uniformly and independently distributed inside the arbitrarily shaped polygon. The implementation is based on the recursive approach proposed by Ahmadi and Pan [1] in order to obtain the **distance** **distributions** associated with arbitrary triangles. The algorithm in [1] is extended for arbitrarily shaped polygons by using a modified form of the shoelace formula. This modification allows tractable computation of the overlap area between a disk of radius r centered at the arbitrary reference point and the arbitrarily shaped polygon, which is a key part of the

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For the comparison above, MMM was run in default mode (assuming a temperature of 175 K) and in 298 K mode. In 175 K mode we found that MMM often produces very sharp but spiky **distance** **distributions**, which can be difficult to interpret and that are usually not found in PELDOR experiments. At 298 K the MMM **distributions** are much more smooth and rather wide, which means that most of the MTSSL rotamers that MMM predicts for a certain site are assumed to be populated at this temperature (Supplementary Figure 1). In essence, this comes close to the mtsslWizard strategy of sampling the whole conformational space of the label at this site and calculating an average **distance**. Furthermore, Fig. 3 shows that for both mtsslWizard and MMM the predictions within our dataset are more reliable (smaller standard deviation) if the average of the calculated distribution is compared to the average of the experimental distribution as opposed to the peak values of experiment and prediction. This is especially obvious for MMM when run in 178 K mode where the weighting that MMM applies to the distinct rotamers becomes more apparent. This might on one hand be due to errors in the experimental **distance** **distributions** themselves (see above and [20]) or on the other hand this may indicate, that the MTSSL rotamer libraries need to be combined with a more sophisticated energy scoring function taking the protein environment, solvent and electrostatics explicitly into account. This would however come at great computational costs and only slight variations between experiment and simulation (ionic strength, pH, temperature, concentration of ethylene glycol,…) might render the outcome of such efforts futile. The influence of the protein environment on the conformation of the label becomes apparent in Fig. 4 which shows Chi-angles from PDB entries that contain MTSSL in comparison with the computationally derived rotamer library used in MMM [27]. Although the overall fit of the computational library to the experimentally observed conformations is good, there are experimental Chi-angles that are not contained in the libraries or are predicted to have a very low probability. For whatever reason—the local environment of the spin label seems to promote Chi- angles that are energetically unfavorable for the free label. We believe that such Chi-angles ought not to be excluded without good reason. Thus, mtsslWizard searches all possible Chi-angles restricted only by vdW clashes.

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sub-subtypes, the former FSU-cluster (herein called A6) and a well separated cluster of 2 sequences (herein called A7). All these clades were supported by a strong branch support at 100%. Four sequences also clustered with the A3 sub-subtypes but were poorly supported (branch sup- port of 3%) and could not be unambiguously included into A3 nor any of the observed clades in the near full genome nor gag, pol and env specific phylogenies. The same tree topology was observed with both neighbour- joining phylogenetic and maximum likelihood recon- struction. To assess if A3 and A4 not formally retained sub-subtypes, as well as FSU-cluster (herein renamed A6) and the newly described A7 clade, all felt in the range of formally retained sub-subtypes, near full genome pair- wise genetic distances were calculated. Their distribution supported all these A sub-subtype as candidates with the exception of the A3 sub-subtype presenting a genetic dis- tance distribution with A1 slightly lower than other sub- subtypes (Additional file 1: Fig. S1, Tables S2 and S3). The same patterns of phylogenetic tree topology and genetic **distance** **distributions** were also observed when analysing the gag, pol and env genes separately.

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Raw data was fitted by a monoexponential decay to remove the intermolecular background, followed by Tikhonov regularization in DeerAnalysis2013. 30 The optimum regularization parameter α was chosen by the L-curve criterion: α = 10 was found to be optimum for all cases except for tetraradical 107 where α = 1 was required. In 107 two equivalent short distances (ortho), two equivalent medium distances (meta) and two equivalent long distances (para) are present. As similar angular fluctuations will broaden the ortho-**distance** more than the para-**distance** each of the three **distance** pairs would require different Tikhonov regularization parameters to capture their distribution. A value of 1 was found not to broaden the long distances and not to split the short **distance** **distributions**. 32 Traces were power-scaled 78a as indicated using the implementation in DeerAnalysis2013. **Distance** **distributions** were validated by varying the background start point using the validation tool in DeerAnalysis2013. For all traces in Chapter 3 validations were performed by varying the start time from 5% to 95% of the total time window length, and 19 trials (every 5%) were performed, followed by pruning of the trial results with a prune factor of 1.15 (i.e. retaining only those data sets exceeding the lowest rmsd (root mean square deviation) by a maximum of 15%). If less than 50% of trials were retained upon pruning, traces were cut in steps of 15% of the time window length (here, resulting either in cuts of 15 or 30%) until at least half of the trials were within 15% of the lowest rmsd. **Distance** **distributions** show the 2 × σ confidence interval (± 2 × rmsd). For all traces reported in Chapter 4 the start time was varied from 5% to 80% of the total time window length, and 16 trials (every 5%) were performed, followed by pruning of the trial results with a prune factor of 1.15. The noise was increased to a level of 1.5 (i.e. by 50%) and 50 trials were performed.

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The maxima of the line-of-sight **distance** **distributions** in the Galactic plane occur at distances somewhat further than the maxima of the line-of-sight density **distributions**, due to the volume effect in the star counts. This effect is stronger in the galactic plane (Fig. 2 right). Assuming a plausible orientation ( = 25 ◦ ), this explains part of the observational signature which was previously used to infer the existence of a second long bar. If in addition we choose a model snapshot where the bar has leading ends, as seen in Fig. 1, most of the long bar signature in the star count data can be reproduced. While not made specially to fit to the MW, this model thus illustrates that the traditional Galactic bar (the boxy bulge) and the more recently inferred long bar can plausibly be explained by a single boxy bulge/bar structure (more details in [10]).

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Impact of gene ﬂow . A summary of CAPs for populations with asymmetric gene ﬂow is presented in Table 4. We illus- trate the simulation results with example CAPs for sets of ten individuals (Figure 4). These CAPs are ‘cryptic’, in that any simulated population structure is ignored and a subsample of individuals is drawn without consideration of population afﬁliation. Overall, the average genetic **distance** increases with increasing gene ﬂow, as does raggedness. The standard devi- ation of individual genetic **distance** **distributions** decreases, as does the sample heterozygosity, with increasing gene ﬂow. These results reﬂect the appearance of weight in the central region of the CAP distribution (Figure 4b), between the average genetic **distance** for the within-population compari- sons and the average genetic **distance** for the between-popu- lation comparisons. Intermediate peaks correspond to comparisons between focal individuals in the reference population (which receives gene ﬂow) and migrant individuals (individuals with a high proportion of immigrant ancestry) of the reference population. The weight in this intermediate portion of the distribution (averaged over 50 randomly selected CAPs) increases with gene ﬂow (Table 4). Table 2. List of individuals removed from analysis because of

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It has been previously reported that the Rx label gives rise to more restricted **distance** **distributions** than the R1 label. 10 The label sites used in this study gave rise to spin-pairs due to the dimeric nature of Vps75 with spin–spin distances of between 30 and 60 Å. The X-band PELDOR data had strong and persistent echo oscillations (Fig. 3). Apart from for the shortest **distance** the oscillations continued to be significant up to the maximum time measurable. The quality of the Tikhonov derived **distance** **distributions** was generally good (Fig. 3) but varied somewhat, possibly due to the truncated oscillations (experiments with varied pump pulse position did not show significant change in the **distributions**). L-curves indicating the choice of broadening factor used in the processing are shown in ESI,† Fig. S6. Because the conformational dynamics of the spin label is extremely direc- tional, the effect on experimentally measured **distance** distribu- tions will vary, depending on the relative directions of tilt. MD trajectories were used to simulate **distance** **distributions** to compare with the X-band PELDOR derived **distributions**. The a-helical sites showed good agreement between simulation and experimental **distance** **distributions** (Fig. 3), with the i–i + 1 Fig. 2 Combined frames taken from molecular dynamics on spin labelled

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improves prey location in small juvenile rainbow trout. To this end, we observed rainbow trout foraging freely on Daphnia magna, a cladoceran present in some water bodies that salmonids inhabit. Experiments were carried out under two white light illuminations of low intensity (one diffuse, the other 100 % linearly polarized) and under low-intensity short- wavelength illumination of varying percent polarization. Foraging performance was assessed by measuring prey location **distance**, and the vertical and horizontal components of prey location angle for each attack on prey. If polarized light increases prey contrast, then the frequency **distributions** of prey location **distance** and angles should be different under polarized and unpolarized illumination. Likewise, the frequency **distributions** under low percent polarizations (those below the fish detection threshold) should be different from those under higher percent polarizations (those that fall within the fish’s detection threshold).

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Implications for field studies: Join-count measures of spatial structure can also be used for making infer- ences about real populations. The extremely high val- ues of [r]

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Given an implementation which uses a cryptographic protocol that processes parts (subkeys) of a private key (master key) k ∗ separately and independently, one can try to derive information about the subkeys by looking at information that the implementation leaks through side channels. For instance, in AES- 128 [11], we view the 128-bit master key as being divided into 16 byte-sized subkeys that are separately processed in S-boxes. These bytes can be targeted independently by a side-channel attack (SCA, see e.g. [3,4,8]). Common side channels are power consumption, electromagnetic radiation and acoustics. An attacker measures traces of these channels: the amount of power, radiation or noise that the implementation emits at points in time during the measurement. The next step is to extract information from these measurements. By use of statistical methods the measurements are converted into posterior probabilities for each of the values of each of the attacked subkeys. To come back to AES-128, an attack of an S-box leads to a probability distribution of the 256 possibilities for the subkey byte that was processed in that S-box. If we are able to get these **distributions** for multiple subkeys, then this information can be combined to find the master key: Calculate which master key has the highest probability subkeys and check if this was the key used in the implementation. If it was not, check the next most likely one, and the next, etc.

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candidate blocks are just the displaced versions of the original block. The best (least distorted, i.e., most matched) candidate block is found, and its displacement (motion vector) is recorded. In a typical interframe coder, the input frame is subtracted from the prediction of the reference frame. Consequently the motion vector and the resulting error can be transmitted instead of the original luminance block; thus, interframe redundancy is removed and data compression is achieved. At the receiver end, the decoder builds the frame di ﬀ erence signal from the received data and adds it to the reconstructed reference frames. The summation gives an exact replica of the current frame. The better the prediction, the smaller the error signal and hence the transmission bit rate [13]. Despite the success of block matching standards method, these techniques are only based on the luminosity, and one can find misleading cases where the hypothesis of constant levels of gray is not verified. Some models take into account a factor of change of brightness in the scene. Thus the change in brightness is supposed to oﬀset during the estimation. Such adjustments can improve the result of global changes in brightness, for which it is possible to estimate the change in a reliable manner, as against it does not take into account local variations, such as shadows. Therefore, we propose a statistical method to estimate the motion based on modeling image blocks by a mixture of Gaussian **distributions**. These mixtures are robust, relatively easy to use, and have traditionally learned independently, class by class, using a criterion of maximum likelihood [14–16]. The optimization is then performed using the algorithm EM (Expectation-Maximization) based on an iterative optimization of the model parameters (a priori probability, vectors means, and covariances matrices). Then we resort to the Extended Mahalanobis distances to measure the similarity and to search for the best matching between two windows spaces (or blocks) located in consecutive frames.

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In this work, we first extend the framework of (Solomon et al. 2014) to hypergraphs using Wasserstein barycenter (Agueh and Carlier 2011; Asoodeh, Gao, and Evans 2018). For 2-Wasserstein distances this is equivalent to solving a multi-marginal optimal transport (Carlier and Ekeland 2010) problem with a naturally constructed cost function. The hypergraph extension of Wasserstein propagation is based on a novel interpretation of the original algorithm on graphs (Solomon et al. 2014) as a message-passing algo- rithm. Next, we take a deeper look at the statistical learn- ing aspects of our proposed algorithm, and establish general- ization error bounds for propagating one-dimensional distri- butions on graphs and hypergraphs using the 2-Wasserstein **distance**. One dimensional **distributions** such as histograms are among the most frequent application scenarios of soft la- bel propagation. The main technical ingredient is algorith- mic stability (Bousquet and Elisseeff 2002). To our knowl- edge, our generalization bound is the first of its type in the literature of Wasserstein **distance** based soft label propaga- tion; on graphs these results generalize the generalization error bounds in (Belkin, Matveeva, and Niyogi 2004). As no general semi-supervised learning algorithm is available for large dataset (Petegrosso et al. 2017), the new connection between Wasserstein barycenter and semi-supervised learn- ing might be of theoretical as well as computational interest. In the supplemental material, we provide promising nu- merical results for both synthetic and real data. In particular, we apply our hypergraph soft label propagation algorithm to random uniform hypergraphs as well as several UCI datasets adopting hypergraph representations.

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High-quality seismograms recorded by dense regional seismic networks for various distances and wide dynamic ranges enable us to investigate frequency- and **distance**- dependent characteristics of the apparent radiation pat- tern. Takemura et al. (2009, 2015) and Kobayashi et al. (2015) reported that the apparent P- and S-wave radia- tion patterns are distorted with increasing **distance** but still preserving the original four-lobe pattern at hypocen- tral distances less than 40 km even for high frequencies. In this study, we firstly investigated the frequency- and **distance**-dependent characteristics of the apparent P- and S-wave radiation patterns using dense and large number seismograms. On the basis of observed char- acteristics, then we propose a frequency- and **distance**- dependent model of the apparent radiation pattern to predict the spatial **distributions** of maximum P- and S-wave amplitudes of local earthquakes.

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Abstract Estimation of elemental distribution based on geochemical data is important for determination of elemental prospects in studied areas. The main aim of this study is to estimate Cu, Mo, Au and Ag with respect to lithogeochemical data in Kahang porphyry deposit, Central Iran, using combination of Inverse **Distance** Weighted (IDW) and Artiﬁcial Neural Network (ANN). The results obtained by the combination methods show that the proper elemental anomalies are associated with geological particulars including lithological units, alteration zones and faults. Moreover, correlation between raw data and the results reveals that the combination method can be applicable for interpretation of elemental **distributions**.

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Figure 2B shows the inferred parameter **distributions** for the various parameter settings. As the full posterior distribution is four dimensional, we plotted the marginals only. The inferred parameter **distributions** showed varying behavior: The distribu- tions for U were well-tuned to values close to the true parameter values. For the D parameter the shifts in the **distributions** fol- lowed the changes in the true parameter, becoming broader for depressing dynamics. Both F and f were not narrowly tuned to the true parameter. Although f was tuned to small values for facilitating synapses, its distribution became broader for depress- ing synapses. The F parameter was not particularly tuned to any value, being close to an uniform distribution for both depress- ing and facilitating synapses. We explored the possibility that the broadness of F depended on the prior boundary by extending it to 5 s and 10 s. However, the distribution remained uniform and merely grew wider, suggesting that the broad distribution was not caused by an improper choice of prior. In summary, the inference procedure shows that—depending on the dynamics— the inferred parameter **distributions** can be narrow or broad and that some parameters are much more tightly constrained than others.

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Nowadays, it is common for one natural person to join mul- tiple social networks to enjoy different kinds of services. Linking identical users across multiple social networks, also known as social network alignment, is an important prob- lem of great research challenges. Existing methods usually link social identities on the pairwise sample level, which may lead to undesirable performance when the number of avail- able annotations is limited. Motivated by the isomorphism information, in this paper we consider all the identities in a social network as a whole and perform social network align- ment from the distribution level. The insight is that we aim to learn a projection function to not only minimize the dis- tance between the **distributions** of user identities in two so- cial networks, but also incorporate the available annotations as the learning guidance. We propose three models SNNA u ,

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The three most important nutrient distributions were noted: – in case the Danube runoff spreads to the East for a considerable distance 30 – 50 miles, the content of nutrients in the oxy[r]

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This process works for different measures of interest (e.g. pedestrian flow, fundamental diagram, trajectories), as long as a suitable **distance** function linking data to simulation can be found (step 4 above). Provided the tolerance 𝜀𝜀 is chosen small enough and enough simulations are performed (large 𝑛𝑛 ), ABC will find an accurate estimate of the posterior parameter distribution [9]. The posterior parameter distribution indicates both the most likely parameter values (e.g. mean or mode of posterior) and the uncertainty associated with it (e.g. variance of posterior). A particularly useful feature of ABC is that it can be used to compare the quality of models in explaining data. If ABC is performed for different models on the same data using the same value of 𝜀𝜀 , then the rate at which parameters are accepted into the posterior distribution (step 4) for each model can be used to approximate the Bayes Factor – a commonly used measure for model selection [9]. Model complexity, i.e. the number of parameters a model has, is inherently accounted for in ABC [9].

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surface charge. Inner-sphere and outer-sphere complexes with different types (termed inner and outer) of silanol and siloxide oxygens were suggested to be responsible for the various peaks in the profiles of ion density as a function of vertical **distance** from the surface. Although the patterns in Na + and Rb + vertical ion densities were similar, the larger ionic radius of the Rb + ion compared to Na + shifted the peaks to larger dis- tances from the surface. The more highly charged Sr 2+ ion had a more tightly bound hydration shell and as a result different bonding preferences to the monovalent ions, with adsorption to the ’outer’ silanols comparatively dominant. Lateral ion density pro- files in the xy plane revealed preferences for particular adsorption sites. For example, Na + ions had a greater affinity for protonated oxygens compared to deprotonated due to the stronger solvation of the latter. Voitchovsky and co-workers investigated lat- eral ion structure at the interface between mica and several aqueouselectrolytes (RbCl, NaCl and KCl) at a range of electrolyte concentrations using MD in combination with AFM. 96 It was suggested that the interfacial ion structuring was driven by interfacial water structure. Computational studies have provided detailed structural information on the subnanometer scale for the quartz/aqueous electrolyte interface and the influence of ions on the orientational behavior of nearby water molecules was clear.

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In Section 3 a characterization of the joint multinomial of two identically distributed random vectors based on one conditional multinomial... distribution is given.[r]