Elliptic curves of large rank and small conductor

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page break

Alternating groups and moduli space lifting Invariants

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp. odd) theta functions when r is even (resp. odd). For inner spaces the result is independent of r. Another use appears in, http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for the prime p=2 lying over Hurwitz spaces first studied by, http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*) High tower levels are general-type varieties and have no rational points.For infinitely many of those MTs, the tree of cusps contains a subtree -- a spire -- isomorphic to the tree of cusps on a modular curve tower. This makes plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs. Establishing these modular curve-like properties opens, to MTs, modular curve-like thinking where modular curves have never gone before. A fuller html description of this paper is at http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from proof sheets, but does include some proof simplification in \S

An Unusual Case of Locally Advanced Glycogen-Rich Clear Cell Carcinoma of the Breast

Glycogen-rich clear cell (GRCC) is a rare subtype of breast carcinoma characterized by carcinoma cells containing an optically clear cytoplasm and intracytoplasmic glycogen. We present the case of a 55-year-old woman with a palpable mass in the right breast and clinical signs of locally advanced breast cancer (LABC). The diagnosis of GRCC carcinoma was based on certain histopathological characteristics of the tumor and immunohistochemical analysis. To our knowledge, this is the first case of GRCC LABC with intratumoral calcifications. There is no evidence of recurrence or metastatic disease after 14 months’ follow-up

Testing Hardy nonlocality proof with genuine energy-time entanglement

We show two experimental realizations of Hardy ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)]. Unlike, previous energy-time Bell experiments, these tests require precise tailored nonmaximally entangled states. One of them is equivalent to the two-setting two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-time and time-bin Bell tests.Comment: 5 pages, revtex4, 6 figure

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Classtalk: A Classroom Communication System for Active Learning

This pdf file is an article describing the advantages of using Classtalk technology in the classroom to enhance classroom communication. Classtalk technology cab facilitate the presentation of questions for small group work, collec the student answers and then display histograms showing how the class answered. This new communication technology can help instructors create a more interactive, student centered classroom, especially when teaching large courses. The article describes Classtalk as a very useful tool not only for engaging students in active learning, but also for enhancing the overall communication within the classroom. This article is a selection from the electronic Journal for Computing in Higher Education. Educational levels: Graduate or professional

Learning physics in context: a study of student learning about electricity and magnetism

This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel university class in electricity and magnetism are analyzed to demonstrate the central and inextricable role of context in student learning. This work sits within a broader effort to create and analyze environments which support student learning in the sciencesComment: 36 pages, 4 Figure

Current HHT genetic overview in Spain and its phenotypic correlation: Data from RiHHTa registry

Background: Hereditary hemorrhagic telangiectasia (HHT) is a rare vascular disease with autosomal dominant inheritance. Disease-causing variants in endoglin (ENG) and activin A receptor type II-like 1 (ACVRL1) genes are detected in more than 90% of cases submitted to molecular diagnosis. Methods: We used data from the RiHHTa (Computerized Registry of Hereditary Hemorrhagic Telangiectasia) registry to describe genetic variants and to assess their genotype-phenotype correlation among HHT patients in Spain. Results: By May 2019, 215 patients were included in the RiHHTa registry with a mean age of 52.5 ± 16.5 years and 136 (63.3%) were women. Definitive HHT diagnosis defined by the Curaca¸o criteria were met by 172 (80%) patients. Among 113 patients with genetic test, 77 (68.1%) showed a genetic variant in ACVRL1 and 36 (31.8%) in ENG gene. The identified genetic variants in ACVRL1 and ENG genes and their clinical significance are provided. ACVRL1 mutations were more frequently nonsense (50%) while ENG mutations were more frequently, frameshift (39.1%). ENG patients were significantly younger at diagnosis (36.9 vs 45.7 years) and had pulmonary arteriovenous malformations (AVMs) (71.4% vs 24.4%) and cerebral AVMs (17.6% vs 2%) more often than patients with ACVRL1 variants. Patients with ACVRL1 variants had a higher cardiac index (2.62 vs 3.46), higher levels of hepatic functional blood tests, and anemia (28.5% vs 56.7%) more often than ENG patients. Conclusions: ACVRL1 variants are more frequent than ENG in Spain. ACVRL1 patients developed symptomatic liver disease and anemia more often than ENG patients. Compared to ACVRL1, those with ENG variants are younger at diagnosis and show pulmonary and cerebral AVMs more frequently

Unknotting the polarized vacuum of quenched QED

A knot-theoretic explanation is given for the rationality of the quenched QED beta function. At the link level, the Ward identity entails cancellation of subdivergences generated by one term of the skein relation, which in turn implies cancellation of knots generated by the other term. In consequence, each bare three-loop diagram has a rational Laurent expansion in the Landau gauge, as is verified by explicit computation. Comparable simplification is found to occur in scalar electrodynamics, when computed in the Duffin-Kemmer-Petiau formalism.Comment: 11 pages, LaTe

Ambiguities in QED: Renormalons versus Triviality

We point out that, contrary to what is believed to hold for QCD, renormalons are genuine in QED; i.e. the ambiguities which come with them do not require cancellation by hypothetical non-perturbative contributions. They are just the ambiguities characteristic of any trivial ---and thus effective--- theory. If QED remained an isolated theory up to an energy close to its triviality scale, these ambiguities would surely hint at new physics. This not being so, the renormalon ambiguities in QED lead to no new physics, not even to non-perturbative contributions within QED itself.Comment: 8 LaTeX pages. No figure