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Our open-source Python package BoFire combines Bayesian Optimization (BO) with other design of experiments (DoE) strategies focusing on developing and optimizing new chemistry. Previous BO implementations, for example as they exist in the literature or software, require substantial adaptation for effective real-world deployment in chemical industry. BoFire provides a rich feature-set with extensive configurability and realizes our vision of fast-tracking research contributions into industrial use via maintainable open-source software. Owing to quality-of-life features like JSON-serializability of problem formulations, BoFire enables seamless integration of BO into RESTful APIs, a common architecture component for both self-driving laboratories and human-in-the-loop setups. This paper discusses the differences between BoFire and other BO implementations and outlines ways that BO research needs to be adapted for real-world use in a chemistry setting., Comment: 6 pages, 1 figure, 1 listing

We consider the localization of the $\infty$-category of spaces at the $v_n$-periodic equivalences, the case $n=0$ being rational homotopy theory. We prove that this localization is for $n\geq 1$ equivalent to algebras over a certain monad on the $\infty$-category of $T(n)$-local spectra. This monad is built from the Bousfield--Kuhn functor., Comment: 8 pages

Goodwillie's calculus of homotopy functors associates a tower of polynomial approximations, the Taylor tower, to a functor of topological spaces over a fixed space. We define a new tower, the varying center tower, for functors of categories with a fixed initial object, such as algebras under a fixed ring spectrum. We construct this new tower using elements of the Taylor tower constructions of Bauer, Johnson, and McCarthy for functors of simplicial model categories, and show how the varying center tower differs from Taylor towers in terms of the properties of its individual terms and convergence behaviour. We prove that there is a combinatorial model for the varying center tower given as a pro-equivalence between the varying center tower and towers of cosimplicial objects; this generalizes Eldred's cosimplicial models for finite stages of Taylor towers. As an application, we present models for the de Rham complex of rational commutative ring spectra due to Rezk on the one hand, and Goodwillie and Waldhausen on the other, and use our result to conclude that these two models will be equivalent when extended to $E_{\infty}$-ring spectra., Comment: 29 pages. Replaces an earlier version after significant changes to Sections 1 and 3. These changes add motivation for the varying center tower, and add a detailed explanation of an application to the de Rham complex

Goodwillie's homotopy functor calculus constructs a Taylor tower of approximations to F, often a functor from spaces to spaces. Weiss's orthogonal calculus provides a Taylor tower for functors from vector spaces to spaces. In particular, there is a Weiss tower associated to the functor which sends a vector space V to F evaluated at the one-point compactification of V. In this paper, we give a comparison of these two towers and show that when F is analytic the towers agree up to weak equivalence. We include two main applications, one of which gives as a corollary the convergence of the Weiss Taylor tower of BO. We also lift the homotopy level tower comparison to a commutative diagram of Quillen functors, relating model categories for Goodwillie calculus and model categories for the orthogonal calculus., Comment: 28 pages, sequel to Capturing Goodwillie's Derivative, arXiv:1406.0424

Recently, the Johnson-McCarthy discrete calculus for homotopy functors was extended to include functors from an unbased simplicial model category to spectra. This paper completes the constructions needed to ensure that there exists a discrete calculus tower for functors from an unbased simplicial model category to chain complexes over a fixed commutative ring. Much of the construction of the Taylor tower for functors to spectra carries over to this context. However, one of the essential steps in the construction requires proving that a particular functor is part of a cotriple. For this, one needs to prove that certain identities involving homotopy limits hold up to isomorphism, rather than just up to weak equivalence. As the target category of chain complexes is not a simplicial model category, the arguments for functors to spectra need to be adjusted for chain complexes. In this paper, we take advantage of the fact that we can construct an explicit model for iterated fibers, and prove that the functor is a cotriple directly. We use related ideas to provide concrete infinite deloopings of the first terms in the resulting Taylor towers when evaluated at the initial object in the source category., Comment: 20 pages

Recent work of Biedermann and R\"ondigs has translated Goodwillie's calculus of functors into the language of model categories. Their work focuses on symmetric multilinear functors and the derivative appears only briefly. In this paper we focus on understanding the derivative as a right Quillen functor to a new model category. This is directly analogous to the behaviour of Weiss's derivative in orthogonal calculus. The immediate advantage of this new category is that we obtain a streamlined and more informative proof that the n-homogeneous functors are classified by spectra with an action of the symmetric group on n objects. In a later paper we will use this new model category to give a formal comparison between the orthogonal calculus and Goodwillie's calculus of functors., Comment: Final version, to appear. Substantially shortened from earlier version, with a significantly expanded introduction, new results and examples. 27 pages

We call a diagram D absolutely cartesian if F(D) is homotopy cartesian for all homotopy functors F. This is a sensible notion for diagrams in categories C where Goodwillie's calculus of functors may be set up for functors with domain C. We prove a classification theorem for absolutely cartesian squares of spaces and state a conjecture of the classification for higher dimensional cubes., Comment: 8 pages, accepted to the Arolla Conference Proceedings

In this paper, we show that for reduced homotopy endofunctors of spaces, F, and for all $n \geq 1$ there are adjoint functors $R_n, L_n$ with $T_n F \simeq R_n F L_n$, where $P_n F$ is the $n$-excisive approximation to $F$, constructed by taking the homotopy colimit over iterations of $T_n F$. This then endows $T_n$ of the identity with the structure of a monad and the $T_n F$'s are the functor version of bimodules over that monad. It follows that each $T_n F$ (and $P_nF$) takes values in spaces of symmetric Lusternik-Schnirelman cocategory $n$, as defined by Hopkins. This also recovers recent results of Chorny-Scherer. The spaces $T_n F(X)$ are in fact classically nilpotent (in the sense of Berstein-Ganea) but not nilpotent in the sense of Biedermann and Dwyer. We extend the original constructions of dual calculus to our setting, establishing the $n$-co-excisive approximation for a functor, and dualize our constructions to obtain analogous results concerning constructions $T^n$, $P^n$,and LS category., Comment: 29 pages. Final version. To appear in HHA

We call attention to the intermediate constructions $\T_n F$ in Goodwillie's Calculus of homotopy functors, giving a new model which naturally gives rise to a family of towers filtering the Taylor Tower of a functor. We also establish a surprising equivalence between the homotopy inverse limits of these towers and the homotopy inverse limits of certain cosimplicial resolutions. This equivalence gives a greatly simplified construction for the homotopy inverse limit of the Taylor tower of a functor $F$ under general assumptions., Comment: Reformatted for publication (this is the mockup), 23 pages, small typos and formatting corrected as well