Series of Hessian-Vector Products for Tractable Saddle-Free Newton Optimisation of Neural Networks

Despite their popularity in the field of continuous optimisation, second-order quasi-Newton methods are challenging to apply in machine learning, as the Hessian matrix is intractably large. This computational burden is exacerbated by the need to address non-convexity, for instance by modifying the Hessian's eigenvalues as in Saddle-Free Newton methods. We propose an optimisation algorithm which addresses both of these concerns - to our knowledge, the first efficiently-scalable optimisation algorithm to asymptotically use the exact (eigenvalue-modified) inverse Hessian. Our method frames the problem as a series which principally square-roots and inverts the squared Hessian, then uses it to precondition a gradient vector, all without explicitly computing or eigendecomposing the Hessian. A truncation of this infinite series provides a new optimisation algorithm which is scalable and comparable to other first- and second-order optimisation methods in both runtime and optimisation performance. We demonstrate this in a variety of settings, including a ResNet-18 trained on CIFAR-10.Comment: 36 pages, 10 figures, 5 tables. Submitted to TMLR. First two authors' order randomise

Influence of bicarbonate, other anions and carbon dioxide in the activity of Pd-Cu catalysts for nitrate reduction in drinking water

Synthetic and commercial drinking waters with different composition were studied as reaction media to study the influence of salts in NO3- catalytic reduction using a Pd-Cu catalyst supported on a carbon black. As a general trend, a decrease in NO3- conversion and an increase in NH4+ selectivity were observed for high HCO3- concentration media in mixed salts waters. Literature has commonly ascribed HCO3- effect to competitive adsorption with NO3-. However, in the current work, the mechanism for effect HCO3- is reconsidered basis on HCO2- formation during NO3- catalytic reduction, here reported for the first time. HCO2- formation indicates that hydrogenation of HCO3- occurs in addition to adsorption. Likewise, decomposition of HCO2- on the catalysts surface releases hydrogen leading to increased spill-over and relevant hydrogenation of NO3- to NH4+. The presence of SO42-, Cl- reduces NH4+ selectivity due to competition for active sites and lower HCO2- generation. Furthermore, it was observed that the use of CO2 as buffer also contribute to the hydrogenation of NO3- to NH4+ through HCO2- routeThe authors greatly appreciate the support from Spanish Agencia Estatal de Investigacion ´ RTI2018-098431-B-I00 (MCIU/AEI/FEDER, UE). Dydia Tanisha Gonzalez ´ thanks the Regional Government of Madrid a research grant (PEJ-2020-AI/AMB-17551

Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation

We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.Comment: 4 pages,REVTeX, including 4 Figures. Latex (or postscript) version with figures available at http://formentor.uib.es/~montagne/textos/nupt

Lenalidomide and dexamethasone with or without clarithromycin in patients with multiple myeloma ineligible for autologous transplant: a randomized trial

Mieloma; Assajos controlats aleatorisMieloma; Ensayos controlados aleatoriosMyeloma; Randomized controlled trialsAlthough case-control analyses have suggested an additive value with the association of clarithromycin to continuous lenalidomide and dexamethasone (Rd), there are not phase III trials confirming these results. In this phase III trial, 286 patients with MM ineligible for ASCT received Rd with or without clarithromycin until disease progression or unacceptable toxicity. The primary endpoint was progression-free survival (PFS). With a median follow-up of 19 months (range, 0–54), no significant differences in the median PFS were observed between the two arms (C-Rd 23 months, Rd 29 months; HR 0.783, p = 0.14), despite a higher rate of complete response (CR) or better in the C-Rd group (22.6% vs 14.4%, p = 0.048). The most common G3–4 adverse events were neutropenia [12% vs 19%] and infections [30% vs 25%], similar between the two arms; however, the percentage of toxic deaths was higher in the C-Rd group (36/50 [72%] vs 22/40 [55%], p = 0.09). The addition of clarithromycin to Rd in untreated transplant ineligible MM patients does not improve PFS despite increasing the ≥CR rate due to the higher number of toxic deaths in the C-Rd arm. Side effects related to overexposure to steroids due to its delayed clearance induced by clarithromycin in this elderly population could explain these results. The trial was registered in clinicaltrials.gov with the name GEM-CLARIDEX: Ld vs BiRd and with the following identifier NCT02575144. The full trial protocol can be accessed from ClinicalTrials.gov. This study received financial support from BMS/Celgene

Wound-up phase turbulence in the Complex Ginzburg-Landau equation

We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to states within a range of allowed winding numbers. The analogy with the Eckhaus instability for non-turbulent waves is stressed. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of allowed winding numbers vanishes. We explain the states reached at long times in terms of three basic states, namely quasiperiodic states, frozen turbulence states, and riding turbulence states. Justification and some insight into them is obtained from an analysis of a phase equation for nonzero winding number: rigidly moving solutions of this equation, which correspond to quasiperiodic and frozen turbulence states, are understood in terms of periodic and chaotic solutions of an associated system of ordinary differential equations. A short report of some of our results has been published in [Montagne et al., Phys. Rev. Lett. 77, 267 (1996)].Comment: 22 pages, 15 figures included. Uses subfigure.sty (included) and epsf.tex (not included). Related research in http://www.imedea.uib.es/Nonlinea

Dynamics of localized structures in vector waves

Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev. Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been replaced by a better on

Global monitoring of soil multifunctionality in drylands using satellite imagery and field data

Models derived from satellite image data are needed to monitor the status of terrestrial ecosystems across large spatial scales. However, a remote sensing-based approach to quantify soil multifunctionality at the global scale is missing despite significant research efforts on this topic. A major constraint for doing so is the availability of suitable global-scale field data to calibrate remote sensing indicators (RSI) and, to a lesser extent, the sensitivity of spectral data of available satellite sensors to soil background and atmospheric conditions. Here, we aimed to develop a soil multifunctionality model to monitor global drylands coupling ground data on 14 soil functions of 222 dryland areas from six continents to 18 RSI derived from a time series (2006–2013) Landsat dataset. Among the RSI evaluated, the chlorophyll absorption ratio index was the best predictor of soil multifunctionality in single-variable-based models (r = 0.66, P < 0.01, NMRSE = 0.17). However, a multi-variable RSI model combining the chlorophyll absorption ratio index, the global environment monitoring index and the canopy-air temperature difference improved the accuracy of quantifying soil multifunctionality (r = 0.73, P < 0.01, NMRSE = 0.15). Furthermore, the correlation between RSI and soil variables shows a wide range of accuracy with upper and lower values obtained for AMI (r = 0.889, NMRSE = 0.05) and BGL (r = 0.685, NMRSE = 0.18) respectively. Our results provide new insights on assessing soil multifunctionality using RSI that may help to monitor temporal changes in the functioning of global drylands effectively.Field data were obtained with the support of the European Research Council (ERC) grant agreement 242658 (BIOCOM). Hernández-Clemente R was supported by the Ramón y Cajal program (RYC2020-029187-I) and the State Plan for Scientific and Subprogram for Knowledge Generation (PID2021-124058OA-I00) from the Spanish Ministry of Science and Innovation (RYC2020-029187-I). Maestre FT acknowledges support from Generalitat Valenciana (CIDEGENT/2018/041) and the Spanish Ministry of Science and Innovation (EUR2022-134048)

Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO

The Complex Ginzburg-Landau Equation in the Presence of Walls and Corners

We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern. Corners between walls provide additional synchronization mechanisms and associated selection criteria. The numerical results fit well with the theoretical predictions in the parameter range studied.Comment: 10 pages, 9 figures; for related work visit http://www.nbi.dk/~martine