相关论文: Multicritical points for the spin glass models on …

We exhibit the multicritical phase structure of the loop gas model on a random surface. The dense phase is reconsidered, with special attention paid to the topological points $g=1/p$. This phase is complementary to the dilute and higher…

We study the multicritical behavior arising from the competition of two distinct types of ordering characterized by O(n) symmetries. For this purpose, we consider the renormalization-group flow for the most general $O(n_1)\oplus…

Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry…

Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…

This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)) where the tools of the field theoretical renormalization group were employed to explain…

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle:…

We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also…

We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero…

The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two…

We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near…

Nontrivial fixed points of the hierarchical renormalization group are computed by numerically solving a system of quadratic equations for the coupling constants. This approach avoids a fine tuning of relevant parameters. We study the…

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…

We study the putative multicritical point in 2+1D $\mathbb{Z}_k$ gauge theory where the Higgs and confinement transitions meet. The presence of an $e$-$m$ duality symmetry at this critical point forces anyons with nontrivial braiding to…

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…

We present a novel approach for relocalization or place recognition, a fundamental problem to be solved in many robotics, automation, and AR applications. Rather than relying on often unstable appearance information, we consider a situation…

We consider $N$ two-dimensional Ising models coupled in presence of quenched disorder and use scale invariant scattering theory to exactly show the presence of a line of renormalization group fixed points for any fixed value of $N$ other…

Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…

Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…

Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…

Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…