Free Energy Wells and Overlap Gap Property in Sparse PCA

We study a variant of the sparse PCA (principal component analysis) problem in the “hard” regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio, has conjectured a precise expression for the best possible (subexponential) runtime throughout the hard regime. Following instead a statistical physics-inspired point of view, we show bounds on the depth of free energy wells for various Gibbs measures naturally associated to the problem. These free energy wells imply hitting time lower bounds that corroborate the low-degree conjecture: we show that a class of natural MCMC (Markov chain Monte Carlo) methods (with worst-case initialization) cannot solve sparse PCA with less than the conjectured runtime. These lower bounds apply to a wide range of values for two tuning parameters: temperature and sparsity misparametrization. Finally, we prove that the overlap gap property (OGP), a structural property that implies failure of certain local search algorithms, holds in a significant part of the hard regime. © 2022 Wiley Periodicals, Inc.     

Electro-Optical and Thermophysical Characterization of Poly (Tripropylene Glycol Di-Acrylate)/Liquid Crystal Composite Materials Prepared by Polymerization Induced Phase Separation

Abstract

This work examines the development and characterization of tripropylene glycol di-acrylate/liquid crystal E7 (TPGDA/LC E7) PDLCs composite materials (polymer-dispersed-liquid-crystals). These systems were produced by UV irradiation photopolymerization (PIPS) of a mixture of the monomer tripropylene glycol di-acrylate (TPGDA) and the liquid crystal E7 (LC E7, a mixture of three cyano-biphenyl and one cyano-terphenyl LCs), in the presence of 2?wt% (of the acrylate/E7 mixture) of a photoinitiator. Electro-optical, thermal and optical characterization was used to understand the effect of the LC concentration on the electro-optical and thermo-physical properties of these materials. Polarizing optical microscopy (POM) and differential scanning calorimetry (DSC) studies were performed to observe the system morphology and to determine the transition temperatures of these materials, both as a function of their composition. The findings showed a slight variation of the nematic-isotropic transition temperature, T_NI, of the LC E7 and of the glass transition temperature, T_g, of the TPGDA polymeric matrix as a function of the mass percentage of the LC E7. A very good electro-optical response for the composition 30/70?wt % TPGDA/LC E7 was obtained.     

Matrix reactions of alkaline earth metal atoms with ozone : Infrared spectra of the metal ozonide and metal oxide molecules

The 15°K deposition of alkaline earth metal atoms and ozone molecules at high dilution in argon yielded intense bands near 800 cm⁻¹ and in the region, 450–650 cm⁻¹. The bands near 800 cm⁻¹ showed the appropriate oxygen isotopic shifts for assignment to ν₃ of the ozonide ion; the use of scrambled isotopic ozones indicated that the metal cation is symmetrically bound to the ozonide anion which contains three oxygen atoms with two equivalent oxygens. For the case of Ca and Ba atoms and ozone, infrared absorptions appeared between 450–650 cm⁻¹ which showed appropriate oxygen isotopic shifts for vibrational assignment to several metal oxide species. In the calcium experiments, bands at 635.7 and 575.5 cm⁻¹ which showed diatomic oxygen-18 isotopic shifts were tentatively identified as (CaO)₂ species; a pair of bands at 593.0 and 592.2 cm⁻¹ were tentatively assigned to CaO₂. For the barium reactions, bands at 634.7, 571.3, and 460.0 showed appropriate oxygen-18 frequency shifts for assignment to BaO, BaO₂, and (BaO)₂, respectively. The BaO assignment was confirmed by the N₂O-nitrogen matrix reaction which yielded a nitrogen matrix counterpart for BaO at 612.4 cm⁻¹.     

γ-Keto Esters and γ-Butyrolactones From the Reaction of Dialkoxydihydrofurans With Trimethylsilyl Iodide

Dimethoxydihydrofurans are converted into γ-keto esters and γ-butyrolactones by a new procedure using an equimolar quantity and an excess of trimethylsilyl iodide, respectively.     

Responsive hyperbranched poly(formyl-1,2,3-triazole)s toward quadruple-modal information security protection

Science China Chemistry - Secrecy has received tremendous attention in modern information society. Innovative polymer-based fluorescent materials with multiple mode emission are quite desirable to...     

Neumann-like integrable models

A countable class of integrable dynamical systems, with four-dimensional phase space and conserved quantities in involution (Hn,In)$(H_n,I_n)$ are exhibited. For n=1$n=1$ we recover Neumann system on T^∗S²$T^{\ast }{S}^2$. All these systems are also integrable at the quantum level.     

Phosphorylated cellulose for water purification: a promising material with outstanding adsorption capacity towards methylene blue

Cellulose - Enhancing the sorption properties of cellulose is a prerequisite for its efficient use in water purification as an alternative to costly activated carbon. Here, solvent-free...     

Magnetic Coupling Constants of Self‐Assembled CuII [3×3] Grids: Alternative Spin Model from Theoretical Calculations

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a ferromagnetic Cu^II [3×3] grid. A two‐step strategy, combining calculations on the whole grid and on binuclear fragments, has been employed to evaluate all the magnetic interactions in the grid. The calculations confirm an S=7/2 ground state, which is in accordance with the magnetisation versus field curve and the thermal dependence of the magnetic moment data. Only the first‐neighbour coupling terms present non‐negligible amplitudes, all of them in agreement with the structure and arrangement of the Cu 3d magnetic orbitals. The results indicate that the dominant interaction in the system is the antiferromagnetic coupling between the ring and the central Cu sites (J₃=J₄≈?31 cm^?1). In the ring two different interactions can be distinguished, J₁=4.6 cm^?1 and J₂=?0.1 cm^?1, in contrast to the single J model employed in the magnetic data fit. The calculated J values have been used to determine the energy level distribution of the Heisenberg magnetic states. The effective magnetic moment versus temperature plot resulting from this ab initio energy profile is in good agreement with the experimental curve and the fitting obtained with the simplified spin model, despite the differences between these two spin models. This study underlines the role that the theoretical evaluations of the coupling constants can play on the rationalisation of the magnetic properties of these complex polynuclear systems.     

Preparation of Stereoregular Isotactic Poly(mandelic acid) through Organocatalytic Ring‐Opening Polymerization of a Cyclic O‐Carboxyanhydride

Poly(mandelic acid) (PMA) is an aryl analogue of poly(lactic acid) (PLA) and a biodegradable analogue of polystyrene. The preparation of stereoregular PMA was realized using a pyridine/mandelic acid adduct (Py?MA) as an organocatalyst for the ring‐opening polymerization (ROP) of the cyclic O‐carboxyanhydride (manOCA). Polymers with a narrow polydispersity index and excellent molecular‐weight control were prepared at ambient temperature. These highly isotactic chiral polymers exhibit an enhancement of the glass‐transition temperature (T_g) of 15 °C compared to the racemic polymer, suggesting potential future application as high‐performance commodity and biomedical materials.     

New complex macromolecular architectures based on organosilicon chemistry

Polycarbosilane networks were prepared from well-defined α, ω-difunctional oligomers: X-[Si(CH₃)₂-CH₂-CH₂]_n-X with X = H ( 1 ) and X = CH=CH₂ ( 2 ). Crosslinking reactions were performed by hydrosilylation of tetramethyltetravinylcyclotetrasiloxane (V₄) or of tetravinylsilane with SiH end groups of 1 . Hydrosilylation of Si-CH=CH₂ end groups of 2 with tetramethyltetrahydrocyclotetrasiloxane (D₄H) was also successfully tried. Some physicochemical properties of these new networks will be presented.¹⁾ Interpenetrating networks based on polysiloxanes and polycarbonates were synthesized by the in situ method: a polysiloxane bearing various proportions of room temperature crosslinkable -Si(OEt)₃ side groups was mixed with bis(allyl ethylene glycol) biscarbonate and a free-radical initiator. After the formation of the first network at room temperature, the cross-linking of the polycarbonate network was performed by raising the temperature up to 80°C. Various chemical modifications of the polysiloxane component in the IPN were performed in order to improve the degree of interpenetration as estimated from turbidity, density, refractive index and DSC measurements.²⁾