Random l-colourable structures with a pregeometry

We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: 1. A zero-one law. 2. The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. 3. There is a formula $\xi(x,y)$ (not directly speaking about colours) such that, with asymptotic probability 1, the relation "there is an $l$-colouring which assigns the same colour to $x$ and $y$" is defined by $\xi(x,y)$. 4. With asymptotic probability 1, an $l$-colourable structure has a unique $l$-colouring (up to permutation of the colours).Comment: 35 page

An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace transform theory. As an application we offer a free of contradictions alternative in the framework of our algebra of generalized functions. The article is aimed at mathematicians, physicists and engineers who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page

A p-adic analogue of Siegel's Theorem on sums of squares

Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields. The p ‐adic Kochen operator provides a p ‐adic analogue of squaring, and a certain localisation of the ring generated by this operator consists of precisely the totally p ‐integral elements of K . We use this to formulate and prove a p ‐adic analogue of Siegel's theorem, by introducing the p ‐Pythagoras number of a general field, and showing that this number is uniformly bounded across number fields. We also generally study fields with finite p ‐Pythagoras number and show that the growth of the p ‐Pythagoras number in finite extensions is bounded

Cinematic and aesthetic cartographies of subjective mutation

This article exmaines the use of cinema as a mapping of subjective mutation in the work of Deleuze, Gauttari and Berardi. Drawing on Deleuze's distinciton between the reduction of the art-work to the symptom and the idea of art as symptomatology, the article focuses on Berardi's use of cinematic examples, posing the quesiton in each case of to what extent they function as symptomatologies or mere symptoms of cultural and subjective mutations in examples ranging from Bergman's Persona to Van Sant's Elephant to finish on speculations about Fincher's The Social Network as a cirtical engagement with subjective mutation in the 21st Century

Constructible motivic functions and motivic integration

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. These results have been announced in math.AG/0403349 and math.AG/0403350. Main results and statements unchanged. Many minor slips corrected and some details added.Comment: Final versio

Rapid disease progression in a patient with mismatch repair-deficient and cortisol secreting adrenocortical carcinoma treated with pembrolizumab

Context: Metastatic adrenocortical carcinoma (ACC) is an aggressive malignancy with a poor prognosis and limited therapeutic options. A subset of ACC is due to Lynch syndrome, an inherited tumour syndrome resulting from germline mutations in mismatch repair (MMR) genes. It has been demonstrated that several cancers characterised by MMR-deficiency are sensitive to immune checkpoint inhibitors that target PD-1. Here, we provide the first report of PD-1 blockade by pembrolizumab in a patient with Lynch syndrome and progressive cortisol-secreting metastatic ACC. Case report: A 58-year old female with known Lynch syndrome who presented with severe Cushing’s syndrome was diagnosed with a cortisol-secreting ACC. Three months following surgical resection and adjuvant mitotane therapy the patient developed metastatic disease and persistent hypercortisolaemia. She commenced pembrolizumab, but her second cycle was delayed due to a transient transaminitis. Computed tomography performed after twelve weeks and 2 cycles of pembrolizumab administration revealed significant disease progression and treatment was discontinued. Seven weeks later, the patient became jaundiced and died rapidly with fulminant liver failure. Conclusion: Treatment of MMR-deficient cortisol-secreting ACC with pembrolizumab may be ineffective due to supra-physiological levels of circulating corticosteroids, which may in turn mask severe drug-induced organ damage

The SCRIPT trial: study protocol for a randomised controlled trial of a polygenic risk score to tailor colorectal cancer screening in primary care

BACKGROUND: Polygenic risk scores (PRSs) can predict the risk of colorectal cancer (CRC) and target screening more precisely than current guidelines using age and family history alone. Primary care, as a far-reaching point of healthcare and routine provider of cancer screening and risk information, may be an ideal location for their widespread implementation. METHODS: This trial aims to determine whether the SCRIPT intervention results in more risk-appropriate CRC screening after 12 months in individuals attending general practice, compared with standard cancer risk reduction information. The SCRIPT intervention consists of a CRC PRS, tailored risk-specific screening recommendations and a risk report for participants and their GP, delivered in general practice. Patients aged between 45 and 70 inclusive, attending their GP, will be approached for participation. For those over 50, only those overdue for CRC screening will be eligible to participate. Two hundred and seventy-four participants will be randomised to the intervention or control arms, stratified by general practice, using a computer-generated allocation sequence. The primary outcome is risk-appropriate CRC screening after 12 months. For those in the intervention arm, risk-appropriate screening is defined using PRS-derived risk; for those in the control arm, it is defined using family history and national screening guidelines. Timing, type and results of the previous screening are considered in both arms. Objective health service data will capture screening behaviour. Secondary outcomes include cancer-specific worry, risk perception, predictors of CRC screening behaviour, screening intentions and health service use at 1, 6 and 12 months post-intervention delivery. DISCUSSION: This trial aims to determine whether a PRS-derived personalised CRC risk estimate delivered in primary care increases risk-appropriate CRC screening. A future population risk-stratified CRC screening programme could incorporate risk assessment within primary care while encouraging adherence to targeted screening recommendations. TRIAL REGISTRATION: Australian and New Zealand Clinical Trial Registry ACTRN12621000092897p. Registered on 1 February 2021. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13063-022-06734-7

The FIELDS Instrument Suite for Solar Probe Plus: Measuring the Coronal Plasma and Magnetic Field, Plasma Waves and Turbulence, and Radio Signatures of Solar Transients.

NASA's Solar Probe Plus (SPP) mission will make the first in situ measurements of the solar corona and the birthplace of the solar wind. The FIELDS instrument suite on SPP will make direct measurements of electric and magnetic fields, the properties of in situ plasma waves, electron density and temperature profiles, and interplanetary radio emissions, amongst other things. Here, we describe the scientific objectives targeted by the SPP/FIELDS instrument, the instrument design itself, and the instrument concept of operations and planned data products

Gravitational Collapse in Higher Dimensional Husain Space-Time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure $p$ and density $\rho$ are related by the following relations (i) $p=k\rho$, (ii) $p=k\rho-\frac{B(v)}{\rho^{\alpha}}$ (variable modified Chaplygin) and (iii) $p=k\rho^{\alpha}$ (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters $k$ and $B$ namely, (i) $k=0$, $B=$ constant (generalized Chaplygin), (ii) $B=$ constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space-time is done.Comment: 12 latex pages, No figure, RevTex styl