Pore formation during dehydration of polycrystalline gypsum observed and quantified in a time-series synchrotron radiation based X-ray micro-tomography experiment

We conducted an in-situ X-ray micro-computed tomography heating experiment at the Advanced Photon Source (USA) to dehydrate an unconfined 2.3 mm diameter cylinder of Volterra Gypsum. We used a purpose-built X-ray transparent furnace to heat the sample to 388 K for a total of 310 min to acquire a three-dimensional time-series tomography dataset comprising nine time steps. The voxel size of 2.2 μm3 proved sufficient to pinpoint reaction initiation and the organization of drainage architecture in space and time. We observed that dehydration commences across a narrow front, which propagates from the margins to the centre of the sample in more than four hours. The advance of this front can be fitted with a square-root function, implying that the initiation of the reaction in the sample can be described as a diffusion process. Novel parallelized computer codes allow quantifying the geometry of the porosity and the drainage architecture from the very large tomographic datasets (20483 voxels) in unprecedented detail. We determined position, volume, shape and orientation of each resolvable pore and tracked these properties over the duration of the experiment. We found that the pore-size distribution follows a power law. Pores tend to be anisotropic but rarely crack-shaped and have a preferred orientation, likely controlled by a pre-existing fabric in the sample. With on-going dehydration, pores coalesce into a single interconnected pore cluster that is connected to the surface of the sample cylinder and provides an effective drainage pathway. Our observations can be summarized in a model in which gypsum is stabilized by thermal expansion stresses and locally increased pore fluid pressures until the dehydration front approaches to within about 100 μm. Then, the internal stresses are released and dehydration happens efficiently, resulting in new pore space. Pressure release, the production of pores and the advance of the front are coupled in a feedback loop.

Three-dimensional reconstruction of an ancient Egyptian mummy

A complete series of cross-sectional computed tomography (CT) scans were obtained of a mummy of an Egyptian priestess, Tjenmutengebtiu, (Jeni), who lived in the twenty-second Dynasty (c. 945-715 BC). The purpose of this joint British Museum and St. Thomas’ Hospital project was effectively to ‘unwrap’ a mummy using cross-sectional X-rays. Jeni is encased in a beautifully decorated anthropomorphic cartonnage coffin. The head and neck were scanned with 2mm slices, the teeth with 1mm slices and the rest of the body with 4 mm slices, a 512 x 512 matrix was used. The 2D CT images, and 3D surface reconstruction’s, demonstrate many features of the embalming techniques and funerary customs of the XXII Dynasty. The presence of cloth protruding from the nasal cavities into the otherwise empty cranial cavity indicates that the brain was extracted via the nose. The remains of the heart can be seen as well as four organ packs corresponding to the mummified and repackaged lungs, intestines, stomach and liver. Each of the organ packs encloses a wax figurine representing one of the four sons of Horus. The teeth are in very good condition with little signs of wear, which, considering the gritty diet of the Egyptians, indicates that Jeni must have been very young when she died. A young age of death is also suggested by analysis of the shape of the molar teeth. The body is generally in very good condition demonstrating the consummate skill of the twenty-second Dynasty embalmers.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Three-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of L-tartaric acid with the associative-group monosubstituted pyridines 3-minopyridine, 3-carboxypyridine (nicotinic acid) and 2-carboxypyridine (picolinic acid).

The 1:1 proton-transfer compounds of L-tartaric acid with 3-aminopyridine [3-aminopyridinium hydrogen (2R,3R)-tartrate dihydrate, C5H7N2+·C4H5O6-·2H2O, (I)], pyridine-3-carboxylic acid (nicotinic acid) [anhydrous 3-carboxypyridinium hydrogen (2R,3R)-tartrate, C6H6NO2+·C4H5O6-, (II)] and pyridine-2-carboxylic acid [2-carboxypyridinium hydrogen (2R,3R)-tartrate monohydrate, C6H6NO2+·C4H5O6-·H2O, (III)] have been determined. In (I) and (II), there is a direct pyridinium-carboxyl N+-HO hydrogen-bonding interaction, four-centred in (II), giving conjoint cyclic R12(5) associations. In contrast, the N-HO association in (III) is with a water O-atom acceptor, which provides links to separate tartrate anions through Ohydroxy acceptors. All three compounds have the head-to-tail C(7) hydrogen-bonded chain substructures commonly associated with 1:1 proton-transfer hydrogen tartrate salts. These chains are extended into two-dimensional sheets which, in hydrates (I) and (III) additionally involve the solvent water molecules. Three-dimensional hydrogen-bonded structures are generated via crosslinking through the associative functional groups of the substituted pyridinium cations. In the sheet struture of (I), both water molecules act as donors and acceptors in interactions with separate carboxyl and hydroxy O-atom acceptors of the primary tartrate chains, closing conjoint cyclic R44(8), R34(11) and R33(12) associations. Also, in (II) and (III) there are strong cation carboxyl-carboxyl O-HO hydrogen bonds [OO = 2.5387 (17) Å in (II) and 2.441 (3) Å in (III)], which in (II) form part of a cyclic R22(6) inter-sheet association. This series of heteroaromatic Lewis base-hydrogen L-tartrate salts provides further examples of molecular assembly facilitated by the presence of the classical two-dimensional hydrogen-bonded hydrogen tartrate or hydrogen tartrate-water sheet substructures which are expanded into three-dimensional frameworks via peripheral cation bifunctional substituent-group crosslinking interactions.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Hydrogen bonding in proton-transfer compounds of 5-sulfosalicylic acid with a series of aliphatic nitrogen Lewis bases

The crystal structures of the proton-transfer compounds of 5-sulfosalicylic acid (3-carboxy-4-hydroxybenzenesulfonic acid) with the aliphatic nitrogen Lewis bases, hydroxylamine, triethylamine, pyrrolidine, morpholine, N-methylmorpholine and piperazine, viz. hydroxyammonium 3-carboxy-4-hydroxybenzenesulfonate (1), triethylaminium 3-carboxy-4-hydroxybenzenesulfonate (2), pyrrolidinium 3-carboxy-4-hydroxybenzenesulfonate monohydrate (3), morpholinium 3-carboxy-4-hydroxybenzenesulfonate monohydrate (4), N-methylmorpholinium 3-carboxy-4-hydroxybenzenesulfonate monohydrate (5) and piperazine-1,4-diium bis(3-carboxy-4-hydroxybenzenesulfonate) hexahydrate (6) have been determined and their comparative structural features and hydrogen-bonding patterns described. Crystals of 4 are triclinic, space group P-1 while the remainder are monoclinic with space group either P21/c (1 - 3) or P21/n (5, 6). Unit cell dimensions and contents are: for 1, a = 5.0156(3), b = 10.5738(6), c = 18.4785(9) Å, β = 96.412(5)o, Z = 4; for 2, a = 8.4998(4), b = 12.3832(6), c = 15.4875(9) Å, β = 102.411(5)o, Z = 4; for 3, a = 6.8755(2), b = 15.5217(4), c = 12.8335(3) Å, β = 92.074(2)o, Z = 4; for 4, a = 6.8397(2), b = 12.9756(5), c = 15.8216(6) Å, α = 90.833(3), β = 95.949(3), γ = 92.505(3)o, Z = 4; for 5, a = 7.0529(3), b = 13.8487(7), c = 15.6448(6) Å, β = 90.190(6)o, Z = 4; for 6, a = 7.0561(2), b = 15.9311(4), c = 12.2102(3) Å, β = 100.858(3)o, Z = 2. The hydrogen bonding generates structures which are either two-dimensional (2 and 5) or three-dimensional (1, 3, 4 and 6). Compound 6 represents the third reported structure of a salt of 5-sulfosalicylic acid having a dicationic piperazine species.

Synthesis of one-dimensional nanocomposites based on alumina nanofibres and their catalytic applications

Materials with one-dimensional (1D) nanostructure are important for catalysis. They are the preferred building blocks for catalytic nanoarchitecture, and can be used to fabricate designer catalysts. In this thesis, one such material, alumina nanofibre, was used as a precursor to prepare a range of nanocomposite catalysts. Utilising the specific properties of alumina nanofibres, a novel approach was developed to prepare macro-mesoporous nanocomposites, which consist of a stacked, fibrous nanocomposite with a core-shell structure. Two kinds of fibrous ZrO2/Al2O3 and TiO2/Al2O3 nanocomposites were successfully synthesised using boehmite nanofibers as a hard temperate and followed by a simple calcination. The alumina nanofibres provide the resultant nanocomposites with good thermal stability and mechanical stability. A series of one-dimensional (1D) zirconia/alumina nanocomposites were prepared by the deposition of zirconium species onto the 3D framework of boehmite nanofibres formed by dispersing boehmite nanofibres into a butanol solution, followed by calcination at 773 K. The materials were characterised by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Transmission electron microscope (TEM), N2 adsorption/desorption, Infrared Emission Spectroscopy (IES), and Fourier Transform Infrared spectroscopy (FT-IR). The results demonstrated that when the molar percentage, X, X=100*Zr/(Al+Zr), was > 30%, extremely long ZrO2/Al2O3 composite nanorods with evenly distributed ZrO2 nanocrystals formed on their surface. The stacking of such nanorods gave rise to a new kind of macroporous material without the use of any organic space filler\template or other specific drying techniques. The mechanism for the formation of these long ZrO2/Al2O3 composite nanorods is proposed in this work. A series of solid-superacid catalysts were synthesised from fibrous ZrO2/Al2O3 core and shell nanocomposites. In this series, the zirconium molar percentage was varied from 2 % to 50 %. The ZrO2/Al2O3 nanocomposites and their solid superacid counterparts were characterised by a variety of techniques including 27Al MAS-NMR, SEM, TEM, XPS, Nitrogen adsorption and Infrared Emission Spectroscopy. NMR results show that the interaction between zirconia species and alumina strongly correlates with pentacoordinated aluminium sites. This can also be detected by the change in binding energy of the 3d electrons of the zirconium. The acidity of the obtained superacids was tested by using them as catalysts for the benzolyation of toluene. It was found that a sample with a 50 % zirconium molar percentage possessed the highest surface acidity equalling that of pristine sulfated zirconia despite the reduced mass of zirconia. Preparation of hierarchically macro-mesoporous catalyst by loading nanocrystallites on the framework of alumina bundles can provide an alternative system to design advanced nanocomposite catalyst with enhanced performance. A series of macro-mesoporous TiO2/Al2O3 nanocomposites with different morphologies were synthesised. The materials were calcined at 723 K and were characterised by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Transmission electron microscope (TEM), N2 adsorption/desorption, Infrared Emission Spectroscopy (IES), and UV-visible spectroscopy (UV-visible). A modified approach was proposed for the synthesis of 1D (fibrous) nanocomposite with higher Ti/Al molar ratio (2:1) at lower temperature (<100oC), which makes it possible to synthesize such materials on industrial scale. The performances of a series of resultant TiO2/Al2O3 nanocomposites with different morphologies were evaluated as a photocatalyst for the phenol degradation under UV irradiation. The photocatalyst (Ti/Al =2) with fibrous morphology exhibits higher activity than that of the photocatalyst with microspherical morphology which indeed has the highest Ti to Al molar ratio (Ti/Al =3) in the series of as-synthesised hierarchical TiO2/Al2O3 nanocomposites. Furthermore, the photocatalytic performances, for the fibrous nanocomposites with Ti/Al=2, were optimized by calcination at elevated temperatures. The nanocomposite prepared by calcination at 750oC exhibits the highest catalytic activity, and its performance per TiO2 unit is very close to that of the gold standard, Degussa P 25. This work also emphasizes two advantages of the nanocomposites with fibrous morphology: (1) the resistance to sintering, and (2) good catalyst recovery.

Investigating the change in three dimensional deformity for idiopathic scoliosis using axially loaded MRI

Background: Adolescent idiopathic scoliosis is a complex three-dimensional deformity, involving a lateral deformity in the coronal plane and axial rotation of the vertebrae in the transverse plane. Gravitational loading plays an important biomechanical role in governing the coronal deformity, however, less is known about how they influence the axial deformity. This study investigates the change in three-dimensional deformity of a series of scoliosis patients due to compressive axial loading. Methods: Magnetic resonance imaging scans were obtained and coronal deformity (measured using the coronal Cobb angle) and axial rotations measured for a group of 18 scoliosis patients (Mean major Cobb angle was 43.4 o). Each patient was scanned in an unloaded and loaded condition while compressive loads equivalent to 50% body mass were applied using a custom developed compressive device. Findings: The mean increase in major Cobb angle due to compressive loading was 7.4 o (SD 3.5 o). The most axially rotated vertebra was observed at the apex of the structural curve and the largest average intravertebral rotations were observed toward the limits of the coronal deformity. A level-wise comparison showed no significant difference between the average loaded and unloaded vertebral axial rotations (intra-observer error = 2.56 o) or intravertebral rotations at each spinal level. Interpretation: This study suggests that the biomechanical effects of axial loading primarily influence the coronal deformity, with no significant change in vertebral axial rotation or intravertebral rotation observed between the unloaded and loaded condition. However, the magnitude of changes in vertebral rotation with compressive loading may have been too small to detect given the resolution of the current technique.

An analytical tool that quantifies cellular morphology changes from three-dimensional fluorescence images

The most common software analysis tools available for measuring fluorescence images are for two-dimensional (2D) data that rely on manual settings for inclusion and exclusion of data points, and computer-aided pattern recognition to support the interpretation and findings of the analysis. It has become increasingly important to be able to measure fluorescence images constructed from three-dimensional (3D) datasets in order to be able to capture the complexity of cellular dynamics and understand the basis of cellular plasticity within biological systems. Sophisticated microscopy instruments have permitted the visualization of 3D fluorescence images through the acquisition of multispectral fluorescence images and powerful analytical software that reconstructs the images from confocal stacks that then provide a 3D representation of the collected 2D images. Advanced design-based stereology methods have progressed from the approximation and assumptions of the original model-based stereology(1) even in complex tissue sections(2). Despite these scientific advances in microscopy, a need remains for an automated analytic method that fully exploits the intrinsic 3D data to allow for the analysis and quantification of the complex changes in cell morphology, protein localization and receptor trafficking. Current techniques available to quantify fluorescence images include Meta-Morph (Molecular Devices, Sunnyvale, CA) and Image J (NIH) which provide manual analysis. Imaris (Andor Technology, Belfast, Northern Ireland) software provides the feature MeasurementPro, which allows the manual creation of measurement points that can be placed in a volume image or drawn on a series of 2D slices to create a 3D object. This method is useful for single-click point measurements to measure a line distance between two objects or to create a polygon that encloses a region of interest, but it is difficult to apply to complex cellular network structures. Filament Tracer (Andor) allows automatic detection of the 3D neuronal filament-like however, this module has been developed to measure defined structures such as neurons, which are comprised of dendrites, axons and spines (tree-like structure). This module has been ingeniously utilized to make morphological measurements to non-neuronal cells(3), however, the output data provide information of an extended cellular network by using a software that depends on a defined cell shape rather than being an amorphous-shaped cellular model. To overcome the issue of analyzing amorphous-shaped cells and making the software more suitable to a biological application, Imaris developed Imaris Cell. This was a scientific project with the Eidgenössische Technische Hochschule, which has been developed to calculate the relationship between cells and organelles. While the software enables the detection of biological constraints, by forcing one nucleus per cell and using cell membranes to segment cells, it cannot be utilized to analyze fluorescence data that are not continuous because ideally it builds cell surface without void spaces. To our knowledge, at present no user-modifiable automated approach that provides morphometric information from 3D fluorescence images has been developed that achieves cellular spatial information of an undefined shape (Figure 1). We have developed an analytical platform using the Imaris core software module and Imaris XT interfaced to MATLAB (Mat Works, Inc.). These tools allow the 3D measurement of cells without a pre-defined shape and with inconsistent fluorescence network components. Furthermore, this method will allow researchers who have extended expertise in biological systems, but not familiarity to computer applications, to perform quantification of morphological changes in cell dynamics.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

Made by motion, Series one

“Made by Motion” is a collaboration between digital artist Paul Van Opdenbosch and performer and choreographer Elise May; a series of studies on captured motion data used to generating experimental visual forms that reverberate in space and time. The project investigates the invisible forces generated by and influencing the movement of a dancer. Along with how the forces can be captured and applied to generating visual outcomes that surpass simple data visualisation, projecting the intent of the performer’s movements. The source or ‘seed’ comes from using an Xsens MVN - Inertial Motion Capture system to capture spontaneous dance movements, with the visual generation conducted through a customised dynamics simulation. In this first series the visual investigation focused on manipulating the movement date at the instance of capture, capture been the recording of three-dimensional movement as ‘seen’ by the hardware and ‘understood’ through the calibration of software. By repositioning the capture hardware on the body we can effectively change how the same sequence of movements is ‘seen’ by the motion capture system thus generating a different visual result from effetely identical movement. The outcomes from the experiments clearly demonstrates the effectiveness of using motion capture hardware as a creative tool to manipulate the perception of the capture subject, in this case been a sequence of dance movements. The creative work exhibited is a cross-section of the experiments conducted in practice with the first animated work (Movement A - Control) using the motion capture hardware in its default ‘normal’ configuration. Following this is the lower body moved to the upper body (Lb-Ub), right arm moved onto the left arm (Ra-La), right leg moved onto the left leg (Rl-Ll) and finally the left leg moved onto a object that is then held in the left hand (Ll-Pf (Lh)).

The structures of the isomorphous potassium and rubidium salts of 4-nitrobenzoic acid and an overview of the metal complex stereochemistries of the alkali metal salt series with this ligand

The structures of the isomorphous potassium and rubidium polymeric coordination complexes with 4-nitrobenzoic acid, poly[mu2-aqua-aqua-mu3-(4-nitrobenzoato)-potassium], [K(C7H4N2O2)(H2O)2]n, (I) and poly[mu3-aqua-aqua-mu5-(4-nitrobenzoato)-rubidium], [Rb(C7H4N2O2)(H2O)2]n, (II) have been determined. In (I) the very distorted KO6 coordination sphere about the K+ centres in the repeat unit comprise two bridging nitro O-atom donors, a single bridging carboxyl O-atom donor and two water molecules, one of which is bridging. In the the Rb complex (II), the same basic MO6 coordination is found in the repeat unit but is expanded to RbO9 through a slight increase in the accepted Rb-O bond length range and includes an additional Rb-O(carboxyl) bond, completing a bidentate O,O'-chelate interaction, and additional bridging Rb-Onitro) and Rb-O(water) bonds. The comparative K-O and Rb-O bond length ranges are 2.738(3)-3.002(3)Ang. (I) and 2.884(2)-3.182(2)Ang. (II). The structure of (II) is also isomorphous as well as isostructural with the known structure of the nine-coordinate caesium 4-nitrobenzoate analogue, [Cs(C7H4N2O~2~)(H~2~O)2]n, (III) in which the Cs---O range is 3.047(4)-3.338(4)Ang. In all three complexes, common basic polymeric extensions are found, including two different centrosymmetric bridging interactions through both water and nitro groups as well as extensions along c through the p-related carboxyl group, giving a two-dimensional structure in (I). In (II) and (III), three-dimensional structures are generated through additional bridges through the nitro and water O-atoms. In all structures, both water molecules are involved in similar intra-polymer O-H...O hydrogen-bonding interactions to both carboxyl as well as water O-atom acceptors. A comparison of the varied coordination behaviour of the full set of Li-Cs salts with 4-nitrobenzoic acid is also made.