Related papers: On the Composition of Randomized Query Complexity …
This paper is concerned with existence of big tight closure test elements for a commutative Noetherian ring $R$ of prime characteristic $p$. Let $R^{\circ}$ denote the complement in $R$ of the union of the minimal prime ideals of $R$. A big…
Let $R$ be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do \emph{not} assume that their quotient has finite…
Let $0 < \epsilon < 1/2$ be a noise parameter, and let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$. We upper bound the entropy of $T_{\epsilon}…
We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
This dissertation builds a compositional cyber-physical systems theory to develop concrete semantics relating the above diverse views necessary for safety and security assurance. In this sense, composition can take two forms. The first is…
One means of fitting functions to high-dimensional data is by providing smoothness constraints. Recently, the following smooth function approximation problem was proposed: given a finite set $E \subset \mathbb{R}^d$ and a function $f: E…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…
This paper investigates guesswork over ordered statistics and formulates the achievable guesswork complexity of ordered statistics decoding (OSD) in binary additive white Gaussian noise (AWGN) channels. The achievable guesswork complexity…
Approximating functions of a large number of variables poses particular challenges often subsumed under the term ``Curse of Dimensionality'' (CoD). Unless the approximated function exhibits a very high level of smoothness the CoD can be…
We study functions satisfying the composition law $F(xy)+F(x/y)=P(F(x),F(y))$ with a symmetric polynomial combiner $P$. We prove that symmetry together with a quadratic degree bound on $P$ forces a composition law of d'Alembert type. We…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
Composition and demonic refinement $\sqsubseteq$ of binary relations are defined by \begin{align*} (x, y)\in (R;S)&\iff \exists z((x, z)\in R\wedge (z, y)\in S) R\sqsubseteq S&\iff (dom(S)\subseteq dom(R) \wedge…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
We compute the motivic nearby cycles of functions obtained by composition with a polynomial which is non-degenerate with respect to its Newton polyhedron. Our result involves new convolution operators and generalized nearby cycles.
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
Compositionality is an important explanatory target in emergent communication and language evolution. The vast majority of computational models of communication account for the emergence of only a very basic form of compositionality:…