Index of refraction measurements are made by means of an optical device in which a coherent light beam is divided into an object beam and a reference beam, each of which is directed through a separate path in a common light transmitting medium. The object beam is also transmitted en route through a test volume that accommodates a substance to be tested. It is subsequently recombined with the reference beam to form a single output beam. The output beam is received by a photo detector and its intensity is measured. The intensity of the detected output beam is related to any phase shift between the object and reference beams. The phase shift in turn is a measure of the index of refraction of the test substance. Information relating to density, temperature and pressure of the test substance can be derived from measured index of refraction values by using conventional conversion formulas. An operating range control is provided by introducing a volume of pressurized gas into the paths of the object and reference beams. The operating range of the instrument is set by adjusting the pressure of the gas in the absence of a test substance.
Statistical mechanics methods allowed to derive a very precise picture of the solution set @cite_31 @cite_17 @cite_11 . This inspired a new message passing algorithm dubbed @cite_15 . In conjunction with decimation, this algorithm allowed to solve random instances of unprecedentedly large sizes, in difficult regimes of @math and @math .
@cite_31 @cite_11 @cite_15 @cite_17
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Let @math be a uniformly distributed random @math -SAT formula with @math variables and @math clauses. For clauses variables ratio @math the formula @math is satisfiable with high probability. However, no efficient algorithm is known to provably find a satisfying assignment beyond @math with a non-vanishing probability. Non-rigorous statistical mechanics work on @math -CNF led to the development of a new efficient "message passing algorithm" called [M ', Science 2002]. Experiments conducted for @math suggest that the algorithm finds satisfying assignments close to @math . However, in the present paper we prove that the basic version of Survey Propagation Guided Decimation fails to solve random @math -SAT formulas efficiently already for @math with @math almost a factor @math below @math . While the use of statistical physics methods to analyze large corpora has been useful to unveil many patterns in texts, no comprehensive investigation has been performed on the interdependence between syntactic and semantic factors. In this study we propose a framework for determining whether a text (e.g., written in an unknown alphabet) is compatible with a natural language and to which language it could belong. The approach is based on three types of statistical measurements, i.e. obtained from first-order statistics of word properties in a text, from the topology of complex networks representing texts, and from intermittency concepts where text is treated as a time series. Comparative experiments were performed with the New Testament in 15 different languages and with distinct books in English and Portuguese in order to quantify the dependency of the different measurements on the language and on the story being told in the book. The metrics found to be informative in distinguishing real texts from their shuffled versions include assortativity, degree and selectivity of words. As an illustration, we analyze an undeciphered medieval manuscript known as the Voynich Manuscript. We show that it is mostly compatible with natural languages and incompatible with random texts. We also obtain candidates for keywords of the Voynich Manuscript which could be helpful in the effort of deciphering it. Because we were able to identify statistical measurements that are more dependent on the syntax than on the semantics, the framework may also serve for text analysis in language-dependent applications. Decimation is a simple process for solving constraint satisfaction problems, by repeatedly fixing variable values and simplifying without reconsidering earlier decisions. We investigate different decimation strategies, contrasting those based on local, syntactic information from those based on message passing, such as statistical physics based Survey Propagation (SP) and the related and more well-known Belief Propagation (BP). Our results reveal that once we resolve convergence issues, BP itself can solve fairly hard random k-SAT formulas through decimation; the gap between BP and SP narrows down quickly as k increases. We also investigate observable differences between BP SP and other common CSP heuristics as decimation proceeds, exploring the hardness of the decimated formulas and identifying a somewhat unexpected feature of message passing heuristics, namely, unlike other heuristics for satisfiability, they avoid unit propagation as variables are fixed. We study the satisfiability of randomly generated formulas formed by M clauses of exactly K literals over N Boolean variables. For a given value of N the problem is known to be most difficult when α = M N is close to the experimental threshold αc separating the region where almost all formulas are SAT from the region where all formulas are UNSAT. Recent results from a statistical physics analysis suggest that the difficulty is related to the existence of a clustering phenomenon of the solutions when α is close to (but smaller than) αc. We introduce a new type of message passing algorithm which allows to find efficiently a satisfying assignment of the variables in this difficult region. This algorithm is iterative and composed of two main parts. The first is a message-passing procedure which generalizes the usual methods like Sum-Product or Belief Propagation: It passes messages that may be thought of as surveys over clusters of the ordinary messages. The second part uses the detailed probabilistic information obtained from the surveys in order to fix variables and simplify the problem. Eventually, the simplified problem that remains is solved by a conventional heuristic. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005