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Velocity plays a central role in classical mechanics, yet quantum mechanics deals with the variables E,t,p and x. P nonrelativistically is mo v, but a given p value corresponds to various m1v1=m2v2=m3v3 and so does not determine v uniquely. (A p, E pair or a p,mo pair is needed for this.). Here we consider a quantum particle in a square well potential. If detection of a particle occurs through impulse= Integral F dt, then m1v1=p and m2v2=p yield the same impulse although the velocities may be completely different. If one seeks a “time-independent” scenario then one would expect the two to yield the same spatial probability distribution even though E is different for each. In such a case E1 and E2 distinguish between v1 and v2. For a particle in an infinite well v1 and v2 represent different frequencies and so this “frequency” information role is taken on by energy. What happens if one considers two different average momenta levels for the same single particle? In such a case mo is fixed and p1 and p2 correspond to different v1 and v2 i.e. to different frequencies. There is no time in a time-independent scenario so how does one represent the relative frequencies? One may do this spatially, we argue. If p1=n1 3.14/L and p2=n2 3.14/L where L is the well size then p1 has n1 crests and p2, n2 crests. Thus in one case relative velocity for the same p is distinguished by E1 and E2, but not by any spatial distribution. In the second for the same mo and different v1 and v2, there is both a different spatial distribution describing the relative frequencies, but also different E’s which also distinguish and are linked to frequency. This leads to the idea of probability crests with certain base widths proportional to 1/p. What happens in the case of a free particle? Such a particle should also be associated with crests linked to 1/p, but the particle is traveling through space. It is not restricted to L and so its probability density should mimic classical mechanics i.e. be a constant everywhere. To allow for this one considers a probability distribution of crests and troughs together with a second spatially shifted distribution indicating the direction and nature motion , but with the constraint that the modulus is 1. This suggests cos(px) and sin(px) for the two distributions. This is very different from the classical mechanical scenario of a bound state spatial density (1) which is proportional to dt with fixed dx i.e. Cdx/v(x) where v(x) is velocity. Such a picture only accounts for relative densities in space. Thus for two different constant velocities v1 and v2 which represent different frequencies of traversing a distance L, the spatial density is the same classically. Thus important information is lost and we argue that Cdx/v(x) is incomplete. In quantum mechanics the envelope of P(x)=W*(x)W(x)dx approaches the classical value for high n (energy level), but quantum mechanics contains much more information, namely the idea that different v for the same mo have different frequencies which must be manifested spatially. &nbsp

Let (C(t)) t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ 2 is also. We show by counterexample that the converse is false in general.

In San Francisco Bay (SFB), light availability is largely determined by the concentration of suspended particulate matter (SPM) in the water column. SPM exhibits substantial variation with time, depth, and location. To study how SPM influences light and phytoplankton growth, we coupled a sediment transport model with a hydrodynamic model and a biogeochemical model. The coupled models were used to simulate conditions for the year of 2011 with a focus on northern SFB. For comparison, two simulations were conducted with ecosystem processes driven by SPM concentrations supplied by the sediment transport model and by applying a constant SPM concentration of 20 mg l–1. The sediment transport model successfully reproduced the general pattern of SPM variation in northern SFB, which improved the chlorophyll-a simulation resulting from the biogeochemical model, with vertically integrated primary productivity varying greatly, from 40 g[C] m–2year–1over shoals to 160 g[C] m–2year–1in the deep channel. Primary productivity in northern SFB is influenced by euphotic zone depth (Ze). Our results show thatZein shallow water regions (Zein deep water regions is controlled by SPM concentration. As a result,Zehas low (high) values in shallow (deep) water regions. Large (small) differences in primary productivity exist between the two simulations in deep (shallow) water regions. Furthermore, we defined a new parameterFlightfor “averaged light limitation” in the euphotic zone. The averaged chlorophyll-a concentration in the euphotic zone andFlightshare a similar distribution such that both have high (low) values in shallow (deep) water regions. Our study demonstrates that light is a critical factor in regulating the phytoplankton growth in northern SFB, and a sediment transport model improves simulation of light availability in the water column.

The article describes the experiments and their results using two Deep Learning (DL) models and four measures of similarity/distance, determining the similarity of documents from the three publicly available corpuses of paraphrased documents. As DL models, Word2Vec was used in two variants and FastText in one. The article explains the existence of a multitude of hyperparamethers and defines their values, selection of effective way of text processing, the use of some non- standard parameters in Natural Language Processing (NLP), the characteristics of the corpuses used, the results of the pairs (DL model, similarity measure) processing corpuses, and seeks to determine combinations of conditions under which use of exactly certain pairs yields the best results (presented in the article), measured by standard evaluation measures Accuracy, Precision, Recall and primarily F-measure.

Today, military analysts receive far more information than they can process in the time available for mission planning or decision-making. Operational demands have outpaced the analytical capacity of the Department of Defense. To address this problem, this work applies natural language processing to cluster reports based on the topics they contain, provides automatic text summarizations, and then demonstrates a prototype of a system that uses graph theory to visualize the results. The major findings reveal that the cosine similarity algorithm applied to vector-based models of documents produced statistically significant predictions of document similarity; the Term Frequency-Inverse Document Frequency algorithm improved similarity algorithm performance and produced topic models as document summaries; and a high degree of analytic efficiency was achieved using visualizations based on centrality measures and graph theory. From these results, one can see that clustering reports based on semantic similarity offers substantial advantages over current analytical procedures, which rely on manual reading of individual reports. On this basis, this thesis provides a prototype of a system to improve the utility of operational reporting as well as an analytical framework that can assist in the development of future capabilities for military planning and decision-making. http://archive.org/details/improvingoperati1094566578 Major, United States Army Approved for public release. distribution is unlimited

We propose four methods for finding local subspaces in large spectral libraries. The proposed four methods include (a) cosine angle spectral matching; (b) hit quality index spectral matching; (c) self-organizing maps and (d) archetypal analysis methods. Then evaluate prediction accuracies for global and subspaces calibration models. These methods were tested on a mid-infrared spectral library containing 1907 soil samples collected from 19 different countries under the Africa Soil Information Service project. Calibration models for pH, Mehlich-3 Ca, Mehlich-3 Al, total carbon and clay soil properties were developed for the whole library and for the subspace. Root mean square error of prediction was used to evaluate predictive performance of subspace and global models. The root mean square error of prediction was computed using a one-third-holdout validation set. Effect of pretreating spectra with different methods was tested for 1st and 2nd derivative Savitzky–Golay algorithm, multiplicative scatter correction, standard normal variate and standard normal variate followed by detrending methods. In summary, the results show that global models outperformed the subspace models. We, therefore, conclude that global models are more accurate than the local models except in few cases. For instance, sand and clay root mean square error values from local models from archetypal analysis method were 50% poorer than the global models except for subspace models obtained using multiplicative scatter corrected spectra with which were 12% better. However, the subspace approach provides novel methods for discovering data pattern that may exist in large spectral libraries., Highlights • Global model performed better than local models. • MSC preprocessed spectra gave poor models, 1st and 2nd derivative spectra gave stable models. • Mehlich-3 calcium gave the highest coefficient of variation. • Total carbon global and subspace models using first derivative preprocessed spectra are similar.

This study examined the interactive relationship between two measures of association (direct and indirect associations) when predicting relatedness judgments and cued-recall performance. Participants were recruited from Amazon's Mechanical Turk and were given word pairs of varying relatedness to judge for their semantic, thematic, and associative strength. After completing a distractor task, participants then completed a cued recall task. First, we sought to expand previous work on judgments of associative memory (JAM) to include semantic and thematic based judgments (judgments of relatedness, JOR), while also replicating bias and sensitivity findings. Next, we tested for an interaction between direct and indirect association when predicting participant judgments while also expanding upon previous work by examining that interaction when predicting recall. The interaction between direct and indirect association was significant for both judgments and recall. For low indirect association, direct association was the primary predictor of both judgment strength and recall proportions. However, this trend reversed for high indirect association, as higher levels of indirect relation decreased the effectiveness of direct relation as a predictor. Overall, our findings indicate the degree to which the processing of similarity information impacts cognitive processes such as retrieval and item judgments, while also parsing apart the underlying, interactive relationship that exists between the norms used to represent concept information.

Similarity measures, such as the ones of Jaccard, Dice, or Cosine, measure the similarity between two vectors. A good property for similarity measures would be that, if we add a constant vector to both vectors, then the similarity must increase. We show that Dice and Jaccard satisfy this property while Cosine and both overlap measures do not. Adding a constant vector is called, in Lorenz concentration theory, nominal increase and we show that the stronger transfer principle is not a required good property for similarity measures. Another good property is that, when we have two vectors and if we add one of these vectors to both vectors, then the similarity must increase. Now Dice, Jaccard, Cosine, and one of the overlap measures satisfy this property, while the other overlap measure does not. Also a variant of this latter property is studied.

The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of increasingly straight lines which together form a cloud of points, being the investigated relation. The theoretical results are tested against the author co-citation relations among 24 informetricians for whom two matrices can be constructed, based on co-citations: the asymmetric occurrence matrix and the symmetric co-citation matrix. Both examples completely confirm the theoretical results. The results enable us to specify an algorithm that provides a threshold value for the cosine above which none of the corresponding Pearson correlations would be negative. Using this threshold value can be expected to optimize the visualization of the vector space.

We give a short proof to characterize the cases when arccos(r), the arccosine of the squareroot of a rational number r [0, 1], is a rational multiple of : This happens exactly if r is an integer multiple of 1/4. The proof relies on the well-known recurrence relation for the Chebyshev polynomials of the first kind. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2006.