Related papers: On the strict comparison theorem for $G$-expectati…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
E prover is a state-of-the-art theorem prover for first-order logic with equality. E prover is built around a saturation loop, where new clauses are derived by inference rules from previously derived clauses. Selection of clauses for the…
The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…
Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…
This paper develops a new framework, \emph{simultaneous saturation}, designed to quantify the size of sets whose elements are simultaneously large. The framework establishes a correspondence between the magnitude of such sets and a system…
In this paper we extend the notion of g-evaluation, in particular g-expectation, to the case where the generator g is allowed to have a quadratic growth. We show that some important properties of the g-expectations, including a…
General Equilibrium Theory is the benchmark of economics, especially its results concerning the efficient allocation of resources, known as the First and Second Welfare Theorems. Yet, General Equilibrium Theory is beyond the scope of most…
This paper presents a theory of error in cross-validation testing of algorithms for predicting real-valued attributes. The theory justifies the claim that predicting real-valued attributes requires balancing the conflicting demands of…
We offer an interpretation of super-quantum correlations in terms of a "doubly" quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension \alpha' and the string coupling…
We show that the weak and strong forms of the Generalized Spectral Conjecture (GSC) of Boyle and Handelman are equivalent. The GSC asserts that well understood necessary spectral conditions on a square matrix A over a subring S of the reals…
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a…
In this note, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional stochastic differential equations (SDEs) with jumps and for matrix-valued SDEs with jumps.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
In the article 'Criteria for Strong and Weak Random Attractors' necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…
In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.
A {\em maximal inequality} seeks to estimate $\mathbb{E}\max_i X_i$ in terms of properties of the $X_i$. When the latter are independent, the union bound (in its various guises) can yield tight upper bounds. If, however, the $X_i$ are…
We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or…
Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type: {tabular}{rlll} $-dY_t$ &=& $f(t, Y_t, Z_t, Y_{t+\delta(t)}, Z_{t+\zeta(t)})dt-Z_tdB_t, $ & $ t\in[0, T];$ $Y_t$…