Finding the global minimum: a fuzzy end elimination implementation

The ‘fuzzy end elimination theorem’ (FEE) is a mathematicallyproven theorem that identifies rotameric states in proteinswhich are incompatible with the global minimum energy conformation.While implementing the FEE we noticed two different aspectsthat directly affected the final results at convergence. First,the identification of a single dead-ending rotameric state cantrigger a ‘domino effect’ that initiates the identificationof additional rotameric states which become dead-ending. A recursivecheck for deadending rotameric states is therefore necessaryevery time a dead-ending rotameric state is identified. It isshown that, if the recursive check is omitted, it is possibleto miss the identification of some dead-ending rotameric statescausing a premature termination of the elimination process.Second, we examined the effects of removing dead-ending rotamericstates from further considerations at different moments of time.Two different methods of rotameric state removal were examinedfor an order dependence. In one case, each rotamer found tobe incompatible with the global minimum energy conformationwas removed immediately following its identification. In theother, dead-ending rotamers were marked for deletion but retainedduring the search, so that they influenced the evaluation ofother rotameric states. When the search was completed, all markedrotamers were removed simultaneously. In addition, to expandfurther the usefulness of the FEE, a novel method is presentedthat allows for further reduction in the remaining set of conformationsat the FEE convergence. In this method, called a tree-basedsearch, each dead-ending pair of rotamers which does not leadto the direct removal of either rotameric state is used to reducesignificantly the number of remaining conformations. In thefuture this method can also be expanded to triplet and quadrupletsets of rotameric states. We tested our implementation of theFEE by exhaustively searching ten protein segments and foundthat the FEE identified the global minimum every time. For eachsegment, the global minimum was exhaustively searched in twodifferent environments: (i) the segments were extracted fromthe protein and exhaustively searched in the absence of thesurrounding residues; (ii) the segments were exhaustively searchedin the presence of the remaining residues fixed at crystal structureconformations. We also evaluated the performance of the methodfor accurately predicting side chain conformations. We examinedthe influence of factors such as type and accuracy of backbonetemplate used, and the restrictions imposed by the choice ofpotential function, parameterization and rotamer database. Conclusionsare drawn on these results and future prospects are given     

Some statistical aspects of binary measuring systems

Qualitative analysis is often used to determine whether or not a particular feature appears or is absent in tests, in quality control procedures, identification scans, go/no go measurements and many other fields. Generally, such analysis uses simple measuring methods that classify the analyzed property value into two comprehensive and exclusive classes/categories. The performance reliability of such binary measurement systems (BMSs) is usually assessed by false positive and false negative rates. The article presents some additional aspects related to metrological properties of BMS: traceability – described in terms of sequential hierarchical chain of consecutive BMSs calibrations – error accumulation, distribution of test results, consistency and repeatability problems. It is shown that some intuitively plausible at a first glance concepts such as hypotheses about the binomial distribution of test results or consistency testing by sequentially repeated sorting are wrong if the objective is to conduct a deep examination, and therefore, should be avoided.     

Pozzolanic reactions of six principal clay minerals: Activation, reactivity assessments and technological effects

Six standard clays, before and after calcination at 3 or 4 temperatures and being mixed with Ca(OH)₂ [CH] in the presence of simulated cement pore solution, and with ordinary Portland cement, respectively, were studied in detail. Chemical compositions of most clays conform well to the requirement in ASTM C 618. Water demand of clay-containing mortar varies, depending on the crystal chemistry of raw clays, and on the specific surface area of calcined clays. Measurements of XRD background or alkali soluble Si are rapid methods in evaluation of the pozzolanic activity of clays. Compressive strength of mortars based on the raw clays is affected by structure of clays. Calcination increases the pozzolanic activity of clays and the compressive strength of the Portland cement — clay mortars. A close correlation exists between compressive strength of mortars and particle size distribution of the dehydroxylated clays. The most common reaction products of clay — CH mixtures are C-S-H² and C₄AH_x, while C₂ASH_j8 and C₃AH₆ were also detected with clays rich in Al.     

ASER analysis of generalized hexagonal QAM schemes for NOMA systems over Nakagami-m fading channels

To achieve high data rates expected from beyond 5G communications, higher-order modulation techniques have been explored. The energy-efficient modulation technique with a high data rate has encouraged researches towards an optimum two-dimensional hexagonal-shaped constellation, namely, hexagonal quadrature amplitude modulation (HQAM). Thus, in this work, we analyze the average symbol error rate (ASER) of HQAM schemes by considering a two-user nonorthogonal multiple access (NOMA) pair. Closed-form expressions for ASER of HQAM schemes for users are derived over generalized Nakagami- $m$ fading channels. Further, for the HQAM constellation feasibility in two-user downlink NOMA systems, the power allocation criterion for the users is presented. Furthermore, the impact of modulation order of the users over the systems ASER analysis is investigated and valuable insights are drawn.