The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties

A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary one-error-correcting codes of length 15: Part I--Classification," IEEE Trans. Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying work, the classified codes are studied in great detail, and their main properties are tabulated. The results include the fact that 33 of the 80 Steiner triple systems of order 15 occur in such codes. Further understanding is gained on full-rank codes via switching, as it turns out that all but two full-rank codes can be obtained through a series of such transformations from the Hamming code. Other topics studied include (non)systematic codes, embedded one-error-correcting codes, and defining sets of codes. A classification of certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of coordinates fixed by symmetries of codes), added and extended many other result

Building safe software

Murphy is a set of techniques and tools under investigation for their potential in enhancing the safety of software. This paper describes some of the work which has been done and some which is planned

The genetic basis for adaptation of model-designed syntrophic co-cultures.

Understanding the fundamental characteristics of microbial communities could have far reaching implications for human health and applied biotechnology. Despite this, much is still unknown regarding the genetic basis and evolutionary strategies underlying the formation of viable synthetic communities. By pairing auxotrophic mutants in co-culture, it has been demonstrated that viable nascent E. coli communities can be established where the mutant strains are metabolically coupled. A novel algorithm, OptAux, was constructed to design 61 unique multi-knockout E. coli auxotrophic strains that require significant metabolite uptake to grow. These predicted knockouts included a diverse set of novel non-specific auxotrophs that result from inhibition of major biosynthetic subsystems. Three OptAux predicted non-specific auxotrophic strains-with diverse metabolic deficiencies-were co-cultured with an L-histidine auxotroph and optimized via adaptive laboratory evolution (ALE). Time-course sequencing revealed the genetic changes employed by each strain to achieve higher community growth rates and provided insight into mechanisms for adapting to the syntrophic niche. A community model of metabolism and gene expression was utilized to predict the relative community composition and fundamental characteristics of the evolved communities. This work presents new insight into the genetic strategies underlying viable nascent community formation and a cutting-edge computational method to elucidate metabolic changes that empower the creation of cooperative communities

Rational Design of DNA Sequences with Non-Orthogonal Binding Interactions

Molecular computation involving promiscuous, or non-orthogonal, binding interactions between system components is found commonly in natural biological systems, as well as some proposed human-made molecular computers. Such systems are characterized by the fact that each computational unit, such as a domain within a DNA strand, may bind to several different partners with distinct, prescribed binding strengths. Unfortunately, implementing systems of molecular computation that incorporate non-orthogonal binding is difficult, because researchers lack a robust, general-purpose method for designing molecules with this type of behavior. In this work, we describe and demonstrate a process for the rational design of DNA sequences with prescribed non-orthogonal binding behavior. This process makes use of a model that represents large sets of non-orthogonal DNA sequences using fixed-length binary strings, and estimates the differential binding affinity between pairs of sequences through the Hamming distance between their corresponding binary strings. The real-world applicability of this model is supported by simulations and some experimental data. We then select two previously described systems of molecular computation involving non-orthogonal interactions, and apply our sequence design process to implement them using DNA strand displacement. Our simulated results on these two systems demonstrate both digital and analog computation. We hope that this work motivates the development and implementation of new computational paradigms based on non-orthogonal binding

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry