One-Loop Helicity Amplitudes for ttbar Production at Hadron Colliders

We present compact analytic expressions for all one-loop helicity amplitudes contributing to ttbar production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation.Comment: 29 pages, 5 figures, v2 typos corrected (journal version

CANONICITY AND HOMOTOPY CANONICITY FOR CUBICAL TYPE THEORY

Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. We present in this article two canonicity results, both proved by a sconing argument: a homotopy canonicity result, every natural number is path equal to a numeral, even if we take away the equations defining the lifting operation on the type structure, and a canonicity result, which uses these equations in a crucial way. Both proofs are done internally in a presheaf model

Homotopy Canonicity for Cubical Type Theory

Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. In this paper we show by a sconing argument that if we remove these equations for the path lifting operation from the system, we still retain homotopy canonicity: every natural number is path equal to a numeral

The effective model structure and ∞\infty-groupoid objects

For a category $\mathcal E$ with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simplicial objects in $\mathcal E$, generalising the Kan--Quillen model structure on simplicial sets. We then prove that the effective model structure is left and right proper and satisfies descent in the sense of Rezk. As a consequence, we obtain that the associated $\infty$-category has finite limits, colimits satisfying descent, and is locally Cartesian closed when $\mathcal E$ is, but is not a higher topos in general. We also characterise the $\infty$-category presented by the effective model structure, showing that it is the full sub-category of presheaves on $\mathcal E$ spanned by Kan complexes in $\mathcal E$, a result that suggests a close analogy with the theory of exact completions

Sparse Binary Compression: Towards Distributed Deep Learning with minimal Communication

Currently, progressively larger deep neural networks are trained on ever growing data corpora. As this trend is only going to increase in the future, distributed training schemes are becoming increasingly relevant. A major issue in distributed training is the limited communication bandwidth between contributing nodes or prohibitive communication cost in general. These challenges become even more pressing, as the number of computation nodes increases. To counteract this development we propose sparse binary compression (SBC), a compression framework that allows for a drastic reduction of communication cost for distributed training. SBC combines existing techniques of communication delay and gradient sparsification with a novel binarization method and optimal weight update encoding to push compression gains to new limits. By doing so, our method also allows us to smoothly trade-off gradient sparsity and temporal sparsity to adapt to the requirements of the learning task. Our experiments show, that SBC can reduce the upstream communication on a variety of convolutional and recurrent neural network architectures by more than four orders of magnitude without significantly harming the convergence speed in terms of forward-backward passes. For instance, we can train ResNet50 on ImageNet in the same number of iterations to the baseline accuracy, using $\times 3531$ less bits or train it to a $1\%$ lower accuracy using $\times 37208$ less bits. In the latter case, the total upstream communication required is cut from 125 terabytes to 3.35 gigabytes for every participating client

Constructing a universe for the setoid model

The setoid model is a model of intensional type theory that validates certain extensionality principles, like function extensionality and propositional extensionality, the latter being a limited form of univalence that equates logically equivalent propositions. The appeal of this model construction is that it can be constructed in a small, intensional, type theoretic metatheory, therefore giving a method to boostrap extensionality. The setoid model has been recently adapted into a formal system, namely Setoid Type Theory (SeTT). SeTT is an extension of intensional Martin-L\uf6f type theory with constructs that give full access to the extensionality principles that hold in the setoid model. Although already a rich theory as currently defined, SeTT currently lacks a way to internalize the notion of type beyond propositions, hence we want to extend SeTT with a universe of setoids. To this aim, we present the construction of a (non-univalent) universe of setoids within the setoid model, first as an inductive-recursive definition, which is then translated to an inductive-inductive definition and finally to an inductive family. These translations from more powerful definition schemas to simpler ones ensure that our construction can still be defined in a relatively small metatheory which includes a proof-irrelevant identity type with a strong transport rule

Evaluating the Benefits: Quantifying the Effects of TCP Options, QUIC, and CDNs on Throughput

To keep up with increasing demands on quality of experience, assessing and understanding the performance of network connections is crucial for web service providers. While different measures, like TCP options, alternative transport layer protocols like QUIC, or the hosting of services in CDNs, are expected to improve connection performance, no studies are quantifying such impacts on connections on the Internet. This paper introduces an active Internet measurement approach to assess the impacts of mentioned measures on connection performance. We conduct downloads from public web servers considering different vantage points, extract performance indicators like throughput, RTT, and retransmission rate, and survey speed-ups due to TCP option usage. Further, we compare the performance of QUIC-based downloads to TCP-based downloads considering different option configurations. Next to significant throughput improvements due to TCP option usage, in particular TCP window scaling, and QUIC, our study shows significantly increased performance for connections to domains hosted by different giant CDNs.Comment: Presented at the ACM/IRTF Applied Networking Research Workshop 2023 (ANRW23

Canonicity and homotopy canonicity for cubical type theory

Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. We present in this article two canonicity results, both proved by a sconing argument: a homotopy canonicity result, every natural number is path equal to a numeral, even if we take away the equations defining the lifting operation on the type structure, and a canonicity result, which uses these equations in a crucial way. Both proofs are done internally in a presheaf model

Stereoselective synthesis of γ-hydroxynorvaline through combination of organo- and biocatalysis

An efficient route for the synthesis of all four diastereomers of PMP-protected α-amino-γ-butyrolacton to access γ-hydroxynorvaline was established. The asymmetric key steps comprise an organocatalytic Mannich reaction and an enzymatic ketone reduction. Three reaction steps could be integrated in a one-pot process, using 2-PrOH both as solvent and as reducing agent. The sequential construction of stereogenic centres gave access to each of the four stereoisomers in high yield and with excellent stereocontrol