Indicator function and complex coding for mixed fractional factorial designs

In a general fractional factorial design, the $n$-levels of a factor are coded by the $n$-th roots of the unity. This device allows a full generalization to mixed-level designs of the theory of the polynomial indicator function which has already been introduced for two level designs by Fontana and the Authors (2000). the properties of orthogonal arrays and regular fractions are discussed

The use of blocking sets in Galois geometries and in related research areas

Blocking sets play a central role in Galois geometries. Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research areas. This article focusses on these applications to motivate researchers to investigate blocking sets, and to motivate researchers to investigate the problems that can be solved by using blocking sets. By showing the many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets in fact open the door to improvements on the solution of many other problems

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

Improving the fatigue resistance of adhesive joints in laminated wood structures

The premature fatigue failure of a laminated wood/epoxy test beam containing a cross section finger joint was the subject of a multi-disciplinary investigation. The primary objectives were to identify the failure mechanisms which occurred during the finger joint test and to provide avenues for general improvements in the design and fabrication of adhesive joints in laminated wood structures

Progressive Crushing of Polymer Matrix Composite Tubular Structures: Review

The present paper reviews crushing process of fibre-reinforced polymer (FRPs) composites tubular structures. Working with anisotropic material requires consideration of specific parameter definition in order to tailor a well-engineered composite structure. These parameters include geometry design, strain rate sensitivity, material properties, laminate design, interlaminar fracture toughness and off-axis loading conditions which are reviewed in this paper to create a comprehensive data base for researchers, engineers and scientists in the field. Each of these parameters influences the structural integrity and progressive crushing behaviour. In this extensive review each of these parameters is introduced, explained and evaluated. Construction of a well-engineered composite structure and triggering mechanism to strain rate sensitivity and testing conditions followed by failure mechanisms are extensively reviewed. Furthermore, this paper has mainly focused on experimental analysis that has been carried out on different types of FRP composites in the past two decades

High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits

Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find

The dynamics of morphogenesis in stem cell-based embryology: Novel insights for symmetry breaking

Breaking embryonic symmetry is an essential prerequisite to shape the initially symmetric embryo into a highly organized body plan that serves as the blueprint of the adult organism. This critical process is driven by morphogen signaling gradients that instruct anteroposterior axis specification. Despite its fundamental importance, what triggers symmetry breaking and how the signaling gradients are established in time and space in the mammalian embryo remain largely unknown. Stem cell-based in vitro models of embryogenesis offer an unprecedented opportunity to quantitatively dissect the multiple physical and molecular processes that shape the mammalian embryo. Here we review biochemical mechanisms governing early mammalian patterning in vivo and highlight recent advances to recreate this in vitro using stem cells. We discuss how the novel insights from these model systems extend previously proposed concepts to illuminate the extent to which embryonic cells have the intrinsic capability to generate specific, reproducible patterns during embryogenesis