Single- and Multi-Distribution Dimensionality Reduction Approaches for a Better Data Structure Capturing

In recent years, the huge expansion of digital technologies has vastly increased the volume of data to be explored, such that reducing the dimensionality of data is an essential step in data exploration. The integrity of a dimensionality reduction technique relates to the goodness of maintaining the data structure. Dimensionality reduction techniques such as Principal Component Analyses (PCA) and Multidimensional Scaling (MDS) globally preserve the distance ranking at the expense of neglecting small-distance preservation. Conversely, the structure capturing of some other methods such as Isomap, Locally Linear Embedding (LLE), Laplacian Eigenmaps t-Stochastic Neighbour Embedding (t-SNE), Uniform Manifold Approximation and Projection (UMAP), and TriMap rely on the number of neighbours considered. This paper presents a dimensionality reduction technique, Same Degree Distribution (SDD) that does not rely on the number of neighbours, thanks to using degree-distributions in both high and low dimensional spaces. Degree-distribution is similar to Student-t distribution and is less expensive than Gaussian distribution. As such, it enables better global data preservation in less computational time. Moreover, to improve the data structure capturing, SDD has been extended to Multi-SDDs (MSDD), which employs various degree distributions on top of SDD. The proposed approach and its extension demonstrated a greater performance compared with eight other benchmark methods, tested in several popular synthetics and real datasets such as Iris, Breast Cancer, Swiss Roll, MNIST, and Make Blob evaluated by the co-ranking matrix and Kendall’s Tau coefficient. For further work, we aim to approximate the number of distributions and their degrees in relation to the given dataset. Reducing the computational complexity is another objective for further work

Texas Crop Profile: Spinach

11 pp., 18 tablesThis profile of spinach production in Texas gives an overview of basic commodity information; discusses insect, disease and weed pests; and covers cultural and chemical control methods

79. The Modern Pottery Industry in Malta.

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Grazing catfish, fishing birds, and attached algae in a Panamanian stream

In streams where algivorous fishes abound, striking variation of attached algae often develops along depth gradients, with bands of high standing crops in shallow water (<20 cm) and sparse standing crops on deeper substrates. Experimental results from a stream in central Panama support the hypothesis that vertical variation in algal standing crops arises when grazing fishes avoid predators in shallow water by forgoing food resources that accumulate there. When 38 rocks bearing algae in a stream in central Panama were transferred from shallow (<20 cm) to deeper (>20 cm) water, algae were rapidly consumed by grazing catfish. Catfish were removed from three stream pools and left in place in three control pools. Ten days after catfish removal, algal standing crops in deep and shallow areas of removal pools were similar, while algal standing crops were higher in shallow than in deep areas of control pools. Catfish were exposed to fishing birds in open-topped enclosures. In one of three series of these pens, most catfish in shallow pens (10 and 20 cm) disappeared after 14 days, while catfish in deeper pens (30 and 50 cm) did not. Other groups of catfish which were caged 8 days showed differences in behavior depending on whether they had been fed or starved. After their release into their home pool, starved catfish spent more time feeding than did fed catfish. Despite their apparently increased hunger levels, starved catfish did not venture into shallow water to obtain algae. These results support the view that predator induced avoidance by grazers of certain areas can produce spatial pattern in the flora of flowing water communities. © 1989 Kluwer Academic Publishers

Intermittent magnetic field excitation by a turbulent flow of liquid sodium

The magnetic field measured in the Madison Dynamo Experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.Comment: 5 pages, 7 figure

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in Rd\R^d

We consider a class of second order linear nonautonomous parabolic equations in R^d with time periodic unbounded coefficients. We give sufficient conditions for the evolution operator G(t,s) be compact in C_b(R^d) for t>s, and describe the asymptotic behavior of G(t,s)f as t-s goes to infinity in terms of a family of measures mu_s, s in R, solution of the associated Fokker-Planck equation