The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations

We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta=1 is the unique invariant distribution for this Markov chain. Our proof uses a combination of probabilistic, combinatoric, and representation-theoretic arguments.Comment: To appear in Annals Probab. 6 figures Only change in new version is addition of proof (at end of article) that the state (1,0,0,...) is transien

Specialized Hidden Markov Model Databases for Microbial Genomics

As hidden Markov models (HMMs) become increasingly more important in the analysis of biological sequences, so too have databases of HMMs expanded in size, number and importance. While the standard paradigm a short while ago was the analysis of one or a few sequences at a time, it has now become standard procedure to submit an entire microbial genome. In the future, it will be common to submit large groups of completed genomes to run simultaneously against a dozen public databases and any number of internally developed targets. This paper looks at some of the readily available HMM (or HMM-like) algorithms and several publicly available HMM databases, and outlines methods by which the reader may develop custom HMM targets

On The Edge

Vol. 1 On the edge: Major work -- Vol. 2 On the edge: ExegesisMy creative work is a cycle of thirteen short stories entitled On the Edge. Each story is located in what might be described as Greater Port Adelaide. This is an area which stretches from Alberton and West Lakes northward through the historical port adjacent to the Port River and its Inner Harbour, and thence along the Le Fevre Peninsula from Birkenhead and Semaphore to North Haven and the Outer Harbour. Apart from a number of mansions and holiday homes built close to the beach by wealthy Adelaide businessmen around the turn of the 20th century the area has predominantly been occupied by members of the working class. By working class I mean that group of individuals normally regarded as wage labourers and their families, although under modern economic conditions many of its members are unemployed. Most employment in the area has traditionally been linked to shipping, the wharfs and numerous related maritime trades. Containerisation and other technical innovations drastically reduced the need for labour on the docks, just as globalisation has curtailed opportunities for local employment in manufacturing. It is the results of such shifts that my work seeks to illustrate by creating a montage of differing experiences for residents of the area. To emphasise the cyclical nature of the work I have started with the alienation of a school-leaver frustrated by his lack of opportunity and ended with the death of a seaman, a hang-over from the days of a more cohesive and politically committed society. There are also a number of characters who reappear or are at least mentioned in more than one story. As I was unaware of the existence of such a genre as a ‘cycle’ of short stories I have used my exegesis to undertake a brief enquiry into its history, concentrating on my proposition that such a genre is particularly suited to the exposition of social criticism. To this end I have traced its development from the ancient epic cycles, through the collections of the middle ages, to the final establishment of the cycle as a genre in its own right at the beginning of the 20th century. Subsequently I have concentrated on the works of two Australian authors, Frank Hardy and John Morrison, as I believe that each created a work that should be considered as a ‘cycle’ rather than as a ‘collection’ of short stories. It was reading Morrison’s Stories of the Waterfront that inspired me to write On the Edge. The exegesis begins with a short consideration of the differing modes of ‘realistic’ writing as this is the area I consider myself to be operating in. Indeed, in an era coming to be described as one of ‘post-truth’, I consider realism to be the method incumbent for a socially committed writer to utilise. The final chapter of my exegesis is concerned with those writers whom I feel have had a major influence on my own practice.Thesis (Ph.D.) -- University of Adelaide, School of Humanities, 201

Connectivity of Markoff mod-p graphs and maximal divisors

Markoff mod-$p$ graphs are conjectured to be connected for all primes $p$. In this paper, we use results of Chen and Bourgain, Gamburd, and Sarnak to confirm the conjecture for all $p > 3.448\cdot10^{392}$. We also provide a method that quickly verifies connectivity for many primes below this bound. In our study of Markoff mod-$p$ graphs we introduce the notion of \emph{maximal divisors} of a number. We prove sharp asymptotic and explicit upper bounds on the number of maximal divisors, which ultimately improves the Markoff graph $p$-bound by roughly 140 orders of magnitude as compared with an approach using all divisors

Comportamiento sísmico de un muro de contención de cinco metros y su desplazamiento – Carabayllo, 2021

La presente investigación “Comportamiento sísmico de un muro de contención de cinco metros y su desplazamiento- Carabayllo, 2021” tuvo como propósito: Evaluar el comportamiento sísmico de un muro de contención de cinco metros para verificar el desplazamiento, la población de estudio son los muros de contención de cinco metros del distrito de Carabayllo. La muestra es un muro de contención de cinco metros de altura del asentamiento humano El Progreso sector 4. El muestreo de del tipo no probabilístico, a criterio discrecional o criterio del investigador. El tipo de investigación es básica y el diseño es explicativo. La interacción muro- suelo es un proceso en el que la respuesta del suelo ante una carga dinámica (cargas por sismos, etc.) influye en el movimiento de la estructura y esta a su vez influye en el movimiento del suelo. Se determinaron los efectos de los empujes sísmicos de Mononobe-Okabe para la verificación de los máximos desplazamientos en un muro de gravedad, en voladizo y con contrafuerte de cinco metros de altura, obteniéndose que el máximo desplazamiento se da en el muro en voladizo con un desplazamiento de 0.68 cm. También se pudo hacer las comparaciones con el máximo asentamiento producido en la zapata en donde el muro por gravedad obtiene como resultado un asentamiento máximo de 0.197 cm. También se obtuvieron los valores de los esfuerzos máximos en compresión de las zapatas donde el muro de gravedad obtiene un resultado de 1.38 kg/cm2, todos estos resultados se dan en condición pseudoestatica, resultados que fueron obtenidos en el modelamiento con ayuda del programa SAP 2000 y con los empujes sísmicos de Mononobe-Okabe

Gene3D: comprehensive structural and functional annotation of genomes

Gene3D provides comprehensive structural and functional annotation of most available protein sequences, including the UniProt, RefSeq and Integr8 resources. The main structural annotation is generated through scanning these sequences against the CATH structural domain database profile-HMM library. CATH is a database of manually derived PDB-based structural domains, placed within a hierarchy reflecting topology, homology and conservation and is able to infer more ancient and divergent homology relationships than sequence-based approaches. This data is supplemented with Pfam-A, other non-domain structural predictions (i.e. coiled coils) and experimental data from UniProt. In order to enhance the investigations possible with this data, we have also incorporated a variety of protein annotation resources, including protein–protein interaction data, GO functional assignments, KEGG pathways, FUNCAT functional descriptions and links to microarray expression data. All of this data can be accessed through a newly re-designed website that has a focus on flexibility and clarity, with searches that can be restricted to a single genome or across the entire sequence database. Currently Gene3D contains over 3.5 million domain assignments for nearly 5 million proteins including 527 completed genomes. This is available at: http://gene3d.biochem.ucl.ac.uk

Integrating genetic markers and adiabatic quantum machine learning to improve disease resistance-based marker assisted plant selection

The goal of this research was to create a more accurate and efficient method for selecting plants with disease resistance using a combination of genetic markers and advanced machine learning algorithms. A multi-disciplinary approach incorporating genomic data, machine learning algorithms and high-performance computing was employed. First, genetic markers highly associated with disease resistance were identified using next-generation sequencing data and statistical analysis. Then, an adiabatic quantum machine learning algorithm was developed to integrate these markers into a single predictor of disease susceptibility. The results demonstrate that the integrative use of genetic markers and adiabatic quantum machine learning significantly improved the accuracy and efficiency of disease resistance-based marker-assisted plant selection. By leveraging the power of adiabatic quantum computing and genetic markers, more effective and efficient strategies for disease resistance-based marker-assisted plant selection can be developed

Guidance of sentinel lymph node biopsy decisions in patients with T1-T2 melanoma using gene expression profiling.

AIM: Can gene expression profiling be used to identify patients with T1-T2 melanoma at low risk for sentinel lymph node (SLN) positivity? PATIENTS & METHODS: Bioinformatics modeling determined a population in which a 31-gene expression profile test predicted \u3c5% SLN positivity. Multicenter, prospectively-tested (n = 1421) and retrospective (n = 690) cohorts were used for validation and outcomes, respectively. RESULTS: Patients 55-64 years and ≥65 years with a class 1A (low-risk) profile had SLN positivity rates of 4.9% and 1.6%. Class 2B (high-risk) patients had SLN positivity rates of 30.8% and 11.9%. Melanoma-specific survival was 99.3% for patients ≥55 years with class 1A, T1-T2 tumors and 55.0% for class 2B, SLN-positive, T1-T2 tumors. CONCLUSION: The 31-gene expression profile test identifies patients who could potentially avoid SLN biopsy

Tax and occupancy of business properties : theory and evidence from UK business rates

We study the impact of commercial property taxation on vacancy rates and rents in the UK, using a new data-set, and exploiting exogenous variations in property tax rates from reliefs in the UK system: small business rate relief (SBRR), retail relief and empty property relief. We estimate that the retail relief reduces vacancies by 85%, and SBRR relief by up to 49%, while empty property exemption increases them by up to 89%. The effect of retail relief on clusters of urban properties (the "High St") is no different to its overall effect. SBRR increases (decreases) the likelihood that a property is occupied by a small (large) business. We also use data on asking prices for rental properties to study the effect of reliefs on rental rates. Rental rates move in the opposite direction to vacancy rates, except in the case of empty property relief. All these findings are consistent with a novel model of directed search in the commercial property market, also presented in the paper