Related papers: RCF4: Inconsistent Quantification

In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…

We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of <phi…

Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently…

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating…

Assessing consistency in Pairwise Comparison Matrices (PCMs) within the Analytical Hierarchy Process (AHP) poses significant challenges when using the traditional Consistency Ratio (CR) method. This study introduces a novel alternative that…

The theory of symmetry of quantum mechanical systems is applied to study the structure and properties of several classes of relevant maps in quantum information theory: CPTP, PPT and Schwarz maps. First, we develop the general structure…

Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However,…

In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on…

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…

In this article I investigate the phenomenon of minimum models of second-order set theories, focusing on Kelley--Morse set theory $\mathsf{KM}$, G\"odel--Bernays set theory $\mathsf{GB}$, and $\mathsf{GB}$ augmented with the principle of…

Kruskal's theorem famously states that finite trees (ordered using an infima-preserving embeddability relation) form a well partial order. Freund, Rathjen, and Weiermann extended this result to general recursive data types with their…

The main results of this paper are already known (V.V. Shokurov, the non-vanishing theorem, 1985). Moreover, the non-$\mathbb{Q}$-factorial MMP was more recently considered by O~Fujino, in the case of toric varieties (Equivariant…

We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been…

A binary matrix satisfies the consecutive ones property (COP) if its columns can be permuted such that the ones in each row of the resulting matrix are consecutive. Equivalently, a family of sets F = {Q_1,..,Q_m}, where Q_i is subset of R…

Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…

We prove the following two results. Theorem A: Let alpha be a limit ordinal. Suppose that 2^{|alpha|}<aleph_alpha and 2^{|alpha|^+}<aleph_{|alpha|^+}, whereas aleph_alpha^{|alpha|}>aleph_{|alpha|^+}. Then for all n< omega and for all…

The fact that the euclidean algorithm eventually terminates is pervasive in mathematics. In the language of continued fractions, it can be stated by saying that the orbits of rational points under the Gauss map x-->{1/x} eventually reach…

Invertible map equivalences are approximations of graph isomorphism that refine the well-known Weisfeiler-Leman method. They are parametrised by a number k and a set Q of primes. The intuition is that two graphs G and H which are equivalent…

We consider four prototypes of variational problems and prove the existence of fractal minimizers through the direct method in the calculus of variations. By design these minimizers are H\"older curves or H\"older parametrizations of…

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…