A statistical physics approach to a multi-channel Wigner spiked model

Abstract In this letter we present a ﬁnite temperature approach to a high-dimensional inference problem, the Wigner spiked model, with group dependent signal-to-noise ratios. For two classes of convex and non-convex network architectures the error in the reconstruction is described in terms of the solution of a mean-ﬁeld spin-glass on the Nishimori line. In the cases studied the order parameters do not ﬂuctuate and are the solution of ﬁnite dimensional variational problems. The deep architecture is optimized in order to conﬁne the high temperature phase where reconstruction fails.

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Detailed study of the phase transition in [Ni(H2O)6](NO3)2·(15-crown-5)·H2O and analysis in terms of mean-field theory

Acta Crystallographica Section B Structural Science ◽

10.1107/s010876811100526x ◽

2011 ◽

Vol 67 (2) ◽

pp. 130-143 ◽

Cited By ~ 3

Author(s):

Maxime A. Siegler ◽

Sean Parkin ◽

Ross J. Angel ◽

Carolyn Pratt Brock

Keyword(s):

High Temperature ◽

Order Parameter ◽

Energy Surface ◽

Lattice Water Molecule ◽

Mean Field Theory ◽

Mean Field ◽

Structural Evolution ◽

High Temperature Phase ◽

Group Symmetry ◽

Temperature Phase

The transition between 190 and 200 K in [Ni(H2O)6](NO3)2·(15-crown-5)·H2O has been followed by determining the structure at 22 temperatures in the range 90–273 K. The structural change is a zone-boundary transition with a critical point at (½, 0, ½) in the Brillouin zone of the high-temperature phase; both phases have space-group symmetry P21 but the volume of the unit cell is halved when a crystal is heated through the transition. The only obvious disorder in the high-temperature phase is of the lattice water molecule, which occupies two sites; some disorder persists below the transition. The greatest changes in the structure below the transition are the rotations of one of the two 15-crown-5 molecules and of one of the two nitrate ions; above the transition the two molecules are related by symmetry as are the two ions. Below the transition these two rotation angles evolve linearly with one another, and can thus be associated with a single order parameter that describes the structural evolution. The evolution of the spontaneous strain arising from the transition does not, however, follow the same evolution as the structural order parameter. This observation indicates that the transition cannot be described in terms of a Landau-type expansion that is characterized by a single order parameter, perhaps because the potential-energy surface for this essentially molecular crystal is more complicated than for the inorganic and framework structures in which such simple behaviour is observed.

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INTERACTIONS AND MOLECULAR ORIENTATIONS IN SOLID C60

International Journal of Modern Physics B ◽

10.1142/s0217979299000163 ◽

1999 ◽

Vol 13 (03) ◽

pp. 253-281 ◽

Cited By ~ 21

Author(s):

P. LAUNOIS ◽

S. RAVY ◽

R. MORET

Keyword(s):

Review Paper ◽

Mean Field ◽

High Temperature Phase ◽

Scattering Data ◽

Intermolecular Potential ◽

Temperature Phase ◽

Single Model ◽

Molecular Dynamics Calculations ◽

The Mean ◽

Present Understanding

In spite of recent progress, our present understanding of the intermolecular interactions in solid C 60 is still imperfect and no single model is able to describe correctly its whole physical properties. These interactions induce elaborate orientational properties which have motivated thorough investigations. In this review paper we concentrate on the orientational properties in the high temperature phase. It is shown how the preferred orientations and the orientational correlations could be accessed through the analysis of the Bragg and diffuse scattering intensity data. The results obtained using either mean-field treatments or molecular dynamics calculations have brought information on the existence of competing local orientational orders. The scattering data have also been exploited to discriminate between different models of intermolecular potential. Within the mean-field treatment, necessary conditions for any model to satisfy scattering results are put forward.

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High temperature phase transitions in barium sodium niobate: the wall roughening 1q–2qincommensurate transition and mean field tricritical behaviour in a disordered exclusion model

Journal of Physics Condensed Matter ◽

10.1088/0953-8984/17/37/026 ◽

2005 ◽

Vol 17 (37) ◽

pp. 5911-5926 ◽

Cited By ~ 10

Author(s):

J F Scott ◽

S A Hayward ◽

M Miyake

Keyword(s):

Phase Transitions ◽

High Temperature ◽

Mean Field ◽

High Temperature Phase ◽

Temperature Phase ◽

Sodium Niobate

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Formation of high temperature phase in flash-evaporated SnSe films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100176629 ◽

1990 ◽

Vol 48 (4) ◽

pp. 698-699

Author(s):

J.P.S. Hanjra

Keyword(s):

Thin Films ◽

Electrical Properties ◽

Energy Gap ◽

Dominant Role ◽

Fine Powder ◽

High Temperature Phase ◽

Temperature Phase ◽

Water Mixture ◽

Flash Evaporation ◽

Photovoltaic Applications

Tin mono selenide (SnSe) with an energy gap of about 1 eV is a potential material for photovoltaic applications. Various authors have studied the structure, electronic and photoelectronic properties of thin films of SnSe grown by various deposition techniques. However, for practical photovoltaic junctions the electrical properties of SnSe films need improvement. We have carried out investigations into the properties of flash evaporated SnSe films. In this paper we report our results on the structure, which plays a dominant role on the electrical properties of thin films by TEM, SEM, and electron diffraction (ED).Thin films of SnSe were deposited by flash evaporation of SnSe fine powder prepared from high purity Sn and Se, onto glass, mica and KCl substrates in a vacuum of 2Ø micro Torr. A 15% HF + 2Ø% HNO3 solution was used to detach SnSe film from the glass and mica substrates whereas the film deposited on KCl substrate was floated over an ethanol water mixture by dissolution of KCl. The floating films were picked up on the grids for their EM analysis.

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