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Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition.
Registry-based trials have emerged as a potentially cost-saving study methodology. Early estimates of cost savings, however, conflated the benefits associated with registry utilisation and those associated with other aspects of pragmatic trial designs, which might not all be as broadly applicable. In this study, we sought to build a practical tool that investigators could use across disciplines to estimate the ranges of potential cost differences associated with implementing registry-based trials versus standard clinical trials.
We built simulation Markov models to compare unique costs associated with data acquisition, cleaning, and linkage under a registry-based trial design versus a standard clinical trial. We conducted one-way, two-way, and probabilistic sensitivity analyses, varying study characteristics over broad ranges, to determine thresholds at which investigators might optimally select each trial design.
Registry-based trials were more cost effective than standard clinical trials 98.6% of the time. Data-related cost savings ranged from $4300 to $600,000 with variation in study characteristics. Cost differences were most reactive to the number of patients in a study, the number of data elements per patient available in a registry, and the speed with which research coordinators could manually abstract data. Registry incorporation resulted in cost savings when as few as 3768 independent data elements were available and when manual data abstraction took as little as 3.4 seconds per data field.
Registries offer important resources for investigators. When available, their broad incorporation may help the scientific community reduce the costs of clinical investigation. We offer here a practical tool for investigators to assess potential costs savings.
In recent years, investigations of the phase transition behavior of semiconducting nanoparticles under high pressure has attracted increasing attention due to their potential applications in sensors, electronics, and optics. However, current understanding of how the size of nanoparticles influences this pressure-dependent property is somewhat lacking. In particular, phase behaviors of semiconducting CdS nanoparticles under high pressure have not been extensively reported. Therefore, in this work, CdS nanoparticles of different sizes are used as a model system to investigate particle size effects on high-pressure-induced phase transition behaviors. In particular, 7.5, 10.6, and 39.7 nm spherical CdS nanoparticles are synthesized and subjected to controlled high pressures up to 15 GPa in a diamond anvil cell. Analysis of all three nanoparticles using in-situ synchrotron wide-angle X-ray scattering (WAXS) data shows that phase transitions from wurtzite to rocksalt occur at higher pressures than for bulk material. Bulk modulus calculations not only show that the wurtzite CdS nanomaterial is more compressible than rocksalt, but also that the compressibility of CdS nanoparticles depends on their particle size. Furthermore, sintering of spherical nanoparticles into nanorods was observed for the 7.5 nm CdS nanoparticles. Our results provide new insights into the fundamental properties of nanoparticles under high pressure that will inform designs of new nanomaterial structures for emerging applications.
Herd immunity, a concept normally applied in vaccinated populations, is a preventative measure to determine if a significant portion of a population can protect vulnerable individuals against a certain disease. Like vaccines, tourniquet education can be a form of herd immunity to protect vulnerable individuals in a population and prevent the loss of life from a peripheral hemorrhage. The authors have identified a deficiency in simple, quick, and effective hemorrhage control education. Therefore, to maximize herd immunity, the novel educational platform evaluates the efficacy of “Just-in-Time” (JiT) tourniquet application training.
The authors hypothesize that the utilization of JiT training will be effective in promoting both competence and confidence for individuals to utilize tourniquets in response to a disaster environment.
This Institutional Review Board-approved study recruited medical students who were trained in hemorrhage control measures at a Level 1 Trauma Center. Tourniquet training sessions were held, and naïve civilians received tourniquet education. The subjects received a five- to ten-minute lesson on indications, contraindications, and application techniques of commercial and improvisational tourniquets. Participants subsequently applied a tourniquet to an instructor’s arm to demonstrate proper tourniquet application for a brachial artery hemorrhage. Pre- and post-educational surveys were completed to test participant competency and confidence.
Of the 104 subjects who completed the course, 97 had no prior training in hemorrhage control techniques, including commercial and improvisational tourniquet application. The mean pre-test score was 2.27/5.00 and the mean post-test score was 4.38/5.00, P <.001 (n = 97). When queried “How competent would you feel applying a tourniquet (commercial or improvisational) on an individual with a bleeding wound?” 92/97 felt confident (95%), one felt less confident, and four felt no difference in confidence levels (P <.001).
Just-in-Time training is an effective method in teaching naïve civilians proper tourniquet application. This platform could serve as an alternative to more extensive training programs and requires less time, costs, and resources. If a significant number of individuals in a local community can effectively apply a tourniquet in a disaster scenario, a “herd immunity” effect could be achieved to control peripheral hemorrhages.
Leafy spurge (Euphorbia esula L.) is an invasive perennial weed infesting range and recreational lands of North America. Previous research and omics projects with E. esula have helped develop it as a model for studying many aspects of perennial plant development and response to abiotic stress. However, the lack of an assembled genome for E. esula has limited the power of previous transcriptomics studies to identify functional promoter elements and transcription factor binding sites. An assembled genome for E. esula would enhance our understanding of signaling processes controlling plant development and responses to environmental stress and provide a better understanding of genetic factors impacting weediness traits, evolution, and herbicide resistance. A comprehensive transcriptome database would also assist in analyzing future RNA-seq studies and is needed to annotate and assess genomic sequence assemblies. Here, we assembled and annotated 56,234 unigenes from an assembly of 589,235 RNA-seq-derived contigs and a previously published Sanger-sequenced expressed sequence tag collection. The resulting data indicate that we now have sequence for >90% of the expressed E. esula protein-coding genes. We also assembled the gene space of E. esula by using a limited coverage (18X) genomic sequence database. In this study, the programs Velvet and Trinity produced the best gene-space assemblies based on representation of expressed and conserved eukaryotic genes. The results indicate that E. esula contains as much as 23% repetitive sequences, of which 11% are unique. Our sequence data were also sufficient for assembling a full chloroplast and partial mitochondrial genome. Further, marker analysis identified more than 150,000 high-quality variants in our E. esula L-RNA–scaffolded, whole-genome, Trinity-assembled genome. Based on these results, E. esula appears to have limited heterozygosity. This study provides a blueprint for low-cost genomic assemblies in weed species and new resources for identifying conserved and novel promoter regions among coordinately expressed genes of E. esula.
A clinically compatible fluorescence lifetime imaging microscopy (FLIM) system was developed. The system was applied to intraoperative in vivo imaging of head and neck squamous cell carcinoma (HNSCC). The endoscopic FLIM prototype integrates a gated (down to 0.2 ns) intensifier imaging system and a fiber-bundle endoscope (0.5-mm-diameter, 10,000 fibers with a gradient index lens objective 0.5 NA, 4-mm field of view), which provides intraoperative access to the surgical field. Tissue autofluorescence was induced by a pulsed laser (337 nm, 700 ps pulse width) and collected in the 460 ± 25 nm spectral band. FLIM experiments were conducted at 26 anatomic sites in ten patients during head and neck cancer surgery. HNSCC exhibited a weaker florescence intensity (~50% less) when compared with healthy tissue and a shorter average lifetime (τHNSCC = 1.21 ± 0.04 ns) than the surrounding normal tissue (τN = 1.49 ± 0.06 ns). This work demonstrates the potential of FLIM for label-free head and neck tumor demarcation during intraoperative surgical procedures.
For a class of ℤ2 Markov Random Fields (MRFs) μ, we show that the sequence of successive differences of entropies of induced MRFs on strips of height n converges exponentially fast (in n) to the entropy of μ. These strip entropies can be computed explicitly when μ is a Gibbs state given by a nearest-neighbor interaction on a strongly irreducible nearest-neighbor ℤ2 shift of finite type X. We state this result in terms of approximations to the (topological) pressures of certain functions on such an X, and we show that these pressures are computable if the values taken on by the functions are computable. Finally, we show that our results apply to the hard core model and Ising model for certain parameter values of the corresponding interactions, as well as to the topological entropy of certain nearest-neighbor ℤ2 shifts of finite type, generalizing a result in [R. Pavlov. Approximating the hard square entropy constant with probabilistic methods. Ann. Probab. to appear].
This volume is a collection of papers on hidden Markov processes (HMPs) involving connections with symbolic dynamics and statistical mechanics. The subject was the focus of a five-day workshop held at the Banff International Research Station (BIRS) in October 2007, which brought together thirty mathematicians, computer scientists, and electrical engineers from institutions throughout the world. Most of the papers in this volume are based either on work presented at the workshop or on problems posed at the workshop.
From one point of view, an HMP is a stochastic process obtained as the noisy observation process of a finite-state Markov chain; a simple example is a binary Markov chain observed in binary symmetric noise, i.e., each symbol (0 or 1) in a binary state sequence generated by a two-state Markov chain may be flipped with some small probability, independently from time instant to time instant. In another (essentially equivalent) viewpoint, an HMP is a process obtained from a finite-state Markov chain by partitioning its state set into groups and completely “hiding” the distinction among states within each group; more precisely, there is a deterministic function on the states of the Markov chain, and the HMP is the process obtained by observing the sequences of function values rather than sequences of states (and hence such a process is sometimes called a “function of a Markov chain”).
HMPs are encountered in an enormous variety of applications involving phenomena observed in the presence of noise.
Abstract. In this article, we show that small complex perturbations of positive matrices are contractions, with respect to a complex version of the Hilbert metric, on a neighborhood of the interior of the real simplex within the complex simplex. We show that this metric can be used to obtain estimates of the domain of analyticity of the entropy rate for a hidden Markov process when the underlying Markov chain has strictly positive transition probabilities.
The purpose of this article is twofold. First, in Section 2, we introduce a new complex version of the Hilbert metric on the standard real simplex. This metric is defined on a complex neighborhood of the interior of the standard real simplex, within the standard complex simplex. We show that if the neighborhood is sufficiently small, then any sufficiently small complex perturbation of a strictly positive square matrix acts as a contraction, with respect to this metric. While this article was nearing completion, we were informed of a different complex Hilbert metric, which was recently introduced. We briefly discuss the relation between this metric  and our metric in Remark 2.7.
Secondly, we show how one can use a complex Hilbert metric to obtain lower estimates of the domain of analyticity of the entropy rate for a hidden Markov process when the underlying Markov chain has strictly positive transition probabilities.
Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.
New technologies have resulted in transmission lines that deviate significantly from the intended rectangular cross sections. Trapezoidal cross sections and roughness that penetrate a significant depth into the surface in comparison to the skin-depth of the conductor can cause a very significant deviation in transmission line parameters from predicted values. Proximity effect further complicates the analysis by increasing losses and changing the impact of surface roughness by changing the current distribution. A skin-effect filament model that combines a traditional skin-effect filament modeling concept with traditional surface roughness modeling concepts is presented that accounts for surface roughness effects and non-ideal cross sections. The new technique models the transmission line non-idealities in a combined way with the current density in the signal and return current paths. This adapted filament model shows an average deviation of less than 2% above 1 GHz with one given transmission line measurement and does not have the computational challenges seen in a 3D full-wave solver.