Discrete Steps Research Articles

Computer-aided simulation of high-dimensional event-continuous systems

A comparative analysis of efficiency of explicit methods with error and stability control, semi-implicit (m, k)-methods, and implicit methods implemented in the modelling and simulation environment ISMA is presented. The Akzo Nobel Central Research laboratory’s model of a tumour penetrated by antibodies is used as the test problem. The computer model in the LISMA language after applying the method of lines is given. Performance of the numerical integration algorithms is measured for different spatial variable discretization steps.

Discrete steps of successional pathways differ in kelp forest and urchin barren communities

The role of organisms in community assembly and functioning is a crucial question of community ecology. We address this issue in a particular marine coastal ecosystem at SE Pacific: although kelp forests and urchin barrens are conspicuous benthic systems in rocky habitats, only a few studies have been focused on studying their successional patterns (especially following disturbances). In this work, we present successional pathways from micro-periphyton to macro-organisms observed during a 14-month period in kelp forests and urchin barrens in the Antofagasta Peninsula, Chile. The community composition and structure showed habitat-specific successional pathways with different dominant organisms in these two communities. Likewise, during their successional trajectories, both communities showed different number of discrete temporal stages. Kelp forests displayed a longer successional pathway of 7 discrete stages, while the barren bed succession pathway was composed only of 4 stages. We argue that this difference would be due to self-organising processes. This finding may have relevant implications for conservation and monitoring, since the intensive harvest of kelp species will not only increase the dominance of urchin barrens, but it would also facilitate its own, self-determined, more efficient (with few steps) successional pattern and the consequent persistence.

Neighborhood based decision theoretic rough set under dynamic granulation for BCI motor imagery classification

Brain Computer Interface is an interesting and important research field that has contributed widespread application systems. In the medical field, it is important for physically challenged persons to aid in rehabilitation and restoration. In Brain Computer Interface, computer acts as interface between brain signals and external device. The computer processes the brain signals and sends necessary instructions to external device. The external device helps in restoring the movement ability of patient. Motor imagery is the imagination of motor movements like hand, foot and tongue. There is an associated brain signal when the normal person moves their hand, foot and tongue. Similarly, there is an associated brain signal when the physically challenged person imagines moving their hand, foot and tongue. When this brain signal is analyzed by brain computer interface, it can facilitate motor movements through external device. The aim of this work is to analyze and classify the brain signals for motor movements to aid in rehabilitation and restoration. In this paper BCI Competition IV Dataset I, Dataset IIa, BCI Competition III Dataset IIIa and Neuroprosthetic EEG Dataset are analyzed A novel optimization technique with Neighborhood Decision Theoretic Rough Set under Dynamic Granulation is proposed for motor imagery classification. Neighborhood based Decision Theoretic Rough Set under Dynamic Granulation (NDTRS under DG) is hybrid approach combining two algorithms Neighborhood Rough Set and Decision Theoretic Rough Set under Dynamic Granulation ((DTRS under DG). Neighborhood Rough Set overcomes the drawback of discretization step in Rough Set. Decision Theoretic Rough Set under Dynamic Granulation algorithm has loss function for classification. The effectiveness of classification is improved since the loss function is involved in the construction of algorithm. The proposed method Neighborhood based Decision Theoretic Rough Set under Dynamic Granulation gives higher classification accuracy compared to existing approaches.

Dissociation Constant of Integrin-RGD Binding in Live Cells from Automated Micropipette and Label-Free Optical Data.

The binding of integrin proteins to peptide sequences such as arginine-glycine-aspartic acid (RGD) is a crucial step in the adhesion process of mammalian cells. While these bonds can be examined between purified proteins and their ligands, live-cell assays are better suited to gain biologically relevant information. Here we apply a computer-controlled micropipette (CCMP) to measure the dissociation constant (Kd) of integrin-RGD-binding. Surface coatings with varying RGD densities were prepared, and the detachment of single cells from these surfaces was measured by applying a local flow inducing hydrodynamic lifting force on the targeted cells in discrete steps. The average behavior of the populations was then fit according to the chemical law of mass action. To verify the resulting value of Kd2d = (4503 ± 1673) 1/µm2, a resonant waveguide grating based biosensor was used, characterizing and fitting the adhesion kinetics of the cell populations. Both methods yielded a Kd within the same range. Furthermore, an analysis of subpopulations was presented, confirming the ability of CCMP to characterize cell adhesion both on single cell and whole population levels. The introduced methodologies offer convenient and automated routes to quantify the adhesivity of living cells before their further processing.

Photon-excitation photon-emission maps (PhexPhem maps) with rovibronic resolution as a data base for theory and astrophysics part I: method and first results for H2

Dispersed fluorescence of wavelengths between 75 and 180 nm has been recorded after excitation of room temperature by narrow bandwidth monochromatized synchrotron radiation. Spectra have been taken in the exciting-photon energy range between 11 and 18 eV for discrete energy steps of 2.5 meV at a bandwidth of about 10 meV. The exciting-photon energy bandwidth has been narrow enough to induce transitions between individual rovibronic states. The resolution in the dispersed fluorescence detection was partly sufficient to resolve fluorescent transitions between individual rovibronic states. The recorded intensities are presented as two-dimensional photon-excitation photon-emission (PhexPhem) maps. They give a complete overview of experimental dispersed VUV/ FUV fluorescence spectra of H2 for these excitation energies, covering excitation from to all known singly excited states. The presented proof of principle experiments show a way to generate spectroscopic reference data for theory benchmarking and the interpretation of astrophysical observations.

The epigenetic and morphogenetic effects of molecular oxygen and its derived reactive species in development

The development of multicellular organisms involves the unpacking of a complex genetic program. Extensive characterization of discrete developmental steps has revealed the genetic program is controlled by an epigenetic state. Shifting the epigenome is a group of epigenetic enzymes that modify DNA and proteins to regulate cell type specific gene expression. While the role of these modifications in development has been established, the input(s) responsible for electing changes in the epigenetic state remains unknown. Development is also associated with dynamic changes in cellular metabolism, redox, free radical production, and oxygen availability. It has previously been postulated that these changes are causal in development by affecting gene expression. This suggests that oxygen is a morphogenic compound that impacts the removal of epigenetic marks. Likewise, metabolism and reactive oxygen species influence redox signaling through iron and glutathione to limit the availability of key epigenetic cofactors such as α-ketoglutarate, ascorbate, NAD+ and S-adenosylmethionine. Given the close relationship between these cofactors and epigenetic marks it seems likely that the two are linked. Here we describe how changing these inputs might affect the epigenetic state during development to drive gene expression. Combined, these cofactors and reactive oxygen species constitute the epigenetic landscape guiding cells along differing developmental paths.

Power Quality Analysis of the Output Voltage of AC Voltage and Frequency Controllers Realized with Various Voltage Control Techniques

Single-phase and three-phase AC-AC converters are employed in variable speed drive, induction heating systems, and grid voltage compensation. They are direct frequency and voltage controllers having no intermediate power conversion stage. The frequency controllers govern the output frequency (low or high) in discrete steps as per the requirements. The voltage controllers only regulate the RMS value of the output voltage. The output voltage regulation is achieved on the basis of the various voltage control techniques such as phase-angle, on-off cycle, and pulse-width modulation (PWM) control. The power quality of the output voltage is directly linked with its control techniques. Voltage controllers implemented with a simple control technique have large harmonics in their output voltage. Different control techniques have various harmonics profiles in the spectrum of the output voltage. Traditionally, the evaluation of power quality concerns is based on the simulation platform. The validity of the simulated values depends on the selection of the period of a waveform. Any deficiency in the selection of the period leads to incorrect results. A mathematical analytical approach can tackle this issue. This becomes important to analytically analyze the harmonious contents generated by various switching control algorithms for the output voltage so that these results can be successfully used for power quality analysis and filtering of harmonics components through various harmonics suppression techniques. Therefore, this research is focused on the analytical computation of the harmonics coefficients in the output voltage realized through the various voltage and frequency control techniques. The mathematically computed results are validated with the simulation and experimental results.

A South-to-South Cultural Adaptation of an Evidence-Based Parenting Program for Families in the Philippines.

Rates of child maltreatment are higher in low‐ and middle‐income countries due to risk factors such as social inequities, economic adversity, and sociocultural norms. Given the evidence showing the effectiveness of parenting interventions to prevent child maltreatment, this study embarked on a cultural adaptation of an evidence‐based parenting program with the eventual goal of integrating it within a nationwide conditional cash transfer program for low‐income Filipino parents with children aged 2–6 years. We document the systematic adaptation of the Parenting for Lifelong Health for Young Children program that was developed and tested in South Africa, for low‐resource Filipino families using the heuristic framework for the cultural adaptation of interventions. We underscore the merits of conducting a multistage top‐down and bottom‐up process that uses a participatory approach among cultural insiders and outsiders to develop a parenting intervention that reflects the contextual realities and cultural values of end users. The adapted program, Masayang Pamilya Para sa Batang Pilipino, is the product of a delicate and deliberate effort to balance Filipino childrearing goals and values with the scientific evidence on components of parenting interventions known to promote positive parenting and prevent child maltreatment.

Displacement Effect and Ratchet Effect: Testing of Two Alternative Hypotheses

This article empirically tests the displacement effect of Peacock and Wiseman (PW) and the ratchet effect of Bird, both of which are alternatives to Wagner’s law on the growth of public expenditure. The displacement effect explains why the (horizontal) trend line moves upward in discrete steps over time, whereas the ratchet effect affirms that public expenditure “ratchets” during drops in the economy and remains at a higher level after the economy stabilizes. The following innovations are introduced in the present study: (a) empirical testing was conducted for Spain and an extensive time period, 1880–2016; (b) the relationship between PR and expenditure was considered, introducing Gross Domestic Product (GDP) as a control variable; and (c) testing was performed using two differentiated methodologies. More specifically, the two methodologies employed were unit roots and cointegration with structural breakpoints and the more recent wavelet methodology. Given that PW refer to situations of social upheaval and its consequences, this study places its focus on analyzing the changes produced in Spain’s public expenditure with respect to the Spanish Civil War of 1936–1939 and to other disruptions both before and after this date. It was concluded that the displacement effect explains the development of Spanish public expenditure for the crises of 1982 and 1998. Meanwhile, wavelet methodology explains growth that took place in 1920 and 1980. In contrast, the ratchet effect does not explain the development of Spanish public expenditure over the study period.

Conditions for accretion disc formation and observability of wind-accreting X-ray binaries

Abstract We explore the effect of anisotropic wind driving on the properties of accretion onto black holes (BHs) in close binaries. We specifically focus on line-driven winds, which are common in high-mass X-ray binaries (HMXBs). In close binary systems, the tidal force from the companion star can modify the wind structure in two different ways. One is the reduction of wind terminal velocity due to the weaker effective surface gravity. The other is the reduction in mass flux due to gravity darkening (GD). We incorporate these effects into the so-called CAK theory in a simple way and investigate the wind flow around the accretor on the orbital scale. We find that a focused accretion stream is naturally formed when the Roche lobe filling factor is ${\gtrsim}0.8$ –0.9, analogous to that of wind Roche lobe overflow, but only when the velocity reduction is taken into account. The formation of a stream is necessary to bring in sufficient angular momentum to form an accretion disc around the BH. GD effects reduce the amount of accreted angular momentum, but not enough to prevent the formation of a disc. Based on these results, we expect there to be a discrete step in the observability of HMXBs depending on whether the donor Roche lobe filling factor is below or above ${\sim}$ 0.8–0.9.

An information entropy and latent Dirichlet allocation approach to noise patent filtering

Defining valid patents in a particular technological field is an indispensable step in patent analysis. To minimise the risk of missing valid patents, domain experts manually exclude irrelevant patents, known as noise patents, from an initial patent set derived using a loose retrieval query. However, this task has become time-consuming and labour intensive due to the increasing number of patents and rising complexity of technological knowledge. This study proposes a semi-automated approach to noise patent filtering based on information entropy theory and latent Dirichlet allocation. The proposed approach comprises four discrete steps: (1) structuring patents using a term-weighting method; (2) recommending noise patent seeds based on the information quantity of patents in terms of focal keyword groups; (3) measuring text similarities for patent clustering using latent Dirichlet allocation; and (4) identifying potential noise patent clusters with respect to the noise patent seeds. Our case study confirms that the proposed approach is valuable as a complementary noise patent filtering tool that will enable domain experts to focus more on their own knowledge-intensive tasks such as prior art analysis and research and development (R&D) strategy formulation.

Dynamics of interdependent critical infrastructures - a prioritised distribution model

Previous research articles about interdependent critical infrastructures developed different mathematical models describing the dynamic direct and indirect interactions of these infrastructures. Many of these models use discrete time steps to show how a reduced operability of one infrastructure C at time t will lead at time t + 1 to reductions in all infrastructures to which C distributes its output; and many of them use a standard mode of distribution which will be called proportional. According to a recent result, with this proportional distribution a reduced operability in only one infrastructure will lead to an enduring reduction of all operabilities even after full repairs of all damages. This research replaces this proportional mode by a newly defined prioritised one. It shows that a system with prioritised distribution mode leads in nearly all practical cases to an increased behaviour of the whole system: after repair of all damages, all infrastructures will return automatically to full operability.

Hamiltonian Monte Carlo method for estimating variance components.

A Hamiltonian Monte Carlo algorithm is a Markov chain Monte Carlo method, and the method has a potential to improve estimating parameters effectively. Hamiltonian Monte Carlo is based on Hamiltonian dynamics, and it follows Hamilton's equations, which are expressed as two differential equations. In the sampling process of Hamiltonian Monte Carlo, a numerical integration method called leapfrog integration is used to approximately solve Hamilton's equations, and the integration is required to set the number of discrete time steps and the integration stepsize. These two parameters require some amount of tuning and calibration for effective sampling. In this study, we applied the Hamiltonian Monte Carlo method to animal breeding data and identified the optimal tunings of leapfrog integration for normal and inverse chi-square distributions. Then, using real pig data, we revealed the properties of the Hamiltonian Monte Carlo method with the optimal tuning by applying models including variance explained by pedigree information or genomic information. Compared with the Gibbs sampling method, the Hamiltonian Monte Carlo method had superior performance in both models. We have provided the source codes of this method written in the Fortran language at https://github.com/A-ARAKAWA/HMC.

A minimizing Movement approach to a class of scalar reaction–diffusion equations

The purpose of this paper is to introduce a Minimizing Movement approach to scalar reaction–diffusion equations of the form [see formula in PDF] with parameters Λ, Σ > 0 and no-flux boundary condition [see formula in PDF] which is built on their gradient-flow-like structure in the space [see formula in PDF] of finite nonnegative Radon measures on [see formula in PDF], endowed with the recently introduced Hellinger-Kantorovich distance HKΛ,Σ. It is proved that, under natural general assumptions on [see formula in PDF] and [see formula in PDF], the Minimizing Movement scheme [see formula in PDF] for [see formula in PDF] yields weak solutions to the above equation as the discrete time step size τ ↓ 0. Moreover, a superdifferentiability property of the Hellinger-Kantorovich distance HKΛ,Σ, which will play an important role in this context, is established in the general setting of a separable Hilbert space; that result will constitute a starting point for the study of the differentiability of HKΛ,Σ along absolutely continuous curves which will be carried out in a subsequent paper.

О СОВМЕСТНОМ ПРИМЕНЕНИИ КОЛЛОКАЦИОННОГО МЕТОДА ГРАНИЧНЫХ ЭЛЕМЕНТОВ И МЕТОДА ФУРЬЕ ДЛЯ РЕШЕНИЯ ЗАДАЧ ТЕПЛОПРОВОДНОСТИ В КОНЕЧНЫХ ЦИЛИНДРАХ С ГЛАДКИМИ НАПРАВЛЯЮЩИМИ

Here we consider the initial-boundary value problems in a homogeneous cylindrical domain YI Ω ×+ ( Ω+ is an open two-dimensional bounded simply connected domain with a boundary 5 ∂Ω ∈C , 2 \ Ω≡ Ω − + R is the open exterior of the domain Ω+ , [0, ] YI ≡ Y is the height of the cylinder) on a time interval [0, ] TI ≡ T . The initial conditions and the boundary conditions on the bases of the cylinder are zero, and the boundary conditions on the lateral surface of the cylinder are given by the function 1 2 wx x yt ( , , ,) ( 1 2 (, ) x x ∈∂Ω , Y y ∈ I , T t I ∈ ). An approximate solution of such problems is obtained through the combined use of the Fourier method and the collocation boundary element method based on piecewise quadratic interpolation (PQI). The solution to the problem in the cylinder is expanded in a Fourier series in terms of eigenfunctions of the operator 2 By yy ≡ ∂ with the corresponding zero boundary conditions. The coefficients of such a Fourier series are solutions of problems for two-dimensional heat equations 2 2 t ∇ =∂ + u u ku . With a low smoothness of the functions w in the variable y, the weight of solutions at large values of k increases and the accuracy of solving the problem in the cylinder decreases. To maintain accuracy on a uniform grid, the step of discretization of the boundary function w with respect to the variable y is decreased by a factor of j. Here j is an averaged value of the quantity Y k π depending on the function w. In addition, the steps of discretization of functions ( ) 2 exp − τ k with respect to the variable τ in domains τ≤πT k are reduced by a factor of 2 2 k π . The steps in the remaining ranges of values τ and the steps by the other variables remain unchanged. The approximate solutions obtained on the basis of this procedure converge stably to exact solutions in the 2 ( ) LI I Y T × -norm with a cubic velocity uniformly with respect to sets of functions w, bounded by norm of functions with low smoothness in the variable y, uniformly along the length of the generatrix of the cylinder Y , and uniformly in the domain Ω . The latter is also associated with the use of PQI along the curve ∂Ω over the variable 2 2 ρ≡ − r d , which is carried out at small values of r ( d and r are the distances from the observed point of the domain Ω to the boundary ∂Ω and to the current point of integration along ∂Ω , respectively). The theoretical conclusions are confirmed by the results of the numerical solution of the problem in a circular cylinder, where the dependence of the boundary functions w on y is given by the normalized eigenfunctions of the differential operator By which vary in a sufficiently large range of values of k .

Research and development of schemes of the discrete step of reinforcement in the shaft with rope profile conductors

The paper investigates the design of roller guides used in vertical shafts of mining enterprises for rigid reinforcement, consisting of beam and box shots and conductors - rail or box ones. Guiding devices for providing directional movement along the depth of the vertical shaft in cable guides for various lifting vessels (stands, counterweights, skips) have been analyzed, their advantages and disadvantages have been determined. On the basis of the analysis, structures have been developed that provide directional movement using roller guides for double rope-profile conductors connected by a frame and fixed on cantilever-damping firing points, which allow damping horizontal dynamic forces in the frontal and lateral planes. Research, development and implementation of roller guide structures for double rope-profile conductors, providing a reliable connection between the vessel and the guide double rope-profile conductor, makes it possible to achieve: a) high smoothness when moving in double rope-profile conductors; b) reducing the influence of the twisting of the ropes; c) extending the service life of roller guides, due to the use of more rollers in one device and rubber material; d) increasing the service life and trouble-free operation of the guides; e) a significant reduction in the level of vibrations in the frontal and lateral planes; f) reducing the frequency of contact of the safety guide paw with the enclosing profile of the rope-profile conductor, therefore, reducing its wear as a result of abrasion; g) reducing the effect of stitching with coal or ore dust on the durability of the bearing assemblies of roller guides; i) increasing the service life of the roller guide axles due to the simultaneous contact of the rollers and the rope-profile conductor and the redistribution of the load; j) reducing the effect of the curvature of the conductors on the wear of the system elements in case of violation of the shaft lining; k) ensuring standard gaps at a safe level between the guide foot and the rope-profile guide.

Looking for Black Swans

This article examines the basis for testing historical claims and proffers the observation that the historical method is akin to the scientific method in that it utilizes critical elimination rather than justification. Building on the critical rationalism of Karl Popper – and specifically the deductive component of the scientific method called falsification – I examine his tetradic schema and adapt it for the specific purpose of historical analysis by making explicit a discrete step of critical testing, even though the schema is adequate as Popper expresses it and the elimination of error occurs at all steps of analysis. I also add a discrete step of critical elimination to Popper’s schema even though the elimination of error occurs at every step of analysis. The basis for critical elimination history is the demonstrable counterexample. The study of history will never approach the precision of science – history deals with open systems that cannot be replicated like experiments guided by fundamental laws. But just because we cannot know something with the rigor of science does not mean that we cannon know it better than we do. There may be no objective truth in an absolute sense, but there is a distinction to be made between well-tested and poorly tested theories and therefore between history done well and history done with less analytical rigor. What I hope to show is how our historical knowledge may progress through good faith critical discussion – history is discussion – and the elimination of error.

Convenient microfluidic cartridge for single-molecule droplet PCR using common laboratory equipment.

We have previously established a cost-efficient in-house system for single-molecule droplet polymerase chain reaction (PCR) using a polydimethylsiloxane microfluidic cartridge and common laboratory equipment. However, the microfluidic cartridge was only capable of generating monodisperse water-in-oil droplets. Therefore, careful and time-consuming manual droplet handling using a micropipette was required to transfer droplets between the three discrete steps involved in the workflow of droplet PCR-i.e., (1) droplet generation; (2) PCR amplification; and (3) determination of the fluorescence intensity of the thermocycled droplets. In the current study, we developed a new microfluidic cartridge consisting of four layers, with a thin glass slide as the bottom layer. In this cartridge, droplets generated in the uppermost polydimethylsiloxane microfluidic layer are delivered to the glass slide in an online fashion. After the accumulation of many droplets on the glass slide, the cartridge is placed on the flatbed heat block of a thermocycler for PCR amplification. Direct fluorescence imaging of the thermocycled droplets on the glass slide is then carried out using a conventional fluorescence microscope. Efficient heat transfer from the heat block to the settled droplets through the thin glass slide was confirmed by successful PCR amplification inside the droplets, even from single template molecules. The new cartridge eliminates the need for manual droplet transfer between the major steps of droplet PCR analysis, allowing more convenient single-molecule droplet PCR than in our previous studies.

Effects of fuel blending on first stage and overall ignition processes

The effects of blending ratio on mixtures of an alcohol-to-jet (ATJ) fuel and a conventional petroleum-derived fuel on first stage ignition and overall ignition delay are examined at engine-relevant ambient conditions. Experiments are conducted in a high-temperature pressure vessel that maintains a small flow of dry air at the desired temperature (825 K and 900 K) and pressure (6 MPa and 9 MPa) for fuel injections from a custom single-hole, axially-oriented injector, representing medium (7.5 mg) and high (10 mg) engine loading. Formaldehyde, imaged using planar laser-induced fluorescence, is measured at discrete time steps throughout the first and second stage ignition process and is used as a marker of unburned short-chain hydrocarbons formed after the initial breakdown of the fuel. The formaldehyde images are used to calculate the first stage ignition delay for each ambient and fuel loading condition. Chemiluminescence imaging of excited hydroxyl radical at 75 kHz is used to determine the overall ignition delay. At all conditions, increased volume fraction of ATJ resulted in longer, but non-linearly increasing, overall ignition delay. Across all of the blends, first stage ignition delay accounted for about 15% of the increase in overall ignition delay compared to the military's aviation kerosene, F-24, which is Jet A with additives, while extended first stage ignition duration accounted for 85% of the increase. It is observed that blends consisting of 0–60% by volume of the low cetane number ATJ fuel produced nearly identical first stage ignition delays. These results will inform the development of ignition models that can capture the non-linear effects of fuel blending on ignition processes.

Structural Transformations and Spin-Crossover in [FeL2 ]2+ Salts (L=4-{tert-Butylsulfanyl}-2,6-di{pyrazol-1-yl}pyridine): The Influence of Bulky Ligand Substituents.

4-(tert-Butylsulfanyl)-2,6-di(pyrazol-1-yl)pyridine (L) was obtained in low yield from a one-pot reaction of 2,4,6-trifluoropyridine with 2-methylpropane-2-thiolate and sodium pyrazolate in a 1:1:2 ratio. The materials [FeL2 ][BF4 ]2 ⋅solv (1[BF4 ]2 ⋅solv) and [FeL2 ][ClO4 ]2 ⋅solv (1[ClO4 ]2 ⋅solv; solv=MeNO2 , MeCN or Me2 CO) exhibit a variety of structures and spin-state behaviors including thermal spin-crossover (SCO). Solvent loss on heating 1[BF4 ]2 ⋅x MeNO2 (x≈2.3) occurs in two steps. The intermediate phase exhibits hysteretic SCO around 250 K, involving a "reverse-SCO" step in its warming cycle at a scan rate of 5 K min-1 . The reverse-SCO is not observed in a slower 1 K min-1 measurement, however, confirming its kinetic nature. The final product [FeL2 ][BF4 ]2 ⋅0.75 MeNO2 was crystallographically characterized, and shows abrupt but incomplete SCO at 172 K which correlates with disorder of an L ligand. The asymmetric unit of 1[BF4 ]2 ⋅y Me2 CO (y≈1.6) contains five unique complex molecules, four of which undergo gradual SCO in at least two discrete steps. Low-spin 1[ClO4 ]2 ⋅0.5 Me2 CO is not isostructural with its BF4 - congener, and undergoes single-crystal-to-single-crystal solvent loss with a tripling of the crystallographic unit cell volume, while retaining the P space group. Three other solvate salts undergo gradual thermal SCO. Two of these are isomorphous at room temperature, but transform to different low-temperature phases when the materials are fully low-spin.