The lonely runner with seven runners

Suppose $k+1$ runners having nonzero constant speeds run laps on a unit-length circular track starting at the same time and place. A runner is said to be lonely if she is at distance at least $1/(k+1)$ along the track to every other runner. The lonely runner conjecture states that every runner gets lonely. The conjecture has been proved up to six runners ($k\le 5$). A formulation of the problem is related to the regular chromatic number of distance graphs. We use a new tool developed in this context to solve the first open case of the conjecture with seven runners

Video question answering supported by a multi-task learning objective

Video Question Answering (VideoQA) concerns the realization of models able to analyze a video, and produce a meaningful answer to visual content-related questions. To encode the given question, word embedding techniques are used to compute a representation of the tokens suitable for neural networks. Yet almost all the works in the literature use the same technique, although recent advancements in NLP brought better solutions. This lack of analysis is a major shortcoming. To address it, in this paper we present a twofold contribution about this inquiry and its relation with question encoding. First of all, we integrate four of the most popular word embedding techniques in three recent VideoQA architectures, and investigate how they influence the performance on two public datasets: EgoVQA and PororoQA. Thanks to the learning process, we show that embeddings carry question type-dependent characteristics. Secondly, to leverage this result, we propose a simple yet effective multi-task learning protocol which uses an auxiliary task defined on the question types. By using the proposed learning strategy, significant improvements are observed in most of the combinations of network architecture and embedding under analysis

Learning Video Retrieval Models with Relevance-Aware Online Mining

Due to the amount of videos and related captions uploaded every hour, deep learning-based solutions for cross-modal video retrieval are attracting more and more attention. A typical approach consists in learning a joint text-video embedding space, where the similarity of a video and its associated caption is maximized, whereas a lower similarity is enforced with all the other captions, called negatives. This approach assumes that only the video and caption pairs in the dataset are valid, but different captions - positives - may also describe its visual contents, hence some of them may be wrongly penalized. To address this shortcoming, we propose the Relevance-Aware Negatives and Positives mining (RANP) which, based on the semantics of the negatives, improves their selection while also increasing the similarity of other valid positives. We explore the influence of these techniques on two video-text datasets: EPIC-Kitchens-100 and MSR-VTT. By using the proposed techniques, we achieve considerable improvements in terms of nDCG and mAP, leading to state-of-the-art results, e.g. +5.3% nDCG and +3.0% mAP on EPIC-Kitchens-100. We share code and pretrained models at https://github.com/aranciokov/ranp

Seamless Benchmarking of Mathematical Optimization Problems and Metadata Extensions

Public libraries of problems such as Mixed Integer Programming Library (MIPLIB) are fundamental to creating a common benchmark for measuring algorithmic advances across mathematical optimization solvers. They also often provide metadata on problem structure, hardness with respect to state-of-the-art solvers, and solutions with the best objective function value on record. In this short paper, we discuss some ways in which such metadata can be leveraged to create a seamless testing experience. In particular, we present MIPLIBing: a Python library that automatically downloads queried subsets from the current versions of MIPLIB, MINLPLib, and QPLIB, provides a centralized local cache across projects, and tracks the best solution values and bounds on record for each problem. While inspired by similar use cases from other areas, we reflect on the specific needs of mathematical optimization and discuss opportunities to extend benchmark sets to facilitate experimentation with different model structures

On the quantumness of correlations in nuclear magnetic resonance

Nuclear Magnetic Resonance (NMR) was successfully employed to test several protocols and ideas in Quantum Information Science. In most of these implementations the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this article we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogous of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrate how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present

Non-Hermitian von Roos Hamiltonian's η\eta-weak-pseudo-Hermiticity, isospectrality and exact solvability

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables, the $\eta$-weak-pseudo-Hermitian von Roos Hamiltonians H(x) are mapped into the traditional Schrodinger Hamiltonian form H(q), where exact isospectral correspondence between H(x) and H(q) is obtained. Under a user-friendly position dependent mass settings, it is observed that for each exactly-solvable $\eta$-weak-pseudo-Hermitian reference-Hamiltonian H(q)there is a set of exactly-solvable $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians H(x). A non-Hermitian PT-symmetric Scarf II and a non-Hermitian periodic-type PT-symmetric Samsonov-Roy potentials are used as reference models and the corresponding $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.Comment: 11 pages, no figures