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We study the effect of paternity leave on early child development. We collect sur-vey data on 5,000 children under age six in Spain and exploit several extensions of paternity leave that took place between 2017 and 2021. We follow a differences-in-discontinuities research design, based on the date of birth of each child and using cohorts born in non-reform years as controls. We show that the extensions led to significant increases in the length of leave taken by fathers, without affecting that of mothers, thus increasing parental time at home in the first year after birth. Eligibility for four additional weeks of paternity leave led to a significant 12 percentage-point increase in the fraction of children with developmental delays. We provide evidence for two potential mechanisms. First, children exposed to longer paternity leave spend less time alone with their mother, and more time with their father, during their first year of life. Second, treated children use less formal childcare. Our results suggest that paternity leave replaces higher-quality modes of early care. We conclude that the effects of parental leave policies on children depend crucially on the quality of parental versus counterfactual modes of childcare. [Funding for this report was provided by the Spanish Agencia Estatal de Investigación (AEI) and the Spanish Ministry of Science, Innovation and Universities.]

In recent years, the fifth-generation (5G) mobile network has been developed worldwide to remarkably improve network performance and spectral efficiency. Very recently, reconfigurable intelligent surfaces (RISs) technology has emerged as an innovative solution for controlling the propagation medium of the forthcoming sixth-generation (6G) networks. Specifically, RIS takes advantage of the reflected rays on the propagation environment to redirect them to a desired target, improving wireless coverage. To further improve RIS performance, an interesting technique called synchronized transmission with advanced reconfigurable surfaces (STARS) has appeared to allow simultaneous transmission and reflection of intelligent omni-surfaces. With that in mind, this paper introduces an enhanced strategy for the network planning of 5G and beyond (B5G) mobile networks in dense urban scenarios focused on the city of Quito-Ecuador. The efficacy of RIS and its cutting-edge STARS concept is emphasized, providing useful insights into coverage, quality, and throughput results. In particular, this work considers the 3.5/28 GHz frequency bands, optimizing the radio network and anticipating their applicability in B5G networks. Finally, simulation results are also shown, which allow the identification of the benefits of STAR RIS in terms of coverage, signal quality, and data performance., Comment: 6 pages, 12 figures, 2024 IEEE 29th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), presented in Session 11: Federation of 6G Infrastructures and Experimentation Facilities in a Network of Networks, October 22th - 2024

Operational data in next-generation networks offers a valuable resource for Mobile Network Operators to autonomously manage their systems and predict potential network issues. Machine Learning and Digital Twin can be applied to gain important insights for intelligent decision-making. This paper proposes a framework for Radio Frequency planning and failure detection using Digital Twin reducing the level of manual intervention. In this study, we propose a methodology for analyzing Radio Frequency issues as external interference employing clustering techniques in operational networks, and later incorporating this in the planning process. Simulation results demonstrate that the architecture proposed can improve planning operations through a data-aided anomaly detection strategy.

Nearly K\"ahler and Einstein structures admit a variational characterization, where the second variation is associated with a strongly elliptic operator. This allows us to associate a Morse-like index to each structure. Our study focuses on how these indices behave under the assumption that the nearly K\"ahler structure admits a cohomogeneity one action. Specifically, we investigate elements of the index that also exhibit cohomogeneity one symmetry, reducing the analysis to an ODE eigenvalue problem. We apply our discussion to the two inhomogeneous examples constructed by Foscolo and Haskins. We obtain non-trivial lower bounds on the Hitchin index and Einstein co-index for the inhomogeneous nearly K\"ahler structure on $S^3\times S^3$, answering a question of Karigiannis and Lotay., Comment: 24 pages. Corrected the statements of Lemma 2.15 and Prop. 2.16 from the previous version. No impact on the main resuts of the paper

We investigate generalisations of Hitchin's functionals, whose critical points correspond to nearly K\"ahler and nearly parallel $G_2$-structures. Our focus is on the gradient flow of these functionals and the spectral decomposition of their Hessians with respect to natural indefinite inner products. We introduce a Morse-like index for these functionals, termed the Hitchin index. We prove this index provides a lower bound for the Einstein co-index and explore its relationship with the deformation theory of $G_2$- and $\operatorname{Spin}(7)$-conifolds., Comment: 36 pages; minor typos and references corrected

Goldman defined a symplectic form on the smooth locus of the $G$-character variety of a closed, oriented surface $S$ for a Lie group $G$ satisfying very general hypotheses. He then studied the Hamiltonian flows associated to $G$-invariant functions $G \to \mathbb R$ obtained by evaluation on a simple closed curve and proved that they are generalized twist flows. In this article, we investigate the Hamiltonian flows on (subsets of the) $G$-character variety induced by evaluating a $G$-invariant multi-function $G^k \to \mathbb R$ on a tuple $ \underline{\alpha} \in \pi_1(S)^k$. We introduce the notion of a subsurface deformation along a supporting subsurface $S_0$ for $\underline{\alpha}$ and prove that the Hamiltonian flow of an induced invariant multi-function is of this type. We also give a formula for the Poisson bracket between two functions induced by invariant multi-functions and prove that they Poisson commute if their supporting subsurfaces are disjoint. We give many examples of functions on character varieties that arise in this way and discuss applications, for example, to the flow associated to the trace function for non-simple closed curves on $S$., Comment: 66 pages, 13 figures, comments welcome!

We fully describe all horocycle orbit closures in $ \mathbb{Z} $-covers of compact hyperbolic surfaces. Our results rely on a careful analysis of the efficiency of all distance minimizing geodesic rays in the cover. As a corollary we obtain in this setting that all non-maximal horocycle orbit closures, while fractal, have integer Hausdorff dimension., Comment: 55 pages, 8 figures

We study the geometry of hyperconvex representations of surface groups in ${\rm PSL}(d,\mathbb{C})$ and their deformation spaces: We produce a natural holomorphic extension of the classical Ahlfors--Bers map to a product of Teichm\"uller spaces of a canonical Riemann surface lamination and prove that the limit set of a hyperconvex representation in the full flag space has Hausdorff dimension 1 if and only if the representation is conjugate in ${\rm PSL}(d,\mathbb{R})$., Comment: 70 pages. Comments are welcome!

Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably the most powerful preconditioner for Poisson's equation, and its effectiveness results from the complementary roles played by the smoother, responsible for damping high-frequency error components, and the coarse-grid correction, which in turn reduces low-frequency modes. This work presents several strategies to make AMG more compute-intensive by leveraging reflection, translational and rotational symmetries. AMGR, our final proposal, does not require boundary conditions to be symmetric, therefore applying to a broad range of academic and industrial configurations. It is based on a multigrid reduction framework that introduces an aggressive coarsening to the multigrid hierarchy, reducing the memory footprint, setup and application costs of the top-level smoother. While preserving AMG's excellent convergence, AMGR allows replacing the standard sparse matrix-vector product with the more compute-intensive sparse matrix-matrix product, yielding significant accelerations. Numerical experiments on industrial CFD applications demonstrated up to 70% speed-ups when solving Poisson's equation with AMGR instead of AMG. Additionally, strong and weak scalability analyses revealed no significant degradation.

Deconfined quantum critical points are exotic transition points not predicted by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. They are associated to a one-point gap closing between distinct locally ordered phases, thus to a continuous phase transition. Because of this intrinsic criticality, at deconfined quantum critical points algebraic decay of all the correlation functions is expected. Here, we show that it is possible to go beyond this assumption. Specifically, we consider one dimensional interacting fermions where the phenomenon of spin-charge separation arises. We first explore the low energy regimes where a sine-Gordon Hamiltonian can provide accurate results. By means of a field theory approach we find that continuous phase transitions between different locally ordered phases can occur. As a consequence of the decoupled spin and charge degrees of freedom, we find that in two cases only one gap vanishes while the other remains finite. We then derive a microscopic model where such phase transitions take place. By performing a numerical analysis, we unambiguously find that deconfined quantum critical points can indeed be further characterized by the long-range order of a parity operator signaling the presence of a finite gap. Our results provide new interesting insights on the widely investigated topic of quantum phase transitions., Comment: 12 pages, 6 figures

This work delivers a novel user-server authentication procedure exploiting the features of maximally entangled pairs in both an idealistic noiseless scenario and a moderately noisy one. Additionally, we leverage the specific features of our design, which are conveniently suited for inlaying it into the well known BB84 quantum communication protocol. We first define a trivial extension of our initial proposal allowing for such task (symmetric scheme) to then come up with what we denote as asymmetric scheme, better matching practicality. Furthermore, a realistic simulation of the user-server authentication protocol has been achieved by employing a noisy model for both transmission and storage, the latter relying on cavity-enhanced atomic-frequency comb (AFC) memories. While in a noiseless scenario our proposal is ensured to be airtight, considering a certain degree of noise poses a challenge when aiming to actually implement it. We have implemented a deep neural network to distinguish legitimate users from forgery attempts, outperforming a mere statistical approach designed for the same task. Such method achieved a success rate of 0.75 with storage times of $1$ $\mu s$ and a user-server distance of $10$ km., Comment: 11 pages, 5 figures

Recent work [Sachdeva et al.] presented an iterative hybrid quantum variational optimization algorithm designed by Q-CTRL and executed on IBM gate-based quantum processing units (QPUs), claiming a significant performance advantage against a D-Wave quantum annealer. Here we point out major methodological problems with this comparison. Using a simple unoptimized workflow for quantum annealing, we show success probabilities multiple orders of magnitude higher than those reported by [Sachdeva et al.]. These results, which can be reproduced using open-source code and free trial access to a D-Wave quantum annealer, contradict Q-CTRL's claims of superior performance. We also provide a direct comparison between quantum annealing and a recent demonstration of digitized quantum annealing on an IBM processor, showing that analog quantum annealing on a D-Wave QPU reaches far lower energies than digitized quantum annealing on an IBM QPU.

We address a conjecture of Mirzakhani about the statistical behavior of certain expanding families of ``twist tori'' in the moduli space of hyperbolic surfaces, showing that they equidistribute to a certain Lebesgue-class measure along almost all sequences. We also identify a number of other expanding families of twist tori whose limiting distributions are mutually singular to Lebesgue., Comment: 22 pages, 8 figures. Comments Welcome!

Current datasets for long-form video understanding often fall short of providing genuine long-form comprehension challenges, as many tasks derived from these datasets can be successfully tackled by analyzing just one or a few random frames from a video. To address this issue, we present a novel dataset and benchmark, CinePile, specifically designed for authentic long-form video understanding. This paper details our innovative approach for creating a question-answer dataset, utilizing advanced LLMs with human-in-the-loop and building upon human-generated raw data. Our comprehensive dataset comprises 305,000 multiple-choice questions (MCQs), covering various visual and multimodal aspects, including temporal comprehension, understanding human-object interactions, and reasoning about events or actions within a scene. Additionally, we fine-tuned open-source Video-LLMs on the training split and evaluated both open-source and proprietary video-centric LLMs on the test split of our dataset. The findings indicate that although current models underperform compared to humans, fine-tuning these models can lead to significant improvements in their performance., Comment: Project page with all the artifacts - https://ruchitrawal.github.io/cinepile/. Updated version with adversarial refinement pipeline and more model evaluations

In this work, we present two new methods for Variational Quantum Circuit (VQC) Process Tomography onto $n$ qubits systems: PT_VQC and U-VQSVD. Compared to the state of the art, PT_VQC halves in each run the required amount of qubits for process tomography and decreases the required state initializations from $4^{n}$ to just $2^{n}$, all while ensuring high-fidelity reconstruction of the targeted unitary channel $U$. It is worth noting that, for a fixed reconstruction accuracy, PT_VQC achieves faster convergence per iteration step compared to Quantum Deep Neural Network (QDNN) and tensor network schemes. The novel U-VQSVD algorithm utilizes variational singular value decomposition to extract eigenvectors (up to a global phase) and their associated eigenvalues from an unknown unitary representing a general channel. We assess the performance of U-VQSVD by executing an attack on a non-unitary channel Quantum Physical Unclonable Function (QPUF). U-VQSVD outperforms an uninformed impersonation attack (using randomly generated input states) by a factor of 2 to 5, depending on the qubit dimension. For the two presented methods, we propose a new approach to calculate the complexity of the displayed VQC, based on what we denote as optimal depth.

We study surface subgroups of $\mathrm{SL}(4,\mathbb R)$ acting convex cocompactly on $\mathbb R \textrm P^3$ with image in the coaffine group. The boundary of the convex core is stratified, and the one dimensional strata form a pair of bending laminations. We show that the bending data on each component consist of a convex $\mathbb R \textrm P^2$ structure and an affine measured lamination depending on the underlying convex projective structure on $S$ with (Hitchin) holonomy $\rho: \pi_1S \to \mathrm{SL}(3,\mathbb R)$. We study the space $\mathcal {ML}^\rho(S)$ of bending data compatible with $\rho$ and prove that its projectivization is a sphere of dimension $6g-7$., Comment: 51 pages, 6 figures, Comments welcome! V2: minor revisions

Physical Unclonable Functions (PUFs) leverage inherent, non-clonable physical randomness to generate unique input-output pairs, serving as secure fingerprints for cryptographic protocols like authentication. Quantum PUFs (QPUFs) extend this concept by using quantum states as input-output pairs, offering advantages over classical PUFs, such as challenge reusability via public channels and eliminating the need for trusted parties due to the no-cloning theorem. Recent work introduced a generalized mathematical framework for QPUFs. It was shown that random unitary QPUFs cannot achieve existential unforgeability against Quantum Polynomial Time (QPT) adversaries. Security was possible only with additional uniform randomness. To avoid the cost of external randomness, we propose a novel measurement-based scheme. Here, the randomness naturally arises from quantum measurements. Additionally, we introduce a second model where the QPUF functions as a nonunitary quantum channel, which guarantees existential unforgeability. These are the first models in the literature to demonstrate a high level of provable security. Finally, we show that the Quantum Phase Estimation (QPE) protocol, applied to a Haar random unitary, serves as an approximate implementation of the second type of QPUF by approximating a von Neumann measurement on the unitary's eigenbasis., Comment: 20 pages, 6 figures

Large Language Models (LLMs) are already as persuasive as humans. However, we know very little about how they do it. This paper investigates the persuasion strategies of LLMs, comparing them with human-generated arguments. Using a dataset of 1,251 participants in an experiment, we analyze the persuasion strategies of LLM-generated and human-generated arguments using measures of cognitive effort (lexical and grammatical complexity) and moral-emotional language (sentiment and moral analysis). The study reveals that LLMs produce arguments that require higher cognitive effort, exhibiting more complex grammatical and lexical structures than human counterparts. Additionally, LLMs demonstrate a significant propensity to engage more deeply with moral language, utilizing both positive and negative moral foundations more frequently than humans. In contrast with previous research, no significant difference was found in the emotional content produced by LLMs and humans. These findings contribute to the discourse on AI and persuasion, highlighting the dual potential of LLMs to both enhance and undermine informational integrity through communication strategies for digital persuasion.

Spontaneously symmetry-broken (SSB) phases are locally ordered states of matter characterizing a large variety of physical systems. Because of their specific ordering, their presence is usually witnessed by means of local order parameters. Here, we propose an alternative approach based on statistical correlations of noise after the ballistic expansion of an atomic cloud. We indeed demonstrate that probing such noise correlators allows one to discriminate among different SSB phases characterized by spin-charge separation. As a particular example, we test our prediction on a 1D extended Fermi-Hubbard model, where the competition between local and nonlocal couplings gives rise to three different SSB phases: a charge density wave, a bond-ordering wave, and an antiferromagnet. Our numerical analysis shows that this approach can accurately capture the presence of these different SSB phases, thus representing an alternative and powerful strategy to characterize strongly interacting quantum matter., Comment: 5 pages, 3 figures, and Supplemental Material. Accepted version of the manuscript

We study the geometry of hyperconvex representations of hyperbolic groups in ${\rm PSL}(d,\mathbb{C})$ and establish two structural results: a group admitting a hyperconvex representation is virtually isomorphic to a Kleinian group, and its hyperconvex limit set in the appropriate flag manifold has Hausdorff dimension strictly smaller than $2$., Comment: 23 pages. Minor revision, corrected a small inaccuracy in the proof of Proposition 4.16

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. One such problem is the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum phase transition. State-of-the-art classical simulations demand resources that grow exponentially with system size. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schr\"odinger equation. We demonstrate area-law scaling of entanglement in the model quench in two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for classical approaches. We assess approximate methods based on tensor networks and neural networks and conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that classical computers cannot.

We study Thouless pumps, i.e., adiabatic topological transport, in an interacting spin chain described by the dimerized XXZ Hamiltonian. In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In contrast, here we show that, in the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity. We illustrate the robustness of these exotic Thouless pumps through the behavior of the noninteracting singularity, which for sufficiently strong interactions splits into two singularities separated by a spontaneous antiferromagnetic insulator. We perform a numerical benchmark of these phenomena by means of tensor network simulations of ground-state physics and real-time adiabatic dynamics. Finally, we propose an experimental protocol with Floquet-driven Rydberg tweezer arrays., Comment: 7.5 pages, 5 figures. Revised version published in Physical Review A

Amorphous solids, i.e., systems which feature well-defined short-range properties but lack long-range order, constitute an important research topic in condensed matter. While their microscopic structure is known to differ from their crystalline counterpart, there are still many open questions concerning the emergent collective behavior in amorphous materials. This is particularly the case in the quantum regime, where the numerical simulations are extremely challenging. In this article, we instead propose to explore amorphous quantum magnets with an analog quantum simulator. To this end, we first present an algorithm to generate amorphous quantum magnets, suitable for Rydberg simulators of the Ising model. Subsequently, we use semiclassical approaches to get a preliminary insight of the physics of the model. In particular, for ferromagnetic interactions, we calculate mean-field phase diagrams, and use the linear-spin-wave theory to study localization properties and dynamical structure factors of the excitations. For antiferromagnetic interactions, we show that amorphous magnets exhibit a complex classical energy landscape by means of simulated annealing. Finally, we outline an experimental proposal based on Rydberg atoms in programmable tweezer arrays, thus opening the road towards the study of amorphous quantum magnets in regimes difficult to simulate classically., Comment: 10.5 pages, 8 figures

In a previous paper, the authors extended Mirzakhani's (almost-everywhere defined) measurable conjugacy between the earthquake and horocycle flows to a measurable bijection. In this one, we analyze the continuity properties of this map and its inverse, proving that both are continuous at many points and in many directions. This lets us transfer measure convergence between the two systems, allowing us to pull back results from Teichm{\"u}ller dynamics to deduce analogous statements for the earthquake flow., Comment: 64 pages plus references and index, 19 figures

In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metriplectic representation of the dynamics allows us to describe the conservation of energy, as well as to guarantee entropy production. Moreover, we describe the use of discrete gradient systems to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate., Comment: 14 pages, 5 figures

Smart grid interoperability is the means to achieve the twin green and digital transition but re-mains heterogeneous and fragmented to date. This work presents the first ideas and corner-stones of an Interoperability Roadmap for the Energy Transition that is being developed by the Horizon Europe int:net project. This roadmap builds on four cornerstones that address open interoperability issues. These are a knowledge base to address the lack of convergence among existing initiatives, a maturity model and a network of testing and certification facilities to ad-dress the lack of practical tools for the industry, and a governance process to address the gap between standards-related approaches of Standards Development Organisations and Research and Innovation projects. A community of practice will be set up to ensure the continuity of the ongoing activities related to smart grid interoperability. To outlive the duration of the int:net project, the aim is to formalise the community of practice as a legal entity., Comment: 12. (Hybrid) Symposium Communications for Energy Systems (ComForEn 2023)

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbour interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbour repulsion becomes sizeable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously-symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of non-local interactions, geometrical frustration, and quantum fluctuations., Comment: 7+3 pages, 3+3 figures