Beyond CARMA: Building Complex Processes from Lévy Noise
![The correlation functions of supCAR(2)(2)-III processes demonstrate a transition in behavior based on shape parameters; when [latex]\alpha + 3 \in (3,4][/latex], these processes exhibit non-oscillatory long-range dependence, but as the shape parameter increases beyond this range, oscillations emerge, indicating a shift in the underlying dynamic characteristics.](https://arxiv.org/html/2601.15796v1/x4.png)
This review introduces supCARMA processes-superpositions of continuous-time autoregressive moving average models driven by Lévy processes-and details their theoretical properties.
Science
Beyond Bundles: A Formal Framework for Differential Geometry
This review introduces a powerful, category-theoretic approach to differential objects, connections, and bundles, extending classical concepts to broader mathematical settings.
Beyond Averages: Understanding the Impact of Mesoscopic Fluctuations
![The system’s free energy, charted as a function of frustration-with cohesive energy held constant at [latex]u = -1[/latex]-reveals a critical threshold where the energy of frustrated matter intersects that of a pure crystalline solid, indicating a transition point governed by the balance between order and disorder within the material.](https://arxiv.org/html/2601.15782v1/x2.png)
This review details a new theoretical approach for characterizing how fluctuations at the mesoscale fundamentally shape the behavior of complex systems and influence phase transitions.
Smarter Sampling: Adapting to Signals for Efficient Data Capture
A new framework dynamically adjusts sampling rates based on signal characteristics, potentially overcoming limitations of traditional data acquisition methods.
Beyond Conformality: A Path to Carrollian Theories
New research reveals how deforming conformal field theories via a specific operator smoothly connects them to their Carrollian counterparts, unlocking deeper insights into their underlying structure.
Unlocking Neutrino Secrets: The ESSnuSB+ Vision
A new generation of neutrino experiments, spearheaded by the ESSnuSB+ project, is poised to probe the fundamental properties of these elusive particles and address some of the biggest mysteries in physics.
Reading Material Properties From System Response
A new method allows for the unique determination of nonlinear material behavior within a solid system by analyzing measurements taken at its boundaries.
Beyond Hamming: Exploring the Frontiers of Rank-Metric Codes
This review delves into the theory of rank-metric codes, a powerful generalization of traditional Hamming codes with applications in diverse areas of coding theory and cryptography.
Beyond Perturbation: A Novel Quantum Critical Point
![The data demonstrates a successful fit to the Equation of State [latex] (11) [/latex], indicating the model accurately captures the system's thermodynamic behavior under the conditions tested.](https://arxiv.org/html/2601.16051v1/x4.png)
New simulations of the Thirring model reveal a strongly-interacting quantum critical point with scaling exponents that challenge conventional theoretical predictions.
Black Hole Echoes: Nonlinearity’s Subtle Impact
![Nonlinear simulations demonstrate the temporal evolution of massive scalar perturbations, where rescaling the evolved field as [latex]{\Phi\_{lm}}={\lambda^{n}}\phi\_{lm}^{(n)}[/latex] reveals that the [latex](0,0)[/latex] mode arises from the quadratic self-couplings of the linear [latex](1,1)[/latex], [latex](0,0)[/latex], and [latex](2,0)[/latex] modes, and exhibits excellent agreement between intermediate-time analytical predictions and corresponding numerical evolution.](https://arxiv.org/html/2601.16016v1/x14.png)
New research reveals that while massive scalar fields exhibit predictable behavior around black holes, quadratic quasinormal modes may offer a pathway to observe previously hidden nonlinear dynamics.