Related papers: Approximating the Existential Theory of the Reals
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We propose an approach to formally specifying the behavioral properties of systems that rely on a perception model for interactions with the physical world. The key idea is to introduce embeddings -- mathematical representations of a…
The paper addresses an escape of a classical particle from a potential well under harmonic forcing. Most dangerous/efficient escape dynamics reveals itself in conditions of 1:1 resonance and can be described in the framework of isolated…
E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained by thresholding some e-variable. As such, e-variables arise…
We establish the validity of bootstrap methods for empirical likelihood (EL) inference under the density ratio model (DRM). In particular, we prove that the bootstrap maximum EL estimators share the same limiting distribution as their…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…
Polynomial series approximations are a central theme in approximation theory due to their utility in an abundance of numerical applications. The two types of series, which are featured most prominently, are Taylor series expansions and…
We begin by surveying the historical positions in different attempts to understand the material world since the rise of modern science, with specific focus on the role of Cartesian primary qualities in explanatory conceptualisation.…
The $\epsilon$-approximate degree of a Boolean function $f: \{-1, 1\}^n \to \{-1, 1\}$ is the minimum degree of a real polynomial that approximates $f$ to within $\epsilon$ in the $\ell_\infty$ norm. We prove several lower bounds on this…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems…
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen ('EPR') reported on a thought experiment that they believed showed that quantum theory provided an incomplete description of reality. Today we know that quantum theory is a complete…
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
In an empirical logic, an experimentally verifiable proposition P relating to a quantum system is assigned the value of either true of false if the system is in the pure state that belongs or, respectively, does not belong to the Hilbert…