arXiv subjects

Nicolò Cangiotti

Publications and source records attributed to Nicolò Cangiotti.

At least 19 recordsLinked to original sources

arXiv2026

Normalized nonlinear Schrödinger ground states on defected grids with unbounded defects

We study normalized ground states for the nonlinear Schrödinger energy on two-dimensional square grids with unbounded defects. We first show that unbounded defects do not necessarily destroy the dimensional crossover, proving its persistence on the half-grid and the quarter-grid. We then consider a prototypical defected grid where a macroscopically two-dimensional region coexists with an unbounded one-dimensional channel. On this graph, normalized ground states do not exist for sufficiently small or sufficiently large masses, showing that the one-dimensional component can dominate the variational problem and induce loss of compactness. Finally, we show that this mechanism is sensitive to the local geometry of the graph: suitable additional defects preserve small-mass nonexistence but restore the existence of ground states for large masses. Our analysis combines small-mass energy asymptotics with a large-mass blow-up argument.

math.AP↗

arXiv2026

Becoming, Duration, and the Evolving Block Universe

The two-times problem asks how the directed, oriented time of biological and conscious systems relates to the time of fundamental physics. The Evolving Block Universe, in which spacetime grows along Ricci eigenlines through an irreversible quantum dynamics, explains the direction of physical time and its multi-scale emergence up to brain time. It does not explain how this physical time is related to the experience of temporal passage. We argue that Bergson's durée, the continuous qualitative experience of lived time, marks the first-person level beyond brain time at which this hierarchy reaches its limit. This locates the remaining gap between physical time and lived time at the epistemological level.

physics.hist-ph↗

arXiv2026

Profiling vs. Case-specific Evidence: A Probabilistic Analysis

The use of profiling evidence in criminal trials is a longstanding controversy in legal epistemology and evidence law theory. Many scholars, even when they oppose its use at trial, still assume that profiling evidence can be probative of guilt. We reject that assumption. Profiling evidence may support a generic hypothesis, but is not evidence that the defendant is guilty of the specific crime of which they are accused. We contrast profiling evidence with case-specific evidence, which speaks more directly to the facts of the case. Our critique departs from others by grounding the argument in a probabilistic analysis of evidentiary value. We also explore the implications of our account for debates about stereotyping.

stat.OT↗

arXiv2026

Exploring Exponential Runge-Kutta Methods: A Survey

In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.

math.NA↗

arXiv2026

Nonlinear Schrödinger Equation with magnetic potential on metric graphs

In this manuscript, we shall investigate the Nonlinear Magnetic Schrödinger Equation on noncompact metric graphs, focusing on the existence of ground states. We prove that the magnetic Hamiltonian is variationally equivalent to a non-magnetic operator with additional repulsive potentials supported on the graph's cycles. This effective potential is strictly determined by the Aharonov-Bohm flux through the topological loops. Leveraging this reduction, we extend classical existence criteria to the magnetic setting. As a key application, we characterize the ground state structure on the tadpole graph, revealing a mass-dependent phase transition. The ground states exist for sufficiently small repulsion in an intermediate regime of masses while sufficiently strong flux prevents the formation of ground states.

math.AP↗

arXiv2025

Evidence Without Injustice: A New Counterfactual Test for Fair Algorithms

The growing philosophical literature on algorithmic fairness has examined statistical criteria such as equalized odds and calibration, causal and counterfactual approaches, and the role of structural and compounding injustices. Yet an important dimension has been overlooked: whether the evidential value of an algorithmic output itself depends on structural injustice. We contrast a predictive policing algorithm, which relies on historical crime data, with a camera-based system that records ongoing offenses, where both are designed to guide police deployment. In evaluating the moral acceptability of acting on a piece of evidence, we must ask not only whether the evidence is probative in the actual world, but also whether it would remain probative in nearby worlds without the relevant injustices. The predictive policing algorithm fails this test, but the camera-based system passes it. When evidence fails the test, it is morally problematic to use it punitively, more so than evidence that passes the test.

cs.CY↗

arXiv2025

What is so special about analogue simulations?

This paper defends an account of terrestrial analogue simulations in black hole physics as instances of inferences from material analogy in science (Hesse 1963). We outline the main verdicts and recommendations deriving from this analysis, arguing that they not only fit the existing practice but are also more credible than those supported by prominent epistemological alternatives (e.g., Crowther et al. 2019, Dardashti et al. 2019).

physics.hist-ph↗

arXiv2025

Causal Equal Protection as Algorithmic Fairness

By combining the philosophical literature on statistical evidence and the interdisciplinary literature on algorithmic fairness, we revisit recent objections against classification parity in light of causal analyses of algorithmic fairness and the distinction between predictive and diagnostic evidence. We focus on trial proceedings as a black-box classification algorithm in which defendants are sorted into two groups by convicting or acquitting them. We defend a novel principle, causal equal protection, that combines classification parity with the causal approach. In the do-calculus, causal equal protection requires that individuals should not be subject to uneven risks of classification error because of their protected or socially salient characteristics. The explicit use of protected characteristics, however, may be required if it equalizes these risks.

cs.CY↗

arXiv2025

L-mosaics and orthomodular lattices

In this paper, we introduce a class of hypercompositional structures called dualizable L-mosaics. We prove that their category is equivalent to that formed by ortholattices and we formulate an algebraic property characterizing orthomodularity, suggesting possible applications to quantum logic.

math.CT↗

arXiv2023

Morrey-Campanato Functional Spaces for Carnot Groups

We shortly review the historical path of Morrey-Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey-Campanato spaces in the framework of Carnot groups.

math.FA↗

arXiv2023

Schrödinger-Maxwell equations driven by mixed local-nonlocal operators

In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then provide a range of parameter values to ensure the existence of solitary standing waves, obtained as Mountain Pass critical points for the associated energy functionals.

math.AP↗

arXiv2023

On projective spaces over local fields

Let $\mathcal{P}$ be the set of points of a finite-dimensional projective space over a local field $F$, endowed with the topology $τ$ naturally induced from the canonical topology of $F$. Intuitively, continuous incidence abelian group structures on $\mathcal{P}$ are abelian group structures on $\mathcal{P}$ preserving both the topology $τ$ and the incidence of lines with points. We show that the real projective line is the only finite-dimensional projective space over an Archimedean local field which admits a continuous incidence abelian group structure. The latter is unique up to isomorphism of topological groups. In contrast, in the non-Archimedean case we construct continuous incidence abelian group structures in any dimension $n \in \mathbb{N}$. We show that if $n>1$ and the characteristic of $F$ does not divide $n+1$, then there are finitely many possibilities up to topological isomorphism and, in any case, countably many.

math.AG↗

arXiv2023

Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators

Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allowed to be nonpositive definite according to a real parameter. In this paper, we provide a range of parameter values to ensure the existence of solitary (standing) waves, obtained as Mountain Pass critical points for the associated energy functionals in two different settings, by considering two different classes of potentials: constant potentials and continuous, bounded from below, and coercive potentials.

math.AP↗

arXiv2023

Genus Comparisons in the Topological Analysis of RNA Structures

RNA folding prediction remains challenging, but can be also studied using a topological mathematical approach. In the present paper, the mathematical method to compute the topological classification of RNA structures and based on matrix field theory is shortly reviewed, as well as a computational software, McGenus, used for topological and folding predictions. Additionally, two types of analysis are performed: the prediction results from McGenus are compared with topological information extracted from experimentally-determined RNA structures, and the topology of RNA structures is investigated for biological significance, in both evolutionary and functional terms. Lastly, we advocate for more research efforts to be performed at intersection of physics-mathematics and biology, and in particular about the possible contributions that topology can provide to the study of RNA folding and structure.

q-bio.BM↗

arXiv2023

A survey on Lyapunov functions for epidemic compartmental models

In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, together with a commentary on their use. Our aim is to provide a comprehensive starting point to readers who are attempting to prove global stability of systems of ODEs. The focus is on mathematical epidemiology, however some of the functions and strategies presented in this paper can be adapted to a wider variety of models, such as prey-predator or rumor spreading.

math.DS↗

arXiv2022

Reasoning by Analogy in Mathematical Practice

The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of analogical reasoning in mathematics, stating general conditions under which an analogy may provide genuine inductive support to a mathematical conjecture (over and above fulfilling the merely heuristic role of 'suggesting' a conjecture in the psychological sense). The proposed conditions generalize the criteria put forward by Hesse (1963) in her influential work on analogical reasoning in the empirical sciences. By reference to several case-studies, we argue that the account proposed in this paper does a better job in vindicating the use of analogical inference in mathematics than the prominent alternative defended by Bartha (2009). Moreover, our proposal offers novel insights into the practice of extending to the infinite case mathematical properties known to hold in finite domains.

math.HO↗

arXiv2022

Dimensional Universality of Schauder Estimates Constants for Fourth Order Heat-Type Equations

A new method to compute Schauder Estimates for multidimensional fourth order heat-type equations is proposed. In particular, we show how knowing Schauder or Sobolev estimates for the one-dimensional fourth order heat equation allows to derive their multidimensional analogs for equations with time inhomogeneous coefficients with the same constants as in the case of the one-dimensional heat equation. Our method relies on a merger between (Krylov and Priola, 2017), where they actually showed the same result for the classical second order heat equation and (Funaki, 1979), where a probabilistic construction of solutions for the fourth order heat equation is presented.

math.AP↗

arXiv2022

A Generalization of Lanchester's Model of Warfare

The classical Lanchester's model is shortly reviewed and analysed, with particular attention to the critical issues that intrinsically arise from the mathematical formalization of the problem. We then generalize a particular version of such a model describing the dynamics of warfare when three or more armies are involved in the conflict. Several numerical simulations are provided.

physics.soc-ph↗