188 research outputs found

    Pegging Graphs Yields a Small Diameter

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    We consider the following process for generating large random cubic graphs. Starting with a given graph, repeatedly add edges that join the midpoints of two randomly chosen edges. We show that the growing graph asymptotically almost surely has logarithmic diameter. This process is motivated by a particular type of peer-to-peer network. Our method extends to similar processes that generate regular graphs of higher degre

    Generation and properties of random graphs and analysis of randomized algorithms

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    We study a new method of generating random dd-regular graphs by repeatedly applying an operation called pegging. The pegging algorithm, which applies the pegging operation in each step, is a method of generating large random regular graphs beginning with small ones. We prove that the limiting joint distribution of the numbers of short cycles in the resulting graph is independent Poisson. We use the coupling method to bound the total variation distance between the joint distribution of short cycle counts and its limit and thereby show that O(ϵ1)O(\epsilon^{-1}) is an upper bound of the \eps-mixing time. The coupling involves two different, though quite similar, Markov chains that are not time-homogeneous. We also show that the ϵ\epsilon-mixing time is not o(ϵ1)o(\epsilon^{-1}). This demonstrates that the upper bound is essentially tight. We study also the connectivity of random dd-regular graphs generated by the pegging algorithm. We show that these graphs are asymptotically almost surely dd-connected for any even constant d4d\ge 4. The problem of orientation of random hypergraphs is motivated by the classical load balancing problem. Let h>w>0h>w>0 be two fixed integers. Let \orH be a hypergraph whose hyperedges are uniformly of size hh. To {\em ww-orient} a hyperedge, we assign exactly ww of its vertices positive signs with respect to this hyperedge, and the rest negative. A (w,k)(w,k)-orientation of \orH consists of a ww-orientation of all hyperedges of \orH, such that each vertex receives at most kk positive signs from its incident hyperedges. When kk is large enough, we determine the threshold of the existence of a (w,k)(w,k)-orientation of a random hypergraph. The (w,k)(w,k)-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The other topic we discuss is computing the probability of induced subgraphs in a random regular graph. Let 0<s<n0<s<n and HH be a graph on ss vertices. For any S[n]S\subset [n] with S=s|S|=s, we compute the probability that the subgraph of Gn,d\mathcal{G}_{n,d} induced by SS is HH. The result holds for any d=o(n1/3)d=o(n^{1/3}) and is further extended to Gn,d\mathcal{G}_{n,{\bf d}}, the probability space of random graphs with given degree sequence d\bf d. This result provides a basic tool for studying properties, for instance the existence or the counts, of certain types of induced subgraphs

    Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

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    The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed

    Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

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    The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed.business cycle; continuous time econometrics; investment cycle; inventory cycle; maximum entropy spectral analysis; parametric resonance

    Reconstruction of gasoline engine in-cylinder pressures using recurrent neural networks

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    Knowledge of the pressure inside the combustion chamber of a gasoline engine would provide very useful information regarding the quality and consistency of combustion and allow significant improvements in its control, leading to improved efficiency and refinement. While measurement using incylinder pressure transducers is common in laboratory tests, their use in production engines is very limited due to cost and durability constraints. This thesis seeks to exploit the time series prediction capabilities of recurrent neural networks in order to build an inverse model accepting crankshaft kinematics or cylinder block vibrations as inputs for the reconstruction of in-cylinder pressures. Success in this endeavour would provide information to drive a real time combustion control strategy using only sensors already commonly installed on production engines. A reference data set was acquired from a prototype Ford in-line 3 cylinder direct injected, spark ignited gasoline engine of 1.125 litre swept volume. Data acquired concentrated on low speed (1000-2000 rev/min), low load (10-30 Nm brake torque) test conditions. The experimental work undertaken is described in detail, along with the signal processing requirements to treat the data prior to presentation to a neural network. The primary problem then addressed is the reliable, efficient training of a recurrent neural network to result in an inverse model capable of predicting cylinder pressures from data not seen during the training phase, this unseen data includes examples from speed and load ranges other than those in the training case. The specific recurrent network architecture investigated is the non-linear autoregressive with exogenous inputs (NARX) structure. Teacher forced training is investigated using the reference engine data set before a state of the art recurrent training method (Robust Adaptive Gradient Descent – RAGD) is implemented and the influence of the various parameters surrounding input vectors, network structure and training algorithm are investigated. Optimum parameters for data, structure and training algorithm are identified

    Essays on Selected Aspects of European Integration

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    To further strengthen European integration much can be done and is actually needed. The present work provides a wide range of empirical results and corresponding policy recommendations from the perspective of economics. The collection of articles here provides a clear illustration that there is a lot of potential to amend the architecture of the European Union and the euro area, respectively. It is well understood that the process of European integration is a continuous process which requires adjustments from time to time. This thesis provides results which indicate that very specific measures, such as facilitating a catch-up in terms of institutional quality by central and eastern European countries, would be beneficial for the process of European integration. This is in line with the general claim that institutional harmonization has to be enhanced. It is shown that within the more narrow framework of the euro area measures to enhance the functioning of the single currency are needed as well. In sum, this implies a strong need for policy measures in response to the recent developments of European integration. Moreover, it is demonstrated that common rules have to be equally binding for all countries. In fact, a number of necessary policy measures are already being implemented, for example the implementation of Basel III. With respect to implementation, results of this thesis imply that such measures have to be implemented carefully. Policy makers have to take into account country-specific characteristics when implementing one-fits-all policy measures. Nonetheless, the uniform European rules are not questioned here. In addition to the results and corresponding policy recommendations, the bulk of the research done here also contributes methodologically to economics. The increasing availability of micro-data is used to address macroeconomic questions and derive corresponding macroeconomic results and implications. Future research in economics will most likely make more and more use of such data

    Catching Up and EU Accession - Conditions for Fast Real Convergence in the Candidate Countries

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    This is a report about the fifth workshop from the seminar series of IIASAs Economic Transition and Integration Project entitled "The Process of EU Accession: Preparation by Learning and Exchange". The workshop was held in Bratislava on 7-9 February 2002. The first two sections summarize the opening of the workshop and two introductory presentations dealing with economic policies of Slovakia on its way to the EU accession and the historical perspectives of growth, integration and recommended policies for catching-up in transition countries. The next section presents an outline of recent developments in the accession process in ten individual candidate countries. The fourth section concentrates on the analysis of factors determining savings and investments in accession countries and the role of banking intermediation, as illustrated on the case of Hungary. The fifth section is dedicated to questions of competitiveness - to the alternative ways of its measurement and policies that support exports and/or the ability of domestic producers to substitute imports, stressing that policies on the company and industry level are more important than national policies. The sixth section deals with the problems of macroeconomic financial convergence and the requirements on national performance for becoming a member of the European Monetary Union. Its first paper discusses alternative policies of central banks from Eastern and Central Europe for a smooth monetary integration of their countries with the euro-zone. Its second paper tests the empirical evidence on the speed of economic convergence in various transition countries. Its third paper analyses the aspects of the so-called nominal and real convergence and the potential scope of alternative monetary policies in accession countries in order to retain their external balance. The seventh section presents the summary of three presentations that dealt with international institutions. The first one is dealing with the policies and the support for catching up provided by the World Bank. The second paper describes the experiences of Ireland, Latvia and Estonia in preparing the national development plans and in the usage of structural and cohesion funds provided by the European Commission. The third paper concentrates on the problems of domestic agricultural policies and the EU Transfers, as based on the comparison of Slovakia with some other EU candidate countries and with the EU incumbents. The next two sections discuss the questions associated with the R&D, foreign direct investment, human capital and their spillovers. In the first of them the lessons from the Irish experience are summarized and compared with the present situation in accession countries. The paper, that follows next, analyses the data on education, compares the EU candidate countries with some less developed EU member countries and draws conclusion about policies for the human capital development and their association with growth. The last (tenth) section is based the on the comparative analysis of the empirical evidence from transition countries on the indicators of human development and the policies for a more comprehensive convergence of these countries to the levels of present EU member states

    Homogeneous Lean Combustion in Downsized Spark-Ignited Engines

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    Emissions of greenhouse-gasses and noxious compounds from internal combustion engines propelling personal transportation vehicles is an imminent issue in the society. Therefore, it is vital to find means of reducing these emissions to decrease the impacts of transportation. Despite the current rapid electrification of the light duty vehicle fleet, it is expected that there will still be a substantial share of vehicles, produced and sold, that are propelled either solely or partly by combustion engines in the next decades to come. An advantage of combustion engines is that they consume hydrocarbon fuels, which are energy dense and can be produced from renewable sources enabling elimination of net carbon emissions. These fuels can be distributed using the current infrastructure, allowing for a fast transition into a low-carbon transportation system. The sources of renewables are however limited, and production of renewable fuels requires energy, which is why the fuel efficiency of combustion engines is key.This thesis addresses the need for reduced emissions from personal transportation vehicles by investigating homogeneous lean combustion in downsized spark-ignited engines as a means of improving combustion engine fuel efficiency. Lean combustion offers substantial efficiency improvements to the current already well-developed combustion systems. However, historically, it has been proven difficult to achieve robust lean combustion that achieves both efficiency improvements and sufficiently low emissions of nitrogen oxides. In this thesis, the focus has been to investigate the potentially synergetic combination of high engine loads above 10 bar brake mean effective pressure, a common attribute of downsized engines, and lean combustion. The idea is that lean combustion reduces knocking combustion, a harmful event that limits engine efficiency due to cylinder pressure limitations. Simultaneously, it is hypothesized that higher engine loads will lead to faster and more stable combustion, allowing important reductions in nitrogen oxides.Using engine experiments and simulations, homogeneous lean combustion has been investigated. From the experiments it could be concluded that lean combustion can be sustained at high loads. One of the world’s first two-stage turbochargers designed solely for lean combustion was utilized for this purpose and found to be successful. However, it was discovered that lean combustion does not eliminate knocking combustion completelyKeywords: engine, efficiency, emissions, lean, combustion, nor did high load operation eliminate cyclic dispersion of combustion, which imposes limitations. Using improved in-cylinder charge motion and alternative fuels, these limitations can be mitigated, allowing for stable, efficient, low nitrogen oxide high load lean combustion

    Financial integration of NAFTA : measurement and analysis of the North American financial markets convergence / Yueming (Roy) Sun

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    vii, 67 leaves ; 29 cmApplying market arbitrage theory on daily data, we measure the empirical financial market convergence of NAFTA’s financial markets since 1994. Radar diagram and wavelet multi-resolution analysis (MRA) scalogram movies of the statistical moments of the term interest rate differentials visualize the multidimensional convergence. From the radar movies, we find: 1) a uniform disappearance of the average forward premia; 2) a non-uniform decline of bilateral financial market risk; 3) variation of bilateral financial market pressure measured by skewness; and 4) emergence of uniform market microstructures as measured by vanishing excess-kurtosis. From the MRA movies, we find that the national term structures of interest rates converge, since the stochastic resonance coefficients of the interest rate differentials lose significance: market energy at all frequencies dissipates into “white noise.” Testing Obrimah, Prakash and Rangan’s (2009) Lemma, we find that, after 2002, higher financial flow pressure is a necessary condition for lower financial market risk
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