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This work presents a hybrid quantum-classical algorithm to perform clustering aggregation, designed for neutral-atoms quantum computers and quantum annealers. Clustering aggregation is a technique that mitigates the weaknesses of clustering algorithms, an important class of data science methods for partitioning datasets, and is widely employed in many real-world applications. By expressing the clustering aggregation problem instances as a Maximum Independent Set (MIS) problem and as a Quadratic Unconstrained Binary Optimization (QUBO) problem, it was possible to solve them by leveraging the potential of Pasqal's Fresnel (neutral-atoms processor) and D-Wave's Advantage QPU (quantum annealer). Additionally, the designed clustering aggregation algorithm was first validated on a Fresnel emulator based on QuTiP and later on an emulator of the same machine based on tensor networks, provided by Pasqal. The results revealed technical limitations, such as the difficulty of adding additional constraints on the employed neutral-atoms platform and the need for better metrics to measure the quality of the produced clusterings. However, this work represents a step towards a benchmark to compare two different machines: a quantum annealer and a neutral-atom quantum computer. Moreover, findings suggest promising potential for future advancements in hybrid quantum-classical pipelines, although further improvements are needed in both quantum and classical components., Comment: Submitted to ISC25

This paper overviews the economics of scientific grants, focusing on the interplay between the inherent uncertainty in research, researchers' incentives, and grant design. Grants differ from traditional market systems and other science and innovation policy tools, such as prizes and patents. We outline the main economic forces specific to science, noting the limited attention given to grant funding in the economics literature. Using tools from information economics, we identify key incentive problems at various stages of the grant funding process and offer guidance for effective grant design. In the allocation stage, funders aim to select the highest-merit applications while minimizing evaluation costs. The selection rule, in turn, impacts researchers' incentives to apply and invest in their proposals. In the grant management stage, funders monitor researchers to ensure efficient use of funds. We discuss the advantages and potential pitfalls of (partial) lotteries and emphasize the effectiveness of staged grant design in promoting a productive use of grants. Beyond these broadly applicable insights, our overview highlights the need for further research on grantmaking. Understudied areas include, at the micro level, the interplay of different grant funding stages, and at the macro level, the interaction of grants with other instruments in the market for science.

The Hessian map is the rational map that sends a homogeneous polynomial to the determinant of its Hessian matrix. We prove that the Hessian map is birational on its image for ternary forms of degree $d\ge 4$, $d\neq 5$, by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques., Comment: by Ciro Ciliberto, Giorgio Ottaviani, with an appendix by Jerson Caro, Juanita Duque-Rosero

Large bibliometric databases, such as Web of Science, Scopus, and OpenAlex, facilitate bibliometric analyses, but are performative, affecting the visibility of scientific outputs and the impact measurement of participating entities. Recently, these databases have taken up the UN's Sustainable Development Goals (SDGs) in their respective classifications, which have been criticised for their diverging nature. This work proposes using the feature of large language models (LLMs) to learn about the "data bias" injected by diverse SDG classifications into bibliometric data by exploring five SDGs. We build a LLM that is fine-tuned in parallel by the diverse SDG classifications inscribed into the databases' SDG classifications. Our results show high sensitivity in model architecture, classified publications, fine-tuning process, and natural language generation. The wide arbitrariness at different levels raises concerns about using LLM in research practice.

A/B testing methodology is generally performed by private companies to increase user engagement and satisfaction about online features. Their usage is far from being transparent and may undermine user autonomy (e.g. polarizing individual opinions, mis- and dis- information spreading). For our analysis we leverage a crucial case study dataset (i.e. Upworthy) where news headlines were allocated to users and reshuffled for optimizing clicks. Our centre of focus is to determine how and under which conditions A/B testing affects the distribution of content on the collective level, specifically on different social network structures. In order to achieve that, we set up an agent-based model reproducing social interaction and an individual decision-making model. Our preliminary results indicate that A/B testing has a substantial influence on the qualitative dynamics of information dissemination on a social network. Moreover, our modeling framework promisingly embeds conjecturing policy (e.g. nudging, boosting) interventions.

Molecular docking is an essential step in the drug discovery process involving the detection of three-dimensional poses of a ligand inside the active site of the protein. In this paper, we address the Molecular Docking search phase by formulating the problem in QUBO terms, suitable for an annealing approach. We propose a problem formulation as a weighted subgraph isomorphism between the ligand graph and the grid of the target protein pocket. In particular, we applied a graph representation to the ligand embedding all the geometrical properties of the molecule including its flexibility, and we created a weighted spatial grid to the 3D space region inside the pocket. Results and performance obtained with quantum annealers are compared with classical simulated annealing solvers.

This is a revised version of the lecture notes prepared for the workshop on "Plane quartics, Scorza map and related topics", held in Catania, January 19-21, 2016. The last section contains eight Macaulay2 scripts on theta characteristics and the Scorza map, with a tutorial. The first sections give an introduction to these scripts. The tutorial contains a list of the 36 Scorza preimages of the Edge quartic., Comment: 47 pages

The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many complex problems that cannot be solved otherwise with conventional computing methods. These problems include modeling quantum mechanics, logistics, chemical-based advances, drug design, statistical science, sustainable energy, banking, reliable communication, and quantum chemical engineering. The last few years have witnessed remarkable progress in quantum software and algorithm creation and quantum hardware research, which has significantly advanced the prospect of realizing quantum computers. It would be helpful to have comprehensive literature research on this area to grasp the current status and find outstanding problems that require considerable attention from the research community working in the quantum computing industry. To better understand quantum computing, this paper examines the foundations and vision based on current research in this area. We discuss cutting-edge developments in quantum computer hardware advancement and subsequent advances in quantum cryptography, quantum software, and high-scalability quantum computers. Many potential challenges and exciting new trends for quantum technology research and development are highlighted in this paper for a broader debate., Comment: Technical Report: 15 pages, 2 figures

Let $f$ be a homogeneous polynomial of even degree $d$. We study the decompositions $f=\sum_{i=1}^r f_i^2$ where $\mathrm{deg} f_i=d/2$. The minimal number of summands $r$ is called the $2$-rank of $f$, so that the polynomials having $2$-rank equal to $1$ are exactly the squares. Such decompositions are never unique and they are divided into $\mathrm{O}(r)$-orbits, the problem becomes counting how many different $\mathrm{O}(r)$-orbits of decomposition exist. We say that $f$ is $\mathrm{O}(r)$-identifiable if there is a unique $\mathrm{O}(r)$-orbit. We give sufficient conditions for generic and specific $\mathrm{O}(r)$-identifiability. Moreover, we show the generic $\mathrm{O}(r)$-identifiability of ternary forms., Comment: 14 pages, to appear in Journal of Algebra

Over the past six decades, the computing systems field has experienced significant transformations, profoundly impacting society with transformational developments, such as the Internet and the commodification of computing. Underpinned by technological advancements, computer systems, far from being static, have been continuously evolving and adapting to cover multifaceted societal niches. This has led to new paradigms such as cloud, fog, edge computing, and the Internet of Things (IoT), which offer fresh economic and creative opportunities. Nevertheless, this rapid change poses complex research challenges, especially in maximizing potential and enhancing functionality. As such, to maintain an economical level of performance that meets ever-tighter requirements, one must understand the drivers of new model emergence and expansion, and how contemporary challenges differ from past ones. To that end, this article investigates and assesses the factors influencing the evolution of computing systems, covering established systems and architectures as well as newer developments, such as serverless computing, quantum computing, and on-device AI on edge devices. Trends emerge when one traces technological trajectory, which includes the rapid obsolescence of frameworks due to business and technical constraints, a move towards specialized systems and models, and varying approaches to centralized and decentralized control. This comprehensive review of modern computing systems looks ahead to the future of research in the field, highlighting key challenges and emerging trends, and underscoring their importance in cost-effectively driving technological progress., Comment: Preprint submitted to Telematics and Informatics Reports, Elsevier (2024)

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 65 pages, 15 figures; comments welcome

Neutral atoms devices represent a promising technology that uses optical tweezers to geometrically arrange atoms and modulated laser pulses to control the quantum states. A neutral atoms Noisy Intermediate Scale Quantum (NISQ) device is developed by Pasqal with rubidium atoms that will allow to work with up to 100 qubits. All NISQ devices are affected by noise that have an impact on the computations results. Therefore it is important to better understand and characterize the noise sources and possibly to correct them. Here, two approaches are proposed to characterize and correct noise parameters on neutral atoms NISQ devices. In particular the focus is on Pasqal devices and Machine Learning (ML) techniques are adopted to pursue those objectives. To characterize the noise parameters, several ML models are trained, using as input only the measurements of the final quantum state of the atoms, to predict laser intensity fluctuation and waist, temperature and false positive and negative measurement rate. Moreover, an analysis is provided with the scaling on the number of atoms in the system and on the number of measurements used as input. Also, we compare on real data the values predicted with ML with the a priori estimated parameters. Finally, a Reinforcement Learning (RL) framework is employed to design a pulse in order to correct the effect of the noise in the measurements. It is expected that the analysis performed in this work will be useful for a better understanding of the quantum dynamic in neutral atoms devices and for the widespread adoption of this class of NISQ devices., Comment: 11 pages, 5 figures, 3 tables

A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matrices. Inversion of the natural parametrization is known as Pad\'e approximation. We study the dimension and defining ideals of Taylor varieties. Taylor hypersurfaces are interesting for projective geometry, since their Hessians tend to vanish. In three and more variables, there exist defective Taylor varieties whose dimension is smaller than the number of parameters. We explain this with Fr\"oberg's Conjecture in commutative algebra., Comment: 20 pages

Traditional and lightweight cryptography primitives and protocols are insecure against quantum attacks. Thus, a real-time application using traditional or lightweight cryptography primitives and protocols does not ensure full-proof security. Post-quantum Cryptography is important for the Internet of Things (IoT) due to its security against Quantum attacks. This paper offers a broad literature analysis of post-quantum cryptography for IoT networks, including the challenges and research directions to adopt in real-time applications. The work draws focus towards post-quantum cryptosystems that are useful for resource-constraint devices. Further, those quantum attacks are surveyed, which may occur over traditional and lightweight cryptographic primitives., Comment: Accepted version

We study the problem of how many different sums of squares decompositions a general polynomial $f$ with SOS-rank $k$ admits. We show that there is a link between the variety $\mathrm{SOS}_k(f)$ of all SOS-decompositions of $f$ and the orthogonal group $\mathrm{O}(k)$. We exploit this connection to obtain the dimension of $\mathrm{SOS}_k(f)$ and show that its degree is bounded from below by the degree of $\mathrm{O}(k)$. In particular, for $k=2$ we show that $\mathrm{SOS}_2(f)$ is isomorphic to $\mathrm{O}(2)$ and hence the degree bound becomes an equality. Moreover, we compute the dimension of the space of polynomials of SOS-rank $k$ and obtain the degree in the special case $k=2$.

Construction project governance relies on agreements between the actors along the construction industry value chain. The mutual obligations arising from these contracts rely on timely monetary transactions. Despite the advantages of automation in payment systems and improved access to digital progress data, several payment applications rely nonetheless on inefficient and time-consuming procedures and documentation. This study examines the present technological advancements that can lead to fix this problem. A smart contract-based approach is ideal for managing construction progress payments that support autonomous process, it fills the gap between payments and project site progress evaluations. This article offers a way for automating construction payments by formalizing smart contracts execution on a decentralized block-chain-based system.

Autonomic computing investigates how systems can achieve (user) specified control outcomes on their own, without the intervention of a human operator. Autonomic computing fundamentals have been substantially influenced by those of control theory for closed and open-loop systems. In practice, complex systems may exhibit a number of concurrent and inter-dependent control loops. Despite research into autonomic models for managing computer resources, ranging from individual resources (e.g., web servers) to a resource ensemble (e.g., multiple resources within a data center), research into integrating Artificial Intelligence (AI) and Machine Learning (ML) to improve resource autonomy and performance at scale continues to be a fundamental challenge. The integration of AI/ML to achieve such autonomic and self-management of systems can be achieved at different levels of granularity, from full to human-in-the-loop automation. In this article, leading academics, researchers, practitioners, engineers, and scientists in the fields of cloud computing, AI/ML, and quantum computing join to discuss current research and potential future directions for these fields. Further, we discuss challenges and opportunities for leveraging AI and ML in next generation computing for emerging computing paradigms, including cloud, fog, edge, serverless and quantum computing environments., Comment: Accepted for Publication in Elsevier IoT Journal, 2022