Search

Let $m,n,s,k$ be four integers such that $1\leqslant s \leqslant n$, $1\leqslant k\leqslant m$ and $ms=nk$. A signed magic array $SMA(m,n; s,k)$ is an $m\times n$ partially filled array whose entries belong to the subset $\Omega\subset \mathbb{Z}$, where $\Omega=\{0,\pm 1, \pm 2,\ldots, \pm (nk-1)/2\}$ if $nk$ is odd and $\Omega=\{\pm 1, \pm 2, \ldots, \pm nk/2\}$ if $nk$ is even, satisfying the following requirements: $(a)$ every $\omega \in \Omega$ appears once in the array; $(b)$ each row contains exactly $s$ filled cells and each column contains exactly $k$ filled cells; $(c)$ the sum of the elements in each row and in each column is $0$. In this paper we construct these arrays when $n$ is even and $s,k\geqslant 5$ are odd coprime integers. This allows us to give necessary and sufficient conditions for the existence of an $SMA(m,n; s,k)$ for all admissible values of $m,n,s,k$.

A $\Gamma$-magic rectangle set $\mathrm{MRS}_\Gamma (a, b; c)$ is a collection of $c$ arrays of size $a\times b$ whose entries are the elements of an abelian group $\Gamma$ of order $abc$, each one appearing once and in a unique array in such a way that the sum of the elements of each row is equal to a constant $\omega \in \Gamma$ and the sum of the elements of each column is equal to a constant $\delta \in \Gamma$. In this paper we provide new evidences for the validity of a conjecture proposed by Sylwia Cichacz and Tomasz Hinc on the existence of an $\mathrm{MRS}_\Gamma(a,b;c)$. We also generalize this problem, describing constructions of $\Gamma$-magic rectangle sets, whose elements are partially filled arrays.

In this paper we introduce Y, a new-generation digital twin designed to replicate an online social media platform. Digital twins are virtual replicas of physical systems that allow for advanced analyses and experimentation. In the case of social media, a digital twin such as Y provides a powerful tool for researchers to simulate and understand complex online interactions. {\tt Y} leverages state-of-the-art Large Language Models (LLMs) to replicate sophisticated agent behaviors, enabling accurate simulations of user interactions, content dissemination, and network dynamics. By integrating these aspects, Y offers valuable insights into user engagement, information spread, and the impact of platform policies. Moreover, the integration of LLMs allows Y to generate nuanced textual content and predict user responses, facilitating the study of emergent phenomena in online environments. To better characterize the proposed digital twin, in this paper we describe the rationale behind its implementation, provide examples of the analyses that can be performed on the data it enables to be generated, and discuss its relevance for multidisciplinary research., Comment: 29 pages, 5 figures

Recommendation systems and assistants (in short, recommenders) are ubiquitous in online platforms and influence most actions of our day-to-day lives, suggesting items or providing solutions based on users' preferences or requests. This survey analyses the impact of recommenders in four human-AI ecosystems: social media, online retail, urban mapping and generative AI ecosystems. Its scope is to systematise a fast-growing field in which terminologies employed to classify methodologies and outcomes are fragmented and unsystematic. We follow the customary steps of qualitative systematic review, gathering 144 articles from different disciplines to develop a parsimonious taxonomy of: methodologies employed (empirical, simulation, observational, controlled), outcomes observed (concentration, model collapse, diversity, echo chamber, filter bubble, inequality, polarisation, radicalisation, volume), and their level of analysis (individual, item, model, and systemic). We systematically discuss all findings of our survey substantively and methodologically, highlighting also potential avenues for future research. This survey is addressed to scholars and practitioners interested in different human-AI ecosystems, policymakers and institutional stakeholders who want to understand better the measurable outcomes of recommenders, and tech companies who wish to obtain a systematic view of the impact of their recommenders.

Following recent policy changes by X (Twitter) and other social media platforms, user interaction data has become increasingly difficult to access. These restrictions are impeding robust research pertaining to social and political phenomena online, which is critical due to the profound impact social media platforms may have on our societies. Here, we investigate the reliability of polarization measures obtained from different samples of social media data by studying the structural polarization of the Polish political debate on Twitter over a 24-hour period. First, we show that the political discussion on Twitter is only a small subset of the wider Twitter discussion. Second, we find that large samples can be representative of the whole political discussion on a platform, but small samples consistently fail to accurately reflect the true structure of polarization online. Finally, we demonstrate that keyword-based samples can be representative if keywords are selected with great care, but that poorly selected keywords can result in substantial political bias in the sampled data. Our findings demonstrate that it is not possible to measure polarization in a reliable way with small, sampled datasets, highlighting why the current lack of research data is so problematic, and providing insight into the practical implementation of the European Union's Digital Service Act which aims to improve researchers' access to social media data.

We study the isoperimetric problem for capillary surfaces with a general contact angle $\theta \in (0, \pi)$, outside convex infinite cylinders with arbitrary two-dimensional convex section. We prove that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. In this class of convex sets, our result extends for the first time the well-known Choe-Ghomi-Ritor\'e relative isoperimetric inequality, corresponding to the case $\theta = \pi/2$, to general angles.

We study the asymptotic behavior of the volume preserving mean curvature and the Mullins-Sekerka flat flow in three dimensional space. Motivated by this we establish a 3D sharp quantitative version of the Alexandrov inequality for $C^2$-regular sets with a perimeter bound.

The emergence of Centralized-RAN (C-RAN) has revolutionized mobile network infrastructure, offering streamlined cell-site engineering and enhanced network management capabilities. As C-RAN gains momentum, the focus shifts to optimizing fronthaul links. While fiber fronthaul guarantees performance, wireless alternatives provide cost efficiency and scalability, making them preferable in densely urbanized areas. However, wireless fronthaul often requires expensive over-dimensioning to overcome the challenging atmospheric attenuation typical of high frequencies. We propose a framework designed to continuously align radio access capacity with fronthaul link quality to overcome this rigidity. By gradually adapting radio access capacity to available fronthaul capacity, the framework ensures smooth degradation rather than complete service loss. Various strategies are proposed, considering factors like functional split and beamforming technology and exploring the tradeoff between adaptation strategy complexity and end-to-end system performance. Numerical evaluations using experimental rain attenuation data illustrate the framework's effectiveness in optimizing radio access capacity under realistically variable fronthaul link quality, ultimately proving the importance of adaptive capacity management in maximizing C-RAN efficiency.

This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in [Curtis2019, Curtis2022]. A theoretical analysis that complements the results in the literature is presented, and the issue of tuning the involved hyper-parameters is investigated. Our study also focuses on a practical version of the method, which computes the stochastic gradient by means of the inner product test and the orthogonality test proposed by Bollapragada et al. in [Bollapragada2018]. It is shown experimentally that this implementation improves the performance of TRish and reduces its sensitivity to the choice of the hyper-parameters.

Industrial datapath designers consider dynamic power consumption to be a key metric. Arithmetic circuits contribute a major component of total chip power consumption and are therefore a common target for power optimization. While arithmetic circuit area and dynamic power consumption are often correlated, there is also a tradeoff to consider, as additional gates can be added to explicitly reduce arithmetic circuit activity and hence reduce power consumption. In this work, we consider two forms of power optimization and their interaction: circuit area reduction via arithmetic optimization, and the elimination of redundant computations using both data and clock gating. By encoding both these classes of optimization as local rewrites of expressions, our tool flow can simultaneously explore them, uncovering new opportunities for power saving through arithmetic rewrites using the e-graph data structure. Since power consumption is highly dependent upon the workload performed by the circuit, our tool flow facilitates a data dependent design paradigm, where an implementation is automatically tailored to particular contexts of data activity. We develop an automated RTL to RTL optimization framework, ROVER, that takes circuit input stimuli and generates power-efficient architectures. We evaluate the effectiveness on both open-source arithmetic benchmarks and benchmarks derived from Intel production examples. The tool is able to reduce the total power consumption by up to 33.9%.

Social media platforms are online fora where users engage in discussions, share content, and build connections. This review explores the dynamics of social interactions, user-generated contents, and biases within the context of social media analysis (analyzing works that use the tools offered by complex network analysis and natural language processing) through the lens of three key points of view: online debates, online support, and human-AI interactions. On the one hand, we delineate the phenomenon of online debates, where polarization, misinformation, and echo chamber formation often proliferate, driven by algorithmic biases and extreme mechanisms of homophily. On the other hand, we explore the emergence of online support groups through users' self-disclosure and social support mechanisms. Online debates and support mechanisms present a duality of both perils and possibilities within social media; perils of segregated communities and polarized debates, and possibilities of empathy narratives and self-help groups. This dichotomy also extends to a third perspective: users' reliance on AI-generated content, such as the ones produced by Large Language Models, which can manifest both human biases hidden in training sets and non-human biases that emerge from their artificial neural architectures. Analyzing interdisciplinary approaches, we aim to deepen the understanding of the complex interplay between social interactions, user-generated content, and biases within the realm of social media ecosystems.

We consider here a fully discrete variant of the implicit variational scheme for mean curvature flow [AlmTayWan,LucStu], in a setting where the flow is governed by a crystalline surface tension defined by the limit of pairwise interactions energy on the discrete grid. The algorithm is based on a new discrete distance from the evolving sets, which prevents the occurrence of the spatial drift and pinning phenomena identified in [BraGelNov] in a similar discrete framework. We provide the first rigorous convergence result holding in any dimension, for any initial set and for a large class of purely crystalline anisotropies, in which the spatial discretization mesh can be of the same order or coarser than the time step.

The spectrum crunch challenge poses a vital threat to the progress of cellular networks and recently prompted the inclusion of millimeter wave (mmWave) and Upper 6GHz (U6G) in the 3GPP standards. These two bands promise to unlock a large portion of untapped spectrum, but the harsh propagation due to the increased carrier frequency might negatively impact the performance of urban Radio Access Network (RAN) deployments. Within the span of a year, two co-located 5G networks operating in these frequency bands were deployed at Politecnico di Milano, Milan, Italy, entirely dedicated to the dense urban performance assessment of the two systems. This paper presents an in-depth analysis of the measurement campaigns conducted on them, with the U6G campaign representing the first of its kind. A benchmark is provided by ray-tracing simulations. The results suggest that networks operating in these frequency bands provide good indoor and outdoor coverage and throughput in urban scenarios, even when deployed in the macro base station setup common to lower frequencies. In addition, a comparative performance analysis of these two key technologies is provided, offering insights on their relative strengths, weaknesses and improvement margins and informing on which bands is better suited for urban macro coverage.

We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when the evaluation of both the function and its gradient is random and a specified accuracy of such evaluations is guaranteed with sufficiently high probability. The proposed algorithm combines the Inexact Restoration framework with a trust-region methodology based on random first-order models. We analyse the properties of the algorithm and provide the expected number of iterations performed to reach an approximate first-order optimality point. Numerical experiments show that the proposed algorithm compares well with a state-of-the-art competitor.

Dual-comb spectroscopy is a powerful technique to measure optical spectra in a wide spectral range with high-frequency resolution. The development of compact systems operating in the long-wave infrared wavelength range is of high interest for spectroscopic and sensing applications. Amongst the different techniques to obtain optical frequency-combs, electro-optic frequency-comb generation presents major advantages thanks to the tunable repetition rate only limited by the bandwidth of the used electro-optical modulator. However, the development of integrated and efficient electro-optical modulators operating in a wide long-wave infrared spectral band is still at its infancy, and electro-optical frequency-comb has not been demonstrated so far beyond the telecom band. In this work, a Schottky-based modulator embedded in a Ge-rich graded SiGe waveguide is used for electro-optic frequency-comb generation. Considering the limited efficiency of the modulator, harmonically-rich RF signals are used to enhance the generation of comb lines around the optical carrier. Interestingly, this allows us to demonstrate the generation of electro-optical combs spanning over 2.4 GHz around 8 {\mu}m wavelength. This paves the way towards fully integrated and tunable mid-infrared electro-optic frequency-comb generation systems., Comment: 10 pages, 9 figures

The flatness of electro-optic frequency combs (EOFCs) generated in a single silicon ring resonator modulator (RRM) is optimized by employing harmonic superposition of the radio-frequency driving signal. A differential evolution algorithm is employed in conjunction with a simplified model of the RRM for offline optimization of the amplitudes and phases of harmonic driving signals and the operating point of the RRM. The optimized driving signals are then applied to a silicon RRM. EOFCs containing 7 and 9 lines are synthesized with a power imbalance between the lines of 2.9 dB and 5.4 dB, respectively, compared to 9.4 dB for an optimized 5-line comb generated from a single sinusoidal driving signal., Comment: 4 pages, 5 figures, submitted to Optics Letters

An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this random approximation technique does not affect the method's convergence nor its evaluation complexity for the search of an $\epsilon$-approximate first-order critical point, which is $\mathcal{O}(\epsilon^{-(p+1)/p})$, where $p$ is the order of derivatives used. A variant of the algorithm using approximate Hessian matrices is also analyzed and shown to require at most $\mathcal{O}(\epsilon^{-2})$ evaluations. Preliminary numerical tests show that the random-subspace technique can significantly improve performance on some problems, albeit, unsurprisingly, not for all., Comment: 23 pages

A comparison theorem by Choe, Ghomi and Ritor\'e states that the exterior isoperimetric profile $I_\mathcal{C}$ of any convex body $\mathcal{C}$ in $\mathbb{R}^N$ lies above that of any half-space $H$. We characterize convex bodies such that $I_\mathcal{C}\equiv I_H$ in terms of a notion of "maximal affine dimension at infinity'', briefly called the asymptotic dimension $d^*(\mathcal{C})$ of $\mathcal{C}$. More precisely, we show that $I_\mathcal{C}\equiv I_H$ if and only if $d^*(\mathcal{C})\ge N-1$. We also show that if $d^*(\mathcal{C})\le N-2$, then, for large volumes, $I_\mathcal{C}$ is asymptotic to the isoperimetric profile of $\mathbb{R}^N$. We then estimate, in terms of $d^*(\mathcal{C})$-dependent power laws, the order as $v\to\infty$ of the difference between $I_\mathcal{C}$ and the isoperimetric profile of $\mathbb{R}^N$.

We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and inexact Newton methods for nonlinear systems of equations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented.

Formal verification of datapath circuits is challenging as they are subject to intense optimization effort in the design phase. Industrial vendors and design companies deploy equivalence checking against a golden or existing reference design to satisfy correctness concerns. State-of-the-art datapath equivalence checking tools deploy a suite of techniques, including rewriting. We propose a rewriting framework deploying bitwidth dependent rewrites based on the e-graph data structure, providing a powerful assistant to existing tools. The e-graph can generate a path of rewrites between the reference and implementation designs that can be checked by a trusted industry tool. We will demonstrate how the intermediate proofs generated by the assistant enable convergence in a state of the art tool, without which the industrial tool runs for 24 hours without making progress. The intermediate proofs automatically introduced by the assistant also reduce the total proof runtime by up to 6x.

Social Network sites are fertile ground for several polluting phenomena affecting online and offline spaces. Among these phenomena are included echo chambers, closed systems in which the opinions expressed by the people inside are exacerbated for the effect of the repetition, while opposite views are actively excluded. This paper offers a framework to explore, in a platform-independent manner, the topological changes through time of echo chambers, while considering the content posted by users and the attitude conveyed in discussing specific controversial issues. The proposed framework consists of four steps: (i) data collection and annotation of users' ideology regarding a controversial topic, (ii) construction of a dynamic network of interactions, (iii) ECs extraction and analysis of their dynamics, and (iv) topic extraction and valence analysis. The paper then enhances the formalization of the framework by conducting a case study on Reddit threads about sociopolitical issues (gun control, American politics, and minorities discrimination) during the first two years and a half of Donald Trump's presidency. The results unveil that users often stay inside echo chambers over time. Furthermore, in the analyzed discussions, the focus is on controversies related to right-wing parties and specific events in American and Canadian politics. The analysis of the attitude conveyed in the discussions shows a slight inclination toward a more negative or neutral attitude when discussing particularly sensitive issues, such as fascism, school shootings, or police violence., Comment: 25 pages

The emergence of new public forums in the shape of online social media has introduced unprecedented challenges to public discourse, including polarization, misinformation, and the emergence of echo chambers. While existing research has extensively studied the behavior of active users within echo chambers, little attention has been given to the hidden audience, also known as lurkers, who passively consume content without actively engaging. This study aims to estimate the share of the hidden audience and investigate their interplay with the echo chamber effect. Using Twitter as a case study, we analyze a polarized political debate to understand the engagement patterns and factors influencing the hidden audience's presence. Our findings reveal a relevant fraction of users that consume content without active interaction, which underscores the importance of considering their presence in online debates. Notably, our results indicate that the engagement of the hidden audience is primarily influenced by factors such as the reliability of media sources mentioned in tweets rather than the ideological stance of the user that produced the content. These findings highlight the need for a comprehensive understanding of the hidden audience's role in online debates and how they may influence public opinion., Comment: This work is the output of the Complexity72h workshop, held at the IFISC in Palma, Spain, 26-30 June 2023. https://www.complexity72h.com. The document contains 12 pages, including one of supplementary information, and it has 5 figures in the main text and 1 in the supplementary information

In this paper we introduce the notion of parabolic $\alpha$-Riesz flow, for $\alpha\in(0,d)$, extending the notion of $s$-fractional heat flows to negative values of the parameter $s=-\frac{\alpha}{2}$. Then, we determine the limit behaviour of these gradient flows as $\alpha \to 0^+$ and $\alpha \to d^-$. To this end we provide a preliminary $\Gamma$-convergence expansion for the Riesz interaction energy functionals. Then we apply abstract stability results for uniformly $\lambda$-convex functionals which guarantee that $\Gamma$-convergence commutes with the gradient flow structure.

In this paper we show for the first time the phenomenon of negative reflection in a simple mechanical structure. The latter is a grating of fixed inclusions embedded in a linear elastic matrix. Numerical analyses for out-of-plane shear waves demonstrate that there exist frequencies at which most of the incident energy is reflected at negative angles. The effect is symmetric with respect to a line that is not parallel to the normal direction to the grating structure. Simulations at different angles of incidence and computations of the energy fluxes show that negative reflection is achievable in a wide range of loading conditions., Comment: 9 pages, 4 figures, 1 link to a video