On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

Lysis mediated by T cells and restricted by H-2 antigen of target cells infected with vaccinia virus

VARIOUS virus infections lead to the formation of cytotoxic lymphocytes (CL), which are capable of killing virus-infected target cells1−4. Specific lysis of target cells infected with 51Cr-labelled vaccinia virus could be observed when investigating the cell-mediated cytotoxic reaction to vaccinia virus5; the CL could be characterised as a T cell. The sensitised lymphocytes from C3H mice could only kill syngeneic L929 cells infected with vaccinia virus, whereas lysis by sensitised lymphocytes derived from DBA/2 mice was restricted to the syngeneic infected mastocytoma P815X2 cells. In the lymphocytic choriomeningitis infection the target cell lysis was shown to be restricted by H-2 antigen6. We report here experiments with primary fibroblasts of the mouse strains C3H, DBA/2 and the (C3H DBA/2)F1 generation were designed to affirm that the effector phase of virus-specific lysis of target cells mediated by T cells is restricted by H-2 antigen even in the vaccinia virus infection. Further experiments with H-2 alloantisera were performed to indicate the close local relationship between H-2 antigens and viral surface antigens

Magma-driven, high-grade metamorphism in the Sveconorwegian Province, southwest Norway, during the terminal stages of Fennoscandian Shield evolution

Recently it has been argued that the Sveconorwegian orogeny in southwest Fennoscandia comprised a series of accretionary events between 1140 and 920 Ma, behind a long-lived, active continental margin characterized by voluminous magmatism and high-grade metamorphism. Voluminous magnesian granitic magmatism is recorded between 1070 and 1010 Ma (Sirdal Magmatic Belt, SMB), with an apparent drop in activity ca. 1010-1000 Ma. Granitic magmatism resumed ca. 1000-990 Ma, but with more ferroan (A type) compositions (hornblende-biotite granites). This ferroan granitic magmatism was continuous until 920 Ma, and included emplacement of an AMCG (anorthosite-mangerite-charnockite-granite) complex (Rogaland Igneous Complex). Mafic rocks with ages corresponding to the spatially associated granites suggest that heat from underplated mafic magma was the main driving force for lower crustal melting and long-lived granitic magmatism. The change from magnesian to ferroan compositions may reflect an increasingly depleted and dehydrated lower crustal source. High-grade metamorphic rocks more than ~20 km away from the Rogaland Igneous Complex yield metamorphic ages of 1070-1015 Ma, corresponding to SMB magmatism, whereas similar rocks closer to the Rogaland Igneous Complex yield ages between 1100 and 920 Ma, with an apparent age peak ca. 1000 Ma. Ti-in-zircon temperatures from these rocks increase from ~760 to 820 °C ca. 970 Ma, well before the inferred emplacement age of the Rogaland Igneous Complex (930 Ma), suggesting that long-lived, high-grade metamorphism was not directly linked to the emplacement of the latter, but rather to the same mafic underplating that was driving lower crustal melting. Structural data suggest that the present-day regional distribution of high- and low-grade rocks reflects late-stage orogenic doming

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

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

Computer-aided diagnosis for (123I)FP-CIT imaging: impact on clinical reporting

BACKGROUND: For (123I)FP-CIT imaging, a number of algorithms have shown high performance in distinguishing normal patient images from those with disease, but none have yet been tested as part of reporting workflows. This study aims to evaluate the impact on reporters' performance of a computer-aided diagnosis (CADx) tool developed from established machine learning technology. Three experienced (123I)FP-CIT reporters (two radiologists and one clinical scientist) were asked to visually score 155 reconstructed clinical and research images on a 5-point diagnostic confidence scale (read 1). Once completed, the process was then repeated (read 2). Immediately after submitting each image score for a second time, the CADx system output was displayed to reporters alongside the image data. With this information available, the reporters submitted a score for the third time (read 3). Comparisons between reads 1 and 2 provided evidence of intra-operator reliability, and differences between reads 2 and 3 showed the impact of the CADx. RESULTS: The performance of all reporters demonstrated a degree of variability when analysing images through visual analysis alone. However, inclusion of CADx improved consistency between reporters, for both clinical and research data. The introduction of CADx increased the accuracy of the radiologists when reporting (unfamiliar) research images but had less impact on the clinical scientist and caused no significant change in accuracy for the clinical data. CONCLUSIONS: The outcomes for this study indicate the value of CADx as a diagnostic aid in the clinic and encourage future development for more refined incorporation into clinical practice

A retrospective analysis investigating the effects of Telazol® and medetomidine on ejaculate characteristics in cheetahs (Acinonyx jubatus)

Zoo managed cheetahs provide an insurance population for wild cheetahs that are under threat of extinction from habitat loss, lack of prey, competition, pet trade and poaching for skin and bones. Assisted reproductive techniques including artificial insemination, in vitro fertilization, and embryo transfer augment natural breeding programs but rely on good quality semen for best results. It is understood that anesthesia can affect semen characteristics such as ejaculate volume, total sperm count, sperm motility, and incidence of urine contamination. Thus, the aim of this study was to conduct a retrospective analysis of 23 years of data to investigate sperm parameters of semen collected under anesthesia using medetomidine in combination with butorphanol and midazolam or Telazol® alone. Electroejaculation records (Medetomidine, Butorphanol, and Midazolam anesthetized n = 59 ejaculates, from 30 cheetahs, Telazol® anesthetized, n= 169 ejaculates, from 72 cheetahs) were evaluated for incidence of urine contamination. Electroejaculation records (Medetomidine, Butorphanol, and Midazolam anesthetized n = 21 ejaculates, from 17 cheetahs, Telazol® anesthetized, n = 143 ejaculates, from 63 cheetahs) were evaluated for total sperm count, total motility, ejaculate volume, and testicle size. Telazol® treated cheetahs had a numerically higher total sperm count (Median ± SD: 42.58 ± 77.8 × 106 spermatozoa) compared to those treated with medetomidine (Median ± SD: 31.2 ±44.58 × 106 spermatozoa), and a significantly (p < 0.05) higher sperm motility (Median ± SD: 70.0 ± 9.71%) compared to medetomidine (Median ± SD: 53.0 ± 16.41%) treated cheetahs. The findings of this study indicate that medetomidine anesthesia results in significantly lower sperm motility and Telazol® anesthesia results in a higher total sperm count and motility, thus resulting in higher quality ejaculate. This information can aid in the veterinary management of the species when involved in genome resource banking and assisted reproductive technologies

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

Association between KCNJ6 (GIRK2) Gene Polymorphisms and Postoperative Analgesic Requirements after Major Abdominal Surgery

Opioids are commonly used as effective analgesics for the treatment of acute and chronic pain. However, considerable individual differences have been widely observed in sensitivity to opioid analgesics. We focused on a G-protein-activated inwardly rectifying potassium (GIRK) channel subunit, GIRK2, that is an important molecule in opioid transmission. In our initial polymorphism search, a total of nine single-nucleotide polymorphisms (SNPs) were identified in the whole exon, 5′-flanking, and exon-intron boundary regions of the KCNJ6 gene encoding GIRK2. Among them, G-1250A and A1032G were selected as representative SNPs for further association studies. In an association study of 129 subjects who underwent major open abdominal surgery, the A/A genotype in the A1032G SNP and -1250G/1032A haplotype were significantly associated with increased postoperative analgesic requirements compared with other genotypes and haplotypes. The total dose (mean±SEM) of rescue analgesics converted to equivalent oral morphine doses was 20.45±9.27 mg, 10.84±2.24 mg, and 13.07±2.39 mg for the A/A, A/G, and G/G genotypes in the A1032G SNP, respectively. Additionally, KCNJ6 gene expression levels in the 1032A/A subjects were significantly decreased compared with the 1032A/G and 1032G/G subjects in a real-time quantitative PCR analysis using human brain tissues, suggesting that the 1032A/A subjects required more analgesics because of lower KCNJ6 gene expression levels and consequently insufficient analgesic effects. The results indicate that the A1032G SNP and G-1250A/A1032G haplotype could serve as markers that predict increased analgesic requirements. Our findings will provide valuable information for achieving satisfactory pain control and open new avenues for personalized pain treatment