arXiv subjects

Brian Tyrrell

Publications and source records attributed to Brian Tyrrell.

6 recordsLinked to original sources

arXiv2023

Extremely Large Area (88 mm X 88 mm) Superconducting Integrated Circuit (ELASIC)

Superconducting integrated circuit (SIC) is a promising "beyond-CMOS" device technology enables speed-of-light, nearly lossless communications to advance cryogenic (4 K or lower) computing. However, the lack of large-area superconducting IC has hindered the development of scalable practical systems. Herein, we describe a novel approach to interconnect 16 high-resolution deep UV (DUV EX4, 248 nm lithography) full reticle circuits to fabricate an extremely large (88mm X 88 mm) area superconducting integrated circuit (ELASIC). The fabrication process starts by interconnecting four high-resolution DUV EX4 (22 mm X 22 mm) full reticles using a single large-field (44 mm X 44 mm) I-line (365 nm lithography) reticle, followed by I-line reticle stitching at the boundaries of 44 mm X 44 mm fields to fabricate the complete ELASIC field (88 mm X 88 mm). The ELASIC demonstrated a 2X-12X reduction in circuit features and maintained high-stitched line superconducting critical currents. We examined quantum flux parametron (QFP) circuits to demonstrate the viability of common active components used for data buffering and transmission. Considering that no stitching requirement for high-resolution EX4 DUV reticles is employed, the present fabrication process has the potential to advance the scaling of superconducting quantum devices.

cond-mat.supr-con↗

arXiv2022

Finite Undecidability in Fields II: PAC, PRC and PpC Fields

A field $K$ in a ring language $\mathcal{L}$ is finitely undecidable if $\mbox{Cons}(\Sigma)$ is undecidable for every nonempty finite $\Sigma \subseteq \mbox{Th}(K; \mathcal{L})$. We adapt arguments originating with Cherlin-van den Dries-Macintyre/Ershov (for PAC fields) and Haran (for PRC fields) to prove all PAC and PRC fields are finitely undecidable. We describe the difficulties that arise in adapting the proof to P$p$C fields, and show no bounded P$p$C field is finitely axiomatisable. This work is drawn from the author's PhD thesis and is a sequel to arXiv:2210.12729.

math.LO↗

arXiv2022

Finite Undecidability in Fields I: NIP Fields

A field $K$ in a ring language $\mathcal{L}$ is finitely undecidable if $\mbox{Cons}(\Sigma)$ is undecidable for every nonempty finite $\Sigma \subseteq \mbox{Th}(K; \mathcal{L})$. We extend a construction of Ziegler and (among other results) use a first-order classification of Anscombe and Jahnke to prove every NIP henselian nontrivially valued field is finitely undecidable. We conclude (assuming the NIP Fields Conjecture) that every NIP field is finitely undecidable. This work is drawn from the author's PhD thesis.

math.LO↗

arXiv2021

A Note on Hilbert's "Geometric" Tenth Problem

This paper explores undecidability in theories of positive characteristic function fields in the "geometric" language of rings $\mathcal{L}_F = \{0, 1, +, \cdot, F\}$, with a unary predicate $F$ for nonconstant elements. In particular we are motivated by a question of Fehm on the decidability of $\mbox{Th}_{\exists}(\mathbb{F}_p(t); \mathcal{L}_F)$; equivalently, that of $\mbox{Th}_{\exists}(\mathbb{F}_p(t); \mathcal{L}_r)$ without parameters. We indicate how to generalise existing machinery to prove the undecidability of $\mbox{Th}_{\forall^1\exists}(K; \mathcal{L}_F)$ without parameters, where $K$ is the function field of a curve over an algebraic extension of $\mathbb{F}_p$, not algebraically closed. We discuss the problem (and its geometric implications) further in this context too.

math.LO↗

arXiv2019

A New Universal Definition of $\mathbb{F}_q [t]$ in $\mathbb{F}_q (t)$

This paper gives a universal definition of $\mathbb{F}_q [t]$ in $\mathbb{F}_q (t)$ using 89 quantifiers, more direct than those that exist in the current literature. The language $\mathcal{L}_{\mbox{rings}, t}$ we consider here is the language of rings $\{0, 1, +, -, \cdot\}$ with an additional constant symbol $t$. We then modify this definition marginally to universally define $\mathbb{F}_q [t]$ in $\mathbb{F}_q (t)$ without parameters, using 90 quantifiers. We assume throughout that the characteristic of $\mathbb{F}_q$ is odd.

math.LO↗

arXiv2018

Applying Distributional Compositional Categorical Models of Meaning to Language Translation

The aim of this paper is twofold: first we will use vector space distributional compositional categorical models of meaning to compare the meaning of sentences in Irish and in English (and thus ascertain when a sentence is the translation of another sentence) using the cosine similarity score. Then we shall outline a procedure which translates nouns by understanding their context, using a conceptual space model of cognition. We shall use metrics on the category ConvexRel to determine the distance between concepts (and determine when a noun is the translation of another noun). This paper will focus on applications to Irish, a member of the Gaelic family of languages.

cs.CL↗