The application of inelastic neutron scattering to investigate the interaction of methyl propanoate with silica

A modern industrial route for the manufacture of methyl methacrylate involves the reaction of methyl propanoate and formaldehyde over a silica-supported Cs catalyst. Although the process has been successfully commercialised, little is known about the surface interactions responsible for the forward chemistry. This work concentrates upon the interaction of methyl propanoate over a representative silica. A combination of infrared spectroscopy, inelastic neutron scattering, DFT calculations, X-ray diffraction and temperature-programmed desorption is used to deduce how the ester interacts with the silica surface

The Little-Hopfield model on a Random Graph

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement.Comment: 14 pages, 4 figure

Training a perceptron in a discrete weight space

On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous perceptron and prediction following the clipped weights. The learning is described by a new set of order parameters, composed of the overlaps between the teacher and the continuous/clipped students. Different scenarios are examined among them on-line learning with discrete/continuous transfer functions and off-line Hebb learning. The generalization error of the clipped weights decays asymptotically as $exp(-K \alpha^2)$/$exp(-e^{|\lambda| \alpha})$ in the case of on-line learning with binary/continuous activation functions, respectively, where $\alpha$ is the number of examples divided by N, the size of the input vector and $K$ is a positive constant that decays linearly with 1/L. For finite $N$ and $L$, a perfect agreement between the discrete student and the teacher is obtained for $\alpha \propto \sqrt{L \ln(NL)}$. A crossover to the generalization error $\propto 1/\alpha$, characterized continuous weights with binary output, is obtained for synaptic depth $L > O(\sqrt{N})$.Comment: 10 pages, 5 figs., submitted to PR

Hyalotekite, (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2)(Si,B)(2)O28F, a Tectosilicate Related to Scapolite: New Structure Refinement, Phase Transitions and a Short-Range Ordered 3B Superstructure

Hyalotekite, a framework silicate of composition (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2) (Si,B)(2)O28F, is found in relatively high-temperature(greater than or equal to 500 degrees C) Mn skarns at Langban, Sweden, and peralkaline pegmatites at Dara-i-Pioz, Tajikistan. A new paragenesis at Dara-i-Pioz is pegmatite consisting of the Ba borosilicates leucosphenite and tienshanite, as well as caesium kupletskite, aegirine, pyrochlore, microcline and quartz. Hyalotekite has been partially replaced by barylite and danburite. This hyalotekite contains 1.29-1.78 wt.% Y2O3, equivalent to 0.172-0.238 Y pfu or 8-11% Y on the Ca site; its Pb/(Pb+Ba) ratio ranges 0.36-0.44. Electron microprobe F contents of Langban and Dara-i-Pioz hyalotekite range 1.04-1.45 wt.%, consistent with full occupancy of the F site. A new refinement of the structure factor data used in the original structural determination of a Langban hyalotekite resulted in a structural formula, (Pb1.96Ba1.86K0.18)Ca-2(B1.76Be0.24)(Si1.56B0.44)Si8O28F, consistent with chemical data and all cations with positive-definite thermal parameters, although with a slight excess of positive charge (+57.14 as opposed to the ideal +57.00). An unusual feature of the hyalotekite framework is that 4 of 28 oxygens are non-bridging; by merging these 4 oxygens into two, the framework topology of scapolite is obtained. The triclinic symmetry of hyalotekite observed at room temperature is obtained from a hypothetical tetragonal parent structure via a sequence of displacive phase transitions. Some of these transitions are associated with cation ordering, either Pb-Ba ordering in the large cation sites, or B-Be and Si-B ordering on tetrahedral sites. Others are largely displacive but affect the coordination of the large cations (Pb, Ba, K, Ca). High-resolution electron microscopy suggests that the undulatory extinction characteristic of hyalotekite is due to a fine mosaic microstructure. This suggests that at least one of these transitions occurs in nature during cooling, and that it is first order with a large volume change. A diffuse superstructure observed by electron diffraction implies the existence of a further stage of short-range cation ordering which probably involves both (Pb,K)-Ba and (BeSi,BB)-BSi

Statistical Mechanics of Soft Margin Classifiers

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the generalization error towards the asymptotic value, depending on the task and on general characteristics of the distribution of stabilities of the patterns to be learned. The optimal learning curves of the SMCs, which give the minimal generalization error, are obtained by tuning the coefficient controlling the trade-off between the error and the regularization terms in the cost function. If the task is realizable by the SMC, the optimal performance is better than that of a hard margin Support Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review

Slowly evolving geometry in recurrent neural networks I: extreme dilution regime

We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The (fast) neurons and (slow) connectivity variables equilibrate separately, but at different temperatures. Our model is exactly solvable in equilibrium. We obtain phase diagrams upon making the condensed ansatz (i.e. recall of one pattern). These show that, as the connectivity temperature is lowered, the volume of the retrieval phase diverges and the fraction of mis-aligned spins is reduced. Still one always retains a region in the retrieval phase where recall states other than the one corresponding to the `condensed' pattern are locally stable, so the associative memory character of our model is preserved.Comment: 18 pages, 6 figure

Near-Infrared Spectroscopy of Molecular Filaments in the Reflection Nebula NGC 7023

We present near-infrared spectroscopy of fluorescent molecular hydrogen (H_2) emission from molecular filaments in the reflection nebula NGC 7023. We derive the relative column densities of H_2 rotational-vibrational states from the measured line emission and compare these results with several model photodissociation regions covering a range of densities, incident UV-fields, and excitation mechanisms. Our best-fit models for one filament suggest, but do not require, either a combination of different densities, suggesting clumps of 10^6 cm^{-3} in a 10^4 - 10^5 cm^{-3} filament, or a combination of fluorescent excitation and thermally-excited gas, perhaps due to a shock from a bipolar outflow. We derive densities and UV fields for these molecular filaments that are in agreement with previous determinations.Comment: ApJ accepted, 26 pages including 5 embedded figures, uses AASTEX. Also available at http://www-astronomy.mps.ohio-state.edu/~martini/pubs.htm

Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices

We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest neighbour bonds along the ring are ferromagnetic, whereas those corresponding to the Poisonnian graph are allowed to be random. Our models thus generally contain quenched connectivity and bond disorder. Within the replica formalism, calculating the disorder-averaged free energy requires the diagonalization of replicated transfer matrices. In addition to developing the general replica symmetric theory, we derive phase diagrams and calculate effective field distributions for two specific cases: that of uniform sparse long-range bonds (i.e. `small world' magnets), and that of (+J/-J) random sparse long-range bonds (i.e. `small world' spin-glasses).Comment: 22 pages, LaTeX, IOP macros, eps figure

Equilibrium statistical mechanics on correlated random graphs

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents - crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. At least at equilibrium, dilution simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 figure

Clinicopathologic predictors of finding additional inguinal lymph node metastases in penile cancer patients following positive dynamic sentinel node biopsy:a European multicentre evaluation

OBJECTIVES: Following tumour positive sentinel lymph node biopsy (+DSNB), completion inguinal lymph node dissection (ILND) is negative in 84-89% of basins. Thus, ILND after +DSNB may be considered overtreatment resulting in substantial morbidity. This study aimed to develop a predictive model for additional inguinal lymph node metastases (LNM) at ILND following +DSNB using DSNB characteristics to identify a patient group in which ILND might be omitted. PATIENTS AND METHODS: A retrospective study of 407 inguinal basins with a +DSNB of penile cancer patients who underwent subsequent ILND from seven European centres. From the histopathology reports, the number of positive and negative lymph nodes, extranodal extension and size of the metastasis were recorded. Using bootstrapped logistic regression, variables were selected for the clinical prediction model based on the optimisation of Akaike's information criterion. The area under the curve (AUC) of the receiver operating characteristic (ROC) curve was calculated for the resulting model. Decision curve analysis (DCA) was used to evaluate the clinical utility of the model. RESULTS: 64 (16%) of +DSNB harboured additional LNM at ILND. The number of positive nodes at +DSNB (odds ratio (OR) 2.19; 95% confidence interval (CI) 1.17-4.00; p=0.01) and the largest metastasis size in mm (OR 1.06; 95%CI 1.03-1.10; p=0.001) were selected for the clinical prediction model. The AUC was 0.67 (95%CI 0.60-0.74). The DCA showed no clinical benefit of using the clinical prediction model. CONCLUSION: A small but clinically important group of basins harbour additional LNM at completion ILND following +DSNB. While DSNB characteristics were associated with additional LNM, they did not improve the selection of basins in which ILND could be omitted. Thus, completion ILND remains necessary in all basins with a +DSNB