The theory of the exponential differential equations of semiabelian varieties

The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The theory includes necessary and sufficient conditions for a system of equations to have a solution. The necessary condition generalizes Ax's differential fields version of Schanuel's conjecture to semiabelian varieties. There is a purely algebraic corollary, the "Weak CIT" for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties.Comment: 53 pages; v3: Substantial changes, including a completely new introductio

Systemic therapies for intrahepatic cholangiocarcinoma

Intrahepatic cholangiocarcinoma (iCCA) is a highly lethal hepatobiliary neoplasm whose incidence is increasing. Largely neglected for decades as a rare malignancy and frequently misdiagnosed as carcinoma of unknown primary, considerable clinical and investigative attention has recently been focused on iCCA worldwide. The established standard of care includes first-line (gemcitabine and cisplatin), second-line (FOLFOX) and adjuvant (capecitabine) systemic chemotherapy. Compared to hepatocellular carcinoma, iCCA is genetically distinct with several targetable genetic aberrations identified to date. Indeed, FGFR2 and NTRK fusions, and IDH1 and BRAF targetable mutations have been comprehensively characterised and clinical data is emerging on targeting these oncogenic drivers pharmacologically. Also, the role of immunotherapy has been examined and is an area of intense investigation. Herein, in a timely and topical manner, we will review these advances and highlight future directions of research

Diet assessment of the Atlantic Sea Nettle Chrysaora quinquecirrha in Barnegat Bay, New Jersey, using next-generation sequencing

Next-generation sequencing (NGS) methodologies have proven useful in deciphering the food items of generalist predators, but have yet to be applied to gelatinous animal gut and tentacle content. NGS can potentially supplement traditional methods of visual identification. Chrysaora quinquecirrha (Atlantic sea nettle) has progressively become more abundant in Mid-Atlantic United States’ estuaries including Barnegat Bay (New Jersey), potentially having detrimental effects on both marine organisms and human enterprises. Full characterization of this predator’s diet is essential for a comprehensive understanding of its impact on the food web and its management. Here, we tested the efficacy of NGS for prey item determination in the Atlantic sea nettle. We implemented a NGS ‘shotgun’ approach to randomly sequence DNA fragments isolated from gut lavages and gastric pouch/tentacle picks of eight and 84 sea nettles, respectively. These results were verified by visual identification and co-occurring plankton tows. Over 550 000 contigs were assembled from ~110 million paired-end reads. Of these, 100 contigs were confidently assigned to 23 different taxa, including soft-bodied organisms previously undocumented as prey species, including copepods, fish, ctenophores, anemones, amphipods, barnacles, shrimp, polychaete worms, flukes, flatworms, echinoderms, gastropods, bivalves and hemichordates. Our results not only indicate that a ‘shotgun’ NGS approach can supplement visual identification methods, but targeted enrichment of a specific amplicon/gene is not a prerequisite for identifying Atlantic sea nettle prey items

On the weights of binary irreducible cyclic codes

International audienceThis paper is devoted to the study of the weights of binary irreducible cyclic codes. We start from McEliece's interpretation of these weights by means of Gauss sums. Firstly, a dyadic analysis, using the Stickelberger congruences and the Gross-Koblitz formula, enables us to improve McEliece's divisibility theorem by giving results on the multiplicity of the weights. Secondly, in connection with a Schmidt and White's conjecture, we focus on binary irreducible cyclic codes of index two. We show, assuming the generalized Riemann hypothesis, that there are an infinite of such codes. Furthermore, we consider a subclass of this family of codes satisfying the quadratic residue conditions. The parameters of these codes are related to the class number of some imaginary quadratic number fields. We prove the non existence of such codes which provide us a very elementary proof, without assuming G.R.H, that any two-weight binary irreducible cyclic code c(m,v) of index two with v prime greater that three is semiprimitive

Vienna Circle and Logical Analysis of Relativity Theory

In this paper we present some of our school's results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a case-study showing that the Vienna Circle's (VC) approach to doing science is workable and fruitful when performed with using the insights and tools of mathematical logic acquired since its formation years at the very time of the VC activity. We think that logical positivism was based on the insight and anticipation of what mathematical logic is capable when elaborated to some depth. Logical positivism, in great part represented by VC, influenced and took part in the birth of modern mathematical logic. The members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure