Fast Thresholding Algorithms with Feedbacks and Partially Known Support for Compressed Sensing

Some works in modified compressive sensing (CS) show that reconstruction of sparse signals can obtain better results than traditional CS using the partially known support. In this paper, we extend the idea of these works to the null space tuning algorithm with hard thresholding, feedbacks ([Formula: see text]) and derive sufficient conditions for robust sparse signal recovery. The theoretical analysis shows that including prior information of partially known support relaxes the preconditioned restricted isometry property condition comparing with the [Formula: see text]. Numerical experiments demonstrate that the modification improves the performance of the NST+HT+FB, thereby requiring fewer samples to obtain an approximate reconstruction. Meanwhile, a systemic comparison with different methods based on partially known support is shown.

Reconstructing modified gravity with holographic vacuum energy density

A reconstruction of modified gravity is proposed by establishing a correspondence between the effective density of the modified gravity and the holographic density. The nonhomogeneous term in the modified Friedmann equation, generated by the vacuum (holographic) energy density, lead to reconstructed models that contain explicitly, as part of the solution, the Einstein–Hilbert (EH) term. It was shown that the [Formula: see text]CDM-type cosmic histories allow the general relativity Lagrangian with cosmological constant as a particular reconstructed solution. The Starobinsky term appears in some reconstructed solutions, and an approximate reconstruction of the Chaplygin gas cosmology was performed in terms of elementary functions of curvature.

An overview of lithotype associations of Miocene lignite seams exploited in Poland

Currently, three stratigraphically distinct lignite seams of Early to Middle Miocene age are exploited in Poland, namely the third Ścinawa lignite seam (ŚLS-3), the second Lusatian lignite seam (LLS-2) and the first Mid-Polish lignite seam (MPLS-1). All of these are composed of numerous macroscopically distinguishable layers defined as lignite lithotypes. In the present paper, the lithotypes of Polish lignites are grouped into seven major lithotype associations that originated in various types of mire. Therefore, an approximate reconstruction of mire type can be based on lignite lithotypes. Within the Polish lignite seams examined, the commonest in order of importance are: xylodetritic (XDL), detroxylitic (DXL), detritic (DL) and xylitic (XL) lithotype associations, mostly with a massive (m) or horizontal (h) structure. They are particularly dominant in lignite opencasts belonging to the Konin and Adamów mines. However, in the lowermost seams at the Turów and Bełchatów mines, a substantial part of the seams comprises the bitumen-rich (BL) lithotype association. These seams also lignite lithotypes that in large quantities have a gelified (g) and/or nodular (n) structure. In contrast, lignites from the Sieniawa mine are characterised by an admixture of the best-developed lithotype associations of both fusitic (FL) and weathered (WL) lignites. Moreover, the vast majority of these lignites have a folded (fo) and/or faulted (fa) structure, because they were completely deformed by glaciotectonics.

Substratum morphology and significance during the Weichselian Odra ice lobe advance in northeast Germany and northwest Poland

In the Polish Lowlands, three main ice lobes, referred to as Odra, Vistula and Mazury, formed during the Last Scandinavian Glaciation. These lobes protruded at least several kilometres beyond the main ice margin and it is believed that they represent terminal parts of the ice streams. Applied geostatistical analysis based on numerous geological data has allowed an approximate reconstruction of the Odra ice lobe substratum in the area of northwest Poland and northeast Germany. A spatial representation of the Odra lobe substratum clearly illustrates the adverse slope of the glacier bed, but also indicates areas morphologically prone to ice streaming. It is suggested that the ice took advantage of local topography that enabled advance out of the Baltic basin; consequently, the ice followed a topographic low which, in combination with favourable hydraulic conditions of its substratum, likely initiated ice streaming.