相关论文: Unifying Framework for Amplification Mechanisms: C…
We develop a unified matrix-spectral framework for analyzing stability and interpretability in deep neural networks. Representing networks as data-dependent products of linear operators reveals spectral quantities governing sensitivity to…
Interacting random matrix systems are fundamental to modern theoretical physics and data science, yet a unified framework for their analysis has been lacking. This work introduces such a universal framework, built upon two novel concepts:…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
The quantum criticality of the two-lead two-channel pseudogap Anderson model is studied. Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias…
We present a generic system of three harmonic modes coupled parametrically with a time-varying coupling modulated by a combination of two pump harmonics, and show how this system provides the minimal platform to realize nonreciprocal…
Light propagation in a nonlinear optical medium is nonreciprocal for spatially asymmetric linear permittivity. We here examine physical mechanism and properties of such nonreciprocity (NR). For this, we calculate transmission of light…
We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We prove for an infinite array of globally coupled overdamped anharmonic oscillators subject to additive Gaussian white noise the existence of a well-behaved critical manifold in the parameter space which separates a symmetric phase from a…
The $S$ matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given $S$ matrix which describes neutrino oscillation, one can define the two different…
By considering the potential parameter $\Gamma$ as a function of another potential parameter $\lambda$[47], We successfully extend the analysis of two-dimensional autonomous dynamical system of quintessence scalar field model to the…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
We present a semi-analytical framework for studying interactions between quantum emitters and general electromagnetic resonators. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the…
Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…
Accurate determination of the complex effective permittivity is fundamental to optical material engineering, but it remains a critical metrology challenge for heterogeneous systems. In polymer blends and optical composites, scattering and…
While criticality is widely observed in neural networks, its underlying neural mechanism is not known well. We consider a network of $N$ excitatory leaky integrated and fire (LIF) neurons that reside on a regular lattice with periodic…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
We consider the period-doubling and intermittency transitions in iterated nonlinear one-dimensional maps to corroborate unambiguously the validity of Tsallis' non-extensive statistics at these critical points. We study the map…
We stress the importance of the circa 20 parameters in the Standard Model, which are not fixed by the model but only determined experimentally, as a window to the physics beyond the Standard Model. However, it is a tiny window in as far as…