A local limit theorem with speed of convergence for Euclidean algorithms and diophantine costs

For large $N$, we consider the ordinary continued fraction of $x=p/q$ with $1\le p\le q\le N$, or, equivalently, Euclid's gcd algorithm for two integers $1\le p\le q\le N$, putting the uniform distribution on the set of $p$ and $q$s. We study the distribution of the total cost of execution of the algorithm for an additive cost function $c$ on the set $\mathbb{Z}_+^*$ of possible digits, asymptotically for $N\to\infty$. If $c$ is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author. Introducing diophantine conditions on the cost, we are able to control the speed of convergence in the local limit theorem. We use previous estimates of the first author and Vall\'{e}e, and we adapt to our setting bounds of Dolgopyat and Melbourne on transfer operators. Our diophantine condition is generic (with respect to Lebesgue measure). For smooth enough observables (depending on the diophantine condition) we attain the optimal speed.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP140 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Direct method-based statistical limit analysis of wc-co composites

In this paper, a direct method-based prediction of load-bearing capacity of nonperiodic WC-Co composites is presented. The main goal is to generalize the methodology of limit analysis on periodic heterogeneous media to materials with random microstructures. For such materials, the admissible macroscopic loading domains demonstrate remarkable scatter among RVE models of identical size and constituents but different morphologies. Limit analysis is performed on samples of a group of RVE models converted automatically from scanning electron microscopy (SEM) images. The corresponding admissible loading domains are numerically determined and statistically interpreted. The obtained results for plastic limit loads by direct method are compared with those from conventional incremental analysis

Simplified Second-Order Generalized Integrator - Frequency-Locked Loop

Second-Order Generalized Integrator –Frequency-Locked Loop (SOGI-FLL) is a popular technique available in the grid synchronization literature. This technique uses gain normalization in the frequency locked-loop. This increases the computational complex-ity. In this paper, we propose an alternative imple-mentation to reduce the computational complexity of the SOGI-FLL. The proposed implementation modifies mainly the frequency locked-loop part and requires normalized voltage measurement. dSPACE 1104 board-based hardware implementation shows that the proposed implementation executes 20 % faster than the standard implementation. This could be very beneficial for high switching frequency application e.g. ≥ 1 MHz. In ad-dition to the nominal frequency case, multiresonant implementation is also proposed to tackle grid harmonics using a simpler harmonic decoupling network. Small signal dynamical modeling and tuning are performed for both implementations. Dynamical equivalence is also established between the two implementations. Experimental comparative analysis demonstrates similar or better performance (depending on test scenarios) with respect to the standard implementation of the SOGI-FL

Un theoreme de la limite locale pour des algorithmes Euclidiens

We prove a local limit theorem for the Euclidian algorithms ; standard, centred and odd, with any cost function of moderate growth

Molecular analysis of insect stage Trypanosoma brucei

This project used both a genomic and proteomic approach to investigate the molecular and biochemical changes that occur in the insect stage of Trypanosoma brucei. The project had three main aims, the first of which was the application of an already established approach RADES -PCR to investigatc genes expressed during the maturation of established mid -gut infections. The method consisted of two steps, 1) reverse transcription of first strand DNA using oligo (dT) strech and 2) enrichment of parasite material over host material using the splice leader (SL) the miniexon. It was found that the high prevalence of artefacts and the presence of bacterial material from symbionts in the tsetse midgut hampered this investigation. The application of a low and high stringency approach using random anchored primers did not improve the situation. This feature of T brucei maturation could therefore not be investigated further by this approach.Our second aim was to investigate the effect that 8 Br -cGMP has on T brucei procyclic forms. It had been observed in our laboratory that the addition of this chemical to an infected bloodmeal increased the level of T brucei establishment within the fly population to 100 %. An enriched subtractive cDNA library was made to study the effect that this compound has on T brucei, this library provided a full set of the differentially expressed genes resulting from this 8 Br -cGMP treatment. Analysis of over 1000 recombinant clones highlighted the involvement of the polyamine and trypanothione synthesis pathway, in particular the potential role of the antioxidant response.Our third aim was to investigate the protein profile of T brucei in response to this treatment. Protein profiles were characterised using surface enhanced laser desorption/ionization time of flight mass spectrophotometry (SELDI- TOF -MS) where proteins are separated according to their biochemical properties. This approach revealed a number of potential differences that resulted in response to the treatment. Therefore there is a response at the proteomic level that may reflect those genes identified by the subtractive library

Erin Flynn, Oral History Interview, 2022

In October and November of 2022, You Li\u27s Journalism 313 students conducted oral history interviews with one another to document the student experience of the COVID-19 pandemic. In this interview, EMU undergraduate Erin Flynn talks about dealing with COVID sickness and the transition to being back on campus.https://commons.emich.edu/covidoralhist/1014/thumbnail.jp

Microchannel fluid flow and heat transfer by lattice boltzmann method

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Micro flow has become a popular field of interest due to the advent of micro electromechanical systems (MEMS). In this work, the lattice Boltzmann method, a particle-based approach, is applied to simulate the two-dimensional micro channel fluid flow. We simulated fluid flow and heat transfer inside microchannel, the prototype application of this study is micro-heat exchangers. The main incentive to look at fluidic behaviour at micron scale is that micro devices tend to behave much differently from the objects we are used to handling in daily life. The choice of using LBM for micro flow simulation is a good one owing to the fact that it is based on the Boltzmann equation which is valid for the whole range of the Knudsen number. Slip velocity and temperature jump boundary conditions are used for the microchannel simulations with Knudsen number values covering the slip flow. The lattice Bhatnagar-Gross-Krook single relaxation time approximation was used. The results found are compared with the Navier-Stokes analytical and numerical results available in the literature and good matches are observed

Money, income and causality: An open economy reexamination

The positive relationship between the rate of growth of the money supply and the rate of growth of aggregate income is a widely accepted principle in macroeconomics. However, the direction of the causality between these two variables has been an enduring subject of controversy. Recent developments in time series analysis, particularly those relating to the concepts of integration and cointegration, and the stationary nature of economic time series, promise to help settle the debate on the statistical relationship between money supply growth and income growth. Most of the recent work on this issue, however, has been confined to a closed economy framework and has dealt only with US data. This dissertation extends the scope of the recent work on money-income causality to an open economy framework. Three distinctly different economies are investigated: the United States (large economy), Canada (smaller, fairly open economy), and the Netherlands (small, very open economy). The impact of two international variables (world money supply and world aggregate income) on the direction of causality between domestic money supply and domestic income are explicitly examined, using monthly data over the period 1960-1990 and optimally selected lags for the model specifications. Money-income causality is tested over the full sample (1960-1990), and over sample periods corresponding to alternative exchange rate regimes. For all three economies, the exchange rate regime is found to be a critical factor in the direction of the causality between domestic money supply and domestic income. In most cases, however, the two international variables (world money supply and world income) do not appear to have a significant impact on the direction of the causality. The empirical results from this study support the predictions of the standard open economy macroeconomic theory (the Mundell-Fleming model) in one half of the cases. This dissertation also confirms earlier findings on the sensitivity of Granger causality tests to lag length selection