Related papers: On Group Averaging for SO(n,1)
We present an averaging process for sections of a torsor under a unipotent group. This process allows one to integrate local sections of such a torsor into a global simplicial section. The results of this paper have applications to…
We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
Batch normalization has been widely used to improve optimization in deep neural networks. While the uncertainty in batch statistics can act as a regularizer, using these dataset statistics specific to the training set impairs generalization…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
In this paper, a subgroup least squares and a convex clustering are introduced for inferring a partially heterogenous linear regression that has potential application in the areas of precision marketing and precision medicine. The…
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
The renormalization group flow in a general renormalizable gauge theory with a simple gauge group in 3+1 dimensions is analyzed. The flow of the ratios of the Yukawa couplings and the gauge coupling is described in terms of a bounded…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
Numerical approaches are an important tool to study strongly correlated quantum systems. However, their fragility with respect to rounding errors is not well studied and numerically verified enclosures of the results are not available. In…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
This is an earlier, but more general, version of "An L^1 Ergodic Theorem for Sparse Random Subsequences". We prove an L^1 ergodic theorem for averages defined by independent random selector variables, in a setting of general…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…