Understanding the structure and complexity of a polynomial family is a fundamental problem of arithmetic circuit complexity. There are various approaches like studying the lower bounds, which deals with nding the smallest circuit required to compute a polynomial, studying the orbit and stabilizer of a polynomial with respect to an invertible transformation etc to do this. We have a rich understanding of some of the well known polynomial families like determinant, permanent, IMM etc. In this thesis we study some of the structural properties of the polyno-mial family called the Nisan-Wigderson polynomial family. This polynomial family is inspired from a well known combinatorial design called Nisan-Wigderson design and is recently used to prove strong lower bounds on some restricted classes of arithmetic circuits ([KSS14],[KLSS14], [KST16]). But unlike determinant, permanent, IMM etc, our understanding of the Nisan-Wigderson polynomial family is inadequate. For example we do not know if this polynomial family is in VP or VNP complete or VNP-intermediate assuming VP 6= VNP, nor do we have an understanding of the complexity of its equivalence test. We hope that the knowledge of some of the inherent properties of Nisan-Wigderson polynomial like group of symmetries and Lie algebra would provide us some insights in this regard. A matrix A 2 GLn(F) is called a symmetry of an n-variate polynomial f if f(A x) = f(x): The set of symmetries of f forms a subgroup of GLn(F), which is also known as group of symmetries of f, denoted Gf . A vector space is attached to Gf to get the complete understanding of the symmetries of f. This vector space is known as the Lie algebra of group of symmetries of f (or Lie algebra of f), represented as gf . Lie algebra of f contributes some elements of Gf , known as continuous symmetries of f. Lie algebra has also been instrumental in designing e cient randomized equivalence tests for some polynomial families like determinant, permanent, IMM etc ([Kay12], [KNST17]). In this work we completely characterize the Lie algebra of the Nisan-Wigderson polynomial family. We show that gNW contains diagonal matrices of a speci c type. The knowledge of gNW not only helps us to completely gure out the continuous symmetries of the Nisan-Wigderson polynomial family, but also gives some crucial insights into the other symmetries of Nisan-Wigderson polynomial (i.e. the discrete symmetries). Thereafter using the Hessian matrix of the Nisan-Wigderson polynomial and the concept of evaluation dimension, we are able to almost completely identify the structure of GNW . In particular we prove that any A 2 GNW is a product of diagonal and permutation matrices of certain kind that we call block-permuted permutation matrix. Finally, we give explicit examples of nontrivial block-permuted permutation matrices using the automorphisms of nite eld that establishes the richness of the discrete symmetries of the Nisan-Wigderson polynomial family.

Optimization problems involving uncertainties are common in a variety of engineering disciplines such as transportation systems, manufacturing, communication networks, healthcare and finance. The large number of input variables and the lack of a system model prohibit a precise analytical solution and a viable alternative is to employ simulation-based optimization. The idea here is to simulate a few times the stochastic system under consideration while updating the system parameters until a good enough solution is obtained. Formally, given only noise-corrupted measurements of an objective function, we wish to end a parameter which minimises the objective function. Iterative algorithms using statistical methods search the feasible region to improve upon the candidate parameter. Stochastic approximation algorithms are best suited; most studied and applied algorithms for funding solutions when the feasible region is a continuously valued set. One can use information on the gradient/Hessian of the objective to aid the search process. However, due to lack of knowledge of the noise distribution, one needs to estimate the gradient/Hessian from noisy samples of the cost function obtained from simulation. Simple gradient search schemes take much iteration to converge to a local minimum and are heavily dependent on the choice of step-sizes. Stochastic Newton methods, on the other hand, can counter the ill-conditioning of the objective function as they incorporate second-order information into the stochastic updates. Stochastic Newton methods are often more accurate than simple gradient search schemes. We propose enhancements to the Hessian estimation scheme used in two recently proposed stochastic Newton methods, based on the ideas of random directions stochastic approximation (2RDSA) [21] and simultaneous perturbation stochastic approximation (2SPSA-31) [6], respectively. The proposed scheme, inspired by [29], reduces the error in the Hessian estimate by (i) Incorporating a zero-mean feedback term; and (ii) optimizing the step-sizes used in the Hessian recursion. We prove that both 2RDSA and 2SPSA-3 with our Hessian improvement scheme converges asymptotically to the true Hessian. The key advantage with 2RDSA and 2SPSA-3 is that they require only 75% of the simulation cost per-iteration for 2SPSA with improved Hessian estimation (2SPSA-IH) [29]. Numerical experiments show that 2RDSA-IH outperforms both 2SPSA-IH and 2RDSA without the improved Hessian estimation scheme.

Quantization of Neural Networks is popular technique for adopting computation intensive Deep Learning applications to edge devices. In this work, low bit mixed precision quantization of FPN-Resnet18 model trained for the task of semantic segmentation is explored using Cityscapes and Arriver datasets. The Hessian information of each layer in the model is used to determine the bit precision for each layer and in some experiments the bit precision for the layers are determined randomly. The networks are quantization-aware trained with bit combinations 2, 4 and 8. The results obtained for both Cityscapes and Arriver datasets show that the quantization-aware trained networks with the low bit mixed precision technique offer a performance at par with the 8-bit quantization-aware trained networks and the segmentation performance degrades when the network activations are quantized below 8 bits. Also, it was found that the usage of the Hessian information had little effect on the network’s performance. / Kvantisering av Neurala nätverk är populär teknik för att införa beräknings-intensiva Deep Learning -applikationer till edge-enheter. I detta arbete utforskas låg bitmixad precisionskvantisering av FPN-Resnet18-modellen som är utbildad för uppgiften för semantisk segmentering med hjälp av Cityscapes och Arriverdatauppsättningar. Hessisk information från varje lager i modellen, används för att bestämma bitprecisionen för respektive lager. I vissa experiment bestäms bitprecision för skikten slumpmässigt. Nätverken är kvantiserings medvetna utbildade med bitkombinationer 2, 4 och 8. Resultaten som erhållits för både Cityscapes och Arriver datauppsättningar visar att de kvantiserings medvetna utbildade nätverken med lågbit blandad precisionsteknik erbjuder en prestanda i nivå med 8-bitars kvantiseringsmedvetna utbildade nätverk och segmenteringens prestationsgrader när nätverksaktiveringarna kvantiseras under 8 bitar. Det visade sig också att användningen av hessisk information hade liten effekt på nätets prestanda.

Doctor of Philosophy / Department of Entomology / R. Jeff Whitworth / The Hessian fly, Mayetiola destructor (Say), has been a historically significant pest of wheat in Kansas. However, it has been 60+ years since research has been conducted examining the flies’ activity throughout the year. Results of pheromone trapping in 4 counties in Kansas shows that Hessian fly (HF) males are actively flying in the fall, at least 1 month after the historical fly-free dates. Therefore, the Hessian Fly-Free Date is no longer valid and should be referred to as the Best Pest Management Date. Using pheromones for fall and spring trapping also indicated that HF is more active throughout the spring than previously thought, with almost continuous fly emergence and numerous emergence peaks in both spring and fall. The use of resistant wheat cultivars has been adapted to protect seedling plants from HF larval feeding in the fall. However, it is unknown if these cultivars are still providing protection after winter vernalization. Greenhouse trials indicated that ‘Armour’, a cultivar considered intermediately resistant, remains resistant under infestation levels of 1 fly/tiller but significant seed weight losses occured under infestations of 3 flies/tiller. In the field, Armour did not provide protection post-vernalization, with plants containing similar numbers of flaxseeds (pupae) as the susceptible cultivar, ‘Fuller’, and having significant losses of culm height (cm), number of spikelets/spike, number of seeds/spike, and seed weight (grams) when infested. ‘Duster’, a cultivar considered highly resistant, appeared to provide resistance to HF larval feeding in both the greenhouse and the field, and even produced significantly heavier seeds when infested with 3 flies/tiller in the greenhouse. These results suggest that post-vernalization screening should be conducted on all HF resistant cultivars to determine if each continues to provide protection. Little information is available showing if and how HF larval feeding on more mature wheat (Feekes 7-10), post-vernalization, impact plants, aside from lodging. Greenhouse and field infestations of a susceptible cultivar, Fuller, showed that significant losses of culm height (cm), number of seeds/spikelet, and seed weight will result from as few as 1 larva /culm. Yield losses averaged 0.13g/spike (65 kg/ha) compared to non-infested plants.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Doctor of Philosophy / Department of Entomology / Ming-Shun Chen / John C. Reese / Keeping in view the important roles of bacteria in almost every aspect of insect’s life, the current study is the first systemic and intensive work on microbes associated with Hessian fly, a serious pest of wheat crop. A whole body analysis of Hessian fly larvae, pupae, or adults suggested that a remarkable diversity of bacteria is associated with different stages of the insect life cycle. The overriding detection of genera Acinetobacter and Enterobacter throughout the life cycle of Hessian fly suggested a stable and intimate relationship with the insect host. Adult Hessian flies have the most dissimilar bacterial composition from other stages with Bacillus as the most dominant genus. Analysis of 5778 high quality sequence reads obtained from larval gut estimated 187, 142, and 262 operational taxonomic units at 3% distance level from the 1st, 2nd, and 3rd instar respectively. Pseudomonas was the most dominant genus found in the gut of all three instars. The 3rd instar larval gut had the most diverse bacterial composition including genera Stenotrophomonas, Pantoea, Enterobacter, Ensifer, and Achromobacter. The transovarial transmission of major bacterial groups provided evidence of their intimate relationship with the Hessian fly. The Hessian fly is known to manipulate wheat plants to its own advantage. This study demonstrated that the combination of a decrease in carbon compounds and an increase in nitrogen compounds in the feeding tissues of Hessian fly-infested plants results in a C/N ratio of 17:1, nearly 2.5 times less than the C/N ratio (42:1) observed in control plants. We propose that bacteria associated with Hessian fly perform nitrogen fixation in the infested wheat, which was responsible for shifting the C/N ratio. The following findings made in the current study i.e. the presence of bacteria encoding nitrogenase (nifH) genes both in Hessian fly and infested wheat, exclusive expression of nifH in infested wheat, presence of diverse bacteria (including the nitrogen fixing genera) in the Hessian fly larvae, presence of similar bacterial microbiota in Hessian fly larvae and at the feeding site tissues in the infested wheat, and reduction in survival of Hessian fly larvae due to loss of bacteria are consistent with this hypothesis. The reduction in Hessian fly longevity after the loss of Alphaproteobacteria in first instar larvae, highest proportion of Alphaproteobacteria in insects surviving after the antibiotic treatments and the nitrogen fixation ability of associated Alphaproteobacteria strongly implies that Alphaproteobacteria are critical for the survival of Hessian fly larvae. This study provides a foundation for future studies to elucidate the role of associated microbes on Hessian fly virulence and biology. A better understanding of Hessian fly-microbe interactions may lead to new strategies to control this pest.

<p>This report presents work done in the field of output error identification, with application to spark ignition (SI) engine identification for the purpose of air to fuel ratio control. The generic parts of the project consist mainly in setting out the basis for the design of output error identification software. Efficiency issues related to linear state space models have also been explored, and although the software design is not made explicit in this report, many of the important concepts have been implemented in order to provide powerful abstractions for the application to SI engine identification. </p><p>The SI engine identification data was obtained under normal operating conditions. The goal is to re- estimate models without utilizing a virtual measurement which has been used successfully to estimate models in the past. This turns out to be a difficult problem much related to the lack of excitation in the system input, shortcomings of the fuel dynamics model and the unknown and hard to estimate exhaust sensor characteristics. Indeed, the larger of the previously estimated models are found not to be identifiable in the present situation. However, trivial restrictions of the models (not meaning restriction to trivial models) avoid that problem.</p>

ABSTRACT The rapid development of structural materials and their successful applications in various sectors of industry have led to increasing demands for assessing their mechanical properties in small volumes. If the size dimensions are below micron, it is difficult to perform traditional tensile and compression tests at such small scales. Indentation testing as one of the advanced technologies to characterize the mechanical properties of material has already been widely employed since indentation technology has emerged as a cost-effective, convenient and non-destructive method to solve this problem at micro- and nanoscales. In spite of the advances in indentation testing, the theory and development on indentation testing are still not completely mature. Many factors affect the accuracy and reliability of identified material parameters. For instance, when the material properties are determined utilizing the inverse analysis relying on numerical modelling, the procedures often suffer from a strong material parameter correlation, which leads to a non-uniqueness of the solution or high errors in parameter identification. In order to overcome that problem, an approach is proposed to reduce the material parameter correlation by designing appropriate indenter tip shapes able to sense indentation piling-up or sinking-in occurring in non-linear materials. In the present thesis, the effect of indenter tip geometry on parameter correlation in material parameter identification is investigated. It may be helpful to design indenter tip shapes producing a minimal material parameter correlation, which may help to improve the reliability of material parameter identification procedures based on indentation testing combined with inverse methods. First, a method to assess the effect of indenter tip geometry on the identification of material parameters is proposed, which contains a gradient-based numerical optimization method with sensitivity analysis. The sensitivities of objective function computed by finite difference method and by direct differentiation method are compared. Subsequently, the direct differentiation method is selected to use because it is more reliable, accurate and versatile for computing the sensitivities of the objective function. Second, the residual imprint mappings produced by different indenters are investigated. In common indentation experiments, the imprint data are not available because the indenter tip itself shields that region from access by measurement devices during loading and unloading. However, they include information about sinking-in and piling-up, which may be valuable to reduce the correlation of material parameter. Therefore, the effect of the imprint data on identification of material parameters is investigated. Finally, some strategies for improvement of the identifiability of material parameter are proposed. Indenters with special tip shapes and different loading histories are investigated. The sensitivities of material parameters toward indenter tip geometries are evaluated on the materials with elasto-plastic and elasto-visoplastic constitutive laws. The results of this thesis have shown that first, the correlations of material parameters are related to the geometries of indenter tip shapes. The abilities of different indenters for determining material parameters are significantly different. Second, residual imprint mapping data are proved to be important for identification of material parameters, because they contain the additional information about plastic material behaviour. Third, different loading histories are helpful to evaluate the material parameters of time-dependent materials. Particularly, a holding cycle is necessary to determine the material properties of time-dependent materials. These results may be useful to enable a more reliable material parameter identification.

This report presents work done in the field of output error identification, with application to spark ignition (SI) engine identification for the purpose of air to fuel ratio control. The generic parts of the project consist mainly in setting out the basis for the design of output error identification software. Efficiency issues related to linear state space models have also been explored, and although the software design is not made explicit in this report, many of the important concepts have been implemented in order to provide powerful abstractions for the application to SI engine identification. The SI engine identification data was obtained under normal operating conditions. The goal is to re- estimate models without utilizing a virtual measurement which has been used successfully to estimate models in the past. This turns out to be a difficult problem much related to the lack of excitation in the system input, shortcomings of the fuel dynamics model and the unknown and hard to estimate exhaust sensor characteristics. Indeed, the larger of the previously estimated models are found not to be identifiable in the present situation. However, trivial restrictions of the models (not meaning restriction to trivial models) avoid that problem.

The research presented in this dissertation pertains to the evaluation of stiffness of carbon nanotubes (CNTs) in a multiscale framework and modeling of the interfacial mechanical behavior in CNT-polymer nanocomposites. The goal is to study the mechanical behavior of CNTs and CNT-polymer interfaces at the atomic level, and utilize this information to develop predictive capabilities of material behavior at the macroscale. Stiffness of CNTs is analyzed through quantum mechanical (QM) calculations while the CNT-polymer interface is examined using molecular dynamics (MD) simulations. CNT-polymer-matrix composites exhibit promising properties as structural materials and constitutive models are sought to predict their macroscale behavior. The reliability of determining the homogenized response of such materials depends upon the ability to accurately capture the interfacial behavior between the nanotubes and the polymer matrix. In the proposed work, atomistic methods are be used to investigate the behavior of the interface by utilizing appropriately chosen atomistic representative volume elements (RVEs). Atomistic simulations are conducted on the RVEs to study mechanical separation with and without covalent functionalization between the polymeric matrix and two filler materials, namely graphite and a (12,0) Single Wall zig zag CNT. The information obtained from atomistic studies of separation is applicable for higher level length scale models as cohesive zone properties. The results of the present research have been correlated with available experimental data from characterization efforts.