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

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

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

BioLPG for Clean Cooking in Sub-Saharan Africa: Present and Future Feasibility of Technologies, Feedstocks, Enabling Conditions and Financing

Energy supply for clean cooking is a priority for Sub-Saharan Africa (SSA). Liquefied petroleum gas (LPG, i.e., propane or butane or a mixture of both) is an economically efficient, cooking energy solution used by over 2.5 billion people worldwide and scaled up in numerous low- and middle-income countries (LMICs). Investigation of the technical, policy, economic and physical requirements of producing LPG from renewable feedstocks (bioLPG) finds feasibility at scale in Africa. Biogas and syngas from the circular economic repurposing of municipal solid waste and agricultural waste can be used in two groundbreaking new chemical processes (Cool LPG or Integrated Hydropyrolysis and Hydroconversion (IH2)) to selectively produce bioLPG. Evidence about the nature and scale potential of bioLPG presented in this study justifies further investment in the development of bioLPG as a fuel that can make a major contribution toward enabling an SSA green economy and universal energy access. Techno-economic assessments of five potential projects from Ghana, Kenya and Rwanda illustrate what might be possible. BioLPG technology is in the early days of development, so normal technology piloting and de-risking need to be undertaken. However, fully developed bioLPG production could greatly reduce the public and private sector investment required to significantly increase SSA clean cooking capacity

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

A Postulate for Tiger Recovery: The Case of the Caspian Tiger

Recent genetic analysis has shown that the extinct Caspian Tiger (P. t. virgata) and the living Amur Tigers (P. t. altaica) of the Russian Far East are actually taxonomically synonymous and that Caspian and Amur groups historically formed a single population, only becoming separated within the last 200 years by human agency. A major conservation implication of this finding is that tigers of Amur stock might be reintroduced, not only back into the Koreas and China as is now proposed, but also through vast areas of Central Asia where the Caspian tiger once lived. However, under the current tiger conservation framework the 12 “Caspian Tiger States” are not fully involved in conservation planning. Equal recognition as “Tiger Range States” should be given to the countries where the Caspian tiger once lived and their involvement in tiger conservation planning encouraged. Today, preliminary ecological surveys show that some sparsely populated areas of Central Asia preserve natural habitat suitable for tigers. In depth assessments should be completed in these and other areas of the Caspian range to evaluate the possibility of tiger reintroductions. Because tigers are a charismatic umbrella species, both ecologically and politically, reintroduction to these landscapes would provide an effective conservation framework for the protection of many species in addition to tigers. And for today’s Amur Tigers this added range will provide a buffer against further loss of genetic diversity, one which will maintain that diversity in the face of selective pressures that can only be experienced in the wild

Distant sequences determine 5′ end formation of cox3 transcripts in Arabidopsis thaliana ecotype C24

The genomic environments and the transcripts of the mitochondrial cox3 gene are investigated in three Arabidopsis thaliana ecotypes. While the proximate 5′ sequences up to nucleotide position −584, the coding regions and the 3′ flanking regions are identical in Columbia (Col), C24 and Landsberg erecta (Ler), genomic variation is detected in regions further upstream. In the mitochondrial DNA of Col, a 1790 bp fragment flanked by a nonanucleotide direct repeat is present beyond position −584 with respect to the ATG. While in Ler only part of this insertion is conserved, this sequence is completely absent in C24, except for a single copy of the nonanucleotide direct repeat. Northern hybridization reveals identical major transcripts in the three ecotypes, but identifies an additional abundant 60 nt larger mRNA species in C24. The extremities of the most abundant mRNA species are identical in the three ecotypes. In C24, an extra major 5′ end is abundant. This terminus and the other major 5′ ends are located in identical sequence regions. Inspection of Atcox3 transcripts in C24/Col hybrids revealed a female inheritance of the mRNA species with the extra 5′ terminus. Thus, a mitochondrially encoded factor determines the generation of an extra 5′ mRNA end