A class of deep Boltzmann machines is considered in the simplified framework a quenched system with Gaussian noise and independent entries. The pressure $K$-layers spin glass model studied allowing interactions only among consecutive layers. lower bound for found terms convex combination $K$ Sherrington-Kirkpatrick models used to study annealed replica symmetric regimes system. map one dimensio...

Tomographic images of the distribution of shear wave speed beneath the northwestern Pacific delineate the configuration of the subducted oceanic lithosphere beneath the western Aleutian Arc. At ~100 km depth, a fast shear wave speed anomaly lies beneath the Aleutian Arc everywhere east of 173E. Between 164E and 173E, however, seismic velocities at this depth are slow relative to the surrounding...

We define a notion of depth for an inclusion of multimatrix algebras B ⊆ A based on a comparison of powers of the inductionrestriction table M (and its transpose matrix). The depth of the semisimple subalgebra B in the semisimple algebra A is the least positive integer n ≥ 2 for which M ≤ qM for some q ∈ Z+. We prove that a depth two subalgebra is a normal subalgebra, and conversely. As a corol...

Abstract Optical imaging has the potential to reveal high-resolution information with minimal photodamage. The recent renaissance of super-resolution, widefield, ultrafast, and computational methods broadened its horizons even further. However, a remaining grand challenge is at depth over widefield high spatiotemporal resolution. This achievement would enable observation fast collective biologi...

In this study the depth of the atmospheric boundary layer (ABL) over the Tibetan Plateau was measured during a regional radiosonde observation campaign in 2008 and found to be deeper than indicated by previously measurements. Results indicate that during fair weather conditions on winter days, the top of the mixed layers can be up to 5 km above the ground (9.4 km above sea level). Measurements ...

soil compaction reduces growth of secondary roots, soil aeration and water and mineral uptake by plant, and decreases chlorophyll content as well as root yield and sugar content. hence, the effect of soil compaction on sugar beet yield and sugar content farms determined by penetrometer using 40 plots of 100 m2 in 40 sugar beet field of hamedan, asadabad, malayer and bahar at the depth of 0-80 c...

In the stratified ocean, vertical motions arise from both adiabatic and diabatic mechanisms. Diapycnal advection is the vertical component of flow across an isopycnal surface which occurs when mixing produces a divergent flux of buoyancy. Buoyancy forcing of the lateral flow by vortex stretching occurs when diapycnal advection rates vary with depth. Microstructure observations of enhanced turbu...