arXiv subjects

Martin Dyer

Publications and source records attributed to Martin Dyer.

At least 19 recordsLinked to original sources

arXiv2026

V407 Vul: a triple star system with an AM CVn detectable by gravitational wave observatories

The AM CVn class includes mass transferring, ultra-compact double white dwarf binaries with orbital periods on the timescale of minutes. A long-standing puzzle is that none of the roughly fifty ultra-compact, "verification binaries" which are easily detectable in the millihertz gravitational wave regime reside in a triple star configuration. Much evidence has hinted at V407 Vul being an inspiraling, double white dwarf AM CVn with an orbital period of 569s. Yet, a decisive confirmation has proved challenging since a main sequence star dominates its visible spectrum. We present a clear confirmation of the triple star nature of the source by detecting a significant astrometric wobble of the photocentre on the 569s orbital period of the binary. The AM CVn and the main sequence components are gravitationally bound with a spatial separation of roughly 0.03-0.04'', equating to an orbital separation of approximately 120AU. A total of 23 years of orbital timing constrained the orbital decay of the AM CVn as being precise to the 1% level, critical in understanding if this class of binary survives through a period minimum or coalesce. New Hubble Space Telescope ultra-violet imaging and spectroscopic data allowed the isolated detection of the AM CVn at shorter wavelengths, revealing an approximately 58000 K accretor white dwarf, while placing a firm distance constraint of 3510+140-110 pc. At this distance, we predict that the Laser Interferometer Space Antenna (LISA) will detect V407 Vul with a 28.4+-9.2 signal-to-noise ratio in a 4yr mission time, making it the first verification binary with an outer tertiary, or "verification triple", detectable for millihertz gravitational wave observatories.

astro-ph.SR↗

arXiv2026

An eclipsing 8.56 minute orbital period mass-transferring binary

We report the discovery of ATLAS J101342.5-451656.8 (hereafter ATLAS J1013-4516), an 8.56 minute orbital period mass transferring AM Canum Venaticorum binary with mean Gaia magnitude G=19.51. The system was identified via periodic variability in Asteroid Terrestrial-impact Last Alert System light curves of Gaia white dwarf candidates. Follow-up spectroscopy with the Large Lenslet Array Magellan Spectrograph reveals a helium dominated accretion disk, while high speed ULTRACAM photometry shows pronounced primary and secondary eclipses. We construct a decade long orbital timing baseline using ATLAS and Gaia survey photometry together with high speed observations from ULTRACAM on the NTT and proto Lightspeed on the Magellan Clay telescope. From this baseline we measure an orbital period derivative Pdot = -1.60 +/- 0.07 x 10^-12 seconds per second. Interpreted in the context of stable mass transfer, the magnitude and sign of Pdot indicate orbital evolution governed by the interplay between gravitational wave driven angular momentum losses and mass transfer, directly probing the donor star structural response to mass loss. Assuming angular momentum loss dominated by gravitational radiation, we constrain the component masses and infer the characteristic gravitational wave strain. We predict a four year Laser Interferometer Space Antenna signal to noise ratio greater than 10, establishing ATLAS J1013-4516 as a strong prospective space based gravitational wave source that probes long term orbital evolution in the mass transferring regime.

astro-ph.SR↗

arXiv2024

A gravitational wave detectable candidate Type Ia supernova progenitor

Type Ia supernovae, critical for studying cosmic expansion, arise from thermonuclear explosions of white dwarfs, but their precise progenitor pathways remain unclear. Growing evidence supports the ``double-degenerate'' scenario, where two white dwarfs interact. The absence of other companion types capable of explaining the observed Ia rate, along with observations of hyper-velocity white dwarfs interpreted as surviving companions of such systems provide compelling evidence in favor of this scenario. Upcoming millihertz gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) are expected to detect thousands of double-degenerate systems, though the most compact known candidate Ia progenitors produce only marginally detectable gravitational wave signals. Here, we report observations of ATLAS J1138-5139, a binary white dwarf system with an orbital period of 28 minutes. Our analysis reveals a 1 solar mass carbon-oxygen white dwarf accreting from a helium-core white dwarf. Given its mass, the accreting carbon-oxygen white dwarf is poised to trigger a typical-luminosity Type Ia supernova within a few million years, or to evolve into a stably mass-transferring AM CVn system. ATLAS J1138-5139 provides a rare opportunity to calibrate binary evolution models by directly comparing observed orbital parameters and mass transfer rates closer to merger than any previously identified candidate Type Ia progenitor. Its compact orbit ensures detectability by LISA, demonstrating the potential of millihertz gravitational wave observatories to reveal a population of Type Ia progenitors on a Galactic scale, paving the way for multi-messenger studies offering insights into the origins of these cosmologically significant explosions.

astro-ph.SR↗

arXiv2024

GERry: A Code to Optimise the Hunt for the Electromagnetic Counter-parts to Gravitational Wave Events

The search for the electromagnetic counterparts to gravitational wave (GW) events has been rapidly gathering pace in recent years thanks to the increasing number and capabilities of both gravitational wave detectors and wide field survey telescopes. Difficulties remain, however, in detecting these counterparts due to their inherent scarcity, faintness and rapidly evolving nature. To find these counterparts, it is important that one optimises the observing strategy for their recovery. This can be difficult due to the large number of potential variables at play. Such follow-up campaigns are also capable of detecting hundreds or potentially thousands of unrelated transients, particularly for GW events with poor localisation. Even if the observations are capable of detecting a counterpart, finding it among the numerous contaminants can prove challenging. Here we present the Gravitational wave Electromagnetic RecovRY code (GERry) to perform detailed analysis and survey-agnostic quantification of observing campaigns attempting to recover electromagnetic counterparts. GERry considers the campaign's spatial, temporal and wavelength coverage, in addition to Galactic extinction and the expected counterpart light curve evolution from the GW 3D localisation volume. It returns quantified statistics that can be used to: determine the probability of having detected the counterpart, identify the most promising sources, and assess and refine strategy. Here we demonstrate the code to look at the performance and parameter space probed by current and upcoming wide-field surveys such as GOTO & VRO.

astro-ph.IM↗

arXiv2023

Thick Forests

We consider classes of graphs, which we call thick graphs, that have the vertices of a corresponding thin graph replaced by cliques and the edges replaced by cobipartite graphs In particular, we consider the case of thick forests, which we show to be the largest class of perfect thick graphs. Recognising membership of a class of thick graphs is NP-complete unless the class of thin graphs is triangle-free, so we focus on this case. Even then membership can be NP-complete. However, we show that the class of thick forests can be recognised in polynomial time. We consider two well-studied combinatorial problems on thick graphs, independent sets and proper colourings. Since determining the independence or chromatic number of a perfect graph is known to be tractable, we examine the complexity of counting all independent sets and colourings in thick forests. Finally, we consider two parametric extensions to larger classes of thick graphs: where the parameter is the size of the thin graph, and where the parameter is its treewidth.

math.CO↗

arXiv2023

Triangle processes on graphs with given degree sequence

The switch chain is a well-studied Markov chain which generates random graphs with a given degree sequence and has uniform stationary distribution. Motivated by the high number of triangles seen in some real-world networks, we study a variant of the switch chain which is more likely to produce graphs with higher numbers of triangles. Specifically, we apply a Metropolis scheme designed to have the following stationary distribution: graph $G$ has probability proportional to $\lambda^{\min\{t(G),\nu\}}$, where $t(G)$ is the number of triangles in $G$ and $\nu$ is a cut-off value introduced to moderate the impact of graphs with a very high number of triangles. We assume that the "activity" $\lambda$ satisfies $\lambda\geq 1$, and call the resulting chain the modified Metropolis switch chain. We prove that the modified Metropolis switch chain is rapidly mixing whenever the (standard) switch chain is rapidly mixing, provided that the activity and maximum degree are not too large. The triangle switch (or "$\triangle$-switch") chain is a restriction of the switch chain which only performs switches that change the set of triangles in the graph. We prove that the $\triangle$-switch chain is irreducible for any degree sequence with minimum degree at least 3, and prove a rapid mixing result for the modified Metropolis $\triangle$-switch chain. Finally, we investigate the distribution of triangles in random graphs with given degrees, under both the uniform distribution and the distribution in which graph $G$ has probability proportional to $\lambda^{t(G)}$. Our analysis implies that the imposition of the cut-off $\nu$ does not significantly impact the behaviour of these modified Metropolis chains over polynomially many steps

math.PR↗

arXiv2020

A triangle process on regular graphs

Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at least one triangle. Triangle switches can be used to define Markov chains which generate graphs with a given degree sequence and with many more triangles (3-cycles) than is typical in a uniformly random graph with the same degrees. We show that the set of triangle switches connects the set of all $d$-regular graphs on $n$ vertices, for all $d\geq 3$. Hence, any Markov chain which assigns positive probability to all triangle switches is irreducible on these graphs. We also investigate this question for 2-regular graphs.

math.CO↗

arXiv2020

Machine Learning for Transient Recognition in Difference Imaging With Minimum Sampling Effort

The amount of observational data produced by time-domain astronomy is exponentially in-creasing. Human inspection alone is not an effective way to identify genuine transients fromthe data. An automatic real-bogus classifier is needed and machine learning techniques are commonly used to achieve this goal. Building a training set with a sufficiently large number of verified transients is challenging, due to the requirement of human verification. We presentan approach for creating a training set by using all detections in the science images to be thesample of real detections and all detections in the difference images, which are generated by the process of difference imaging to detect transients, to be the samples of bogus detections. This strategy effectively minimizes the labour involved in the data labelling for supervised machine learning methods. We demonstrate the utility of the training set by using it to train several classifiers utilizing as the feature representation the normalized pixel values in 21-by-21pixel stamps centered at the detection position, observed with the Gravitational-wave Optical Transient Observer (GOTO) prototype. The real-bogus classifier trained with this strategy can provide up to 95% prediction accuracy on the real detections at a false alarm rate of 1%.

astro-ph.IM↗

arXiv2020

Sampling hypergraphs with given degrees

There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm $\mathcal{A}$ for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm $\mathcal{A}$, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a positive constant.

cs.DM↗

arXiv2020

Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs

We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding" technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. Algorithms (SODA16), 514-527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.

cs.DS↗

arXiv2020

A dichotomy for bounded degree graph homomorphisms with nonnegative weights

We consider the complexity of counting weighted graph homomorphisms defined by a symmetric matrix $A$. Each symmetric matrix $A$ defines a graph homomorphism function $Z_A(\cdot)$, also known as the partition function. Dyer and Greenhill [10] established a complexity dichotomy of $Z_A(\cdot)$ for symmetric $\{0, 1\}$-matrices $A$, and they further proved that its #P-hardness part also holds for bounded degree graphs. Bulatov and Grohe [4] extended the Dyer-Greenhill dichotomy to nonnegative symmetric matrices $A$. However, their hardness proof requires graphs of arbitrarily large degree, and whether the bounded degree part of the Dyer-Greenhill dichotomy can be extended has been an open problem for 15 years. We resolve this open problem and prove that for nonnegative symmetric $A$, either $Z_A(G)$ is in polynomial time for all graphs $G$, or it is #P-hard for bounded degree (and simple) graphs $G$. We further extend the complexity dichotomy to include nonnegative vertex weights. Additionally, we prove that the #P-hardness part of the dichotomy by Goldberg et al. [12] for $Z_A(\cdot)$ also holds for simple graphs, where $A$ is any real symmetric matrix.

cs.CC↗

arXiv2019

Counting weighted independent sets beyond the permanent

Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edge-weighted matchings in a bipartite graph. Equivalently, this may be viewed as approximating the partition function of vertex-weighted independent sets in the line graph of a bipartite graph. Line graphs of bipartite graphs are perfect graphs, and are known to be precisely the class of (claw, diamond, odd hole)-free graphs. So how far does the result of Jerrum, Sinclair and Vigoda extend? We first show that it extends to (claw, odd hole)-free graphs, and then show that it extends to the even larger class of (fork, odd hole)-free graphs. Our techniques are based on graph decompositions, which have been the focus of much recent work in structural graph theory, and on structural results of Chvatal and Sbihi (1988), Maffray and Reed (1999) and Lozin and Milanic (2008).

cs.DM↗

arXiv2019

Triangle-creation processes on cubic graphs

An edge switch is an operation which makes a local change in a graph while maintaining the degree of every vertex. We introduce a switch move, called a triangle switch, which creates or deletes at least one triangle. Specifically, a make move is a triangle switch which chooses a path $zwvxy$ of length 4 and replaces it by a triangle $vxwv$ and an edge $yz$, while a break move performs the reverse operation. We consider various Markov chains which perform random triangle switches, and assume that every possible make or break move has positive probability of being performed. Our first result is that any such Markov chain is irreducible on the set of all 3-regular graphs with vertex set $\{1,2,\ldots, n\}$. For a particular, natural Markov chain of this type, we obtain a non-trivial linear upper and lower bounds on the number of triangles in the long run. These bounds are almost surely obtained in linear time, irrespective of the starting graph.

cs.DM↗

arXiv2018

Counting independent sets in graphs with bounded bipartite pathwidth

We show that a simple Markov chain, the Glauber dynamics, can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter called bipartite pathwidth. This result, which we prove for the more general hardcore distribution with fugacity $\lambda$, can be viewed as a strong generalisation of Jerrum and Sinclair's work on approximately counting matchings, that is, independent sets in line graphs. The class of graphs with bounded bipartite pathwidth includes claw-free graphs, which generalise line graphs. We consider two further generalisations of claw-free graphs and prove that these classes have bounded bipartite pathwidth. We also show how to extend all our results to polynomially-bounded vertex weights.

cs.DM↗

arXiv2018

Counting Independent Sets in Cocomparability Graphs

We show that the number of independent sets in cocomparability graphs can be counted in linear time, as can counting cliques in comparability graphs. By contrast, counting cliques in cocomparabilty graphs and counting independent sets in comparability graphs are #P-complete. We extend these results to counting maximal cliques and independent sets. We also consider the fixed-parameter versions of counting cliques and independent sets of given size $k$. Finally, we combine the results to show that both counting cliques and independent sets in permutation graphs are in linear time.

cs.DM↗

arXiv2018

A telescope control and scheduling system for the Gravitational-wave Optical Transient Observer (GOTO)

The Gravitational-wave Optical Transient Observer (GOTO) is a wide-field telescope project aimed at detecting optical counterparts to gravitational wave sources. The prototype instrument was inaugurated in July 2017 on La Palma in the Canary Islands. We describe the GOTO Telescope Control System (G-TeCS), a custom robotic control system written in Python which autonomously manages the telescope hardware and nightly operations. The system comprises of multiple independent control daemons, which are supervised by a master control program known as the "pilot". Observations are decided by a "just-in-time" scheduler, which instructs the pilot what to observe in real time and provides quick follow-up of transient events.

astro-ph.IM↗

arXiv2018

The flip Markov chain for connected regular graphs

Mahlmann and Schindelhauer (2005) defined a Markov chain which they called $k$-Flipper, and showed that it is irreducible on the set of all connected regular graphs of a given degree (at least 3). We study the 1-Flipper chain, which we call the flip chain, and prove that the flip chain converges rapidly to the uniform distribution over connected $2r$-regular graphs with $n$ vertices, where $n\geq 8$ and $r = r(n)\geq 2$. Formally, we prove that the distribution of the flip chain will be within $\varepsilon$ of uniform in total variation distance after $\text{poly}(n,r,\log(\varepsilon^{-1}))$ steps. This polynomial upper bound on the mixing time is given explicitly, and improves markedly on a previous bound given by Feder et al.(2006). We achieve this improvement by using a direct two-stage canonical path construction, which we define in a general setting. This work has applications to decentralised networks based on random regular connected graphs of even degree, as a self-stabilising protocol in which nodes spontaneously perform random flips in order to repair the network.

cs.DM↗

arXiv2018

Counting perfect matchings and the switch chain

We examine the problem of exactly or approximately counting all perfect matchings in hereditary classes of nonbipartite graphs. In particular, we consider the switch Markov chain of Diaconis, Graham and Holmes. We determine the largest hereditary class for which the chain is ergodic, and define a large new hereditary class of graphs for which it is rapidly mixing. We go on to show that the chain has exponential mixing time for a slightly larger class. We also examine the question of ergodicity of the switch chain in a arbitrary graph. Finally, we give exact counting algorithms for three classes.

cs.DM↗