Related papers: Inclusion-exclusion by ordering-free cancellation
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this…
We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
Our earlier publications showed semantic tableau admits partial exceptions to the Second Incompleteness Theorem where a formalism recognizes its self consistency and views multiplication as a 3-way relation (rather than as a total…
In this paper we calibrate the strength of the soundness of a Kripke-Platek set theory with the axioms of Infinity and \Pi_{1}-Collection with the assumption that`there exists an uncountable regular ordinal' in terms of the existence of…
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
We discuss a path toward the generalisation of the nested soft-collinear subtraction scheme to arbitrary $2\rightarrow n$ processes. The scheme is designed to provide an efficient and process-independent procedure to extract and regulate…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
In previous work we provided a method for eliminating cuts in non-wellfounded proofs with a local-progress condition, these being the simplest kind of non-wellfounded proofs. The method consisted of splitting the proof into nicely behaved…
Standard Bayesian inference can build models that combine information from various sources, but this inference may not be reliable if components of a model are misspecified. Cut inference, as a particular type of modularized Bayesian…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
A general scheme for analyzing reductions of Whitham hierarchies is presented. It is based on a method for determining the $S$-function by means of a system of first order partial differential equations. Compatibility systems of…
We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination in multiplicative proof nets corresponds to instances of…
We prove a removal lemma for induced ordered hypergraphs, simultaneously generalizing Alon--Ben-Eliezer--Fischer's removal lemma for ordered graphs and the induced hypergraph removal lemma. That is, we show that if an ordered hypergraph…
We study a fundamental, all order cancellation operating between graphs of distinct kinematic nature, which allows for the construction of gauge-independent effective self-energies, vertices, and boxes at arbitrary order.
In this paper we express the difference of two complementary Beatty sequences, as the sum of two Beatty sequences closely related to them. In the process we introduce a new Algorithm that generalizes the well known Minimum Excluded…
We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model…