Random Coding Bounds for DNA Codes Based on Fibonacci Ensembles of DNA Sequences

We consider DNA codes based on the concept of a weighted 2-stem similarity measure which reflects the ”hybridization potential” of two DNA sequences. A random coding bound on the rate of DNA codes with respect to a thermodynamic motivated similarity measure is proved. Ensembles of DNA strands whose sequence composition is restricted in a manner similar to the restrictions in binary Fibonacci sequences are introduced to obtain the bound

On Critical Relative Distance of DNA Codes for Additive Stem Similarity

We consider DNA codes based on the nearest-neighbor (stem) similarity model which adequately reflects the "hybridization potential" of two DNA sequences. Our aim is to present a survey of bounds on the rate of DNA codes with respect to a thermodynamically motivated similarity measure called an additive stem similarity. These results yield a method to analyze and compare known samples of the nearest neighbor "thermodynamic weights" associated to stacked pairs that occurred in DNA secondary structures.Comment: 5 or 6 pages (compiler-dependable), 0 figures, submitted to 2010 IEEE International Symposium on Information Theory (ISIT 2010), uses IEEEtran.cl

Unreliable and resource-constrained decoding

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 185-213).Traditional information theory and communication theory assume that decoders are noiseless and operate without transient or permanent faults. Decoders are also traditionally assumed to be unconstrained in physical resources like material, memory, and energy. This thesis studies how constraining reliability and resources in the decoder limits the performance of communication systems. Five communication problems are investigated. Broadly speaking these are communication using decoders that are wiring cost-limited, that are memory-limited, that are noisy, that fail catastrophically, and that simultaneously harvest information and energy. For each of these problems, fundamental trade-offs between communication system performance and reliability or resource consumption are established. For decoding repetition codes using consensus decoding circuits, the optimal tradeoff between decoding speed and quadratic wiring cost is defined and established. Designing optimal circuits is shown to be NP-complete, but is carried out for small circuit size. The natural relaxation to the integer circuit design problem is shown to be a reverse convex program. Random circuit topologies are also investigated. Uncoded transmission is investigated when a population of heterogeneous sources must be categorized due to decoder memory constraints. Quantizers that are optimal for mean Bayes risk error, a novel fidelity criterion, are designed. Human decision making in segregated populations is also studied with this framework. The ratio between the costs of false alarms and missed detections is also shown to fundamentally affect the essential nature of discrimination. The effect of noise on iterative message-passing decoders for low-density parity check (LDPC) codes is studied. Concentration of decoding performance around its average is shown to hold. Density evolution equations for noisy decoders are derived. Decoding thresholds degrade smoothly as decoder noise increases, and in certain cases, arbitrarily small final error probability is achievable despite decoder noisiness. Precise information storage capacity results for reliable memory systems constructed from unreliable components are also provided. Limits to communicating over systems that fail at random times are established. Communication with arbitrarily small probability of error is not possible, but schemes that optimize transmission volume communicated at fixed maximum message error probabilities are determined. System state feedback is shown not to improve performance. For optimal communication with decoders that simultaneously harvest information and energy, a coding theorem that establishes the fundamental trade-off between the rates at which energy and reliable information can be transmitted over a single line is proven. The capacity-power function is computed for several channels; it is non-increasing and concave.by Lav R. Varshney.Ph.D

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept borrowed from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical ‘coherence’ and ‘consistency’. In this study, Gabriel Pareyon presents a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. The author analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Accordingly, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature—proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. At the same time, original arguments by Benoît B. Mandelbrot (1924–2010) are revised, alongside a systematic critique of the literature on the subject. In fact, connecting Charles S. Peirce’s ‘synechism’ with Mandelbrot’s ‘fractality’ is one of the main developments of the present study

06. 2005 Seventeenth Annual IMSA Presentation Day

https://digitalcommons.imsa.edu/class_of_2005/1004/thumbnail.jp

2005 Seventeenth Annual IMSA Presentation Day

The Student Inquiry and Research Program fosters the development of students as highly skilled and integrative problem finders, problem solvers, and apprentice investigators, all skills required to succeed in the global workplace of the 21 Century.https://digitalcommons.imsa.edu/archives_sir/1017/thumbnail.jp