Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

A multiplication curriculum : a short outline

Teachers not only know how to multiply, they also know how to teach children multiplication. But at any one time, most teachers are only concerned with a small section of the whole large process of teaching multiplication. It is easy to lose sight of the wood, because of the close attention being given to individual trees. What is the larger picture? How do children learn to multiply, asks the author? The author discusses the progressive stages of ideas and processes that are involved in learning to multiply. He also provides questions to assist teachers with identifying how far students have progressed in their understanding of multiplication.

Legionella pneumophila multiplication is enhanced by chronic AMPK signalling in mitochondrially diseased dictyostelium cells

Human patients with mitochondrial diseases are more susceptible to bacterial infections, particularly of the respiratory tract. To investigate the susceptibility of mitochondrially diseased cells to an intracellular bacterial respiratory pathogen, we exploited the advantages of Dictyostelium discoideum as an established model for mitochondrial disease and for Legionella pneumophila pathogenesis. Legionella infection of macrophages involves recruitment of mitochondria to the Legionella-containing phagosome. We confirm here that this also occurs in Dictyostelium and investigate the effect of mitochondrial dysfunction on host cell susceptibility to Legionella. In mitochondrially diseased Dictyostelium strains, the pathogen was taken up at normal rates, but it grew faster and reached counts that were twofold higher than in the wild-type host. We reported previously that other mitochondrial disease phenotypes for Dictyostelium are the result of the activity of an energy-sensing cellular alarm protein, AMP-activated protein kinase (AMPK). Here, we show that the increased ability of mitochondrially diseased cells to support Legionella proliferation is suppressed by antisense-inhibiting expression of the catalytic AMPKα subunit. Conversely, mitochondrial dysfunction is phenocopied, and intracellular Legionella growth is enhanced, by overexpressing an active form of AMPKα in otherwise normal cells. These results indicate that AMPK signalling in response to mitochondrial dysfunction enhances Legionella proliferation in host cells.

Dean's great discovery : multiplication, division and fractions

Multiplication, division and fractions are 'hotspots' for students in the middle years with many students experiencing difficulty with these concepts (Siemon, Virgona & Cornielle, 2001). Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts (Young-Loveridge, 2005). In this article we show how an open-ended array problem enabled a Grade 5/6 student to think about the relationship between multiplication, division and fractions. In the article we describe the project and 'hot spot' mathematical tasks that we used and provide some background on multiplicative thinking before presenting the case and a commentary (Western Melbourne Roundtable, 1997) of one student's exploration. This case was documented whilst we were working on a collaborative project with a team of upper primary teachers and a group of pre-service teachers at a local primary school.

A low-voltage low-power analog memory cell with built-in 4-quadrant multiplication

An accurate switched-current (SI) memory cell and suitable for low-voltage low-power (LVLP) applications is proposed. Information is memorized as the gate-voltage of the input transistor, in a tunable gain-boosting triode-transconductor. Additionally, four-quadrant multiplication between the input voltage to the transconductor regulation-amplifier (X-operand) and the stored voltage (Y-operand) is provided. A simplified 2 x 2-memory array was prototyped according to a standard 0.8 mum n-well CMOS process and 1.8-V supply. Measured current-reproduction error is less than 0.26% for 0.25 muA less than or equal to I-SAMPLE less than or equal to 0.75 muA. Standby consumption is 6.75 muW per cell @I-SAMPLE = 0.75 muA. At room temperature, leakage-rate is 1.56 nA/ms. Four-quadrant multiplier (4QM) full-scale operands are 2x(max) = 320 mV(pp) and 2y(max). = 448 mV(pp), yielding a maximum output swing of 0.9 muA(pp). 4QM worst-case nonlinearity is 7.9%.

SUPPORT OF PARACOCCIDIOIDES-BRASILIENSIS MULTIPLICATION BY HUMAN MONOCYTES OR MACROPHAGES - INHIBITION BY ACTIVATED PHAGOCYTES

The interaction of human monocytes or monocyte-derived macrophages and yeast-form Paracoccidioides brasiliensis was studied in vitro. Yeast cells were readily ingested by adherent monocytes or macrophages. Multiplication of P. brasiliensis, measured by growth as colony forming units (cfu) on a supplemented medium with good plating efficiency, was greater in monocyte co-cultures compared to the number of cfu obtained from complete tissue-culture medium (CTCM). Multiplication increased with time in macrophage cocultures, e.g., from two-six-fold in 24 h to nine-fold in 72 h. Microscopic observations indicated that ingested yeast cells multiplied inside macrophages. When monocytes were treated with supernate cytokines (CK) from concanavalin-A-stimulated mononuclear cells, then co-cultured with P. brasiliensis, multiplication was significantly inhibited compared with control monocyte co-cultures. Treatment of macrophages-derived from monocytes by culture in vitro for 3 days-for a further 3 days with CK resulted in maximal inhibition of multiplication over the subsequent 72 h. Similarly, when monocyte-derived macrophages (after culture for 7 days) were treated for 3 days with recombinant human gamma-interferon (IFN; 300 U/ml) or CK they restricted multiplication of P. brasiliensis by 65% and 95%, respectively, compared with control macrophages, Antibody to IFN abrogated the effect of IFN or CK treatment. These findings show that ingested P. brasiliensis can multiply in human monocytes or macrophages and that this multiplication can be restricted by activated monocytes or macrophages.

An accurate low-voltage analog memory-cell with built-in multiplication

A CMOS memory-cell for dynamic storage of analog data and suitable for LVLP applications is proposed. Information is memorized as the gate-voltage of input-transistor of a gain-boosting triode-transconductor. The enhanced output-resistance improves accuracy on reading out the sampled currents. Additionally, a four-quadrant multiplication between the input to regulation-amplifier of the transconductor and the stored voltage is provided. Designing complies with a low-voltage 1.2μm N-well CMOS fabrication process. For a 1.3V-supply, CCELL=3.6pF and sampling interval is 0.25μA≤ ISAMPLE ≤ 0.75μA. The specified retention time is 1.28ms and corresponds to a charge-variation of 1% due to junction leakage @75°C. A range of MR simulations confirm circuit performance. Absolute read-out error is below O.40% while the four-quadrant multiplier nonlinearity, at full-scale is 8.2%. Maximum stand-by consumption is 3.6μW/cell.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.