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In this paper we obtain complexity bounds for computational problems on algebraic power series over several commuting variables. The power series are specified by systems of polynomial equations: a formalism closely related to weighted context-free grammars. We focus on three problems -- decide whether a given algebraic series is identically zero, determine whether all but finitely many coefficients are zero, and compute the coefficient of a specific monomial. We relate these questions to well-known computational problems on arithmetic circuits and thereby show that all three problems lie in the counting hierarchy. Our main result improves the best known complexity bound on deciding zeroness of an algebraic series. This problem is known to lie in PSPACE by reduction to the decision problem for the existential fragment of the theory of real closed fields. Here we show that the problem lies in the counting hierarchy by reduction to the problem of computing the degree of a polynomial given by an arithmetic circuit. As a corollary we obtain new complexity bounds on multiplicity equivalence of context-free grammars restricted to a bounded language, language inclusion of a nondeterministic finite automaton in an unambiguous context-free grammar, and language inclusion of a non-deterministic context-free grammar in an unambiguous finite automaton., Comment: full technical report of a LICS'23 paper

Urban vibrancy is the dynamic activity of humans in urban locations. It can vary with urban features and the opportunities for human interactions, but it might also differ according to the underlying social conditions of city inhabitants across and within social surroundings. Such heterogeneity in how different demographic groups may experience cities has the potential to cause gender segregation because of differences in the preferences of inhabitants, their accessibility and opportunities, and large-scale mobility behaviours. However, traditional studies have failed to capture fully a high-frequency understanding of how urban vibrancy is linked to urban features, how this might differ for different genders, and how this might affect segregation in cities. Our results show that (1) there are differences between males and females in terms of urban vibrancy, (2) the differences relate to `Points of Interest` as well as transportation networks, and (3) that there are both positive and negative `spatial spillovers` existing across each city. To do this, we use a quantitative approach using Call Detail Record data--taking advantage of the near-ubiquitous use of mobile phones--to gain high-frequency observations of spatial behaviours across the seven most prominent cities of Italy. We use a spatial model comparison approach of the direct and `spillover` effects from urban features on male-female differences. Our results increase our understanding of inequality in cities and how we can make future cities fairer., Comment: 20 pages, 10 figures: 1 figure and 1 table in main, 7 figures in supplementary material, 3 tables in supplementary material. Submitted to Environment and Planning B: Urban Analytics and City Science special issue on Spatial Inequalities and Cities

Reconfigurable Intelligent Surfaces (RISs) constitute the key enabler for programmable electromagnetic propagation environments, and are lately being considered as a candidate physical-layer technology for the demanding connectivity, reliability, localization, and sustainability requirements of next generation wireless networks. In this paper, we first present the deployment scenarios for RIS-enabled smart wireless environments that have been recently designed within the ongoing European Union Horizon 2020 RISE-6G project, as well as a network architecture integrating RISs with existing standardized interfaces. We identify various RIS deployment strategies and sketch the core architectural requirements in terms of RIS control and signaling, depending on the RIS hardware architectures and respective capabilities. Furthermore, we introduce and discuss, with the aid of simulations and reflectarray measurements, two novel metrics that emerge in the context of RIS-empowered wireless systems: the RIS bandwidth and area of influence. Their extensive investigation corroborates the need for careful deployment and planning of the RIS technology in future networks., Comment: 43 pages, 21 figures, sumbitted for a journal publication. arXiv admin note: text overlap with arXiv:2203.13478

The use of Attention Layers has become a trend since the popularization of the Transformer-based models, being the key element for many state-of-the-art models that have been developed through recent years. However, one of the biggest obstacles in implementing these architectures - as well as many others in Deep Learning Field - is the enormous amount of optimizing parameters they possess, which make its use conditioned on the availability of robust hardware. In this paper, it's proposed a new method of attention mechanism that adapts the Dot-Product Attention, which uses matrices multiplications, to become element-wise through the use of arrays multiplications. To test the effectiveness of such approach, two models (one with a VGG-like architecture and one with the proposed method) have been trained in a classification task using Fashion MNIST and CIFAR10 datasets. Each model has been trained for 10 epochs in a single Tesla T4 GPU from Google Colaboratory. The results show that this mechanism allows for an accuracy of 92% of the VGG-like counterpart in Fashion MNIST dataset, while reducing the number of parameters in 97%. For CIFAR10, the accuracy is still equivalent to 60% of the VGG-like counterpart while using 50% less parameters.

Dynamic Time Wrapping (DTW) is a widely used algorithm for measuring similarities between two time series. It is especially valuable in a wide variety of applications, such as clustering, anomaly detection, classification, or video segmentation, where the time-series have different timescales, are irregularly sampled, or are shifted. However, it is not prone to be considered as a loss function in an end-to-end learning framework because of its non-differentiability and its quadratic temporal complexity. While differentiable variants of DTW have been introduced by the community, they still present some drawbacks: computing the distance is still expensive and this similarity tends to blur some differences in the time-series. In this paper, we propose a fast and differentiable approximation of DTW by comparing two architectures: the first one for learning an embedding in which the Euclidean distance mimics the DTW, and the second one for directly predicting the DTW output using regression. We build the former by training a siamese neural network to regress the DTW value between two time-series. Depending on the nature of the activation function, this approximation naturally supports differentiation, and it is efficient to compute. We show, in a time-series retrieval context on EEG datasets, that our methods achieve at least the same level of accuracy as other DTW main approximations with higher computational efficiency. We also show that it can be used to learn in an end-to-end setting on long time series by proposing generative models of EEGs.

The energy consumption, the transfer of resources through the international trade, the transition towards renewable energies and the environmental sustainability appear as key drivers in order to evaluate the resilience of the energy systems. Concerning the consumptions, in the literature a great attention has been paid to direct energy, but the production of goods and services also involves indirect energy. Hence, in this work we consider different types of embodied energy sources and the time evolution of the sectors' and countries' interactions. Flows are indeed used to construct a directed and weighted temporal multilayer network based respectively on renewable and non-renewable sources, where sectors are nodes and layers are countries. We provide a methodological approach for analysing the network reliability and resilience and for identifying critical sectors and economies in the system by applying the Multi-Dimensional HITS algorithm. Then, we evaluate central arcs in the network at each time period by proposing a novel topological indicator based on the maximum flow problem. In this way, we provide a full view of economies, sectors and connections that play a relevant role over time in the network and whose removal could heavily affect the stability of the system. We provide a numerical analysis based on the embodied energy flows among countries and sectors in the period from 1990 to 2016. Results prove that the methods are effective in catching the different patterns between renewable and non-renewable energy sources.

The analysis of the central compact object within the supernova remnant HESS J1731-347 suggests that it has a small radius and, even more interestingly, a mass of the order or smaller than one solar mass. This raises the question of which astrophysical process could lead to such a small mass, since the analysis of various types of SN explosions indicate that is it not possible to produce a neutron star with a mass smaller than about $1.17 M_\odot$. Here we show that masses of the order or smaller than one solar mass can be obtained in the case of strange quark stars and that it is possible to build a coherent model explaining not only the mass and the radius of that object, but also its slow cooling suggested in various analyses. We also show that an astrophysical path exists which leads to the formation of such an object, and we discuss the role played in that scenario by strangelets assumed to constitute the dark matter., Comment: 7 pages, 2 Figures, 1 Table. Final version accepted for publication

Wireless traffic is exploding, due to the myriad of new connections and the exchange of capillary data at the edge of the networks to operate real-time processing and decision making. The latter especially affects the uplink traffic, which will grow in 6G and beyond networks, calling for new optimization metrics that include energy, service delay, and electromagnetic field (EMF) exposure (EMFE). To this end, reconfigurable intelligent surfaces (RISs) represent a promising solution to mitigate the EMFE, thanks to their ability of shaping and manipulating the impinging electromagnetic waves. In line with this vision, this paper proposes an online adaptive method to mitigate the EMFE under end-to-end delay constraints of a computation offloading service, in the context of RIS and multi-access edge computing (MEC)-aided wireless networks. The goal is to minimize the long-term average of the EMF human exposure under such constraints, investigating the advantages of RISs towards blue (i.e. low EMFE) communications. A multiple-input multiple-output (MIMO) system is investigated as part of the visions towards 6G. Focusing on a typical scenario of computation offloading, the method jointly and adaptively optimizes user precoding, transmit power, RIS reflectivity parameters, and receiver combiner, with theoretical guarantees on the desired long-term performance. Besides the theoretical results, numerical simulations assess the performance of the proposed algorithm, when exploiting accurate antenna patterns, thus showing the advantage of the RIS and that of our method, compared to benchmark solutions., Comment: Accepted at IEEE Globecom 2022

A local flavour symmetry acting on the quarks of the Standard Model can automatically give rise to an accidental global $U(1)$ which remains preserved from sources of explicit breaking up to a large operator dimension, while it gets spontaneously broken together with the flavour symmetry. Such non-fundamental symmetries are often endowed with a mixed QCD anomaly, so that the strong CP problem is automatically solved via the axion mechanism. We illustrate the general features required to realise this scenario, and we discuss a simple construction based on the flavour group $SU(3)\times SU(2) \times U(1)_F$ to illustrate how mass hierarchies can arise while ensuring at the same time a high quality Peccei-Quinn symmetry., Comment: 11 pages, no figures

The QCD topological observables are essential inputs to obtain theoretical predictions about axion phenomenology, which are of utmost importance for current and future experimental searches for this particle. Among them, we focus on the topological susceptibility, related to the axion mass. We present lattice results for the topological susceptibility in QCD at high temperatures obtained by discretizing this observable via spectral projectors on eigenmodes of the staggered Dirac operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral discretization is motivated by the large lattice artifacts affecting the standard gluonic susceptibility, related to the choice of non-chiral fermions in the lattice action., Comment: 6 pages, 3 eps figures, Proceedings of the 41st International Conference on High Energy physics, ICHEP2022, 6th-13th July, 2022, Bologna, Italy

This letter is about confinement in QCD. At the moment we have pictures of confinement to complete our understanding of the physics of strongly interacting particles, interaction which asks for confinement. As it is said in [1] : " In principle it should be possible to derive the confinement hypothesis from the QCD Lagrangian. At this time, no rigorous derivation exists, so it is not absolutely clear that the confinement hypothesis is a bone fide prediction of QCD" . In this letter we show that a sufficient (of course not necessary) condition for confinement is that topological structure of vacuum in Nature does not correspond to the $\theta$-vacuum. Therefore, if different vacua with nontrivial winding number cannot be connected by tunneling, we obtain confinement as a consequence., Comment: 10 pages