We define and study a learning paradigm that sits between identification in the limit and classification. More precisely, we expect a learner to determine in the limit which members of a finite set D of possible data belong to a target language L, where D is arbitrary. So as D becomes larger and larger, the task becomes closer and closer to identifying L. But as D is always finite and L can be ...

With recent calls for expanding the scope and rigor of engineering education research, use of qualitative methods to answer research questions that can not be answered through quantitative methods is taking on increasing significance. Well-designed qualitative studies often build on epistemological consistency across theoretical perspectives, research questions, and research methods. We examine...

Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of the popular family of spectral clustering algorithms, which clusters the data with the help of eigenvectors of graph Laplacian matrices. We develop new meth...

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find tha...

We study quadratically divergent radiative corrections to the oblique parameters at CERN LEP1 induced by non-standard vector boson self-couplings. We work in the Stückelberg formalism and regulate the divergences through a gauge-invariant higher derivative scheme. Using consistency arguments together with the data we find a limit on the anomalous magnetic moment ∆κ of the W-boson, |∆κ| ∼< 0.26.

We construct a string field Hamiltonian for a noncritical string theory with the continuum limit of the Ising model or its generalization as the matter theory on the worldsheet. It consists of only three string vertices as in the case for c = 0. We also discuss a general consistency condition that should be satisfied by this kind of string field Hamiltonian.

We demonstrate existence of optimal controls with respect to a quadratic cost criterion for the equation u t ? u = F(u; ') | rst for F aanely dependent on the control ' and then for a more fully nonlinear setting in which weak convergence for ' no longer suuces to give consistency in the limit.

1. Some aspects of classical empirical process theory: uniform laws of large numbers, process convergence and uniform central limit theorems. 2. M-estimation. Asymptotic theory of consistency, rates of convergence and limiting distribution. 3. Non-asymptotic theory of penalized empirical risk minimization; nonasymptotic deviation inequalities for suprema of empirical processes, oracle inequalit...