Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.

BREAKING CODES: MAKING THEORIES ON MENSTRUATION ACCESSIBLE THROUGH THIRD-WAVE FEMINISM

Men and women respond to situations according to their community’s social codes. With menstruation, people adhere to “menstrual codes”. Within academic communities, people adhere to “academic codes”. This report paper investigates performances of academic codes and menstrual codes. Implications of gender identity and race are missing and/or minimal in past feminist work regarding menstruation. This paper includes considerations for gender identity and race. Within the examination of academic codes, this paper discusses the inhibitive process of idea creation within the academic sphere, and the limitations to the predominant ways of knowledge sharing within, and outside of, the academic community. The digital project (www.hu.mtu.edu/~creynolds) is one example of how academic and menstrual codes can be broken. The report and project provide a broadly accessible deconstruction of menstrual advertising and academic theories while fostering conversations on menstruation through the sharing of knowledge with others, regardless of gender, race, or academic standing.

Summary of the recommendations of the EFNS/MDS-ES review on therapeutic management of Parkinson's disease.

OBJECTIVE To summarize the 2010 EFNS/MDS-ES evidence-based treatment recommendations for the management of Parkinson's disease (PD). This summary includes the treatment recommendations for early and late PD. METHODS For the 2010 publication, a literature search was undertaken for articles published up to September 2009. For this summary, an additional literature search was undertaken up to December 2010. Classification of scientific evidence and the rating of recommendations were made according to the EFNS guidance. In cases where there was insufficient scientific evidence, a consensus statement ('good practice point') is made. RESULTS AND CONCLUSIONS For each clinical indication, a list of therapeutic interventions is provided, including classification of evidence.

Growth Codes: Intermediate Performance Analysis and Application to Video

Growth codes are a subclass of Rateless codes that have found interesting applications in data dissemination problems. Compared to other Rateless and conventional channel codes, Growth codes show improved intermediate performance which is particularly useful in applications where partial data presents some utility. In this paper, we investigate the asymptotic performance of Growth codes using the Wormald method, which was proposed for studying the Peeling Decoder of LDPC and LDGM codes. Compared to previous works, the Wormald differential equations are set on nodes' perspective which enables a numerical solution to the computation of the expected asymptotic decoding performance of Growth codes. Our framework is appropriate for any class of Rateless codes that does not include a precoding step. We further study the performance of Growth codes with moderate and large size codeblocks through simulations and we use the generalized logistic function to model the decoding probability. We then exploit the decoding probability model in an illustrative application of Growth codes to error resilient video transmission. The video transmission problem is cast as a joint source and channel rate allocation problem that is shown to be convex with respect to the channel rate. This illustrative application permits to highlight the main advantage of Growth codes, namely improved performance in the intermediate loss region.

Cancer intelligence acquired (CIA): tumor glycosylation and sialylation codes dismantling antitumor defense

Aberrant glycosylation is a key feature of malignant transformation and reflects epigenetic and genetic anomalies among the multitude of molecules involved in glycan biosynthesis. Although glycan biosynthesis is not template bound, altered tumor glycosylation is not random, but associated with common glycosylation patterns. Evidence suggests that acquisition of distinct glycosylation patterns evolves from a ‘microevolutionary’ process conferring advantages in terms of tumor growth, tumor dissemination, and immune escape. Such glycosylation modifications also involve xeno- and hypersialylation. Xeno-autoantigens such as Neu5Gc-gangliosides provide potential targets for immunotherapy. Hypersialylation may display ‘enhanced self’ to escape immunosurveillance and involves several not mutually exclusive inhibitory pathways that all rely on protein–glycan interactions. A better understanding of tumor ‘glycan codes’ as deciphered by lectins, such as siglecs, selectins, C-type lectins and galectins, may lead to novel treatment strategies, not only in cancer, but also in autoimmune disease or transplantation.

RC-NDN: Raptor Codes Enabled Named Data Networking

Information-centric networking (ICN) has been proposed to cope with the drawbacks of the Internet Protocol, namely scalability and security. The majority of research efforts in ICN have focused on routing and caching in wired networks, while little attention has been paid to optimizing the communication and caching efficiency in wireless networks. In this work, we study the application of Raptor codes to Named Data Networking (NDN), which is a popular ICN architecture, in order to minimize the number of transmitted messages and accelerate content retrieval times. We propose RC-NDN, which is a NDN compatible Raptor codes architecture. In contrast to other coding-based NDN solutions that employ network codes, RC-NDN considers security architectures inherent to NDN. Moreover, different from existing network coding based solutions for NDN, RC-NDN does not require significant computational resources, which renders it appropriate for low cost networks. We evaluate RC-NDN in mobile scenarios with high mobility. Evaluations show that RC-NDN outperforms the original NDN significantly. RC-NDN is particularly efficient in dense environments, where retrieval times can be reduced by 83% and the number of Data transmissions by 84.5% compared to NDN.

Ancient Semitic Codes and the Mosaic legislation

contributed by the Very Rev, the Chief Rabbi (J. H. Hertz)

CODE’s new ultra-rapid orbit and ERP products for the IGS

The International GNSS Service (IGS) issues four sets of so-called ultra-rapid products per day, which are based on the contributions of the IGS Analysis Centers. The traditional (“old”) ultra-rapid orbit and earth rotation parameters (ERP) solution of the Center for Orbit Determination in Europe (CODE) was based on the output of three consecutive 3-day long-arc rapid solutions. Information from the IERS Bulletin A was required to generate the predicted part of the old CODE ultra-rapid product. The current (“new”) product, activated in November 2013, is based on the output of exactly one multi-day solution. A priori information from the IERS Bulletin A is no longer required for generating and predicting the orbits and ERPs. This article discusses the transition from the old to the new CODE ultra-rapid orbit and ERP products and the associated improvement in reliability and performance. All solutions used in this article were generated with the development version of the Bernese GNSS Software. The package was slightly extended to meet the needs of the new CODE ultra-rapid generation.