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Peter M. Higgins

Publications and source records attributed to Peter M. Higgins.

15 recordsLinked to original sources

A framework for evaluating biosignature potential against the abiotic baseline on ocean worlds

Ocean worlds are considered as targets for life detection missions because they meet several key requirements for habitability. However, identifying potential life on other worlds requires observing clear and unambiguous biosignature signals above the existing abiotic baseline. Consequently, this necessitates evaluating uncertainty and variability in the abiotic baseline, including processes that can overlap, attenuate, or obfuscate biosignatures before they are observed. This article develops a quantitative framework for holistically evaluating abiotic baselines on ocean worlds to guide life detection strategies. Using Enceladus as an example, we assess the potential of using: i) CH$_{4}$ isotopes and their relationship with CO$_{2}$, and ii) amino acid chirality as biosignatures, demonstrating that uncertainties in abiotic processes currently prevent hypothetical future ${\delta}^{13}$C$_{\mathrm{CO2}}$ and ${\delta}^{13}$C$_{\mathrm{CH4}}$ measurements from definitively inferring a biosphere on Enceladus. Additionally, our results quantitatively show that neglecting the abiotic baseline risks false negative life detection claims for both isotopic and chiral biosignatures. Interpreting these and other alternative biosignatures on Enceladus, Europa, Titan, and similar planetary bodies therefore requires complimentary geophysical observations such as constraining internal temperatures to within $\sim$10-100$^{\circ}$C, and improving characterisation of the target's rheology, lithology, initial abiotic organic inventory and ocean transport timescales.

astro-ph.EP

Terrestrial Analogs to Titan for Geophysical Research

Saturn's moon Titan exhibits remarkable parallels to the Earth in many geophysical and geological processes not found elsewhere in the solar system at the present day. These include a nitrogen atmosphere with a condensible gas - methane - replacing the Earth's water, leading to an active meteorology with rainfall and surface manifestations including rivers, lakes and seas, and the dissolution of karstic terrain. Other phenomena such as craters, dunes, and tectonic features are found elsewhere - e.g. on Mars and Venus - but their continuing alteration by pluvial, fluvial and lacustrine processes can be studied only on Earth and Titan. Meanwhile Titan also hosts an interior liquid water ocean with similarities to the Earth as well as to ocean worlds such as Europa and Enceladus. Our focus in this review paper is twofold: to describe the geophysical and geological parallels between Earth and Titan, and to evaluate the yet-underexploited possibilities for field analog research to gain new knowledge about these processes. To date, Titan's much colder temperature and different atmospheric and crustal materials have led to a skepticism that useful analogs can be found on Earth. Our conclusion, however, is that a much larger range of useful analog field work is possible and this work will substantially enhance our knowledge of both worlds. Such investigation will supplement the existing sparse data for Titan returned by space missions, will greatly enhance our understanding of such datasets, and will help to provide science impetus and goals for future missions.

astro-ph.EP

Production optimization by agents of differing work rates

We devise a scheme for producing, in the least possible time, $n$ identical objects with $p$ agents that work at differing speeds. This involves halting the process in order to transfer production across agent types. For the case of two types of agent, we construct a scheme based on the Euclidean algorithm that seeks to minimise the number of pauses in production.

math.CO

Equationally defined classes of semigroups

We apply, in the context of semigroups, the main theorem from~\cite{higjac} that an elementary class $\mathcal{C}$ of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We prove a dual to the Birkhoff theorem in that if the class is also closed under the taking of containing semigroups, some basis of equations of $\mathcal{C}$ is free of the $\forall$ quantifier. Examples are given of EHP-classes that require more than two quantifiers in some equation of any equational basis.

math.LO

The Biker-hiker problem

There are n travellers who have k bicycles and they wish to complete a journey in the shortest possible time. We investigate optimal solutions of this problem, showing they are characterized by a set of words in the Dyck language. Particular solutions with additional desirable properties are introduced and analysed.

math.CO

Orientation-preserving and orientation-reversing mappings: a new description

We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter semigroup coincides with the semigroup of all mappings that preserve intersections of chords on the corresponding circle.

math.CO

Epimorphisms, dominions and H-commutative semigroups

In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from commutative semigroups to H-commutative semigroups by showing that the dominion of an H-commutative semigroup is H-commutative. We then use this to generalise Howie and Isbell's result that any H-commutative semigroup satisfying the minimum condition on principal ideals is saturated.

math.GR

Green's relations and stability for subsemigroups

We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in left-stable semigroups. This is carried out in the context of a survey of the various closely related notions of stability and minimality of Green's classes that have appeared in the literature over the last sixty years, and which have sometimes been presented in different forms.

math.GR

Involution matchings, the semigroup of orientation-preserving and orientation-reversing mappings, and inverse covers of the full transformation semigroup

We continue the study of permutations of a finite regular semigroup that map each element to one of its inverses, providing a complete description in the case of semigroups whose idempotent generated subsemigroup is a union of groups. We show, in two ways, how to construct an involution matching on the semigroup of all transformations which either preserve or reverse orientation of a finite cycle. Finally, by way of application, we prove that finite full transformation semigroups have no cover by inverse semigroups that is closed under intersection.

math.GR

Embedding in a finite 2-generator semigroup

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to finite orthodox semigroups.

math.GR

Burrows-Wheeler transformations and de Bruijn words

We formulate and explain the extended Burrows-Wheeler transform of Mantaci et al from the viewpoint of permutations on a chain taken as a union of partial order-preserving mappings. In so doing we establish a link with syntactic semigroups of languages that are themselves cyclic semigroups. We apply the extended transform with a view to generating de Bruijn words through inverting the transform.

math.GR

Permutations of a semigroup that map to inverses

We investigate the question as to when the members of a finite regular semigroup may be permuted in such a way that each member is mapped to one of its inverses. In general this is not possible. However we reformulate the problem in terms of a related graph and, using an application of Hall's Marriage Lemma, we show in particular that the finite full transformation semigroup does enjoy this property.

math.GR

Orthodox semigroups and permutation matchings

We determine when an orthodox semigroup S has a permutation that sends each member of S to one of its inverses and show that if such a permutation exists, it may be taken to be an involution. In the case of a finite orthodox semigroup the condition is an effective one involving Green's relations on the combinatorial images of the principal factors of S. We also characterise some classes of semigroups via their permutation matchings.

math.GR