Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Development Of New Toolkits For Orbit Determination Codes For Precise Radio Tracking Experiments

This thesis describes the developments of new models and toolkits for the orbit determination codes to support and improve the precise radio tracking experiments of the Cassini-Huygens mission, an interplanetary mission to study the Saturn system. The core of the orbit determination process is the comparison between observed observables and computed observables. Disturbances in either the observed or computed observables degrades the orbit determination process. Chapter 2 describes a detailed study of the numerical errors in the Doppler observables computed by NASA's ODP and MONTE, and ESA's AMFIN. A mathematical model of the numerical noise was developed and successfully validated analyzing against the Doppler observables computed by the ODP and MONTE, with typical relative errors smaller than 10%. The numerical noise proved to be, in general, an important source of noise in the orbit determination process and, in some conditions, it may becomes the dominant noise source. Three different approaches to reduce the numerical noise were proposed. Chapter 3 describes the development of the multiarc library, which allows to perform a multi-arc orbit determination with MONTE. The library was developed during the analysis of the Cassini radio science gravity experiments of the Saturn's satellite Rhea. Chapter 4 presents the estimation of the Rhea's gravity field obtained from a joint multi-arc analysis of Cassini R1 and R4 fly-bys, describing in details the spacecraft dynamical model used, the data selection and calibration procedure, and the analysis method followed. In particular, the approach of estimating the full unconstrained quadrupole gravity field was followed, obtaining a solution statistically not compatible with the condition of hydrostatic equilibrium. The solution proved to be stable and reliable. The normalized moment of inertia is in the range 0.37-0.4 indicating that Rhea's may be almost homogeneous, or at least characterized by a small degree of differentiation.

Design, conduct, and analysis of a multicenter, pharmacogenomic, biomarker study in matched patients with severe sepsis treated with or without drotrecogin Alfa (activated)

A genomic biomarker identifying patients likely to benefit from drotrecogin alfa (activated) (DAA) may be clinically useful as a companion diagnostic. This trial was designed to validate biomarkers (improved response polymorphisms (IRPs)). Each IRP (A and B) contains two single nucleotide polymorphisms that were associated with a differential DAA treatment effect.

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.

Better conduct of clinical trials: the control group in critical care trials

OBJECTIVE: To review trial design issues related to control groups. DESIGN: Review of the literature with specific reference to critical care trials. MAIN RESULTS AND CONCLUSIONS: Performing randomized controlled trials in the critical care setting presents specific problems: studies include patients with rapidly lethal conditions, the majority of intensive care patients suffer from syndromes rather than from well-definable diseases, the severity of such syndromes cannot be precisely assessed, and the treatment consists of interacting therapies. Interactions between physiology, pathophysiology, and therapies are at best marginally understood and may have a major impact on study design and interpretation of results. Selection of the right control group is crucial for the interpretation and clinical implementation of results. Studies comparing new interventions with current ones or different levels of current treatments have the problem of the necessity of defining "usual care." Usual care controls without any constraints typically include substantial heterogeneity. Constraints in the usual therapy may help to reduce some variation. Inclusion of unrestricted usual care groups may help to enhance safety. Practice misalignment is a novel problem in which patients receive a treatment that is the direct opposite of usual care, and occurs when fixed-dose interventions are used in situations where care is normally titrated. Practice misalignment should be considered in the design and interpretation of studies on titrated therapies.