Several authors considered different **numerical** mapping schemes for gene detection. Reference [37] describes the effects of binary **representation**; the integer, real, complex representations; and the DNA walk **representation** for autoregressive modeling and feature analysis of DNA sequences. In [42]-[43] the Voss, the tetrahedron, the real number and its variants, the complex, the quaternion, the EIIP, the paired numeric, the frequency of nucleotide occurrence, and the Z-curve representations are compared using the discrete Fourier transform for period-3 based exon (coding region) prediction. In [74] seven different mapping rules are discussed. In [75] we made an attempt to provide a survey on various **numerical** **representation** methods. We classified various **numerical** representations to two main groups; discussed each **representation** with a **numerical** example, its merits and demerits, applications, and also some concluding remarks.

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In Hemelrijk’s paper (2003), a lot of the design and the results are closely related to the phenomena of concern: the dominance interactions of apes and their spatial distribution. However the “dominance” of an individual, the capacity of an individual to win a confrontation, is represented in terms of a single number. This number is increased if the individual wins its confrontations – it is an indication of where the individual is in the “dominance hierarchy” of the group. This assumes that (1) the dominance relation can be represented as a total order and (2) that an individual’s dominance changes according depending on the whether it wins confrontations in the way that is indicated. In a oral response to the above paper she said that sometimes intransistivities did occur but that this was rare. The implication is that there is a ranking amoung such small groups of apes and that all the members know this ranking. If this is the case, then using a **numerical** **representation** to encode the position of the apes in this ranking might be justified. However, that an individual’s change in position in the ranking can be determined by the equations seems more doubtful as the change in **numerical** value is dependent solely on the interaction of two apes (in a confrontation) whilst the position in the ranking depends on the values of all the apes in the troupe. This brings into doubt what the dominance value means.

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Abstract Genomic signal processing (GSP) is an engineering domain involved with the analysis of genomic data using digital signal processing (DSP) approaches after transformation of the sequence of genome to **numerical** sequence. One challenge of GSP is how to minimize the error of detection of the protein coding region in a specified deoxyribonucleic acid (DNA) sequence with a minimum processing time. Since the type of **numerical** **representation** of a DNA sequence extremely affects the prediction accuracy and precision, this study aimed to compare different DNA **numerical** representations (genetic code context (GCC), atomic number, frequency of nucleotide occurrence in exons (FNO), 2-bit binary and electron ion interaction potential (EIIP)) by measuring the sensitivity, specificity, correlation coefficient (CC) and the processing time for the protein coding region detection. The proposed technique based on digital filters was used to read-out the period 3 components and to eliminate the unwanted noise from DNA sequence. This method applied to 20 human genes demonstrated that the maximum accuracy and minimum processing time are for the 2-bit binary **representation** method comparing to the other used **representation** methods. Results suggest that using 2-bit binary **representation** method significantly enhanced the accuracy of detection and efficiency of the prediction of coding regions using digital filters.

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PAH-driven Hrk induction and its functional requirement in regulation of ovarian pool. (A) Immunohistochemical analysis of Hrk protein (brown staining) in neonatal mouse ovaries following 24 hours of exposure to vehicle or 1 μM DMBA/BaP each during in vitro culture. Induction was observed in oocytes and granulosa cells of both primordial (black and white arrows) and primary follicles. Magnification, ×400. Hrk-deficient ovaries did not show upregulation of immunoreactivity in oocytes after PAH exposure, confirming the specificity of antibody. (B) Western blot analysis of neonate ovaries under the same conditions as described above. Upon adjustment to β-actin ratio, Hrk protein, migrating at approximately 15 kDa, was induced approximately 2.5-fold (P = 0.03). (C) Induction of Hrk transcript in in vitro–treated neonatal ovaries 24 hours after exposure to vehicle, 1 μ M DMBA/BaP each (PAHs), treatment with PAH and 2 μ M resveratrol (PAH/RSV), or 2 μ M resveratrol alone (RSV). The expression data are shown as mean ± SEM of fold change in comparison with the vehicle-treated group and were obtained from 5 sets of independent ovaries per treatment. PAH induced significant (**P = 0.0006) upregulation of Hrk transcript, which was repressed by resveratrol treatment (*P = 0.005). RSV or RSV/PAH groups were not significantly different from vehicle-treated ovaries. (D) Ovaries from Hrk-deficient females were protected from PAH-induced depletion of primordial and primary follicles. **Numerical** **representation** of morphometric analysis of ovarian pool for nonapoptotic oocyte-containing primordial (resting) and primary (growing) follicles in sibling offspring born to heterozygote mothers exposed to PAHs prior to pregnancy and during lactation. Data are expressed as mean number of primordial and primary follicles ± SEM. Each genotype group represents combined data of offspring born to mothers exposed to vehicle (Hrk +/+ , n = 5; Hrk –/– , n = 7) or treated with PAH (Hrk +/+ , n = 4; Hrk –/– , n = 5). A sig-

According to the foundations built in previous sections, a detailed description of applying wavelet analysis in protein classification is given in Section 2.4 to illustrate its usage in cancer research. These information show that a proper combination of the wavelet coefficient-based features and protein physico-chemical property-based features enhances the classification accuracy. In the future, the most vital task will be to enhance the **numerical** **representation** of the protein sequence and the scheme of applying the wavelet transform. Other wavelet transforms, such as Meyer, Haar, Morlet, and Mexican Hat can be considered and the detailed comparison of the performance of using different wavelet-based features can be accomplished. In addition, another research direction is to integrate the rising importance of p53 pathway and interaction set for cancer research related protein sequence information processing.

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145 A suite of sensitivity studies into the effect of different physical processes and model para- 146 meterisations in the context of a high-resolution North Atlantic model has been performed under 147 the US-German ‘Community Modelling Effort’ (CME) in support of the World Ocean Circulation 148 Experiment (for a review see Bo¨ning & Bryan, 1996). The basic model configuration was that 149 of an Atlantic basin between 15 ° S and 65 ° N, with closed walls at the northern and southern 150 boundaries. A focus of the CME analyses was on the dynamics of the current variability in the 151 tropical and subtropical Atlantic, where the model solutions began to reproduce many observed 152 features in a realistic way (e.g., Didden & Schott, 1991; Schott & Molinari, 1996). There were 153 considerable problems, on the other hand, at higher latitudes. Perhaps the most glaring deficit the 154 CME shared with a number of other model studies concerns the failure to simulate the observed 155 current structure (Redler & Bo¨ning, 1997) and eddy variability (Treguier, 1992) in the north- 156 eastern parts of the basin. Sensitivity experiments with different versions of open boundary con- 157 ditions emphasised the need for an improved **representation** of the water exchange with the 158 Norwegian Sea (Redler & Bo¨ning, 1997). The **numerical** **representation** of the outflow of deep 159 water across the Greenland-Iceland-Scotland ridge in turn was found to be of decisive influence 160 on important, basin-scale aspects of the circulation; in particular, the density of the outflow pre- 161 scribed by the northern boundary condition in the CME was a key factor determining the structure 162 and strength of the meridional overturning circulation with its associated northward transport of 163 heat (Do¨scher, Bo¨ning, & Herrmann, 1994; Holland & Bryan, 1994).

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Figure 5 shows the structural **representation** of a RRSC spatial mechanism, where the edge label denotes the link number and the vertex label denotes the joint type. Figure 5 shows that the four links are connected in a closed loop by revolute, revolute, spherical, and calendric joints. Figure 6shows the side view of the planetary gear train in Figure 2 and the corresponding structural **representation**. The kinematic structure in Figure 6 may be sketched in more than one functional schematic. Gear pair can assume either external or internal gear mesh. Hence, there is no one-to-one correspondence between the functional schematic and the structural **representation**. We may use the symbol G i to

intriguing group difference was argued to suggest an ontogenetic reorganization of the underlying neural architecture, shifting from prefrontal regions of the child’s brain to parietal regions (especially the IPS) in adults. As such, the results of this study demonstrated an age-related functional specialization of the IPS that may be related to a change in the underlying **representation** of symbolic **numerical** magnitudes. One possible explanation for the functional specialization of the IPS is a developmental change in the efficiency with which the human brain associates **numerical** magnitudes and their symbolic referents (i.e., the degree of automaticity with which **numerical** magnitudes are associated with their corresponding symbols). In other words, the mapping (i.e., the associative connection) between an initially arbitrary shape and its culturally mediated semantic meaning (i.e., the **numerical** content; the **numerical** magnitude) may be refined over developmental time, increasing the efficiency with which the semantic meaning of **numerical** symbols is retrieved during tasks such as number comparison. In addition to age-related changes in the parietal cortex, the decreased activation in the prefrontal cortex of adults may be indicative of a reduced engagement of cognitive control mechanisms (e.g., working memory), which might play a crucial role in earlier stages when the mapping between **numerical** magnitudes and the **numerical** symbol is established (Cantlon, 2012; Andreas Nieder & Dehaene, 2009).

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Furthermore, our formulation has the following three advantages. First, a heuristic parameter tuning of weights is practically required for convergence of calculations in many cases. However, in conventional me- thods, the weights of error functions such as quadratic terms with respect to states or inputs and penalty func- tions are described as a single objective function. Thus, it is difficult to independently adjust each weight, be- cause solutions in nonlinear optimizations are quite sensitive with respect to such a change. In our method, the constraint is described as a part of control systems by using the transformation between inputs and state va- riables; therefore, the weights can be separately adjusted. Second, in the barrier method (or the interior penalty method), it is not so easy to set initial states of **numerical** calculations in a constrained region in some cases. In the stable manifold method, optimal orbits are calculated from a stable point at the origin to the surrounding area of the origin in the inverse direction of time evolutions. Therefore, we can systematically search solutions inter- secting a given initial condition. Third, cost functions with Lagrange multiplier are used for incorporating equal- ity constraints in addition to penalty functions in the multiplier method. The method is based on a local optimal- ity, i.e., the Karush-Kuhn-Tucker condition, and solutions are approximately calculated by an iterative calcula- tion, e.g., the sequential quadratic programming method [14]. In our method, optimal orbits obtained from the stable manifold method can be regarded as (semi-)global optimal solutions if they sufficiently cover a state space. Furthermore, there is no need to employ any approximation of solutions and any system reduction in the design.

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In addition to the phenomenological expectations, supersymmetry attracts also the theoretical in- terests, for example superstring theory, AdS / CFT correspondence, and Seiberg–Witten theory. As in many other cases, lattice studies are often needed in supersymmetric theories to analyze non- perturbative e ﬀ ects or to confirm theoretical conjectures. However, despite the strong motivation of non-perturbative treatment, one cannot simply apply Monte Carlo simulations to supersymmetric lattice field theories owing to the sign problem. The N = 1 Wess–Zumino model [1, 2] in two dimen- sions is one of the simplest supersymmetric model and suﬀering from the sign problem on the lattice. Even though some **numerical** approaches have been already attempted and reported in Refs. [3–5] for this model, development of non-stochastic methods remains to be an important issue.

In this paper, we have derived the new color path integral **representation** of Wign- er function for the QGP plasma quasiparticle model for canonical ensemble. We have obtained explicit expression of the Wigner function in linear approximation resembling the Maxwell-Boltzmann distribution on momentum variables, but with quantum corrections. This approximation contains also the oscillatory multiplier describing quantum interference. The Monte Carlo calculations of the quark and gluon densities, pair distribution function and the momentum distribu- tion function for strongly coupled QGP plasma in thermal equilibrium at barion chemical potential equal to zero have been done. Comparison with classical Max- well-Boltzmann shows the significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions resulting in appearance of quantum “tails”. As a continuation of this work we are going to do detailed calculations of the spacial pair distribution functions, color correla- tion functions, investigate screening properties of QGP and compare Debye mass with available lattice QCD calculations.

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Abstract: This work is dedicated to the **numerical** results and the implementation of the method coupling a discontinuous Galerkin with an integral **representation** (CDGIR). The originality of this work lies in the choice of discretization by discontinuous Galerkin element and a mixed form for Maxwell’s equations. The **numerical** tests justify the effectiveness of the proposed approach.

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and vibrational states were included in the bath. Herein we employ surrogate Hamiltonian method on a vibronic basis where the effective vibrational mode is explicitly incorporated into the primary system. In addition to the **numerical** advantage of a vibronic-basis de- scription over a grid **representation**, the former can be also more useful for the specific experimental problems where certain vibrational levels and their resonance/off-resonance with electronic states are of interest 12,59,60 and/or the effect of high-frequency vibrational mode is important. 7 The vibronic basis set 61 has been vastly used to describe absorption

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In parallel to these efforts, a particular prolific techni- que at engendering novel sequence analysis algorithms is the Chaos Game **Representation** (CGR), based on Iterated Function Systems (IFS), firstly proposed more than two decades ago [10]. This compact, lossless and computa- tionally efficient **representation** allows the visualization of biological sequences and patterns, with a convenient visual appearance. In fact, CGR captures the patterns arising from distinct L-tuple compositions in DNA sequences [11], enabling whole genome **representation** and visualization [12]. It was also shown that CGR repre- sents a generalization of genomic signatures [13,14], allowing to characterize different species by associating them with distinctive sequence statistics [12].

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When we said, above, that the mental state of agent enhanced with join patterns is not exactly the same as that of the Jason agent we were referring to the fact that beliefs in the proposed language are represented as channels, rather than predicate. This has advantages as well as some drawbacks. The main advantage of this approach is that we have a uniform model, where the beliefs can be simply updated by sending messages, instead of receiving a message and duplicating the information in the belief base. The main drawback is that once a patter in which a belief takes part is fired, the value of the belief is lost. In the case of depleatable resources, such as water or coffee beans in the case of the coffee maker agent, this acts in our favour since we don’t need to manually manage the resource (first add it, then retract it). But for more long-lasting beliefs this is undesirable. If we wish to keep this **representation** model, we need to find a way around this issue. We have come up with two very similar approaches:

Event-related spectral perturbation (ERSP) analysis Unlike the ERP, which contains only information phase- locked to stimulus presentation, the ERSP contains infor- mation both phase-locked and not phase-locked (both evoked and induced activity) to stimulus presentation [35]. Therefore it is a more complete **representation** of the event-related EEG activity than the ERP. Further, the ERSP is able to differentiate between effects happening at differ- ent frequency components of the EEG. Here, time-fre- quency decomposition was performed by short-time Fourier transform in EEGLab [33]. Epochs from the incon- gruent and congruent conditions were used for investigat- ing the ERSP DE. Artifact rejection parameters were the same as for ERP analysis, and the -100 ms to 0 ms interval served as the baseline for the artifact rejection only. Sam- pling points of baseline-uncorrected epochs between -100 and 600 ms relative to stimulus onset were used for ERSP analysis. A sliding temporal window of 128 points was applied 200 times providing output frequency bins at about 2 Hz steps, and output times between -36 to 536 ms with a resolution of 2.87 ms. DEs were detected by within- subject Distance × Task ANOVAs run separately for each group at each point of the time-frequency landscape. To compensate for intensive multiple testing a conservative (p < 0.005) significance level was used. The analysis focused on 50 sampling points (150–300 ms) × 23 fre- quency bins (2–45 Hz). Therefore at a p level of 0.005, 5.75 (50 × 23 × 0.005) points could be detected as signif- icant due to chance at each electrode. This is considerably less than the number of points interpreted as showing sig- nificant effects (see later).

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deed able to use the different **representation** registers – drawing, table and things **numerical**- when they were solving ratio and proportion problems. One is therefore led to point out that work with these interactive activities enabled the students to build the concepts of ratio and proportion, investing them with meaning and sense, ra- ther than just using the algorithm to work on the topics. This is indeed similar to the findings obtained in the stu- dies by Galbraith, P. and Haines, C. [10], Nguyen and Kulm [11], Combs [12] and (Engelbrecht and Harding [15]).

Introduction. The solution of the simulation problems critical to rounding errors, includ- ing the problems of computational mathematics, mathematical physics, optimal control, biochemistry, quantum mechanics, mathematical programming and cryptography, requires the accuracy from 100 to 1 000 decimal digits and more. The main lack of high-precision software libraries is a significant decrease of the speed-in-action, unacceptable for practi- cal problems, in particular, when performing multiplication. A way to increase computa- tion performance over very long numbers is using the residue number system. In this work, we discuss a new fast multiplication method with scaling the result using original hybrid residue positional interval logarithmic floating-point number **representation**.

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are studied. In this work used: method of nonlinear splitting, known previously for non-linear parabolic equations and systems of equations in divergence form, asymptotic theory and asymptotic methods based on diﬀerent transformations. Constructed asymptotic **representation** of self-similar solutions of nonlinear parabolic systems of equations not in divergence form, depending on the value in the system of the **numerical** parameters necessary and suﬃcient signs of their existence. The main purpose of this paper is to find conditions for the existence and non-existence results for global solutions of parabolic equations not in divergence form on the basis of the self-similar analysis. Keywords nonlinear parabolic systems of equations, not in divergence form, global solutions, self-similar solutions, asymptotic **representation** of solution

The control experiment containing all modifications had the highest accuracy of the analyses. However, sometimes the accuracy of the salinity field was still not higher than in the systems with less improvements . This problem might be due to the relatively inaccurate **representation** of the error co- variances between surface elevation, temperature and salinity in the error background matrix. For example we can see in Fig. 6 that the vertical structure of the temperature misfits has seasonal variability with the highest errors close to the bot- tom of the mixed layer which forms in summer. Similarly, we may expect that also salinity errors have a large spatial vari- ability due to the relatively complex dynamics of the surface circulation and relatively high salinity gradients between the Atlantic waters with low and Mediterranean waters with high salinity (Dobricic et al., 2005). Furthermore, the path of the Atlantic water in the Mediterranean may have a high interan- nual variability (e.g. Demirov and Pinardi, 2002). Therefore, in order to improve the estimate of error covariances, in the future they will be updated with a higher temporal frequency. It is important to notice that with the optimal interpola- tion scheme the calculation of seven daily analyses requires a similar amount of computational time as a single weekly analysis, because the computational time mainly depends on