Belousov-Zhabotinsky Reaction Research Articles

Optical Communication among Oscillatory Reactions and Photo‐Excitable Systems: UV and Visible Radiation Can Synchronize Artificial Neuron Models

AbstractNeuromorphic engineering promises to have a revolutionary impact in our societies. A strategy to develop artificial neurons (ANs) is to use oscillatory and excitable chemical systems. Herein, we use UV and visible radiation as both excitatory and inhibitory signals for the communication among oscillatory reactions, such as the Belousov–Zhabotinsky and the chemiluminescent Orban transformations, and photo‐excitable photochromic and fluorescent species. We present the experimental results and the simulations regarding pairs of ANs communicating by either one or two optical signals, and triads of ANs arranged in both feed‐forward and recurrent networks. We find that the ANs, powered chemically and/or by the energy of electromagnetic radiation, can give rise to the emergent properties of in‐phase, out‐of‐phase, anti‐phase synchronizations and phase‐locking, dynamically mimicking the communication among real neurons.

Belousov-Zhabotinsky反応を利用した均質沈澱法による臭化銀粒子の調製 : 溶液成長II

Belousov-Zhabotinsky反応を利用した均質沈澱法による臭化銀粒子の調製 : 溶液成長II

Experimental investigation of a unidirectional network of four chemical oscillators pulse-coupled through an inhibitor

Dynamical synchronous modes in a network of four nearly identical chemical oscillators unidirectionally coupled via inhibitory pulse coupling with time delay τ (when a spike in one oscillator inhibits the next oscillator in the circle after time delay τ), are obtained experimentally. The Belousov–Zhabotinsky reaction is used as a chemical oscillator. The existence of four main modes is confirmed experimentally: in-phase (IP) oscillations; an anti-phase (AP) mode, in which any two neighboring oscillators have a phase shift equal to half of global period T; a walk mode (W), in which oscillators produce consecutive spikes in the direction of the connection with a phase shift between neighboring oscillators equal to T/4; and a walk-reverse mode (WR), when the oscillators produce consecutive spikes (with phase shift T/4), but in the direction opposite the connections (the mode opposite to the W mode). In addition to the main modes, OS modes in which at least one of the four oscillators is suppressed, and “2+1+1” modes in which two neighboring oscillators produce spikes simultaneously and the phases of the third and the fourth oscillators are shifted by T/3 and 2T/3, respectively, are found. It is shown that the modes found experimentally correspond to those found in simulations.

Andrey P. Antonchick

Angewandte Chemie International EditionVolume 56, Issue 40 p. 12042-12042 Author ProfileFree Access Andrey P. Antonchick First published: 10 May 2017 https://doi.org/10.1002/anie.201704212AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Graphical Abstract “The secret of being a successful scientist is patience. My favorite name reaction is the Belousov–Zhabotinsky reaction ...” This and more about Andrey P. Antonchick can be found on page 12042. Andrey P. Antonchick The author presented on this page has recently published his 25th article since 2006 in Angewandte Chemie: “General Enantioselective C−H Activation with Efficiently Tunable Cyclopentadienyl Ligands”: Z.-J. Jia, C. Merten, R. Gontla, C. G. Daniliuc, A. P. Antonchick, H. Waldmann, Angew. Chem. Int. Ed. 2017, 56, 2429; Angew. Chem. 2017, 129, 2469. Date of birth: September 14, 1976 Position: Group leader, Technische Universität Dortmund E-mail: andrey.antonchick@tu-dortmund.de Homepage: http://antonchick.de ORCID: 0000-0003-0435-9443 Education: 2000 Undergraduate degree, Belarusian State University, Minsk 2005 PhD supervised by Prof. Dr. Vladimir Khripach (Institute of Bioorganic Chemistry of the National Academy of Sciences of Belarus) and Dr. Bernd Schneider (Max Planck Institute for Chemical Ecology, Jena) 2005–2008 Postdoctoral fellow with Prof. Dr. Magnus Rueping, University of Frankfurt 2008–2011 Postdoctoral fellow with Prof. Dr. Herbert Waldmann, Max Planck Institute of Molecular Physiology, Dortmund Awards: 2012 Thieme Chemistry Journals Award; 2017 visiting professorship, Peoples’ Friendship University of Russia Research: Reaction methodology, asymmetric catalysis, chemical biology Hobbies: Skiing, soccer The secret of being a successful scientist is patience. My favorite name reaction is the Belousov–Zhabotinsky reaction. My science “heroes” are Sofia V. Kovalevskaya, Alexander Fleming, Christiaan N. Barnard, Paul Ehrlich, Giordano Bruno, and many more. If I had one year of paid leave I would do some experiments in the lab. If I could be a piece of lab equipment, I would be a magnetic stir bar. The principal aspects of my personality are honesty and fairness. My favorite bands are Depeche Mode, The Cure, and Portishead. When I was eighteen I wanted to be a chemist. The most significant historic event of the past 100 years was space flight. My first experiment was the synthesis of nitrogen triiodide. My biggest inspiration is nature. My favorite times of day are early morning and late evening. My favorite way to spend a holiday is skiing. My 5 top papers: References 1“[1+1+1] Cyclotrimerization for the Synthesis of Cyclopropanes”: S. Manna, A. P. Antonchick, Angew. Chem. Int. Ed. 2016, 55, 5290; Angew. Chem. 2016, 128, 5376. (A radical cascade reaction for the simple synthesis of small rings.) 2“Cascade Multicomponent Synthesis of Indoles, Pyrazoles, and Pyridazinones by Functionalization of Alkenes”: K. Matcha, A. P. Antonchick, Angew. Chem. Int. Ed. 2014, 53, 11960; Angew. Chem. 2014, 126, 12154. (A general approach to heterocycle synthesis.) 3“Organocatalytic Oxidative Annulation of Benzamide Derivatives with Alkynes”: S. Manna, A. P. Antonchick, Angew. Chem. Int. Ed. 2014, 53, 7324; Angew. Chem. 2014, 126, 7452. (We demonstrated how transition-metal catalysts can be omitted in C−H bond functionalization.) 4“Metal-Free Cross-Dehydrogenative Coupling of Heterocycles with Aldehydes”: K. Matcha, A. P. Antonchick, Angew. Chem. Int. Ed. 2013, 52, 2082; Angew. Chem. 2013, 125, 2136. (One of the most practical reactions that was developed in my group.) 5“Palladium-Catalyzed Double C−H Activation Directed by Sulfoxides in the Synthesis of Dibenzothiophenes”: R. Samanta, A. P. Antonchick, Angew. Chem. Int. Ed. 2011, 50, 5217; Angew. Chem. 2011, 123, 5323. (Your first independent publication is like your first love!) Volume56, Issue40September 25, 2017Pages 12042-12042 ReferencesRelatedInformation

Kinetics of the Acetaminophen-Based Oscillatory Chemical Reaction with and without Ferroin as Catalyst: An Inorganic Prototype Model for Acetaminophen–Ethanol Syndrome

This paper describes the nonlinear behaviour of the acetaminophen-based uncatalysed Belousov–Zhabotinsky oscillator and its dynamics in the presence of ferroin as catalyst. The role of free metal ions as catalysts was examined and the results compared with those of corresponding complexed catalysts. Free metal ions were found to be sluggish with respect to the evolution of the oscillatory regime as compared to complexed ones. The effect was monitored of change of the ligand moiety of the catalyst complex on the oscillatory parameters. Since ethanol potentiates the hepatotoxicity caused by acetaminophen in vivo, it is thought to understand this interaction by virtue of causing perturbation of the acetaminophen-based oscillator with different concentrations of ethanol with and without ferroin as catalyst. Another dimension to the ethanol effect was examined by perturbation of the system with ethanol at different stages of the reaction so as to get an idea as to whether it is acetaminophen or some reactive intermediate generated in the reaction system which reacts with ethanol. Further, the ferroin-catalysed oscillator is taken as a prototype inorganic model of the acetaminophen–ethanol syndrome, as ferroin and hypobromous acid (HOBr) act as inorganic replacements for cytochrome P450 and nicotinamide adenine dinucleotide phosphate (NADPH) in alcohol metabolism.

Protic Ionic Liquids for the Belousov-Zhabotinsky Reaction: Aspects of the BZ Reaction in Protic Ionic Liquids and Its Use for the Autonomous Coil-Globule Oscillation of a Linear Polymer.

Herein, we describe the physicochemical aspects of the Belousov-Zhabotinsky (BZ) reaction in hydrated protic ionic liquids (PILs) combined with different cations with a hydrogen sulfate ([HSO4-]) anion. PILs were prepared from the neutralization reactions of sulfuric acid with 13 different aliphatic amines. The amine structure was selected to investigate the effect of the number of active protons, alkyl chain length (hydrophilicity), and cationic linearity on the mechanism of the BZ reaction. The pKa values of PILs were significantly higher (pKa = 1.0-2.5) than those of inorganic acids (H2SO4 = -3.0; HNO3 = -1.4), the conventional proton source in a BZ reaction. A periodic redox oscillation was observed in Ru(bpy)3 when appropriate amounts of BZ reaction substrates (NaBrO3 oxidant; malonic acid reductant) were added to the hydrated PILs. A long-lasting BZ oscillation was realized when hydrophilic cations (ammonium, ethylammonium, and dimethylethylammonium) were employed. Interestingly, a large ΔA5000 (oscillation amplitude of absorbance for the scale of the oscillation stability observed after 5000 s from the initiation of the BZ reaction) was achieved for PILs possessing less than four carbon atoms in their cationic structure. The apparent BZ oscillation activation energy (Ea) in the hydrated PILs was estimated to be ∼40 kJ mol-1, which is 30 kJ mol-1 less than that observed in a conventional system. The catalytic reaction in the BZ reaction subprocess suppresses the total activation energy of the reaction. To realize long-lasting self-oscillating polymeric materials acting under milder condition, we demonstrated an autonomous coil-globule polymer chain transition (BZ-driven) that directly converts chemical energy to mechanical motion in hydrated PILs without freely diffusing Ru(bpy)3 metal catalyst. Ethylammonium hydrogen sulfate ([ea-H+][HSO4-]) is selected as the suitable proton source for the BZ reaction. A well-defined self-oscillating polymer that incorporated Ru(bpy)3 metal catalyst into the polymer backbone accompanied by good compatibility in hydrated [ea-H+][HSO4-] is successfully prepared by ATRP, followed by postmodification of the metal catalyst. The rhythmic solubility changes of the polymer under milder conditions, realized by combination with PILs, will expand the potential applications of PILs to novel functional materials.

Robustness of free and pinned spiral waves against breakup by electrical forcing in excitable chemical media.

We present an investigation on the breakup of free and pinned spiral waves under an applied electrical current in the Belousov-Zhabotinsky reaction. Spiral fronts propagating towards the negative electrode are decelerated. A breakup of the spiral waves occurs when some segments of the fronts are stopped by a sufficiently strong electrical current. In the absence of obstacles (i.e., free spiral waves), the critical value of the electrical current for the wave breakup increases with the excitability of the medium. For spiral waves pinned to circular obstacles, the critical electrical current increases with the obstacle diameter. Analysis of spiral dynamics shows that the enhancement of the robustness against the breakup of both free and pinned spiral waves is originated by the increment of wave speed when either the excitability is strengthened or the obstacle size is enlarged. The experimental findings are reproduced by numerical simulations using the Oregonator model. In addition, the simulations reveal that the robustness against the forced breakup increases with the activator level in both cases of free and pinned spiral waves.

Fabrication of Micropatterned Self-Oscillating Polymer Brush for Direction Control of Chemical Waves.

The propagation control of chemical waves via a pentagonal patterned structure in a self-oscillating polymer brush composed of N-isopropylacrylamide and a metal catalyst for the Belousov-Zhabotinsky (BZ) reaction is reported. The patterned self-oscillating polymer brush is prepared by combining surface-initiated atom transfer radical polymerization and maskless photolithography. Surface modification is confirmed by X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, 3D measuring laser microscopy, and fluorescence microscopy. The polymer brush patterns are fabricated with gaps between the pentagonal regions, and investigations on the effect of the gap distance on the BZ reaction reveal that at the appropriate distance, chemical waves propagate across the array from the plane to the corner between the patterns. Unidirectional control is achieved not only in the 1D array, but also in a 2D curved array. This patterned self-oscillating polymer brush is a novel and advantageous approach for creating an autonomous dynamic soft interface.

Front tracking for quantifying advection-reaction-diffusion.

We present an algorithm for measuring the speed and thickness of reaction fronts, and from those quantities, the diffusivity and the reaction rate of the active chemical species. This front-tracking algorithm provides local measurements suitable for statistics and requires only a sequence of concentration fields. Though our eventual goal is front tracking in advection-reaction-diffusion, here we demonstrate the algorithm in reaction-diffusion. We test the algorithm with validation data in which front speed and thickness are prescribed, as well as simulation results in which diffusivity and reaction rate are prescribed. In all tests, measurements closely match true values. We apply the algorithm to laboratory experiments using the Belousov-Zhabotinsky reaction, producing speed, diffusivity, and reaction rate measurements that are statistically more robust than in prior studies. Finally, we use thickness measurements to quantify the concentration profile of chemical waves in the reaction.

Pinning of scroll waves to flat and highly branched unexcitable heterogeneities.

System heterogeneities such as organelles, cells, and anatomical features strongly affect nonlinear wave patterns in biological systems. These effects are more readily studied in otherwise homogeneous chemical reactions that allow the introduction of tailored structures. Following this approach, we investigate the dynamics of three-dimensional excitation vortices pinned to inert sheets with circular holes arranged on a hexagonal lattice. Experiments with the Belousov-Zhabotinsky reaction and numerical simulations of an excitable reaction-diffusion model reveal vortex pinning that circumvents the rapid collapse of free vortex rings. The pinned scroll waves are affected by the topological mismatch between their looplike rotation backbone and the branched pinning structure. Depending on the initial condition, a multitude of stable vortex states exist, all of which obey topological constraints, suggesting spinlike states for the involved obstacle holes.

Fredkin and Toffoli Gates Implemented in Oregonator Model of Belousov–Zhabotinsky Medium

A thin-layer Belousov–Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates — Fredkin gate and Toffoli gate — in a BZ medium network of excitable channels with subexcitable junctions. Local control of the BZ medium excitability is an important feature of the gates’ design. An excitable thin-layer BZ medium responds to a localized perturbation with omnidirectional target or spiral excitation waves. A subexcitable BZ medium responds to an asymmetric perturbation by producing traveling localized excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform the computation. We interpret the wave-fragments as values of Boolean variables. The presence of a wave-fragment at a given site of a circuit represents the logical truth, absence of the wave-fragment — logically false. Fredkin gate consists of ten excitable channels intersecting at 11 junctions, eight of which are subexcitable. Toffoli gate consists of six excitable channels intersecting at six junctions, four of which are subexcitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.

Self-Organization Induced by Self-Assembly in Microheterogeneous Reaction-Diffusion System.

When acrylamide (AA) monomers are added to the Belousov-Zhabotinsky (BZ) reaction incorporated into nanodroplets of water-in-oil aerosol OT (AOT) microemulsion (the BZ-AOT system), free radicals produced in the BZ reaction initiate polymerization of AA monomers and polyacrylamide particles are formed. These particles change the microstructure of the AOT microemulsion thus inducing the transition from Turing patterns to new dissipative patterns which can be either stationary "black" spots or waves.

Weakly and strongly coupled Belousov-Zhabotinsky patterns.

We investigate experimentally and numerically the synchronization of two-dimensional spiral wave patterns in the Belousov-Zhabotinsky reaction due to point-to-point coupling of two separate domains. Different synchronization modalities appear depending on the coupling strength and the initial patterns in each domain. The behavior as a function of the coupling strength falls into two qualitatively different regimes. The weakly coupled regime is characterized by inter-domain interactions that distorted but do not break wave fronts. Under weak coupling, spiral cores are pushed around by wave fronts in the other domain, resulting in an effective interaction between cores in opposite domains. In the case where each domain initially contains a single spiral, the cores form a bound pair and orbit each other at quantized distances. When the starting patterns consist of multiple randomly positioned spiral cores, the number of cores decreases with time until all that remains are a few cores that are synchronized with a partner in the other domain. The strongly coupled regime is characterized by interdomain interactions that break wave fronts. As a result, the wave patterns in both domains become identical.

Self-oscillating microgels with Fe(phen)3 catalyst induced by the BZ reaction under acid-free conditions

A novel self-oscillating microgels were prepared by copolymerization N-isopropylacrylamide (NIPAAm), organic acid and iron(II) 5-acrylamide-1,10-phenanthroline-bi (1,10-phenanthroline) (Fe(phen)3), the catalyst for the Belousov-Zhabotinsky (BZ) reaction. The microgels were characterized by FTIR spectroscopy and scanning electron microscope (SEM). In order to illustrate the self-oscillating mechanism, the static water contact angles of the oxidized and reduced states of self-oscillating microgels were measured. In addition, the self-oscillating behaviors of the microgels were investigated in BZ system under acid-free conditions. Both the redox potential and transmittance self-oscillating were observed at room temperature.

複数の自励振動ゲルから得られる発生力

Coupling polymer gel and Belousov-Zhabotinsky (BZ) reaction makes it possible to create a active polymer gel that swells and shrinks repeatedly (BZ gel). BZ gels are expected as chemical actuators in field of soft robotics. We have studied some chemical actuators using BZ gels. However, they generate only a small force. Herein we attempt to obtain more force using multiple BZ gels. In order to synchronize the period of BZ reaction, we added external force of periodic step waves to two BZ gels, and obtained force of the two gels 1.62 times larger than single one.

Chemical communication and dynamics of droplet emulsions in networks of Belousov-Zhabotinsky micro-oscillators produced by microfluidics.

Chemical communication leading to synchronization and collective behaviour of dynamic elements, such as cell colonies, is a widespread phenomenon with biological, physical and chemical importance. Such synchronization between elements proceeds via chemical communication by emmision, interdiffusion and reception of specific messenger molecules. On a lab scale, these phenomena can be modeled by encapsulating an oscillating chemical reaction, which serves as a signal (information) sender/receiver element, inside microcompartments such as droplet emulsions, liposomes and polymersomes. Droplets can thus be regarded as single units, able to generate chemical messengers that diffuse in the environment and hence can interact with other compartments. The Belousov-Zhabotinsky (BZ) reaction is a well-known chemical oscillator largely used as a model for complex nonlinear phenomena, including chemical, physical and biological examples. When the BZ-reaction is encapsulated inside microcompartments, its chemical intermediates can serve as messengers by diffusing among different microcompartments, to trigger specific reactions leading to a collective behavior between the elements. The geometry and constitution of the diffusion pathways play an important role in governing the collective behaviour of the system. In this context, microfluidics is not only a versatile tool for mastering the encapsulation process of the BZ-reaction in monodisperse microcompartments, but also for creating geometries and networks with well defined boundaries. The individual compartments can be engineered with selected properties using different surfactants in the case of simple emulsions, or with specific membrane properties in the case of liposomes. Furthermore, it enables the arrangement of these microcompartments in various geometric configurations, where the diffusive coupling pathways between individual compartments are both spatially and chemically well-defined. In this tutorial paper, we review a number of articles reporting various approaches to generate networks of compartmentalized Belousov-Zhabotinsky (BZ) chemical oscillators using microfluidics. In contrast to biological cellular networks, the dynamical characteristics of the BZ-reaction is well-known and, when confined in microcompartments arranged in different configurations with a pure interdiffusive coupling, these communicative microreactors can serve to mimic various types of bio-physical networks, aiding to comprehend the concept of chemical communication.

Chemical memory with states coded in light controlled oscillations of interacting Belousov-Zhabotinsky droplets.

The information storing potential of droplets, in which an oscillatory, photosensitive Belousov-Zhabotinsky (BZ) reaction proceeds, is investigated experimentally. We consider coupled oscillations in pairs and triplets of droplets. Droplets are surrounded by a solution of lipids in decane. Oscillations synchronize via diffusion of an activator through a lipid bilayer. The reaction in each droplet can be individually controlled by illumination with blue light through an optical fiber. We found that in pairs of BZ droplets, only the in-phase and the forcing oscillation modes are stable, however switching between these modes is not reliable. In triplets of droplets, switching between two different, stable rotational modes (clockwise and anticlockwise) can be easily implemented. Therefore, such a system is an excellent candidate for a light controlled, reliable, one bit chemical memory unit.

Influence of the Belousov–Zhabotinsky substrate concentration on the lifetime and self-oscillating behavior of a polymer solution

In this study, we synthesized a self-oscillating polymer chain with N-ethylacrylamide (NEAAm) as the main-chain. This exhibits a higher lower critical solution temperature than an N-isopropylacrylamide main chain. We subsequently measured the transmittance self-oscillation of poly[NEAAm-co-Ru(bpy) 3 ] [Ru(bpy) 3 = 4-vinyl-4’-methyl-2,2’-bipyridinebis(2,2’ bipyridine)bis(hexafluorophosphate) ruthenium] solutions comprising three Belousov-Zhabotinsky (BZ) substrates (malonic acid, sodium bromate, and sulfuric acid), under stirring at constant temperature. The soluble-insoluble self-oscillation of the polymer solution originated from the different solubility of the Ru(bpy) 3 moiety as a catalyst of the BZ reaction in the reduced and oxidized states. We demonstrated that the self-oscillating behavior was significantly affected by the initial concentration of the sodium bromate. Moreover, we clarified that the lifetime of the transmittance self-oscillation can be predicted from the initial concentration of malonic acid.

Autonomous unimer-vesicle oscillation by totally synthetic diblock copolymers: effect of block length and polymer concentration on spatio-temporal structures.

In this study, factors controlling autonomous vesicle oscillations exhibited by self-oscillating diblock copolymers were investigated. The self-oscillating diblock copolymer contains poly(ethylene oxide) (PEO) as the hydrophilic block and a random copolymer composed of N-isopropylacrylamide (NIPAAm) with side chains of ruthenium tris(2,2'-bipyridine) (Ru(bpy)3), which catalyzes the Belousov-Zhabotinsky (BZ) reaction, as the self-oscillating block. Recently, our group has reported that a diblock copolymer exhibits a unique autonomous disintegration and reconstruction of the vesicles driven by the periodic redox changes of Ru(bpy)3 in a catalyst-free BZ reaction solution. Nevertheless, the effect of the diblock copolymer architecture on the structure of the vesicles under equilibrium conditions, as well as their oscillation properties under non-equilibrium conditions, has not been clarified thus far. Hence, self-oscillating diblock copolymers with different block lengths were systematically synthesized, and the effects of the block length and polymer concentration on the spatio-temporal vesicle structures were comprehensively discussed.

Lyapunov exponents and the Belousov-Zhabotinsky oscillator: an interactive computational approach

The Belousov-Zhabotinsky (BZ) chemical oscillator is the most studied oscillator. It has been modelled on the basis of single-step mechanisms which have been continuously refined since the seminal manuscript by Field, Koros and Noyes in 1972. This manuscript reports on a unique way of modelling the global dynamics of the oscillator by assuming that the BZ oscillator has shown chaotic behaviour. The unique mathematical definition of chaos is very stringent, and, in this manuscript, we attempt to trace this unique exotic behaviour by the use of ‘onto’ maps of the interval onto itself which are known to exhaustively show a universal sequence of states that has all the hallmarks of chaotic behaviour. A series of one-humped maps of the interval display, through iterations and subsequent symbolic dynamics, a universal sequence of steps that commence with period-doubling, culminating in chaotic behaviour at some accumulation point of an appropriate bifurcation parameter.We put this theory to the test for the BZ oscillator in this manuscript by selecting a unique continuous map of the interval. This was then decomposed by an iterative treatment. Metric entropy and subsequent arbiter of chaotic behaviour was determined by evaluation of Lyapunov exponents which were then compared to observed BZ oscillator states. Our proposed map satisfactorily modelled the global dynamics of the BZ oscillator; predicted period-doubling, and a regime after a critical bifurcation parameter, where chaotic sequences were dense.We also produce, in the Addendum, an iterative MatLab procedure that any reader can utilize to reveal the type of states and behaviour reported here.