A Tsallis’ statistics based neural network model for novel word learning

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.     

Phase transition in the spanning-hyperforest model on complete hypergraphs

By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k2. The case k=2 reduces to the spanning-forest model on the complete graph. Different k are studied at once by using a microcanonical ensemble in which the number of hypertrees is fixed. The low-temperature phase is characterized by the appearance of a giant hyperforest. The phase transition occurs when the number of hyperforests is a fraction (k−1)/k of the total number of vertices. The behaviour at criticality is also studied by means of the coalescence of two saddle points. As the Grassmann formulation exhibits a global supersymmetry we show that the phase transition is second order and is associated to supersymmetry breaking and we explore the pure thermodynamical phase at low temperature by introducing an explicit breaking field.     

Promoting effect of tin oxides on alumina-supported gold catalysts used in CO oxidation

In this study the influence of SnO_x nanoparticles on the catalytic performance of alumina-supported gold catalysts was investigated in CO oxidation. The tin modified supports were prepared by grafting of tetraethyltin onto the surface of alumina via its hydroxyl groups. The decomposition of organometallic surface species in oxygen yielded highly dispersed tin oxide on the surface of alumina. Gold was introduced onto the tin modified alumina support by both deposition-precipitation with urea and direct anionic exchange techniques using HAuCl₄ solution. Based on catalytic and different spectroscopic measurements it is suggested that the presence of “Snⁿ⁺-Au ensemble sites” is responsible for the increased activity of these catalysts.     

Di‐μ‐sulfito‐bis­[(4,4′‐di­methyl‐2,2′‐bi­pyridine)­zinc(II)] dihydrate and poly­[[aqua(1,10‐phenanthroline)­zinc(II)]‐μ3‐sulfito‐zinc(II)‐μ3‐sulfito]

Two different zinc sulfite compounds have been prepared through the decomposition of pyrosulfite–­di­thionite ions in aqueous solution, viz. a dimeric complex, di‐μ‐sulfito‐κ³O,O′:O′′;κ³O:O′,O′′‐bis­[(4,4′‐di­methyl‐2,2′‐bi­pyridine‐κ²N,N′)­zinc(II)] dihydrate, [Zn₂(SO₃)₂(C₁₂H₁₂N₂)₂]·2H₂O, (I), which was solved and refined from a twinned sample, and an extended polymer, poly­[[aqua(1,10‐phenanthroline‐κ²N,N′)­zinc(II)]‐μ₃‐sulfito‐κ²O:O′:O′′‐zinc(II)‐μ₃‐sulfito‐κ³O:O:O′], [Zn₂(SO₃)₂(C₁₂H₁₀N₂)(H₂O)]_n, (II). In (I), the dinuclear Zn^II complex has a center of symmetry. The cation is five‐coordinate in a square‐pyramidal arrangement, the anion fulfilling a bridging chelating role. Compound (II) comprises two different zinc units, one being five‐coordinate (square pyramidal) and the other four‐coordinate (trigonal pyramidal), and two independent sulfite groups with different binding modes to the cationic centers.     

N^N^C platinum(II) and palladium(II) cyclometallates of 6,6′-diphenyl-2,2′-bipyridine, L: Crystal and molecular structure of [Pd(L-H)Cl]

Reaction of K₂[PtCl₄] or Na₂[PdCl₄] with 6,6′-diphenyl-2,2′-bipyridine, L, gives the cyclometallated species [Pt(L-H)Cl], 1, and [Pd(L-H)Cl], 2, respectively, where L-H is a terdentate N^N^C anionic ligand originated by direct activation of a C(sp²)-H bond. The crystal structure of 2 has been solved by X-ray diffraction and compared to that of the analogous complex [Pd(L′-H)Cl] L′ = 6-phenyl-2,2′-bipyridine. The second phenyl ring in 2 entails a considerable distortion of the coordination around the metal. A similar distortion is also to be expected in the analogous compound 1, due to the almost equal covalent radii of palladium(II) and platinum(II).From the complexes 1 and 2 the chloride can be displaced with AgBF₄ and substituted by CO or PPh₃ to give the corresponding cationic species. By reaction of 1 with Na[BH₄] substitution of H⁻ for Cl⁻ can be achieved: the rare hydrido complex [Pt(L-H)H], stabilized only by nitrogen ligands, was isolated in the solid state and fully characterized in solution. It is noteworthy that in the case of the 6-phenyl-2,2′-bipyridine the analogous terminal hydride [Pd(L′-H)H] is unstable. In platinum chemistry the reaction of 6-substituted 2,2′-bipyridines is known to give either N^N^C or N′^C(3) rollover cyclometallation, depending on the nature of the metal precursor. In the case of 6,6′-Ph₂-2,2′-bipy cyclometallation was also shown to undergo multiple C-H activation giving the C^N^C pincer complex [Pt(L-2H)(DMSO)]. The latter species can be related to complex 1: indeed its reaction with HCl produces complex 1 and [Pt(L-H)(DMSO)Cl], a rollover species with a pendant phenyl substituent.     

Development of a non-chromatographic method for the speciation analysis of inorganic antimony in mushroom samples by hydride generation atomic fluorescence spectrometry

A simple and sensitive method has been developed for the direct determination of toxic species of antimony in mushroom samples by hydride generation atomic fluorescence spectrometry (HG AFS). The determination of Sb(III) and Sb(V) was based on the efficiency of hydride generation employing NaBH₄, with and without a previous KI reduction, using proportional equations corresponding to the two different measurement conditions. The extraction efficiency of total antimony and the stability of Sb(III) and Sb(V) in different extraction media (nitric, sulfuric, hydrochloric, acetic acid, methanol and ethanol) were evaluated. Results demonstrated that, based on the extraction yield and the stability of extracts, 0.5 mol L^− 1 H₂SO₄ proved to be the best extracting solution for the speciation analysis of antimony in mushroom samples. The limits of detection of the developed methodology were 0.6 and 1.1 ng g^− 1 for Sb(III) and Sb(V), respectively. The relative standard derivation was 3.8% (14.7 ng g^− 1) for Sb(V) and 5.1% (4.6 ng g^− 1) for Sb(III). The recovery values obtained for Sb(III) and Sb(V) varied from 94 to 106% and from 98 to 105%, respectively. The method has been applied to determine Sb(III), Sb(V) and total Sb in five different mushroom samples; the Sb(III) content varied from 4.6 to 11.4 ng g^− 1 and Sb(V) from 14.7 to 21.2 ng g^− 1. The accuracy of the method was confirmed by the analysis of a certified reference material of tomato leaves.     

p-Adic valued quantization

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ? _p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ? _p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.     

Highly anisotropic distribution of iron nanoparticles within MCM-41 Mesoporous Silica

Electron microscopy techniques are used to visualize the spatial distribution of iron nanoparticles inside a mesoporous MCM-41 molecular sieve. Direct observation of the iron oxide nanoparticles by STEM-HAADF imaging reveals a highly non-uniform spatial distribution inside the mesopores. These particles are retained in the pores after a reduction treatment unlike the behavior found in other similar systems. It is found that thermal treatments induce changes in its morphology, creating nanowires from particle strings.     

The Hilbert series of the one instanton moduli space

The moduli space of k G-instantons on \( {\mathbb{R}^4} \) for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have \( \mathcal{N} = 2 \) supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.