Related papers: Error Bounds and Metric Subregularity
A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
I argue that regularizing terms in standard regression methods not only help against overfitting finite data, but sometimes also yield better causal models in the infinite sample regime. I first consider a multi-dimensional variable…
Based on the work of Romano and Shaikh (2006) and Lehmann and Romano (2005) we give a sufficient criterion for controlling generalised error rates for arbitrarily dependent p-values. This criterion is formulated in terms of matrices…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…
The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for a system of vectors to satisfy the Welch…
This paper concerns the study of a broad class of minimal time functions corresponding to control problems with constant convex dynamics and closed target sets in arbitrary Banach spaces. In contrast to other publications, we do not impose…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
The field-theoretical model describing multicritical phenomena with two coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||}) \oplus O(n_{\perp}) symmetry is considered. Conditions for realization of different types…
A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is…
Generalised dichotomic quantum measurements are fully characterised by two real parameters, dubbed as sharpness parameter and biasedness parameter. The trade-off between the degree of joint measurability, sharpness and biasedness of…
In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include time-varying systems modeled with unbounded state-space operators acting…
Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…
Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of…
The solution to fine tuning is one of the principal motivations for Beyond the Standard Model (BSM) Studies. However constraints on new physics indicate that many of these BSM models are also fine tuned (although to a much lesser extent).…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…