Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Statistical signal extraction using stable processes

The standard models for statistical signal extraction assume that the signal and noise are generated by linear Gaussian processes. The optimum filter weights for those models are derived using the method of minimum mean square error. In the present work we study the properties of signal extraction models under the assumption that signal/noise are generated by symmetric stable processes. The optimum filter is obtained by the method of minimum dispersion. The performance of the new filter is compared with their Gaussian counterparts by simulation.

Studies on polyurethane elastomers based on liquid natural rubber

In the present study, the photochemical depolymerisation of NR in toluene, in presence of H202 and a homogenizing solvent (Methanol/Tetrahydro— furan) so as to get hydroxyl terminated liquid natural rubber (HTNR) has been carried out. The copolymeri— sation of this product with butane 1,4 diol and toluene 2,4 diisocyanate in presence of a catalyst, dibutyl tin dilaurate, to produce polyurethanes with HTNR soft segments is also reported. The preparation of block copolymers based on poly(ethylene oxide) with varying molecular weights and HTNR are also discussed along with a detailed study on their thermal and mechanical properties

Legal regime of quality control in goods

It has long been said that market itself is the ideal regulator of all evils that may come up among traders. Free and fair competition among manufacturers in the market will adequately ensure a fair dealing to the consumers. However, these are pious hopes. that markets anywhere in the world could not accomplish so far. Consumers are being sought to be lured by advertisements issued by manufacturers and sellers that are found often false and misleading. Untrue statements and claims about quality and performance of the products virtually deceive them. The plight of the consumers remains as an unheard cry in the wildemess. In this sorry state of affairs, it is quite natural that the consumers look to the governments for a helping hand. It is seen that the governmental endeavours to ensure quality in goods are diversified. Different tools are formulated and put to use, depending upon the requirements necessitated by the facts and circumstances. This thesis is an enquiry into these measures

Channel Adaptive MAC Protocol with Traffic-Aware Distributed Power Management in Wireless Sensor Networks-Some Performance Issues

In Wireless Sensor Networks (WSN), neglecting the effects of varying channel quality can lead to an unnecessary wastage of precious battery resources and in turn can result in the rapid depletion of sensor energy and the partitioning of the network. Fairness is a critical issue when accessing a shared wireless channel and fair scheduling must be employed to provide the proper flow of information in a WSN. In this paper, we develop a channel adaptive MAC protocol with a traffic-aware dynamic power management algorithm for efficient packet scheduling and queuing in a sensor network, with time varying characteristics of the wireless channel also taken into consideration. The proposed protocol calculates a combined weight value based on the channel state and link quality. Then transmission is allowed only for those nodes with weights greater than a minimum quality threshold and nodes attempting to access the wireless medium with a low weight will be allowed to transmit only when their weight becomes high. This results in many poor quality nodes being deprived of transmission for a considerable amount of time. To avoid the buffer overflow and to achieve fairness for the poor quality nodes, we design a Load prediction algorithm. We also design a traffic aware dynamic power management scheme to minimize the energy consumption by continuously turning off the radio interface of all the unnecessary nodes that are not included in the routing path. By Simulation results, we show that our proposed protocol achieves a higher throughput and fairness besides reducing the delay

A Reinforcement Learning Approach to Economic Dispatch using Neural Networks

This paper presents a Reinforcement Learning (RL) approach to economic dispatch (ED) using Radial Basis Function neural network. We formulate the ED as an N stage decision making problem. We propose a novel architecture to store Qvalues and present a learning algorithm to learn the weights of the neural network. Even though many stochastic search techniques like simulated annealing, genetic algorithm and evolutionary programming have been applied to ED, they require searching for the optimal solution for each load demand. Also they find limitation in handling stochastic cost functions. In our approach once we learn the Q-values, we can find the dispatch for any load demand. We have recently proposed a RL approach to ED. In that approach, we could find only the optimum dispatch for a set of specified discrete values of power demand. The performance of the proposed algorithm is validated by taking IEEE 6 bus system, considering transmission losses

Gewerbeaufsicht im 21. Jahrhundert.

Während zum Genehmigungsrecht zahlreiche Abhandlungen in der juristischen Literatur und eine große Zahl von Urteilen veröffentlicht sind, hält sich die Forschung und praktische Behandlung zum Aufsichtsrecht in Grenzen. Diese Arbeit vertieft das Verständnis, für die spezifische Verknüpfung und gegenseitige Abhängigkeit der Eröffnungskontrollen und der begleitenden Kontrollen im deutschen Arbeits-, Umwelt- und Verbraucherschutzrecht. Zentraler Punkt dieser Arbeit ist die Entwicklung von Grundlinien der begleitenden Aufsicht im Gewerbeaufsichtsrecht. Dazu ist es erforderlich die verschiedenen Randbedingungen gewerbeaufsichtlichen Handelns in den Blick zu nehmen. Es ist ein Blick auf die zu erwartende Ausbildung eines neuen Rationalitätstyps der gesellschaftlichen Entwicklung (2.), auf die Typisierung von Staats-, Gewerbe- und Wirtschaftsaufsicht und deren spezifischen Handlungsmustern, den festgestellten Defiziten des Aufsichtsrechts und des Aufsichtshandelns der begleitenden Kontrollen und den festgestellten tatsächlichen Wirkungen des Aufsichtssystems (3.) zu werfen. Weitere Einflüsse auf das Aufsichtsmodell der Zukunft kommen aus der erwarteten und wünschenswerten Entwicklung des Genehmigungsrechts (4.), der Art und Weise wie die begleitende Aufsicht gehandhabt werden kann und soll (5.) und den Privatisierungstypen und deren verfassungsrechtlichen Grenzen (6.). Die Arbeit schließt mit der Formulierung eines Zukunftsmodells, dass die Gewichte zwischen der Eröffnungs- und der begleitender Kontrolle, sowie das Verhältnis zwischen Staat, Privaten Dritten und Unternehmen, neu ordnet. Insgesamt wird in dieser Arbeit für ein Aufsichtsmodell plädiert, indem der Staat stärker in die Verantwortung für eine risikoorientierte begleitende Aufsicht genommen wird. Maßstäbe für die Risikoregelung sind künftig komplett vom Staat aufzustellen. Staatliche Aufsicht kann sich zukünftig auf Rahmenregelungen und Rahmenprüfungen bei den risikoreichsten Anlagen, Tätigkeiten und Produkten beschränken. Private Dritte können die Detailermittlungen und Freigaben bearbeiten. Private Sachverständige können künftig die Hauptlast detaillierter und zeitintensiver Kontrolltätigkeiten bei Anlagen, Tätigkeiten und Produkten mit mittlerem Risiko übernehmen. Anlagen, Tätigkeiten und Produkte mit geringem Risiko können der Eigenüberwachung überlassen werden. Im Gegenzug muss der Staat in deutlich stärkeren Maß die Aufsicht über die Kontrolleure anhand einheitlicher Maßstäbe organisieren und durchführen. Die Anforderungen an die Kontrolleure müssen künftig allgemein, sowohl für die externen Kontrollpersonen als auch für die internen Aufsichtspersonen, gelten und überprüft werden.

Growth and yield of groundnut, sesame and roselle in an Acacia senegal agroforestry system in North Kordofan, Sudan

A field experiment was conducted under rainfed conditions in western Sudan at El-Obeid Research Farm and Eldemokeya Forest Reserve, North Kordofan State, during the growing seasons 2004/05 and 2005/06. The main objective was to investigate the soil physical and chemical properties and yield of groundnut (Arachis hypogea), sesame (Sesamum indicum) and roselle (Hibiscus sabdariffa) of an Acacia senegal agroforestry system in comparison with the sole cropping system. Data were recorded for soil physical and chemical properties, soil moisture content, number of pods per plant, fresh weight (kg ha^−1) and crop yield (kg ha^−1). The treatments were arranged in Randomized Complete Block Design (RCBD) and replicated four times. Significant differences (P < 0.05) were obtained for sand and silt content on both sites, while clay content was not significantly different on both sites. The nitrogen (N) and organic carbon were significantly (P < 0.05) higher in the intercropping system in Eldemokeya Forest Reserve compared with sole cropping. Soil organic carbon, N and pH were not significant on El-Obeid site. Yet the level of organic carbon, N, P and pH was higher in the intercropping system. Fresh weight was significantly different on both sites. The highest fresh weight was found in the intercropping system. Dry weights were significantly different for sesame and roselle on both sites, while groundnut was not significantly different. On both sites intercropping systems reduced groundnut, sesame and roselle yields by 26.3, 12 and 20.2%, respectively. The reduction in yield in intercropping plots could be attributed to high tree density, which resulted in water and light competition between trees and the associated crops.

Development and Integration of Biocontrol Products in Branched Broomrape (Phelipanche ramosa) management in Tomato

Parasitic weeds of the genera Striga, Orobanche, and Phelipanche pose a severe problem for agriculture because they are difficult to control and are highly destructive to several crops. The present work was carried out during the period October, 2009 to February, 2012 to evaluate the potential of arbuscular mycorrhizal fungi (AMF) to suppress P. ramosa on tomatoes and to investigate the effects of air-dried powder and aqueous extracts from Euphorbia hirta on germination and haustorium initiation in Phelipanche ramosa. The work was divided into three parts: a survey of the indigenous mycorrhizal flora in Sudan, second, laboratory and greenhouse experiments (conducted in Germany and Sudan) to construct a base for the third part, which was a field trial in Sudan. A survey was performed in 2009 in the White Nile state, Sudan to assess AMF spore densities and root colonization in nine fields planted with 13 different important agricultural crops. In addition, an attempt was made to study the relationship between soil physico-chemical properties and AMF spore density, colonization rate, species richness and other diversity indices. The mean percentage of AMF colonization was 34%, ranging from 19-50%. The spore densities (expressed as per 100 g dry soil) retrieved from the rhizosphere of different crops were relatively high, varying from 344 to 1222 with a mean of 798. There was no correlation between spore densities in soil and root colonization percentage. A total of 45 morphologically classifiable species representing ten genera of AMF were detected with no correlation between the number of species found in a soil sample and the spore density. The most abundant genus was Glomus (20 species). The AMF diversity expressed by the Shannon–Weaver index was highest in sorghum (H\= 2.27) and Jews mallow (H\= 2.13) and lowest in alfalfa (H\= 1.4). With respect to crop species, the genera Glomus and Entrophospora were encountered in almost all crops, except for Entrophospora in alfalfa. Kuklospora was found only in sugarcane and sorghum. The genus Ambispora was recovered only in mint and okra, while mint and onion were the only species on which no Acaulospora was found. The hierarchical cluster analysis based on the similarity among AMF communities with respect to crop species overall showed that species compositions were relatively similar with the highest dissimilarity of about 25% separating three of the mango samples and the four sorghum samples from all other samples. Laboratory experiments studied the influence of root and stem exudates of three tomato varieties infected by three different Glomus species on germination of P. ramosa. Root exudates were collected 21or 42 days after transplanting (DAT) and stem exudates 42 DAT and tested for their effects on germination of P. ramosa seeds in vitro. The tomato varieties studied did not have an effect on either mycorrhizal colonization or Phelipanche germination. Germination in response to exudates from 42 day old mycorrhizal plants was significantly reduced in comparison to non-mycorrhizal controls. Germination of P. ramosa in response to root exudates from 21 day old plants was consistently higher than for 42 day-old plants (F=121.6; P<.0001). Stem diffusates from non-mycorrhizal plants invariably elicited higher germination than diffusates from the corresponding mycorrhizal ones and differences were mostly statistically significant. A series of laboratory experiments was undertaken to investigate the effects of aqueous extracts from Euphorbia hirta on germination, radicle elongation, and haustorium initiation in P. ramosa. P. ramosa seeds conditioned in water and subsequently treated with diluted E. hirta extract (10-25% v/v) displayed considerable germination (47-62%). Increasing extract concentration to 50% or more reduced germination in response to the synthetic germination stimulants GR24 and Nijmegen-1 in a concentration dependent manner. P. ramosa germlings treated with diluted Euphorbia extract (10-75 % v/v) displayed haustorium initiation comparable to 2, 5-Dimethoxy-p-benzoquinon (DMBQ) at 20 µM. Euphorbia extract applied during conditioning reduced haustorium initiation in a concentration dependent manner. E. hirta extract or air-dried powder, applied to soil, induced considerable P. ramosa germination. Pot experiments were undertaken in a glasshouse at the University of Kassel, Germany, to investigate the effects of P. ramosa seed bank on tomato growth parameters. Different Phelipanche seed banks were established by mixing the parasite seeds (0 - 32 mg) with the potting medium in each pot. P. ramosa reduced all tomato growth parameters measured and the reduction progressively increased with seed bank. Root and total dry matter accumulation per tomato plant were most affected. P. ramosa emergence, number of tubercles, and tubercle dry weight increased with the seed bank and were, invariably, maximal with the highest seed bank. Another objective was to determine if different AM fungi differ in their effects on the colonization of tomatoes with P. ramosa and the performance of P. ramosa after colonization. Three AMF species viz. GIomus intraradices, Glomus mosseae and Glomus Sprint® were used in this study. For the infection, P. ramosa seeds (8 mg) were mixed with the top 5 cm soil in each pot. No mycorrhizal colonization was detected in un-inoculated control plants. P. ramosa infested, mycorrhiza inoculated tomato plants had significantly lower AMF colonization compared to plants not infested with P. ramosa. Inoculation with G. intraradices, G. mosseae and Glomus Sprint® reduced the number of emerged P. ramosa plants by 29.3, 45.3 and 62.7% and the number of tubercles by 22.2, 42 and 56.8%, respectively. Mycorrhizal root colonization was positively correlated with number of branches and total dry matter of tomatoes. Field experiments on tomato undertaken in 2010/12 were only partially successful because of insect infestations which resulted in the complete destruction of the second run of the experiment. The effects of the inoculation with AMF, the addition of 10 t ha-1 filter mud (FM), an organic residues from sugar processing and 36 or 72 kg N ha-1 on the infestation of tomatoes with P. ramosa were assessed. In un-inoculated control plants, AMF colonization ranged between 13.4 to 22.1% with no significant differences among FM and N treatments. Adding AMF or FM resulted in a significant increase of branching in the tomato plants with no additive effects. Dry weights were slightly increased through FM application when no N was applied and significantly at 36 kg N ha-1. There was no effect of FM on the time until the first Phelipanche emerged while AMF and N application interacted. Especially AMF inoculation resulted in a tendency to delayed P. ramosa emergence. The marketable yield was extremely low due to the strong fruit infestation with insects mainly whitefly Bemisia tabaci and tomato leaf miner (Tuta absoluta). Tomatoes inoculated with varied mycorrhiza species displayed different response to the insect infestation, as G. intraradices significantly reduced the infestation, while G. mosseae elicited higher insect infestation. The results of the present thesis indicate that there may be a potential of developing management strategies for P. ramosa targeting the pre-attachment stage namely germination and haustorial initiation using plant extracts. However, ways of practical use need to be developed. If such treatments can be combined with AMF inoculation also needs to be investigated. Overall, it will require a systematic approach to develop management tools that are easily applicable and affordable to Sudanese farmers. It is well-known that proper agronomical practices such as the design of an optimum crop rotation in cropping systems, reduced tillage, promotion of cover crops, the introduction of multi-microbial inoculants, and maintenance of proper phosphorus levels are advantageous if the mycorrhiza protection method is exploited against Phelipanche ramosa infestation. Without the knowledge about the biology of the parasitic weeds by the farmers and basic preventive measures such as hygiene and seed quality control no control strategy will be successful, however.

Higher Education Governance in Vietnam: University Action, the State and Changing Relationships

Diese Dissertation stellt eine Studie da, welche sich mit den Änderungen in der Governance der Hochschulbildung in Vietnam beschäftigt. Das zentrale Ziel dieser Forschungsarbeit ist die Untersuchung der Herkunft und Änderung in der Beziehung der Mächte zwischen dem vietnamesischen Staat und den Hochschulbildungsinstituten (HI), welche hauptsächlich aus der Interaktion dieser beiden Akteure resultiert. Die Macht dieser beiden Akteure wurde im sozialen Bereich konstruiert und ist hauptsächlich durch ihre Nützlichkeit und Beiträge für die Hochschulbildung bestimmt. Diese Arbeit beschäftigt sich dabei besonders mit dem Aspekt der Lehrqualität. Diese Studie nimmt dabei die Perspektive einer allgemeinen Governance ein, um die Beziehung zwischen Staat und HI zu erforschen. Zudem verwendet sie die „Resource Dependence Theory“ (RDT), um das Verhalten der HI in Bezug auf die sich verändernde Umgebung zu untersuchen, welche durch die Politik und eine abnehmende Finanzierung charakterisiert ist. Durch eine empirische Untersuchung der Regierungspolitik sowie der internen Steuerung und den Praktiken der vier führenden Universitäten kommt die Studie zu dem Schluss, dass unter Berücksichtigung des Drucks der Schaffung von Einkommen die vietnamesischen Universitäten sowohl Strategien als auch Taktiken entwickelt haben, um Ressourcenflüsse und Legitimität zu kontrollieren. Die Entscheidungs- und Zielfindung der Komitees, die aus einer Mehrheit von Akademikern bestehen, sind dabei mächtiger als die der Manager. Daher werden bei initiativen Handlungen der Universitäten größtenteils Akademiker mit einbezogen. Gestützt auf die sich entwickelnden Muster der Ressourcenbeiträge von Akademikern und Studierenden für die Hochschulbildung prognostiziert die Studie eine aufstrebende Governance Konfiguration, bei der die Dimensionen der akademischen Selbstverwaltung und des Wettbewerbsmarktes stärker werden und die Regulation des Staates rational zunimmt. Das derzeitige institutionelle Design und administrative System des Landes, die spezifische Gewichtung und die Koordinationsmechanismen, auch als sogenanntes effektives Aufsichtssystem zwischen den drei Schlüsselakteuren - der Staat, die HI/Akademiker und die Studierenden – bezeichnet, brauchen eine lange Zeit zur Detektion und Etablierung. In der aktuellen Phase der Suche nach einem solchen System sollte die Regierung Management-Tools stärken, wie zum Beispiel die Akkreditierung, belohnende und marktbasierte Instrumente und das Treffen informations-basierter Entscheidungen. Darüber hinaus ist es notwendig die Transparenz der Politik zu erhöhen und mehr Informationen offenzulegen.

Effect of rosemary (Rosmarinus officinalis) extract on weight, hematology and cell-mediated immune response of newborn goat kids

This study aimed at evaluating the effects of different levels of rosemary (Rosmarinus officinalis) extract on growth rate, hematology and cell-mediated immune response in Markhoz newborn goat kids. Twenty four goat kids (aged 7 +/- 3 days) were randomly allotted to four groups with six replicates. The groups included: control, T1, T2 and T3 groups which received supplemented-milk with 0, 100, 200 and 400mg aqueous rosemary extract per kg of live body weight per day for 42 days. Body weights of kids were measured weekly until the end of the experiment. On day 42, 10 ml blood samples were collected from each kid through the jugular vein. Cell-mediated immune response was assessed through the double skin thickness after intradermal injection of phyto-hematoglutinin (PHA) at day 21 and 42. No significant differences were seen in initial body weight, average daily gain (ADG) and total gain. However, significant differences in globulin (P <0.05), and white blood cells (WBC) (P <0.001) were observed. There were no significant differences in haemoglobin (Hb), packed cell volume (PCV), red blood cells (RBC), lymphocytes and neutrophils between the treatments. Skin thickness in response to intra dermal injection of PHA significantly increased in the treated groups as compared to the control group at day 42 (P< 0.01) with the T3 group showing the highest response to PHA injection. In conclusion, the results indicated that aqueous rosemary extract supplemented-milk had a positive effect on immunity and skin thickness of newborn goat kids.

Optimal Unsupervised Learning in Feedforward Neural Networks

We investigate the properties of feedforward neural networks trained with Hebbian learning algorithms. A new unsupervised algorithm is proposed which produces statistically uncorrelated outputs. The algorithm causes the weights of the network to converge to the eigenvectors of the input correlation with largest eigenvalues. The algorithm is closely related to the technique of Self-supervised Backpropagation, as well as other algorithms for unsupervised learning. Applications of the algorithm to texture processing, image coding, and stereo depth edge detection are given. We show that the algorithm can lead to the development of filters qualitatively similar to those found in primate visual cortex.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

“Unmixing” Tissue Gene Expression Signatures from Tumor Biopsies

Emergent molecular measurement methods, such as DNA microarray, qRTPCR, and many others, offer tremendous promise for the personalized treatment of cancer. These technologies measure the amount of specific proteins, RNA, DNA or other molecular targets from tumor specimens with the goal of “fingerprinting” individual cancers. Tumor specimens are heterogeneous; an individual specimen typically contains unknown amounts of multiple tissues types. Thus, the measured molecular concentrations result from an unknown mixture of tissue types, and must be normalized to account for the composition of the mixture. For example, a breast tumor biopsy may contain normal, dysplastic and cancerous epithelial cells, as well as stromal components (fatty and connective tissue) and blood and lymphatic vessels. Our diagnostic interest focuses solely on the dysplastic and cancerous epithelial cells. The remaining tissue components serve to “contaminate” the signal of interest. The proportion of each of the tissue components changes as a function of patient characteristics (e.g., age), and varies spatially across the tumor region. Because each of the tissue components produces a different molecular signature, and the amount of each tissue type is specimen dependent, we must estimate the tissue composition of the specimen, and adjust the molecular signal for this composition. Using the idea of a chemical mass balance, we consider the total measured concentrations to be a weighted sum of the individual tissue signatures, where weights are determined by the relative amounts of the different tissue types. We develop a compositional source apportionment model to estimate the relative amounts of tissue components in a tumor specimen. We then use these estimates to infer the tissuespecific concentrations of key molecular targets for sub-typing individual tumors. We anticipate these specific measurements will greatly improve our ability to discriminate between different classes of tumors, and allow more precise matching of each patient to the appropriate treatment