Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

An evaluation of the distributions of polychlorinated biphenyls and organic matter in coastal sediments

The objective of this thesis is to improve the understanding of what processes and mechanism affects the distribution of polychlorinated biphenyls (PCBs) and organic carbon in coastal sediments. Because of the strong association of hydrophobic organic contaminants (HOCs) such as PCBs with organic matter in the aquatic environment, these two entities are naturally linked. The coastal environment is the most complex and dynamic part of the ocean when it comes to both cycling of organic matter and HOCs. This environment is characterised by the largest fluxes and most diverse sources of both entities. A wide array of methods was used to study these processes throughout this thesis. In the field sites in the Stockholm archipelago of the Baltic proper, bottom sediments and settling particulate matter were retrieved using sediment coring devices and sediment traps from morphometrically and seismically well-characterized locations. In the laboratory, the samples have been analysed for PCBs, stable carbon isotope ratios, carbon-nitrogen atom ratios as well as standard sediment properties. From the fieldwork in the Stockholm Archipelago and the following laboratory work it was concluded that the inner Stockholm archipelago has a low (≈ 4%) trapping efficiency for freshwater-derived organic carbon. The corollary is a large potential for long-range waterborne transport of OC and OC-associated nutrients and hydrophobic organic pollutants from urban Stockholm to more pristine offshore Baltic Sea ecosystems. Theoretical work has been carried out using Geographical Information Systems (GIS) and statistical methods on a database of 4214 individual sediment samples, each with reported individual PCB congener concentrations. From this work it was concluded that the continental shelf sediments are key global inventories and ultimate sinks of PCBs. Depending on congener, 10-80% of the cumulative historical emissions to the environment are accounted for in continental shelf sediments. Further it was concluded that the many infamous and highly contaminated surface sediments of urban harbours and estuaries of contaminated rivers cannot be of importance as a secondary source to sustain the concentrations observed in remote sediments. Of the global shelf PCB inventory < 1% are in sediments near population centres while ≥ 90% is in remote areas (> 10 km from any dwellings). The remote sub-basin of the North Atlantic Ocean contains approximately half of the global shelf sediment inventory for most of the PCBs studied.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Sustainable improvement of water networks : to achieve best decisions for rehabilitation plans using advanced GIS and statistical techniques

Many of developing countries are facing crisis in water management due to increasing of population, water scarcity, water contaminations and effects of world economic crisis. Water distribution systems in developing countries are facing many challenges of efficient repair and rehabilitation since the information of water network is very limited, which makes the rehabilitation assessment plans very difficult. Sufficient information with high technology in developed countries makes the assessment for rehabilitation easy. Developing countries have many difficulties to assess the water network causing system failure, deterioration of mains and bad water quality in the network due to pipe corrosion and deterioration. The limited information brought into focus the urgent need to develop economical assessment for rehabilitation of water distribution systems adapted to water utilities. Gaza Strip is subject to a first case study, suffering from severe shortage in the water supply and environmental problems and contamination of underground water resources. This research focuses on improvement of water supply network to reduce the water losses in water network based on limited database using techniques of ArcGIS and commercial water network software (WaterCAD). A new approach for rehabilitation water pipes has been presented in Gaza city case study. Integrated rehabilitation assessment model has been developed for rehabilitation water pipes including three components; hydraulic assessment model, Physical assessment model and Structural assessment model. WaterCAD model has been developed with integrated in ArcGIS to produce the hydraulic assessment model for water network. The model have been designed based on pipe condition assessment with 100 score points as a maximum points for pipe condition. As results from this model, we can indicate that 40% of water pipeline have score points less than 50 points and about 10% of total pipes length have less than 30 score points. By using this model, the rehabilitation plans for each region in Gaza city can be achieved based on available budget and condition of pipes. The second case study is Kuala Lumpur Case from semi-developed countries, which has been used to develop an approach to improve the water network under crucial conditions using, advanced statistical and GIS techniques. Kuala Lumpur (KL) has water losses about 40% and high failure rate, which make severe problem. This case can represent cases in South Asia countries. Kuala Lumpur faced big challenges to reduce the water losses in water network during last 5 years. One of these challenges is high deterioration of asbestos cement (AC) pipes. They need to replace more than 6500 km of AC pipes, which need a huge budget to be achieved. Asbestos cement is subject to deterioration due to various chemical processes that either leach out the cement material or penetrate the concrete to form products that weaken the cement matrix. This case presents an approach for geo-statistical model for modelling pipe failures in a water distribution network. Database of Syabas Company (Kuala Lumpur water company) has been used in developing the model. The statistical models have been calibrated, verified and used to predict failures for both networks and individual pipes. The mathematical formulation developed for failure frequency in Kuala Lumpur was based on different pipeline characteristics, reflecting several factors such as pipe diameter, length, pressure and failure history. Generalized linear model have been applied to predict pipe failures based on District Meter Zone (DMZ) and individual pipe levels. Based on Kuala Lumpur case study, several outputs and implications have been achieved. Correlations between spatial and temporal intervals of pipe failures also have been done using ArcGIS software. Water Pipe Assessment Model (WPAM) has been developed using the analysis of historical pipe failure in Kuala Lumpur which prioritizing the pipe rehabilitation candidates based on ranking system. Frankfurt Water Network in Germany is the third main case study. This case makes an overview for Survival analysis and neural network methods used in water network. Rehabilitation strategies of water pipes have been developed for Frankfurt water network in cooperation with Mainova (Frankfurt Water Company). This thesis also presents a methodology of technical condition assessment of plastic pipes based on simple analysis. This thesis aims to make contribution to improve the prediction of pipe failures in water networks using Geographic Information System (GIS) and Decision Support System (DSS). The output from the technical condition assessment model can be used to estimate future budget needs for rehabilitation and to define pipes with high priority for replacement based on poor condition. rn

Treatment of soft tissue recessions at titanium implants using a resorbable collagen matrix: a pilot study

OBJECTIVES: To histologically assess the effectiveness of a porcine-derived collagen matrix (CM) and a subepithelial connective tissue graft (CTG) for the coverage of single mucosal recessions at osseointegrated dental implants. MATERIALS AND METHODS: Chronic-type mucosal Miller Class I-like recessions (mean clinical defect height: 0.67 ± 0.33-1.16 ± 0.19 mm) were established at the buccal aspect of titanium implants with platform switch in six beagle dogs. The defects were randomly allocated to either (1) coronally advanced flap surgery (CAF) + CM, (2) CAF + CTG or (3) CAF alone. At 12 weeks, histomorphometrical measurements were made (e.g.) between the implant shoulder (IS) and the mucosal margin (PM) and IS and the outer contour of the adjacent soft tissue (mucosal thickness [MT]). RESULTS: All treatment procedures investigated were associated with an almost complete soft tissue coverage of the defect area (i.e. coronal positioning of PM relative to IS). Mean IS-PM and MT values tended to be increased in both CAF + CM (1.04 ± 0.74 mm/0.71 ± 0.55 mm) and CAF + CTG (0.88 ± 1.23 mm/0.62 ± 0.66 mm) groups when compared with CAF (0.16 ± 0.28 mm/0.34 ± 0.23 mm) alone. These differences, however, did not reach statistical significance. CONCLUSIONS: Within the limits of this pilot study, it was concluded that all treatment procedures investigated were effective in covering soft tissue recessions at titanium implants.

Influence of diurnal hyperosmotic loading on the metabolism and matrix gene expression of a whole-organ intervertebral disc model

It is generally agreed that the mechanical environment of intervertebral disc cells plays an important role in maintaining a balanced matrix metabolism. The precise mechanism by which the signals are transduced into the cells is poorly understood. Osmotic changes in the extracellular matrix (ECM) are thought to be involved. Current in-vitro studies on this topic are mostly short-term and show conflicting data on the reaction of disc cells subjected to osmotic changes which is partially due to the heterogenous and often substantially-reduced culture systems. The aim of the study was therefore to investigate the effects of cyclic osmotic loading for 4 weeks on metabolism and matrix gene expression in a full-organ intervertebral disc culture system. Intervertebral disc/endplate units were isolated from New Zealand White Rabbits and cultured either in iso-osmotic media (335 mosmol/kg) or were diurnally exposed for 8 hours to hyper-osmotic conditions (485 mosmol/kg). Cell viability, metabolic activity, matrix composition and matrix gene expression profile (collagen types I/II and aggrecan) were monitored using Live/Dead cell viability assay, tetrazolium reduction test (WST 8), proteoglycan and DNA quantification assays and quantitative PCR. The results show that diurnal osmotic stimulation did not have significant effects on proteoglycan content, cellularity and disc cell viability after 28 days in culture. However, hyperosmolarity caused increased cell death in the early culture phase and counteracted up-regulation of type I collagen gene expression in nucleus and annulus cells. Moreover, the initially decreased cellular dehydrogenase activity recovered with osmotic stimulation after 4 weeks and aggrecan gene down-regulation was delayed, although the latter was not significant according to our statistical criteria. In contrast, collagen type II did not respond to the osmotic changes and was down-regulated in both groups. In conclusion, diurnal hyper-osmotic stimulation of a whole-organ disc/endplate culture partially inhibits a matrix gene expression profile as encountered in degenerative disc disease and counteracts cellular metabolic hypo-activity.

The effect of matrix bound parathyroid hormone on bone regeneration

INTRODUCTION: Autogenous bone is the most successful bone-grafting material; however, multiple disadvantages continue to drive developments of improved methods for bone regeneration. AIM: The aim of the present study was to test the hypothesis that an arginine-glycine-aspartic acid (RGD) modified polyethylene glycol-based matrix (PEG) containing covalently bound peptides of the parathyroid hormone (PTH(1-34)) enhances bone regeneration to a degree similar to autogenous bone. MATERIAL AND METHODS: Six American foxhounds received a total of 48 cylindrical titanium implants placed in the mandible between the first premolar and the second molar. Five, respectively, 7 months following tooth extraction, implants were placed into the center of surgically created defects. This resulted in a circumferential bone defect simulating an alveolar defect with a circular gap of 1.5 mm. Four treatment modalities were randomly allocated to the four defects per side: (1) PEG-matrix containing 20 microg/ml of PTH(1-34), and 350 microg/ml cys-RGD peptide, (2) PEG alone, (3) autogenous bone and (4) empty defects. Histomorphometric analysis was performed 4 and 12 weeks after implantation. The area fraction of newly formed bone was determined within the former defect and the degree of bone-to-implant contact (BIC) was evaluated both in the defect region and in the apical region of the implant. For statistical analysis ANOVA and subsequent pairwise Student's t-test were applied. RESULTS: Healing was uneventful and all implants were histologically integrated. Histomorphometric analysis after 4 weeks showed an average area fraction of newly formed bone of 41.7+/-1.8% for matrix-PTH, 26.6+/-4.1% for PEG alone, 43.9+/-4.5% for autogenous bone, and 28.9+/-1.5% for empty defects. After 12 weeks, the respective values were 49.4+/-7.0% for matrix-PTH, 39.3+/-5.7% for PEG alone, 50.5+/-3.4% for autogenous bone and 38.7+/-1.9% for empty defects. Statistical analysis after 4 and 12 weeks revealed significantly more newly formed bone in the PTH(1-34) group compared with PEG alone or empty defects, whereas no difference could be detected against autogenous bone. Regarding BIC no significant difference was observed between the four treatment groups neither at 4 nor at 12 weeks. CONCLUSION: It is concluded that an RGD-modified PEG hydrogel containing PTH(1-34) is an effective matrix system to obtain bone regeneration.

Adaptive sensing for target tracking applications

In a statistical inference scenario, the estimation of target signal or its parameters is done by processing data from informative measurements. The estimation performance can be enhanced if we choose the measurements based on some criteria that help to direct our sensing resources such that the measurements are more informative about the parameter we intend to estimate. While taking multiple measurements, the measurements can be chosen online so that more information could be extracted from the data in each measurement process. This approach fits well in Bayesian inference model often used to produce successive posterior distributions of the associated parameter. We explore the sensor array processing scenario for adaptive sensing of a target parameter. The measurement choice is described by a measurement matrix that multiplies the data vector normally associated with the array signal processing. The adaptive sensing of both static and dynamic system models is done by the online selection of proper measurement matrix over time. For the dynamic system model, the target is assumed to move with some distribution and the prior distribution at each time step is changed. The information gained through adaptive sensing of the moving target is lost due to the relative shift of the target. The adaptive sensing paradigm has many similarities with compressive sensing. We have attempted to reconcile the two approaches by modifying the observation model of adaptive sensing to match the compressive sensing model for the estimation of a sparse vector.

Quantitative T2 mapping during follow-up after matrix-associated autologous chondrocyte transplantation (MACT): full-thickness and zonal evaluation to visualize the maturation of cartilage repair tissue

The purpose of this article was to evaluate the potential of in vivo zonal T2-mapping as a noninvasive tool in the longitudinal visualization of cartilage repair tissue maturation after matrix-associated autologous chondrocyte transplantation (MACT). Fifteen patients were treated with MACT and evaluated cross-sectionally, with a baseline MRI at a follow-up of 19.7 +/- 12.1 months after cartilage transplantation surgery of the knee. In the same 15 patients, 12 months later (31.7 +/- 12.0 months after surgery), a longitudinal 1-year follow-up MRI was obtained. MRI was performed on a 3 Tesla MR scanner; morphological evaluation was performed using a double-echo steady-state sequence; T2 maps were calculated from a multiecho, spin-echo sequence. Quantitative mean (full-thickness) and zonal (deep and superficial) T2 values were calculated in the cartilage repair area and in control cartilage sites. A statistical analysis of variance was performed. Full-tickness T2 values showed no significant difference between sites of healthy cartilage and cartilage repair tissue (p < 0.05). Using zonal T2 evaluation, healthy cartilage showed a significant increase from the deep to superficial cartilage layers (p < 0.05). Cartilage repair tissue after MACT showed no significant zonal increase from deep to superficial cartilage areas during baseline MRI (p > 0.05); however, during the 1-year follow-up, a significant zonal stratification could be observed (p < 0.05). Morphological evaluation showed no significant difference between the baseline and the 1-year follow-up MRI. T2 mapping seems to be more sensitive in revealing changes in the repair tissue compared to morphological MRI. In vivo zonal T2 assessment may be sensitive enough to characterize the maturation of cartilage repair tissue.

Variation of cell and matrix morphologies in articular cartilage among locations in the adult human knee

OBJECTIVE: Understanding of articular cartilage physiology, remodelling mechanisms, and evaluation of tissue engineering repair methods requires reference information regarding normal structural organization. Our goals were to examine the variation of cartilage cell and matrix morphology in different topographical areas of the adult human knee joint. METHODS: Osteochondral explants were acquired from seven distinct anatomical locations of the knee joints of deceased persons aged 20-40 years and prepared for analysis of cell, matrix and tissue morphology using confocal microscopy and unbiased stereological methods. Differences between locations were identified by statistical analysis. RESULTS: Medial femoral condyle cartilage had relatively high cell surface area per unit tissue volume in the superficial zone. In the transitional zone, meniscus-covered lateral tibia cartilage showed elevated chondrocyte densities compared to the rest of the knee while lateral femoral condyle cartilage exhibited particularly large chondrocytes. Statistical analyses indicated highly uniform morphology throughout the radial zone (lower 80% of cartilage thickness) in the knee, and strong similarities in cell and matrix morphologies among cartilage from the femoral condyles and also in the mediocentral tibial plateau. Throughout the adult human knee, the mean matrix volume per chondron was remarkably constant at approximately 224,000 microm(3), corresponding to approximately 4.6 x 10(6) chondrons per cm(3). CONCLUSIONS: The uniformity of matrix volume per chondron throughout the adult human knee suggests that cell-scale biophysical and metabolic constraints may place limitations on cartilage thickness, mechanical properties, and remodelling mechanisms. Data may also aid the evaluation of cartilage tissue engineering treatments in a site-specific manner. Results indicate that joint locations which perform similar biomechanical functions have similar cell and matrix morphologies; findings may therefore also provide clues to understanding conditions under which focal lesions leading to osteoarthritis may occur.

Quantifying the periodicty of Inter Movement Intervals of Leg Movements

ims: Periodic leg movements in sleep (PLMS) are a frequent finding in polysomnography. Most patients with restless legs syndrome (RLS) display PLMS. However, since PLMS are also often recorded in healthy elderly subjects, the clinical significance of PLMS is still discussed controversially. Leg movements are seen concurrently with arousals in obstructive sleep apnoea (OSA) may also appear periodically. Quantitative assessment of the periodicity of LM/PLM as measured by inter movement intervals (IMI) is difficult. This is mainly due to influencing factors like sleep architecture and sleep stage, medication, inter and intra patient variability, the arbitrary amplitude and sequence criteria which tend to broaden the IMI distributions or make them even multi-modal. Methods: Here a statistical method is presented that enables eliminating such effects from the raw data before analysing the statistics of IMI. Rather than studying the absolute size of IMI (measured in seconds) we focus on the shape of their distribution (suitably normalized IMI). To this end we employ methods developed in Random Matrix Theory (RMT). Patients: The periodicity of leg movements (LM) of four patient groups (10 to 15 each) showing LM without PLMS (group 1), OSA without PLMS (group 2), PLMS and OSA (group 3) as well as PLMS without OSA (group 4) are compared. Results: The IMI of patients without PLMS (groups 1 and 2) and with PLMS (groups 3 and 4) are statistically different. In patients without PLMS the distribution of normalized IMI resembles closely the one of random events. In contrary IMI of PLMS patients show features of periodic systems (e.g. a pendulum) when studied in normalized manner. Conclusions: For quantifying PLMS periodicity proper normalization of the IMI is crucial. Without this procedure important features are hidden when grouping LM/PLM over whole nights or across patients. The clinical significance of PLMS might be eluded when properly separating random LM from LM that show features of periodic systems.

Statistical inference for the optimal approximating model

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ2-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse-engineering and a colonization-competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co-occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio-temporal samples of assemblages in homogenous environments or environmental gradients.