Search

The effective design of patrol strategies is a difficult and complex problem, especially in medium and large areas. The objective is to plan, in a coordinated manner, the optimal routes for a set of patrols in a given area, in order to achieve maximum coverage of the area, while also trying to minimize the number of patrols. In this paper, we propose a multi-agent reinforcement learning (MARL) model, based on a decentralized partially observable Markov decision process, to plan unpredictable patrol routes within an urban environment represented as an undirected graph. The model attempts to maximize a target function that characterizes the environment within a given time frame. Our model has been tested to optimize police patrol routes in three medium-sized districts of the city of Malaga. The aim was to maximize surveillance coverage of the most crime-prone areas, based on actual crime data in the city. To address this problem, several MARL algorithms have been studied, and among these the Value Decomposition Proximal Policy Optimization (VDPPO) algorithm exhibited the best performance. We also introduce a novel metric, the coverage index, for the evaluation of the coverage performance of the routes generated by our model. This metric is inspired by the predictive accuracy index (PAI), which is commonly used in criminology to detect hotspots. Using this metric, we have evaluated the model under various scenarios in which the number of agents (or patrols), their starting positions, and the level of information they can observe in the environment have been modified. Results show that the coordinated routes generated by our model achieve a coverage of more than $90\%$ of the $3\%$ of graph nodes with the highest crime incidence, and $65\%$ for $20\%$ of these nodes; $3\%$ and $20\%$ represent the coverage standards for police resource allocation.

Crime is one of the greatest threats to urban security. Around 80 percent of the world's population lives in countries with high levels of criminality. Most of the crimes committed in the cities take place in their urban environments. This paper presents the development and validation of a digital shadow platform for modeling and simulating urban crime. This digital shadow has been constructed using data-driven agent-based modeling and simulation techniques, which are suitable for capturing dynamic interactions among individuals and with their environment. Our approach transforms and integrates well-known criminological theories and the expert knowledge of law enforcement agencies (LEA), policy makers, and other stakeholders under a theoretical model, which is in turn combined with real crime, spatial (cartographic) and socio-economic data into an urban model characterizing the daily behavior of citizens. The digital shadow has also been instantiated for the city of Malaga, for which we had over 300,000 complaints available. This instance has been calibrated with those complaints and other geographic and socio-economic information of the city. To the best of our knowledge, our digital shadow is the first for large urban areas that has been calibrated with a large dataset of real crime reports and with an accurate representation of the urban environment. The performance indicators of the model after being calibrated, in terms of the metrics widely used in predictive policing, suggest that our simulated crime generation matches the general pattern of crime in the city according to historical data. Our digital shadow platform could be an interesting tool for modeling and predicting criminal behavior in an urban environment on a daily basis and, thus, a useful tool for policy makers, criminologists, sociologists, LEAs, etc. to study and prevent urban crime.

Photons and optical circuits are among the most promising platforms for implementation of quantum technologies, because of its potential use in quantum computing, quantum cryptography and long-distance quantum communication. One of the main requirements to achieve reliable quantum communications are on-demand sources of highly entangled photon pairs, and semiconductor quantum dots have emerged as prominent candidates to satisfy the necessary conditions of brightness and entanglement fidelity. However, in most cases the biexciton-exciton-vacuum cascade produces a pair of maximally polarization-entangled photons with a dephasing, due to the exciton fine structure splitting. This work focuses on the performance of the E91 quantum key distribution protocol under the variation of two elements: first, the phase in the input state when the protocol is implemented using entangled photons generated via the radiative cascade, and second, the relative directions of the polarization analyzers. We obtain analytical expressions for the protocol's secret key rate and Bell's parameter as functions of the studied phase and angles. Then, we validate those expressions by means of a quantum computational implementation with the IBM's API Qiskit. Our results show that the performance of the quantum transmission is highly impacted by the product between the exciton lifetime and the quantum dot's fine structure splitting and that such an impact may be modulated through the orientation of the polarizers. These findings provide important insight for the scalable implementation of quantum key distribution protocols with quantum dots as entanglement sources., Comment: 5 figures and 10 pages long

Responding to the rapid roll-out and large-scale commercialization of foundation models, large language models, and generative AI, an emerging body of work is shedding light on the myriad impacts these technologies are having across society. Such research is expansive, ranging from the production of discriminatory, fake and toxic outputs, and privacy and copyright violations, to the unjust extraction of labor and natural resources. The same has not been the case in some of the most prominent AI governance initiatives in the global north like the UK's AI Safety Summit and the G7's Hiroshima process, which have influenced much of the international dialogue around AI governance. Despite the wealth of cautionary tales and evidence of algorithmic harm, there has been an ongoing over-emphasis within the AI governance discourse on technical matters of safety and global catastrophic or existential risks. This narrowed focus has tended to draw attention away from very pressing social and ethical challenges posed by the current brute-force industrialization of AI applications. To address such a visibility gap between real-world consequences and speculative risks, this paper offers a critical framework to account for the social, political, and environmental dimensions of foundation models and generative AI. We identify 14 categories of risks and harms and map them according to their individual, social, and biospheric impacts. We argue that this novel typology offers an integrative perspective to address the most urgent negative impacts of foundation models and their downstream applications. We conclude with recommendations on how this typology could be used to inform technical and normative interventions to advance responsible AI., Comment: ACM Conference on Fairness, Accountability, and Transparency (FAccT '24). Association for Computing Machinery, New York, NY, USA, 776-796

AI systems may have transformative and long-term effects on individuals and society. To manage these impacts responsibly and direct the development of AI systems toward optimal public benefit, considerations of AI ethics and governance must be a first priority. In this workbook, we introduce and describe our PBG Framework, a multi-tiered governance model that enables project teams to integrate ethical values and practical principles into their innovation practices and to have clear mechanisms for demonstrating and documenting this.

The sustainability of AI systems depends on the capacity of project teams to proceed with a continuous sensitivity to their potential real-world impacts and transformative effects. Stakeholder Impact Assessments (SIAs) are governance mechanisms that enable this kind of responsiveness. They are tools that create a procedure for, and a means of documenting, the collaborative evaluation and reflective anticipation of the possible harms and benefits of AI innovation projects. SIAs are not one-off governance actions. They require project teams to pay continuous attention to the dynamic and changing character of AI production and use and to the shifting conditions of the real-world environments in which AI technologies are embedded. This workbook is part two of two workbooks on AI Sustainability. It provides a template of the SIA and activities that allow a deeper dive into crucial parts of it. It discusses methods for weighing values and considering trade-offs during the SIA. And, it highlights the need to treat the SIA as an end-to-end process of responsive evaluation and re-assessment.

Reaching consensus on a commonly accepted definition of AI Fairness has long been a central challenge in AI ethics and governance. There is a broad spectrum of views across society on what the concept of fairness means and how it should best be put to practice. In this workbook, we tackle this challenge by exploring how a context-based and society-centred approach to understanding AI Fairness can help project teams better identify, mitigate, and manage the many ways that unfair bias and discrimination can crop up across the AI project workflow. We begin by exploring how, despite the plurality of understandings about the meaning of fairness, priorities of equality and non-discrimination have come to constitute the broadly accepted core of its application as a practical principle. We focus on how these priorities manifest in the form of equal protection from direct and indirect discrimination and from discriminatory harassment. These elements form ethical and legal criteria based upon which instances of unfair bias and discrimination can be identified and mitigated across the AI project workflow. We then take a deeper dive into how the different contexts of the AI project lifecycle give rise to different fairness concerns. This allows us to identify several types of AI Fairness (Data Fairness, Application Fairness, Model Design and Development Fairness, Metric-Based Fairness, System Implementation Fairness, and Ecosystem Fairness) that form the basis of a multi-lens approach to bias identification, mitigation, and management. Building on this, we discuss how to put the principle of AI Fairness into practice across the AI project workflow through Bias Self-Assessment and Bias Risk Management as well as through the documentation of metric-based fairness criteria in a Fairness Position Statement.

Sustainable AI projects are continuously responsive to the transformative effects as well as short-, medium-, and long-term impacts on individuals and society that the design, development, and deployment of AI technologies may have. Projects, which centre AI Sustainability, ensure that values-led, collaborative, and anticipatory reflection both guides the assessment of potential social and ethical impacts and steers responsible innovation practices. This workbook is the first part of a pair that provides the concepts and tools needed to put AI Sustainability into practice. It introduces the SUM Values, which help AI project teams to assess the potential societal impacts and ethical permissibility of their projects. It then presents a Stakeholder Engagement Process (SEP), which provides tools to facilitate proportionate engagement of and input from stakeholders with an emphasis on equitable and meaningful participation and positionality awareness.

The circular unitary ensemble and its generalizations concern a random matrix from a compact classical group $\mathrm{U}(N)$, $\mathrm{SU}(N)$, $\mathrm{O}(N)$, $\mathrm{SO}(N)$ or $\mathrm{USp}(N)$ distributed according to the Haar measure. The eigenvalues are known to be very evenly distributed on the unit circle. In this paper, we study the distance from the empirical measure of the eigenvalues to uniformity in the quadratic Wasserstein metric $W_2$. After finding the exact value of the expected value and the variance, we deduce a limit law for the square of the Wasserstein distance. We reformulate our results in terms of the $L^2$ average of the number of eigenvalues in circular arcs, and also in terms of the characteristic polynomial of the matrix on the unit circle., Comment: 31 pages, 4 tables, 1 figure

This paper analyzes the impact of the integration of the Modular Static Synchronous Series Compensator (M-SSSC) solution that will be deployed in the Santa Marta 220 kV (Colombian substation) by using real-time simulations with Hardware in the Loop (HIL) technique, over the protection coordination schemes in the area of influence. The results show that the M-SSSC devices can be successfully coordinated with the protection schemes, mitigating overloads through the transmission lines during steady state and contingencies, while avoiding potential harmful interactions with the grid and, most importantly, with protection devices. This behavior is achieved by using overcurrent detection logics implemented on M-SSSC devices that trip fast-acting Silicon Controlled Rectifiers (SCRs) that cease the voltage injection in less than 5 ms, Comment: Paper accepted in the XIX ERIAC - CIGRE Iberoamerican Regional Meeting- CIGRE Brazil in section Technical Works -C4. Link to paper: https://www.xixeriac.com.br/artigos-apresentacoes

Limit laws for ergodic averages with a power singularity over circle rotations were first proved by Sinai and Ulcigrai, as well as Dolgopyat and Fayad. In this paper, we prove limit laws with an estimate for the rate of convergence for the sum $\sum_{n=1}^N f(n \alpha)/n^p$ in terms of a $1$-periodic function $f$ with a power singularity of order $p \ge 1$ at integers. Our results apply in particular to cotangent sums related to Dedekind sums, and to sums of reciprocals of fractional parts, which appear in multiplicative Diophantine approximation. The main tools are Schmidt's method in metric Diophantine approximation, the Gauss-Kuzmin problem and the theory of $\psi$-mixing random variables., Comment: 34 pages

Determinantal point processes exhibit an inherent repulsive behavior, thus providing examples of very evenly distributed point sets on manifolds. In this paper, we study the so-called harmonic ensemble, defined in terms of Laplace eigenfunctions on the sphere $\mathbb{S}^d$ and the flat torus $\mathbb{T}^d$, and the so-called spherical ensemble on $\mathbb{S}^2$, which originates in random matrix theory. We extend results of Beltr\'an, Marzo and Ortega-Cerd\`a on the Riesz $s$-energy of the harmonic ensemble to the nonsingular regime $s<0$, and as a corollary find the expected value of the spherical cap $L^2$ discrepancy via the Stolarsky invariance principle. We find the expected value of the $L^2$ discrepancy with respect to axis-parallel boxes and Euclidean balls of the harmonic ensemble on $\mathbb{T}^d$. We also show that the spherical ensemble and the harmonic ensemble on $\mathbb{S}^2$ and $\mathbb{T}^2$ with $N$ points attain the optimal rate $N^{-1/2}$ in expectation in the Wasserstein metric $W_2$, in contrast to i.i.d. random points, which are known to lose a factor of $(\log N)^{1/2}$., Comment: 27 pages

The Diophantine sums $\sum_{n=1}^N \| n \alpha \|^{-1}$ and $\sum_{n=1}^N n^{-1} \| n \alpha \|^{-1}$ appear in many different areas including the ergodic theory of circle rotations, lattice point counting and random walks, often in connection with Fourier analytic methods. Beresnevich, Haynes and Velani gave estimates for these and related sums in terms of the Diophantine approximation properties of $\alpha$ that are sharp up to a constant factor. In the present paper, we remove the constant factor gap between the upper and the lower estimates, and thus find the precise asymptotics for a wide class of irrationals. Our methods apply to sums with the fractional part instead of the distance from the nearest integer function, and to sums involving shifts $\| n \alpha + \beta \|$ as well. We also comment on a higher dimensional generalization of these sums., Comment: 13 pages

We obtain new bounds, pointwisely and on average, for Dedekind sums $\mathsf{s}(\lambda,p)$ modulo a prime $p$ with $\lambda$ of small multiplicative order $d$ modulo $p$. Assuming the infinitude of Mersenne primes, the range of our results is optimal. Moreover, we relate high moments of $L(1,\chi)$ over subgroups of characters to some correlations of Dedekind sums and use our recent results to study these correlations.

We study the distribution of the sequence of continued fraction convergents $p_n/q_n$ to a random irrational number in the group $\mathrm{SL}(2,\mathbb{Z}_m)$, and in particular the distribution of $p_n \pmod{m}$ and $q_n \pmod{m}$ with a fixed modulus $m$. Improving the strong law of large numbers due to Sz\"usz, Moeckel, Jager and Liardet, we establish the central limit theorem and the law of the iterated logarithm, as well as the weak and the almost sure invariance principles. As an application, we find the limit distribution of the maximum and the minimum of the Birkhoff sum for the irrational rotation with the indicator of an interval as test function. We also compute the normalizing constant in a classical limit law for the same Birkhoff sum due to Kesten, and dispel a misconception about its dependence on the test interval., Comment: 26 pages

In this paper, we show how quantum modular forms naturally arise in the ergodic theory of circle rotations. Working with the classical Birkhoff sum $S_N(\alpha)=\sum_{n=1}^N (\{ n \alpha \}-1/2)$, we prove that the maximum and the minimum as well as certain exponential moments of $S_N(r)$ as functions of $r \in \mathbb{Q}$ satisfy a direct analogue of Zagier's continuity conjecture, originally stated for a quantum invariant of the figure-eight knot. As a corollary, we find the limit distribution of $\max_{0 \le N

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the HDF5 library which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for the Fortran, Python, and OCaml programming languages. In addition, a suite of tools has been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data., Comment: 13 pages, 2 figures

Quantum Machine Learning (QML) shows how it maintains certain significant advantages over machine learning methods. It now shows that hybrid quantum methods have great scope for deployment and optimisation, and hold promise for future industries. As a weakness, quantum computing does not have enough qubits to justify its potential. This topic of study gives us encouraging results in the improvement of quantum coding, being the data preprocessing an important point in this research we employ two dimensionality reduction techniques LDA and PCA applying them in a hybrid way Quantum Support Vector Classifier (QSVC) and Variational Quantum Classifier (VQC) in the classification of Diabetes.

In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions $a/N$, where $N$ is fixed and $a$ runs through the set of mod $N$ residue classes which are coprime with $N$. Our methods cover statistics such as the sum of partial quotients, the maximal partial quotient, the empirical distribution of partial quotients, Dedekind sums, and much more. We prove a sharp concentration inequality for the sum of partial quotients, and sharp tail estimates for the maximal partial quotient and for Dedekind sums, all matching the tail behavior in the limit laws which are known under an extra averaging over the set of possible denominators $N$. We show that the distribution of partial quotients of reduced fractions with fixed denominator gives a very good fit to the Gauss-Kuzmin distribution. As corollaries we establish the existence of reduced fractions with a small sum of partial quotients resp. a small maximal partial quotient., Comment: Version 1: 37 pages. Version 2: minor corrections and modifications