Weights Modulo a Prime Power in Divisible Codes and a Related Bound

In this paper, we generalize the theorem given by R. M. Wilson about weights modulo$p^t$in linear codes to a divisible code version. Using a similar idea, we give an upper bound for the dimension of a divisible code by some divisibility property of its weight enumerator modulo$p^e$. We also prove that this bound implies Ward's bound for divisible codes. Moreover, we see that in some cases, our bound gives better results than Ward's bound

Dimension reduction for Gaussian process emulation: an application to the influence of bathymetry on tsunami heights

High accuracy complex computer models, or simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace simulators for various purposes, such as the propagation of uncertainties from inputs to outputs or the calibration of some internal parameters against observations. However, when the input space is of high dimension, the construction of an emulator can become prohibitively expensive. In this paper, we introduce a joint framework merging emulation with dimension reduction in order to overcome this hurdle. The gradient-based kernel dimension reduction technique is chosen due to its ability to drastically decrease dimensionality with little loss in information. The Gaussian process emulation technique is combined with this dimension reduction approach. Our proposed approach provides an answer to the dimension reduction issue in emulation for a wide range of simulation problems that cannot be tackled using existing methods. The efficiency and accuracy of the proposed framework is demonstrated theoretically, and compared with other methods on an elliptic partial differential equation (PDE) problem. We finally present a realistic application to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation) are modeled as high-dimensional realizations of a spatial process using a geostatistical approach. Our dimension-reduced emulation enables us to compute the impact of these uncertainties on resulting possible tsunami wave heights near-shore and on-shore. We observe a significant increase in the spread of uncertainties in the tsunami heights due to the contribution of the bathymetry uncertainties. These results highlight the need to include the effect of uncertainties in the bathymetry in tsunami early warnings and risk assessments.Comment: 26 pages, 8 figures, 2 table

Deep Neural Network Architectures for Modulation Classification

In this work, we investigate the value of employing deep learning for the task of wireless signal modulation recognition. Recently in [1], a framework has been introduced by generating a dataset using GNU radio that mimics the imperfections in a real wireless channel, and uses 10 different modulation types. Further, a convolutional neural network (CNN) architecture was developed and shown to deliver performance that exceeds that of expert-based approaches. Here, we follow the framework of [1] and find deep neural network architectures that deliver higher accuracy than the state of the art. We tested the architecture of [1] and found it to achieve an accuracy of approximately 75% of correctly recognizing the modulation type. We first tune the CNN architecture of [1] and find a design with four convolutional layers and two dense layers that gives an accuracy of approximately 83.8% at high SNR. We then develop architectures based on the recently introduced ideas of Residual Networks (ResNet [2]) and Densely Connected Networks (DenseNet [3]) to achieve high SNR accuracies of approximately 83.5% and 86.6%, respectively. Finally, we introduce a Convolutional Long Short-term Deep Neural Network (CLDNN [4]) to achieve an accuracy of approximately 88.5% at high SNR.Comment: 5 pages, 10 figures, In proc. Asilomar Conference on Signals, Systems, and Computers, Nov. 201

Efficient spatial modelling using the SPDE approach with bivariate splines

Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be gained by doing the computations using Gaussian Markov random fields (GMRFs) as the GFs can be seen as weak solutions to corresponding stochastic partial differential equations (SPDEs) using piecewise linear finite elements. We introduce a new class of representations of GFs with bivariate splines instead of finite elements. This allows an easier implementation of piecewise polynomial representations of various degrees. It leads to GMRFs that can be inferred efficiently and can be easily extended to non-stationary fields. The solutions approximated with higher order bivariate splines converge faster, hence the computational cost can be alleviated. Numerical simulations using both real and simulated data also demonstrate that our framework increases the flexibility and efficiency.Comment: 26 pages, 7 figures and 3 table

APPLICATION OF MICROSATELLITE/SSR MARKERS FOR THE IDENTIFICATION OF PEACH ROOTSTOCKS AND CHROMOSOMAL REGIONS ASSOCIATED WITH THE RESPONSE TO PEACH TREE SHORT LIFE SYNDROME

Peach Tree Short Life (PTSL) is a complicated disease syndrome involving nematodes, temperature, soil conditions, pruning and secondary pathogens. The disease occurs commonly in the southeastern U.S., and possibly in other areas of the U.S., Europe, South America and South Africa as the related Bacterial Canker Complex. PTSL causes premature tree death during the 3rd or 4th year after planting, resulting in large economic losses for growers. Recently, Guardian® &lsquo BY520-9&rsquo rootstock was selected for its tolerance to PTSL; however, the genetic basis for this tolerance remains unknown. Nemaguard, a PTSL susceptible rootstock, and Guardian® selection 3-17-7 were crossed. Each 1 plant was selfed to create segregating 2 populations. One hundred and seventy Simple Sequence Repeat (SSR) markers, each uniquely mapped to chromosomal locations on the Prunus reference genome, were used to screen the parents and F1-11. Forty-seven SSR markers showed polymorphism among the parents, and were heterozygous in F1-11. Segregation data obtained from the F2-11 population for SSR marker inheritance and PTSL-response were compiled to identify nuclear genomic regions associated with the response to PTSL disease syndrome. Of the 47 polymorphic SSRs, nine (distributed on 4 linkage groups) were genetically linked with the response to PTSL. Identified SSR markers would be useful in crop improvement and facilitating tolerance rootstock selection. A QTL was associated with the response to PTSL as well. The upper terminus of linkage group 2 appears to be important because both the individual SSR analysis and the QTL analysis linked this region with the response to PTSL. The genes controlling the tolerance or susceptibility of PTSL may reside in this region. In the future, developing more SSR or other high-resolution markers to saturate this region will further define the specific region, and ultimately lead to identification of the candidate genes. The second project described in this dissertation is the genotyping peach rootstock seedlings using DNA-fingerprinting with microsatellite/SSR markers. Peach seedling rootstocks are usually drived from open pollination. Seedlings are difficult to distinguish morphologically, and once grafted, typically no above-ground material is available for visual identification. To avoid misidentification and to protect plant varieties and patents, DNA fingerprinting was investigated as a robust rootstock identification tool. The objective of this study was to distinguish among progeny from eight peach seedling rootstocks: Bailey, Halford, Lovell, Nemaguard, Nemared, Guardian® (selection 3-17-7), S-37 and Kakamas. Each rootstock could be discriminated by at least one SSR marker. No single perfect marker was found to identify all rootstocks. Rootstock seedling identification was conducted by screening open-pollinated seedlings. It is more difficult than parent genotype identification, because heterozygous patterns obtained in a rootstock clone segregate in its seedlings. However, unique segregation patterns were found in the rootstock seedlings. Single SSR markers could identify seedlings of rootstocks Nemared, Bailey, Kakamas and Nemaguard. Seedlings of 3-17-7 and S-37 could be identified by marker combinations. Seedlings of Lovell and Halford can be identified from the other rootstocks. However, there were no SSRs or marker combinations to uniquely differentiate Lovell from Halford seedlings. The SSR markers presented in this study could be used as a practical fingerprinting system for rootstock seedling identification. This technology is useful to test rootstocks for trueness to type for nursery operators and growers, and also will be helpful in protecting seed propagated proprietary rights (i.e., PVP) for breeders

An Internal Observability Estimate for Stochastic Hyperbolic Equations

This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the $L^2$-space. Different from the deterministic case, a delicate analysis of the adaptedness for some stochastic processes is required in the stochastic setting

Deep Neural Network Architectures for Modulation Classification

This thesis investigates the value of employing deep learning for the task of wireless signal modulation recognition. Recently in deep learning research on AMC, a framework has been introduced by generating a dataset using GNU radio that mimics the imperfections in a real wireless channel, and uses 10 different modulation types. Further, a CNN architecture was developed and shown to deliver performance that exceeds that of expert-based approaches. Here, we follow the framework of O’shea [1] and find deep neural network architectures that deliver higher accuracy than the state of the art. We tested the architecture of O’shea [1] and found it to achieve an accuracy of approximately 75% of correctly recognizing the modulation type. We first tune the CNN architecture and find a design with four convolutional layers and two dense layers that gives an accuracy of approximately 83.8% at high SNR. We then develop architectures based on the recently introduced ideas of Residual Networks (ResNet) and Densely Connected Network (DenseNet) to achieve high SNR accuracies of approximately 83% and 86.6%, respectively. We also introduce a CLDNN to achieve an accuracy of approximately 88.5% at high SNR. To improve the classification accuracy of QAM, we calculate the high order cumulants of QAM16 and QAM64 as the expert feature and improve the total accuracy to approximately 90%. Finally, by preprocessing the input and send them into a LSTM model, we improve all classification success rates to 100% except the WBFM which is 46%. The average modulation classification accuracy got a improvement of roughly 22% in this thesis