In this companion piece to 1712.03573, some variations on the main results there are sketched. particular, recursions in which we interpreted as quantum Lefschetz, is reformulated terms of Givental's quantization formalism, or equivalently, a summation finitely many graphs. Meanwhile, varieties modification auxilliary spaces (masterspaces) for fixed point localization given, leading different (...

The existence of non-trivial periodic solutions of a general family of second order differential equations whose main model is a Hill’s equation with a cubic nonlinear term arising in different physical applications is proved. c © 2005 Elsevier Ltd. All rights reserved.

The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recurs...

Current life cycle impact assessment (LCIA) practices use a characterization factor to linearly scale chemical emission human health assuming homogeneous exposure and toxicological susceptibility for the entire population. However, both may vary within population, making same elicit disproportionate impacts. Here we explore how inter-individual variabilities in interact affect estimated overall...

We study a cyclic proof system C over regular expression types, inspired by linear logic and non-wellfounded theory. Proofs in can be seen as strongly typed goto programs. show that they denote computable total functions we analyse the relative strength of Gödel’s T. In general case, prove two systems capture same on natural numbers. affine i.e., when contraction is removed, precisely primitive...

Given a function f from {0, 1, . . . , N − 1} to {0, 1, . . . , N − 1}, we prove that f(x), the mth iterate of f at x, can be computed in time O(logN) for each natural number m and each x by using O(N) information that is generated in a preprocessing procedure. Two types of optimal orbit decompositions of functional graphs are proposed for the preprocess. Both preprocesses require only linear t...