Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Superharmonic vibrations of order 3 in stretched strings

Superharmonic vibrations of order 3 in stretched strings driven by a single-mode planar simple-harmonic force are investigated. It is shown that planar as well as nonplanar superharmonic resonances can occur. After giving a few analytical results, the problem is thoroughly investigated numerically. The stability analysis shows that the region of stable nonplanar oscillations is much smaller than that of stable planar oscillation. It is observed in the case of nonplanar oscillations that the amplitude of the superharmonic in the plane normal to the plane of excitation is larger than that in the plane of excitation.

Perinatal mortality and maternal health in rural China

Background and context Since the economic reforms of 1978, China has been acclaimed as a remarkable economy, achieving 9% annual growth per head for more than 25 years. However, China's health sector has not fared well. The population health gains slowed down and health disparities increased. In the field of health and health care, significant progress in maternal care has been achieved. However, there still remain important disparities between the urban and rural areas and among the rural areas in terms of economic development. The excess female infant deaths and the rapidly increasing sex ratio at birth in the last decade aroused serious concerns among policy makers and scholars. Decentralization of the government administration and health sector reform impacts maternal care. Many studies using census data have been conducted to explore the determinants of a high sex ratio at birth, but no agreement has been so far reached on the possible contributing factors. No study using family planning system data has been conducted to explore perinatal mortality and sex ratio at birth and only few studies have examined the impact of the decentralization of government and health sector reforms on the provision and organization of maternal care in rural China. Objectives The general objective of this study was to investigate the state of perinatal health and maternal care and their determinants in rural China under the historic context of major socioeconomic reforms and the one child family planning policy. The specific objectives of the study included: 1) to study pregnancy outcomes and perinatal health and their correlates in a rural Chinese county; 2) to examine the issue of sex ratio at birth and its determinants in a rural Chinese county; 3) to explore the patterns of provision, utilization, and content of maternal care in a rural Chinese county; 4) to investigate the changes in the use of maternal care in China from 1991 to 2003. Materials and Methods This study is based on a project for evaluating the prenatal care programme in Dingyuan county in 1999-2003, Anhui province, China and a nationwide household health survey to describe the changes in maternal care utilization. The approaches used included a retrospective cohort study, cross sectional interview surveys, informant interviews, observations and the use of statistical data. The data sources included the following: 1) A cohort of pregnant women followed from pregnancy up to 7 days after birth in 20 townships in the study county, collecting information on pregnancy outcomes using family planning records; 2) A questionnaire interview survey given to women who gave birth between 2001 and 2003; 3) Various statistical and informant surveys data collected from the study county; 4) Three national household health interview survey data sets (1993-2003) were utilized, and reanalyzed to described the changes in maternity care utilization. Relative risks (RR) and their confidence intervals (CI) were calculated for comparison between parity, approval status, infant sex and township groups. The chi-square test was used to analyse the disparity of use of maternal care between and within urban and rural areas and its trend across the years in China. Logistic regression was used to analyse the factors associated with hospital delivery in rural areas. Results There were 3697 pregnancies in the study cohort, resulting in 3092 live births in a total population of 299463 in the 20 study townships during 1999-2000. The average age at pregnancy in the cohort was 25.9 years. Of the women, 61% were childless, 38% already had one child and 0.3% had two children before the current pregnancy. About 90% of approved pregnancies ended in a live birth while 73% of the unapproved ones were aborted. The perinatal mortality rate was 69 per thousand births. If the 30 induced abortions in which the gestational age was more than 28 weeks had been counted as perinatal deaths, the perinatal mortality rate would have been as high as 78 per thousand. The perinatal mortality rate was negatively associated with the wealth of the township. Approximately two thirds of the perinatal deaths occurred in the early neonatal period. Both the still birth rate and the early neonatal death rate increased with parity. The risk of a stillbirth in a second pregnancy was almost four times that for a first pregnancy, while the risk of early neonatal deaths doubled. The early neonatal mortality rate was twice as high for female as for male infants. The sex difference in the early neonatal mortality rate was mainly attributable to mortality in second births. The male early neonatal mortality rate was not affected by parity, while the female early neonatal mortality rate increased dramatically with parity: it was about six times higher for second births than for first births. About 82% early neonatal deaths happened within 24 hours after birth, and during that time, girls were almost three times more likely to die than boys. The death rate of females on the day of birth increased much more sharply with parity than that of males. The total sex ratio at birth of 3697 registered pregnancies was 152 males to 100 females, with 118 and 287 in first and second pregnancies, respectively. Among unapproved pregnancies, there were almost 5 live-born boys for each girl. Most prenatal and delivery care was to be taken care of in township hospitals. At the village level, there were small private clinics. There was no limitation period for the provision of prenatal and postnatal care by private practitioners. They were not permitted to provide delivery care by the county health bureau, but as some 12% of all births occurred either at home or at private clinics; some village health workers might have been involved. The county level hospitals served as the referral centers for the township hospitals in the county. However, there was no formal regulation or guideline on how the referral system should work. Whether or not a woman was referred to a higher level hospital depended on the individual midwife's professional judgment and on the clients' compliance. The county health bureau had little power over township hospitals, because township hospitals had in the decentralization process become directly accountable to the township government. In the township and county hospitals only 10-20% of the recurrent costs were funded by local government (the township hospital was funded by the township government and the county hospital was funded by the county government) and the hospitals collected user fees to balance their budgets. Also the staff salaries depended on fee incomes by the hospital. The hospitals could define the user charges themselves. Prenatal care consultations were however free in most township hospitals. None of the midwives made postnatal home visits, because of low profit of these services. The three national household health survey data showed that the proportion of women receiving their first prenatal visit within 12 weeks increased greatly from the early to middle 1990s in all areas except for large cities. The increase was much larger in the rural areas, reducing the urban-rural difference from more than 4 times to about 1.4 times. The proportion of women that received antenatal care visits meeting the Ministry of Health s standard (at least 5 times) in the rural areas increased sharply from 12% in 1991-1993 to 36% in 2001-2003. In rural areas, the proportion increase was much faster in less developed areas than in developed areas. The hospital delivery rate increased slightly from 90% to 94% in urban areas while the proportion increased from 27% to 69% in rural areas. The fastest change was found to be in type 4 rural areas, where the utilization even quadrupled. The overall difference between rural and urban areas was substantially narrowed over the period. Multiple logistic regression analysis shows that time periods, residency in rural or urban areas, income levels, age group, education levels, delivery history, occupation, health insurance and distance from the nearest health care facilities were significantly associated with hospital delivery rates. Conclusions 1. Perinatal mortality in this study was much higher than that for urban areas as well as any reported rate from specific studies in rural areas of China. Previous studies in which calculations of infant mortality were not based on epidemiological surveys have been shown to underestimate the rates by more than 50%. 2. Routine statistics collected by the Chinese family planning system proved to be a reliable data source for studying perinatal health, including still births, neonatal deaths, sex ratio at birth and among newborns. National Household Health Survey data proved to be a useful and reliable data source for studying population health and health services. Prior to this research there were few studies in these areas available to international audiences. 3.Though perinatal mortality rate was negatively associated with the level of township economic development, the excess female early neonatal mortality rate contributed much more to high perinatal mortality rate than economic factors. This was likely a result of the role of the family planning policy and the traditional preferences for sons, which leads to lethal neglect of female newborns and high perinatal mortality. 4. The selective abortions of female foetuses were likely to contribute most to the high sex ratio at birth. The underreporting of female births seemed to have played a secondary role. The higher early neonatal mortality rate in second-born as compared to first-born children, particularly in females, may indicate that neglect or poorer care of female newborn infants also contributes to the high sex ratio at birth or among newborns. Existing family planning policy proved not to effectively control the steadily increased birth sex ratio. 5. The rural-urban gap in service utilization was on average significantly narrowed in terms of maternal healthcare in China from 1991 to 2003. This demonstrates that significant achievements in reducing inequities can be made through a combination of socio-economic development and targeted investments in improving health services, including infrastructure, staff capacities, and subsidies to reduce the costs of service utilization for the poorest. However, the huge gap which persisted among cities of different size and within different types of rural areas indicated the need for further efforts to support the poorest areas. 6. Hospital delivery care in the study county was better accepted by women because most of women think delivery care was very important while prenatal and postnatal care were not. Hospital delivery care was more systematically provided and promoted than prenatal and postnatal care by township hospital in the study area. The reliance of hospital staff income on user fees gave the hospitals an incentive to put more emphasis on revenue generating activities such as delivery care instead of prenatal and postnatal care, since delivery care generated much profits than prenatal and postnatal care . Recommendations 1. It is essential for the central government to re-assess and modify existing family planning policies. In order to keep national sex balance, the existing practice of one couple one child in urban areas and at-least-one-son a couple in rural areas should be gradually changed to a two-children-a-couple policy throughout the country. The government should establish a favourable social security policy for couples, especially for rural couples who have only daughters, with particular emphasis on their pension and medical care insurance, combined with an educational campaign for equal rights for boys and girls in society. 2. There is currently no routine vital-statistics registration system in rural China. Using the findings of this study, the central government could set up a routine vital-statistics registration system using family planning routine work records, which could be used by policy makers and researchers. 3. It is possible for the central and provincial government to invest more in the less developed and poor rural areas to increase the access of pregnant women in these areas to maternal care services. Central government together with local government should gradually provide free maternal care including prenatal and postnatal as well as delivery care to the women in poor and less developed rural areas. 4. Future research could be done to explore if county and the township level health care sector and the family planning system could be merged to increase the effectiveness and efficiency of maternal and child care. 5. Future research could be done to explore the relative contribution of maternal care, economic development and family planning policy on perinatal and child health using prospective cohort studies and community based randomized trials. Key words: perinatal health, perinatal mortality, stillbirth, neonatal death, sex selective abortion, sex ratio at birth, family planning, son preference, maternal care, prenatal care, postnatal care, equity, China

Pocket Statistics 2011

A compact selection of statistics on the social security programmes administered by the Kela. Including both tables and charts, the Pocket statistics presents key data on the benefits provided by the Kela, supplemented by selected data about programmes administered by other organizations. Most of the data is updated to the end of 2010, with some of the presentations extending into 2011.

Development of foreign direct investment in Finland

During 1990 to 2009, Foreign Direct Investment (FDI henceforth) in Finland has fluctuated greatly. This paper focused on analyzing the overall development and basic characteristics of Foreign Direct Investment in Finland, covering the period from 1990 to present. By comparing FDI in Finland with FDI in other countries, the picture of Finland’s FDI position in the world market is clearer. A lot of statistical data, tables and figures are used to describe the trend of Foreign Direct Investment in Finland. All the data used in this study were obtained from Statistics Finland, UNCTAD, OECD, World Bank and International Labor Office, Investment map website and etc. It is also found that there is a big, long-lasting and increasing imbalance of the inward FDI and outward FDI in Finland, the performance of outward FDI is stronger than the inward FDI in Finland. Finland’s position of FDI in the world is rather modest. And based on existing theories, I tried to analyze the factors that might determine the size of the inflows of FDI in Finland. The econometric model of my thesis is based on time series data ranging from 1990 to 2007. A Log linear regression model is adopted to analyze the impact of each variable. The regression results showed that Labor Cost and Investment in Education have a negative influence on the FDI inflows into Finland. Too high labor cost is the main impediment of FDI in Finland, explaining the relative small size of FDI inflows into Finland. GDP and Economy openness have a significant positive impact on the inflows of FDI into Finland; other variables do not emerge as significant factor in affecting the size of FDI inflows in Finland as expected. Meanwhile, the impacts of the most recent financial and economic crisis on FDI in the world and in Finland are discussed as well. FDI inflows worldwide and in Finland have suffered from a big setback from the 2008 global crisis. The economic crisis has undoubtedly significant negative influence on the FDI flows in the world and in Finland. Nevertheless, apart from the negative impact, the crisis itself also brings in chances for policymakers to implement more efficient policies in order to create a pro-business and pro-investment climate for the recovery of FDI inflows. . The correspondent policies and measures aiming to accelerate the recovery of the falling FDI were discussed correspondently.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

The Mechanics and Statistics of Active Matter

Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles-active matter-with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.

Sign Of The Order Parameter In Oriented Systems And Its Utility In The Study Of The Dynamic Properties Of Molecules

Novel one and two dimensional NMR techniques are proposed and utilized for the determination of the signs of the order parameters used for the study of the mobility of the fatty acid chains. The experiments designed to extract this information involve the use of the intensities of the side bands in the spectra of oriented systems spinning at the magic angle. Advantages of the two dimensional technique over the one dimensional method are discussed. The utility of the method in the study of the dynamic properties of membranes and model systems is pointed out.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

An infrared spectroscopic study of the low-spin-high-spin transition in FexMn1-x(Phen)2(NCS)2: A composition-induced change in the order of the spin-state transition

Infrared spectroscopy provides a valuable tool to investigate the spin-state transition in Fe(II) complexes of the type Fe(Phen)2(NCS)2. With progressive substitution of Fe by Mn, the first-order transition changes over to a second-order transition, with a high residual population of the high-spin state even at very low temperatures