Related papers: Lifting with Inner Functions of Polynomial Discrep…
A resonance theorem providing existence of functions that are counterexamples for all members of a given family of translation invariant differentiation bases is proved. Applications of the theorem to Zygmund problem on a choice of…
Many results in mass partitions are proved by lifting $\mathbb{R}^d$ to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to use lifting arguments to polyhedral surfaces. Among other…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
As further development of earlier works on the $(f,g)$-inversion, the present paper is devoted to the $(f,g)$-difference operator and the representation problem or an expansion formula of analytic functions. A recursive formula and the…
We integrate the Lifting cocycles $\Psi_{2n+1},\Psi_{2n+3},\Psi_{2n+5},...$ ([Sh1], [Sh2]) on the Lie algebra $\Dif_n$ of holomorphic differential operators on an $n$-dimensional complex vector space to the cocycles on the Lie algebra of…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Let $f,g\in\overline{\mathbb{Q}}[z]$ be polynomials of degree $d\geq2$ with disconnected Julia sets. We prove that they have the same Lyapunov exponent $\mathcal{L}_f=\mathcal{L}_g$ if and only if either $f$ and $g$ are intertwined, or $f$…
A non-negative function f, defined on the real line or on a half-line, is said to be directly Riemann integrable (d.R.i.) if the upper and lower Riemann sums of f over the whole (unbounded) domain converge to the same finite limit, as the…
Generalized permutahedra are the polytopes obtained from the permutahedron by changing the edge lengths while preserving the edge directions, possibly identifying vertices along the way. We introduce a "lifting" construction for these…
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
We prove a structural theorem for generalized arithmetic progressions in $\F_p$ which contain a large product set of two other progressions.
Let $(f, g)$ be a pair of complex analytic functions on a singular analytic space $X$. We give ``the correct'' definition of the relative polar curve of $(f, g)$, and we give a very formal generalization of L\^e's attaching result, which…
We study tractability properties of the weighted $L_p$-discrepancy. The concept of {\it weighted} discrepancy was introduced by Sloan and Wo\'{z}\-nia\-kowski in 1998 in order to prove a weighted version of the Koksma-Hlawka inequality for…
The promise of lifted probabilistic inference is to carry out probabilistic inference in a relational probabilistic model without needing to reason about each individual separately (grounding out the representation) by treating the…
In weighted Orlicz type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…