Related papers: On principles between $\Sigma_1$- and $\Sigma_2$-i…
Weighted First Order Model Counting (WFOMC) is fundamental to probabilistic inference in statistical relational learning models. As WFOMC is known to be intractable in general ($\#$P-complete), logical fragments that admit polynomial time…
We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is epsilon_X", and (2) "If X is a well-ordering, then so is phi(alpha,X)", where alpha is a…
This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability…
Let $\Sigma_1,\ldots,\Sigma_k$ be finite alphabets, and let $\mu$ be a distribution over $\Sigma_1 \times \dots \times \Sigma_k$ in which the probability of each atom is at least $\alpha$. We prove that if $\mu$ does not admit Abelian…
Let $(\xi_1, \eta_1)$, $(\xi_2, \eta_2),\ldots$ be independent identically distributed $\mathbb{R}^2$-valued random vectors. We prove a strong law of large numbers, a functional central limit theorem and a law of the iterated logarithm for…
Capretta's delay monad can be used to model partial computations, but it has the "wrong" notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the "right" notion of equality, weak bisimilarity.…
We study preferential attachment (PA) trees with general attachment functions. PA suggests an intuitive monotonicity: if high-degree vertices are rewarded more strongly, then the resulting tree should become shallower. We examine this…
In this article, we introduce higher derivative Lagrangians of this form $\alpha_1 A_{\mu}(x)\dot{x}^\mu$, $\alpha_2 G_{\mu}(x)\ddot{x}^\mu$, $\alpha_3 B_{\mu}(x)\dddot{x}^\mu$, $\alpha_4 K_{\mu}(x)\ddddot{x}^\mu$, $\cdots$, that generalize…
The explicit construction of function fields tower with many rational points relative to the genus in the tower play a key role for the construction of asymptotically good algebraic-geometric codes. In 1997 Garcia, Stichtenoth and Thomas…
The main aim of this paper is to study the functional inequality \begin{equation*} \int_{[0,1]}f\bigl((1-t)x+ty\bigr)d\mu(t)\geq 0, \qquad x,y\in I \mbox{ with } x<y, \end{equation*} for a continuous unknown function $f:I\to{\mathbb R}$,…
An equivalent norm in the weighted Bergman space $A^p_\omega$, induced by an $\omega$ in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood-Paley inequalities are also…
Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topological spaces endowed with the wedge product. We then prove…
The classical theorem of Schnirelmann states that the primes are an additive basis for the integers. In this paper we consider the analogous multiplicative setting of the cyclic group $\left(\mathbb{Z}/ q\mathbb{Z}\right)^{\times}$, and…
The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes larger than any node is…
We introduce bounded category forcing axioms for well-behaved classes $\Gamma$. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe $H_{\lambda_\Gamma^+}$ modulo…
Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…
It was proved few years ago that classes of Boolean functions definable by means of functional equations \cite{EFHH}, or equivalently, by means of relational constraints \cite{Pi2}, coincide with initial segments of the quasi-ordered set…
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of stable set polytope. We apply it to majority functions and…
Simple proofs of the midpoint, trapezoidal and Simpson's rules are proved for numerical integration on a compact interval. The integrand is assumed to be twice continuously differentiable for the midpoint and trapezoidal rules, and to be…
In this paper we obtain Berry-Esse\'en bounds on partial sums of functionals of heavy-tailed moving averages, including the linear fractional stable noise, stable fractional ARIMA processes and stable Ornstein-Uhlenbeck processes. Our rates…