that it correctly distinguishes between finite precursors of metals and insulators., Comment: 5 pages, 1 figure