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Matrix Functions and Network Communicability Measures
Full text linkIn recent years, functions of matrices have played an increasingly important
role in the analysis of graphs and networks, especially in the definition of powerful centrality and communicability measures and
in the analysis of diffusion processes, both local and nonlocal. These techniques are having
a significant impact in a variety of applications, ranging from social network analysis to chemical physics to the
neurosciences. This contribution provides a succinct overview of how matrix functions can be used in the
analysis of communicability in complex networks
On the Kolmogorov equation associated with Volterra equations and fractional Brownian motion
Full text linkWe consider a Volterra convolution equation in Rd perturbed with an additive fractional Brownian motion of Riemann-Liouville type with Hurst parameter H is an element of (0, 1). We show that its solution solves an infinite-dimensional stochastic differential equation (SDE) in the Hilbert space of square-integrable functions. Such an equation motivates our study of an unconventional class of SDEs requiring an original extension of the drift operator and its Fr & eacute;chet differentials. We prove that these infinite-dimensional SDEs generate a Markov stochastic flow which is twice Fr & eacute;chet differentiable with respect to the initial data. This stochastic flow is then employed to solve, in the classical sense of infinite-dimensional calculus, the path-dependent Kolmogorov equation corresponding to the SDEs. In particular, we associate a time-dependent infinitesimal generator with the fractional Brownian motion. In the final section, we show some obstructions in the analysis of the mild formulation of the Kolmogorov equation for SDEs driven by the same infinite-dimensional noise. This problem, which is relevant to the theory of regularization by noise, remains open for future research. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/)
GW Approximation Coupled with Classical Fluctuating Charges and Dipoles
Full text linkWe propose a novel multiscale QM/classical methodology based on the GW approximation combined with the fluctuating charges (FQ) and fluctuating charges and dipoles (FQFμ) force fields. The GW approximation is exploited to capture electron correlation effects, while FQ or FQFμ is used to model the mutual polarization effects between the quantum GW system and its surrounding environment in a multiscale fashion. The model is validated through test calculations of ionization potentials of aqueous phenol and applied to the Green Fluorescent Protein (GFP) chromophore (4-hydroxybenzylidene-1,2-dimethylimidazolinone─p-HDBI) in aqueous solution
Senato sine fine
No full textThis paper opens by examining the demise of the Roman Senate between Justinian’s
reconquest and the early seventh century, when the assembly gradually lost its role within the res publica until it disappeared altogether. The article then turns to later continuist interpretations of the Senate’s history, developed mainly in Italy between the eighteenth and twentieth centuries. This tradition imagined the Senate’s survival into the Middle Ages as a means of legitimising papal authority or a secular civic heritage. Under Fascism, these ideas acquired new political resonances: Pietro Fedele and Arrigo Solmi wove the Senate’s supposed continuity into a narrative of uninterrupted Roman identity, while the recovery of the Curia Iulia provided symbolic staging. In this light, the Senate appears less as a vanished institution than as a lasting emblem of national identity and historical destin
Search for b-hadron decays to long-lived particles in the CMS endcap muon detectors
No full textA search for long-lived particles originating from the decay of b hadrons produced in proton-proton collisions with a center-of-mass energy of 13 TeV at the LHC is presented. The analysis is performed on a dataset recorded in 2018, corresponding to an integrated luminosity of 41.6 fb−1. Interactions of the long-lived particles in the CMS endcap muon system would create hadronic or electromagnetic showers, producing clusters of detector hits. Selected events contain at least one such high-multiplicity cluster in the muon endcaps and require the presence of a displaced muon. The most stringent upper limits to date on the branching fraction B(B →KΦ), where the long-lived particle Φ
decays to a pair of hadrons, are obtained for Φ masses of 0.3–3.0 GeV and Φ mean proper decay lengths in the range of 1–500 cm
Mathematical Foundation of Interpretable Equivariant Surrogate Models
No full textThis paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs), based on Group Equivariant Non-Expansive Operators (GENEOs) transformations. The central concept involves quantifying the distance between GEOs by measuring the non-commutativity of specific diagrams. Additionally, the paper proposes a definition of interpretability of GEOs according to a complexity measure that can be defined according to each user’s preferences. Moreover, we explore the formal properties of this framework and show how it can be applied in classical machine learning scenarios, like image classification with convolutional neural networks
Understanding the householder solar panel consumer : A Markovian model and its societal implications
Full text linkHousehold adoption of rooftop photovoltaic (PV) systems is central to the green energy transition, yet diffusion depends on social influence and behavioral biases, as well as payback economics. This study develops a parsimonious Markovian model in which households move sequentially from being unengaged (“Carbon”) to informed, to planning, and finally to adoption (“Green”). Transition rates are micro-founded by two mechanisms: (i) social contagion/communication, proxied by the current share of adopters, and (ii) economic profitability, proxied by payback time computed from a Net Present Value framework. Novel to this diffusion setting, bounded rationality is introduced via hyperbolic discounting, creating a procrastination loop that delays adoption even when PV is economically attractive in a long-run perspective. Calibrated on the Italian residential PV diffusion path (2006–2020) and assessed in national and regional applications, the model reproduces observed trajectories and enables forward-looking scenario analysis (2020–2026). Results show that policies yielding similar payback improvements can produce different outcomes once present bias is accounted for and that behaviorally informed intervention are stronger. The findings contribute a micro-to-macro bridge between behavioral economics and technology diffusion modeling and imply that effective policy portfolios (and PV business models) should complement incentives with commitment devices and social-norm peer strategies to accelerate PV uptake and its spillover emissions benefits
Observation of Bc+ ->Dh+h- Decays
No full textSearches are presented for Bc+->Dh+h- decays, where D is a charmed meson and h± is a charged pion or kaon, using pp collision data collected by the LHCb experiment corresponding to an integrated luminosity of 9 fb-1. [See attached .pdf file
Noise perturbations of Point Vortex model
No full textThe investigation of stochastic perturbations in fluid dynamics has been a standard procedure in the physical and mathematical
literature. In particular, we recall the use of transport-type noise (advection by a stochastic velocity field) in the development of
the theory of turbulence, due to the work of Kraichnan on stochastic transport of passive scalars.
A very classical particle system in the fluid dynamics context is the Point Vortex model. This system is a discretization of the Euler
equation in the vorticity formulation, and it has been introduced and studied by Helmholtz; however, it is due to the investigation
on two-dimensional turbulence carried on by Onsager that this model reached popularity and recognition in the context of fluid
discretizations. The Point Vortex model is also an object of studies in the context of dynamical systems, due to the Hamiltonian
aspects of vortex dynamics. In this thesis, we too focus on the study of two-dimensional models; this is not a limitation in our
investigation, as many phenomena in nature can be modeled by almost-two-dimensional systems, examples are atmospheric or
geostrophic turbulence; this modelization is possible if the vertical scale of the system is negligible with respect to the horizontal
scale or vice-versa.
By investigating both the Point Vortex model in its standard formulation and its stochastic modifications, we explore two long
standing problems in fluid dynamics: turbulence modeling by stochastic perturbations of transport type and the long time
behavior of an inviscid fluid. In the first case, we investigate both the Point Vortex model with stochastic modification of transport
type, and the motion of a passive scalar transported by a stochastic velocity field. This stochastic velocity field is very similar to
the one studied in the Point Vortex model context, and it is a sum of independent and compactly supported vector fields. This
simplified setting allows us to study more in detail the noise. In the second case, we investigate the long time behavior of a two-
dimensional fluid: we study the equilibrium dynamics’s temporal structure by computing correlation of local observables, function
of the vorticity, of a large number of point vortices under the invariant measure and we exibit evidence of
persistence in time correlations, in the form of power law decay of the latte
The challenges of platform cooperativism and the path ahead
No full textThis chapter explores the legacy and emerging dual challenges of platform cooperatives. The first section examines the longstanding issue of political identity in both traditional and platform cooperativism through an extensive textual analysis of historical and contemporary scholars. The second section delves into the business challenges of cooperatives – namely, scale, finance, and the market – showing how these difficulties persist within platform cooperatives and may even be exacerbated by the characteristics of the platform economy. This analysis draws on qualitative case studies from platform cooperatives in Italy and the United States, as well as data from the first international economic survey of platform cooperatives, which includes responses from 86 legally registered businesses across five continents. The third section outlines potential avenues for future research aimed at addressing these challenges and strengthening the cooperative economy to confront the most urgent issues of our time: the climate crisis, war, and social divisions along gender, race, and class lines