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Ecosystems can fluctuate around a stable equilibrium or be in a transient state (the period toward a stable state). In practical applications, transient states may be mistakenly regarded as stable states, or vice versa, especially when multiple positive feedbacks are involved, which produce much more complex system equilibrium behavior than a single positive feedback. However, our current understanding remains limited. Using a long-term restoration project in the Tengger Desert as the study object, this study employed a minimal model to explain a long "transient state" of a dryland ecosystem after restoration under the effects of two positive feedbacks (water-vegetation and erosion-vegetation). The results indicated that the transient state, a shrub-dominated state, might be an alternative stable state maintained by water-vegetation positive feedback. Shifts in dominance between the two positive feedbacks caused the ecosystem to shift from a shrub-dominated state to an herbaceous-dominated state. The shrub-dominated state was masked due to the mechanisms of dominance shifting by the two positive feedbacks, a phenomenon we refer to as a "concealed alternative stable state." This work proposes a novel perspective to study system dynamics—a switch of multiple positive feedbacks, and discovers a new explanation for a transient state—temporary visits of concealed alternative stable states, which could significantly benefit practical ecosystem interventions. [ABSTRACT FROM AUTHOR]

We construct the Sullivan minimal models of the oriented partial flag manifolds F ~ (n 1 , ... , n k) of type (n 1 , ... , n k) , k ≥ 3 and verify that they are formal. As an application of formality, we state the rational LS category and the rational topological complexity of oriented partial flag manifolds. [ABSTRACT FROM AUTHOR]

This paper investigates Rota–Baxter algebras of of arbitrary weight, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weight, from an operadic viewpoint. Denote by λ RBA the operad of Rota-Baxter associative algebras of weight λ . A homotopy cooperad is explicitly constructed, which can be seen as the Koszul dual of λ RBA as it is proven that the cobar construction of this homotopy cooperad is exactly the minimal model of λ RBA . This enables us to introduce the notion of homotopy Rota-Baxter algebras. The deformation complex of a Rota-Baxter algebra and the underlying L ∞ -algebra structure over it are exhibited as well. [ABSTRACT FROM AUTHOR]

For an arbitrary real nilpotent Lie algebra (nilmanifold) with an integrable complex structure, we propose an algorithm for constructing a special model of this nilmanifold that includes information on the complex structure. As a main application, we obtain a classification of eight-dimensional -generated nilpotent Lie algebras that admit an integrable complex structure. We also describe the moduli spaces of complex structures for each Lie algebra from the resulting classification list. [ABSTRACT FROM AUTHOR]

By making use of Halperin's local systems over simplicial sets and the model structure of the category of diffeological spaces due to Kihara, we introduce a framework of rational homotopy theory for such smooth spaces with arbitrary fundamental groups. As a consequence, we have an equivalence between the homotopy categories of fibrewise rational diffeological spaces and an algebraic category of minimal local systems elaborated by Gómez-Tato, Halperin and Tanré. In the latter half of this article, a spectral sequence converging to the singular de Rham cohomology of a diffeological adjunction space is constructed with the pullback of relevant local systems. In case of a stratifold obtained by attaching manifolds, the spectral sequence converges to the Souriau–de Rham cohomology algebra of the diffeological space. By using the pullback construction, we also discuss a local system model for a topological homotopy pushout. [ABSTRACT FROM AUTHOR]

The phenomenon of rate-dependent adhesion has long been recognized as an intricate problem, and the so-far-developed physics and mechanics-based approaches resulted in analytical relations between the implicit form between the work of adhesion and the contact front velocity which are difficult to implement in practice. To address this issue in the framework of spherical indentation, the adhesion relaxation test in a nominal point contact is introduced to estimate the rate-dependent adhesion. Based on a stretched exponent approximation for the contact radius evolution with time, a relatively simple four-parameter model is proposed for the functional relation between the work of adhesion and the contact front velocity, and its fitting performance is compared to that of the known Greenwood–Johnson and Persson–Brener models. [ABSTRACT FROM AUTHOR]

A locally conformally Kähler (LCK) manifold is a complex manifold M which has a Kähler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the Kähler form is exact on the minimal Kähler cover of M. We prove that any bimeromorphic map M'\rightarrow M is in fact holomorphic; in other words, M has a unique minimal model. This can be applied to a wide class of LCK manifolds, such as the Hopf manifolds, their complex submanifolds and to OT manifolds. [ABSTRACT FROM AUTHOR]

Electroporation is a phenomenon associated with an increased permeability of biological cell membranes following exposure of cells to high-voltage electric pulses. An increased membrane permeability allows an increased transport of ions and molecules into and out of the cell. In medicine, the target tissue of electroporation often consists of excitable cells, such as neurons and muscle cells. Unlike non-excitable cells, excitable cells can trigger electric signals (action potentials, AP). The mechanisms by which electroporation influences AP generation are not yet well understood. To gain a better understanding, a suitable experimental model is needed. The paper presents a cell line of genetically modified HEK cells stably expressing voltage-gated sodium ion channels and conditionally expressing potassium ion channels, that together enable the cells to trigger AP. The cells can be easily grown in a cell culture and thus represent an interesting experimental model for investigating the effect of electroporation on cellular excitability. Monitoring AP with fluorescence microscopy in these cells shows that the duration of the applied electric pulse affects the threshold for triggering AP and the AP characteristics. Moreover, the cell confluency affects the ability of the cells to trigger AP. The presented results open new questions that are important for further research on electroporation of excitable tissues and the development of associated treatments. [ABSTRACT FROM AUTHOR]

Simple Summary: Approximately 50% of patients diagnosed with cancer receive radiotherapy at least once during their disease. Experiments with sophisticated in-cellulo assays to improve radiotherapeutic outcomes are still challenging, and some critical details of tumor cell dynamics still need to be explored. To enhance the informative value of such approaches and support future therapeutic study designs, we developed an efficient mathematical model for three-dimensional multicellular tumor spheroids, which reflect microregions within a large tumor or avascular micrometastases and which are an auspicious experimental framework to pre-assess the curative effect of radio(chemo)therapy. We validate our mathematical model using experimental tumor spheroid growth data of several cell lines with and without radiotherapy and observe equal or better performance than previous models. Moreover, our model allows for efficient parameter calibration within previously reported and/or physiologically reasonable ranges. Based on this data-driven approach, we can explain the mechanism of the characteristic dynamics at small tumor volumes. Understanding the complex dynamics of tumor growth to develop more efficient therapeutic strategies is one of the most challenging problems in biomedicine. Three-dimensional (3D) tumor spheroids, reflecting avascular microregions within a tumor, are an advanced in vitro model system to assess the curative effect of combinatorial radio(chemo)therapy. Tumor spheroids exhibit particular crucial pathophysiological characteristics such as a radial oxygen gradient that critically affect the sensitivity of the malignant cell population to treatment. However, spheroid experiments remain laborious, and determining long-term radio(chemo)therapy outcomes is challenging. Mathematical models of spheroid dynamics have the potential to enhance the informative value of experimental data, and can support study design; however, they typically face one of two limitations: while non-spatial models are computationally cheap, they lack the spatial resolution to predict oxygen-dependent radioresponse, whereas models that describe spatial cell dynamics are computationally expensive and often heavily parameterized, impeding the required calibration to experimental data. Here, we present an effectively one-dimensional mathematical model based on the cell dynamics within and across radial spheres which fully incorporates the 3D dynamics of tumor spheroids by exploiting their approximate rotational symmetry. We demonstrate that this radial-shell (RS) model reproduces experimental spheroid growth curves of several cell lines with and without radiotherapy, showing equal or better performance than published models such as 3D agent-based models. Notably, the RS model is sufficiently efficient to enable multi-parametric optimization within previously reported and/or physiologically reasonable ranges based on experimental data. Analysis of the model reveals that the characteristic change of dynamics observed in experiments at small spheroid volume originates from the spatial scale of cell interactions. Based on the calibrated parameters, we predict the spheroid volumes at which this behavior should be observable. Finally, we demonstrate how the generic parameterization of the model allows direct parameter transfer to 3D agent-based models. [ABSTRACT FROM AUTHOR]

We consider a fractional-order model of glucose and insulin interaction based on the intra-venous glucose tolerance test (IVGTT). We show the existence of the model's solution, uniqueness, non-negativity, and boundadness. In addition, for the proposed fractional-order model, we establish sufficient conditions for stability or instability. Some conditions for bifurcation in the proposed model are presented using bifurcation theory. Further, in the case of first order the model is discretized by applying the forward Euler scheme. We investigate how small the time step size must be chosen to guarantee that the steady state solution is an attractive fixed point of the discretized model. Numerical simulations that we provided support the analytical results.

The particulars of stimulus–response experiments performed on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures—so that modal analysis can be used constructively in systems biology mechanistic model building—for some nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input–output (I-O) data associated with a (mechanistic) structural model—one that includes inputs and outputs explicitly. The methodology establishes model dimensionality (size and complexity) from particular I-O datasets; helps select among multiple candidate models (model distinguishability); helps in designing new I-O experiments to extract "hidden" structure; and helps to simplify (reduce) models to their essentials. These modal analysis tools are introduced to NL enzyme-regulated and protein–protein interaction biosystems via nonlinear normal mode (NNM) and quasi-steady state approximation (QSSA) analyses and unified with linear models on invariant 2-dimensional manifolds in phase space, with properties similarly informative about their dominant dynamical properties. Some automation of these highly technical aspects of biomodeling is also introduced. [ABSTRACT FROM AUTHOR]

We consider a fractional-order model of glucose and insulin interaction based on the intra-venous glucose tolerance test (IVGTT). We show the existence of the model's solution, uniqueness, non-negativity, and boundadness. In addition, for the proposed fractional-order model, we establish sufficient conditions for stability or instability. Some conditions for bifurcation in the proposed model are presented using bifurcation theory. Further, in the case of first order the model is discretized by applying the forward Euler scheme. We investigate how small the time step size must be chosen to guarantee that the steady state solution is an attractive fixed point of the discretized model. Numerical simulations that we provided support the analytical results. [ABSTRACT FROM AUTHOR]

We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms of the filtered and graded formality properties of the Malcev Lie algebra of its fundamental group, while some of the finiteness properties of the space are mirrored in the finiteness properties of algebraic models associated with it. In turn, the formality and finiteness properties of algebraic models have strong implications on the geometry of the cohomology jump loci of the space. We illustrate the theory with examples drawn from complex algebraic geometry, actions of compact Lie groups, and 3-dimensional manifolds. [ABSTRACT FROM AUTHOR]

Using the high symmetry in the geometry of a smooth projective quadric, we construct effectively new families of smooth projective rational surfaces whose nef divisors are regular, and whose effective monoids are finitely generated by smooth projective rational curves of negative self-intersection. Furthermore, the Cox rings of these surfaces are finitely generated, the dimensions of their anticanonical complete linear systems are zero, and their nonzero nef divisors intersect positively the anticanonical ones. And in two special cases, we give efficient ways of describing any effective divisor class in terms of the given minimal generating sets for the effective monoids of these surfaces. The ground field of our varieties is algebraically closed of arbitrary characteristic.

In our research work, we suggest the modified minimal model of fractional order and analyze it using the homotopy decomposition method (HDM). The minimal model is quite a useful mathematical model which describes the behavior of glucose-insulin metabolism. The original model was given in the 80s and has been updated over a different period. In this modified model, we add a one-factor diet which plays an important role in the blood-glucose analysis. We obtained the numerical results by using the homotopy decomposition method. HDM is extremely useful, significant, and very simple. We also discuss the existence and uniqueness of the fractional model. [ABSTRACT FROM AUTHOR]

The dissolution of polymer-coated, controlled-release urea fertilisers by means of a simple, Fickian diffusion-based model is described. This is in contrast to prior contributions that invoke non-Fickian mechanisms or take a more quantitative view. Within a quasi-static approximation, simple expressions for the granule radius and release profile as a function of time are obtained in terms of experimentally accessible parameters. Predictions compare well with available experimental data, although the full model is required to capture the gradual saturation of released urea in the late stages of the process. If scaled appropriately, a wide range of experimental data for different coatings turn out to collapse onto what for all intents and purposes can be called a universal curve. This suggests that extensive experimental testing can be avoided if the properties of the coating are known beforehand. • Diffusion model describes release properties of polymer-coated urea fertilisers. • Easily measurable geometric and kinetic quantities dictate the release profile. • Simple theoretical predictions compare well with available experimental data. • A wide range of experimental data can be collapsed onto a quasi universal curve. [ABSTRACT FROM AUTHOR]

Abstract Aims Application of the latent class analysis to acute heart failure with preserved ejection fraction (HFpEF) showed that the heterogeneous acute HFpEF patients can be classified into four distinct phenotypes with different clinical outcomes. This model‐based clustering required a total of 32 variables to be included. However, this large number of variables will impair the clinical application of this classification algorithm. This study aimed to identify the minimal number of variables for the development of optimal subphenotyping model. Methods and results This study is a post hoc analysis of the PURSUIT‐HFpEF study (N = 1095), a prospective, multi‐referral centre, observational study of acute HFpEF [UMIN000021831]. We previously applied the latent class analysis to the PURSUIT‐HFpEF dataset and established the full 32‐variable model for subphenotyping. In this study, we used the Cohen's kappa statistic to investigate the minimal number of discriminatory variables needed to accurately classify the phenogroups in comparison with the full 32‐variable model. Cohen's kappa statistic of the top‐X number of discriminatory variables compared with the full 32‐variable derivation model showed that the models with ≥16 discriminatory variables showed kappa value of >0.8, suggesting that the minimal number of discriminatory variables for the optimal phenotyping model was 16. The 16‐variable model consists of C‐reactive protein, creatinine, gamma‐glutamyl transferase, brain natriuretic peptide, white blood cells, systolic blood pressure, fasting blood sugar, triglyceride, clinical scenario classification, infection‐triggered acute decompensated HF, estimated glomerular filtration rate, platelets, neutrophils, GWTG‐HF (Get With The Guidelines‐Heart Failure) risk score, chronic kidney disease, and CONUT (Controlling Nutritional Status) score. Characteristics and clinical outcomes of the four phenotypes subclassified by the minimal 16‐variable model were consistent with those by the full 32‐variable model. The four phenotypes were labelled based on their characteristics as ‘rhythm trouble’, ‘ventricular‐arterial uncoupling’, ‘low output and systemic congestion’, and ‘systemic failure’, respectively. Conclusions The phenotyping model with top 16 variables showed almost perfect agreement with the full 32‐variable model. The minimal model may enhance the future clinical application of this clustering algorithm.

The phenomenon brake squeal has been an ongoing topic for decades, both in the automotive industry and in science. Although there is agreement on the excitation mechanism of brake squeal, namely self‐excitation due to frictional forces between the disk and the pad, in the subject of squeal it is very complex to discover all relevant effects and to take them into account. Several of these problems are related to nonlinearities, for example, in the contact between pad and disk or drum or in the behavior of the brake pad material. One of these nonlinear effects, which has been almost completely neglected so far, is that the brake can engage, mainly due to the bushing and joint elements within the brake, different equilibrium positions. This in fact has serious influence on the noise behavior as shown in experimental studies. For example, it is observed in experiments that, despite identical operating parameters, squeal sometimes occurs and sometimes not. In initial experimental studies, this could be related to the engaged equilibrium position. Following these experimental studies, the present paper introduces a minimal model by extending the well‐known minimal model by Hoffmann et al. by corresponding elements and nonlinearities allowing the system to engage different equilibrium positions. As will be presented, the stability behavior strongly depends on the engaged equilibrium position. Therefore, the minimal model represents the key experimentally observed issues. Additionally, a limit cycle behavior can also be observed. [ABSTRACT FROM AUTHOR]

We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Massey products induced on the homology algebra, hence the name of derived universal Massey product. [ABSTRACT FROM AUTHOR]

For virus classification and tracing, one idea is to generate minimal models from the gene sequences of each virus group for comparative analysis within and between classes, as well as classification and tracing of new sequences. The starting point of defining a minimal model for a group of gene sequences is to find their longest common sequence (LCS), but this is a non-deterministic polynomial-time hard (NP-hard) problem. Therefore, we applied some heuristic approaches of finding LCS, as well as some of the newer methods of treating gene sequences, including multiple sequence alignment (MSA) and k-mer natural vector (NV) encoding. To evaluate our algorithms, a five-fold cross validation classification scheme on a dataset of H1N1 virus non-structural protein 1 (NS1) gene was analyzed. The results indicate that the MSA-based algorithm has the best performance measured by classification accuracy, while the NV-based algorithm exhibits advantages in the time complexity of generating minimal models. [ABSTRACT FROM AUTHOR]

Minimal Model (MM) is the top-scoring model for assessing physiological characteristics to diagnose the potential or onset of type 2 diabetes mellitus (T2DM) through the intravenous glucose tolerance test (IVGTT) for the past four decades. Nevertheless it has been arguable that MM method either overestimates glucose effectiveness (GE) or underestimates insulin sensitivity (IS) in some cases by both biologists through in vivo experiments and mathematicians by analysis and/or simulations. We propose a novel model including the interstitial insulin according to physiology and adapted from the well accepted Sturis' model for the glucose-insulin metabolic system suitable to the IVGTT setting. Our model consistently overcomes the aforementioned defects in a subgroup of subjects. In addition, the variable X for insulin action in MM might be appropriately interpreted as an increment of insulin in the interstitial space in response to the bolus stimulus, rather than being proportional to the interstitial insulin as believed. [ABSTRACT FROM AUTHOR]

Abstract The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting upon such a system, even formulating an appropriate research question to address this topic is non-trivial. Here we present an abstraction of a supply and distribution system leading to a minimal model, which only retains stylized facts of the systemic function and, in this way, allows us to investigate the generic properties of robust supply networks. On this level of abstraction, a supply and distribution system is the strategic use of transportation to eliminate mismatches between production patterns (i.e., the amounts of goods produced at each production site of a company) and demand patterns (i.e., the amount of goods consumed at each location). When creating networks based on this paradigm and furthermore requiring the robustness of the system with respect to the loss of transportation routes (edge of the network) we see that robust networks are built from specific sets of subgraphs, while vulnerable networks display a markedly different subgraph composition. Our findings confirm a long-standing hypothesis in the field of network science, namely, that network motifs—statistically over-represented small subgraphs—are informative about the robust functioning of a network. Also, our findings offer a blueprint for enhancing the robustness of real-world supply and distribution systems.

Electrophysiological cell models are used to study and simulate the electrical behavior of cells. These models are presented by considering the characteristics of cells, channels, and ion currents in the cell membrane. This study aimed to provide a minimal model for gastric smooth muscle cells. Using the sensitivity analysis method in this paper, gastric cell current from the colon cell was obtained based on the approach of Yeoh et al. Then, the minimal model was obtained by identifying effective ion currents and eliminating inefficient ion currents. To evaluate the minimal model, the criteria of slow wave index points (initial potential, maximum spike potential, minimum valley potential, maximum plateau potential, and resting potential) and action potential duration of 10, 50, and 90 were used. Then, These values were compared with the slow wave physiological state of gastric smooth muscle cells. Finally, the minimal model obtained was consistent with the physiological model. The largest difference between the index points in both cases was related to the maximum spike potential with 2.21 millivolt and the action potential duration of 10 with 9 milliseconds. The results obtained by comparing two models of gastric smooth muscle cells (physiological and minimal states) showed the same behavior in slow wave.

Aims: Application of the latent class analysis to acute heart failure with preserved ejection fraction (HFpEF) showed that the heterogeneous acute HFpEF patients can be classified into four distinct phenotypes with different clinical outcomes. This model‐based clustering required a total of 32 variables to be included. However, this large number of variables will impair the clinical application of this classification algorithm. This study aimed to identify the minimal number of variables for the development of optimal subphenotyping model. Methods and results: This study is a post hoc analysis of the PURSUIT‐HFpEF study (N = 1095), a prospective, multi‐referral centre, observational study of acute HFpEF [UMIN000021831]. We previously applied the latent class analysis to the PURSUIT‐HFpEF dataset and established the full 32‐variable model for subphenotyping. In this study, we used the Cohen's kappa statistic to investigate the minimal number of discriminatory variables needed to accurately classify the phenogroups in comparison with the full 32‐variable model. Cohen's kappa statistic of the top‐X number of discriminatory variables compared with the full 32‐variable derivation model showed that the models with ≥16 discriminatory variables showed kappa value of >0.8, suggesting that the minimal number of discriminatory variables for the optimal phenotyping model was 16. The 16‐variable model consists of C‐reactive protein, creatinine, gamma‐glutamyl transferase, brain natriuretic peptide, white blood cells, systolic blood pressure, fasting blood sugar, triglyceride, clinical scenario classification, infection‐triggered acute decompensated HF, estimated glomerular filtration rate, platelets, neutrophils, GWTG‐HF (Get With The Guidelines‐Heart Failure) risk score, chronic kidney disease, and CONUT (Controlling Nutritional Status) score. Characteristics and clinical outcomes of the four phenotypes subclassified by the minimal 16‐variable model were consistent with those by the full 32‐variable model. The four phenotypes were labelled based on their characteristics as 'rhythm trouble', 'ventricular‐arterial uncoupling', 'low output and systemic congestion', and 'systemic failure', respectively. Conclusions: The phenotyping model with top 16 variables showed almost perfect agreement with the full 32‐variable model. The minimal model may enhance the future clinical application of this clustering algorithm. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic is one of the major disasters that humanity has ever faced. In this paper, we try to model the effect of vaccination in controlling the pandemic, particularly in context to the third wave which is predicted to hit globally. Here, we have modified the susceptible–exposed–infected–recovered–dead model by introducing a vaccination term. One of our main assumptions is that the infection rate (β (t)) is oscillatory. This oscillatory nature has been discussed earlier in literature with reference to the seasonality of epidemics. However, in our case, we invoke this nature of the infection rate (β (t)) to model the cyclical behavior of the COVID-19 pandemic within a short period. This study focuses on a minimalistic approach where we have logically deduced that the infection rate (β (t)) and the vaccination rate (λ) are the most important parameters while the other parameters can be assumed to be constants throughout the simulation. Finally, we have studied the rich interplay between the infection rate (β (t)) and the vaccination rate (λ) on the infectious cases of COVID-19 and made some robust conclusions regarding the global behavior of this pandemic in near future. [ABSTRACT FROM AUTHOR]

Amino acids (AAs) are well known to be involved in the regulation of glucose metabolism and, in particular, of insulin secretion. However, the effects of different AAs on insulin release and kinetics have not been completely elucidated. The aim of this study was to propose a mathematical model that includes the effect of AAs on insulin kinetics during a mixed meal tolerance test. To this aim, five different models were proposed and compared. Validation was performed using average data, derived from the scientific literature, regarding subjects with normal glucose tolerance (CNT) and with type 2 diabetes (T2D). From the average data of the CNT and T2D people, data for two virtual populations (100 for each group) were generated for further model validation. Among the five proposed models, a simple model including one first-order differential equation showed the best results in terms of model performance (best compromise between model structure parsimony, estimated parameters plausibility, and data fit accuracy). With regard to the contribution of AAs to insulin appearance/disappearance (kAA model parameter), model analysis of the average data from the literature yielded 0.0247 (confidence interval, CI: 0.0168 – 0.0325) and -0.0048 (CI: -0.0281 – 0.0185) μU·ml-1/(μmol·l-1·min), for CNT and T2D, respectively. This suggests a positive effect of AAs on insulin secretion in CNT, and negligible effect in T2D. In conclusion, a simple model, including single first-order differential equation, may help to describe the possible AAs effects on insulin kinetics during a physiological metabolic test, and provide parameters that can be assessed in the single individuals.

Exercise training at low intensity in the zone where lipid oxidation reaches a maximum (LIPOXmax training) has a slight but prolonged weight-lowering effect and improves both carbohydrate and lipid metabolism. We investigated in patients followed for long term LIPOXmax training which were the effect on body weight after 4 years and which were the early effects of 10 weeks of training on lipid oxidation during exercise and on insulin secretion and glucose disposal parameters measured with a standard meal. We thus present here the extension over 4 years of a preceding series of 28 obese subjects followed for 3 years to assess long-term weight-lowering effects of LIPOXmax training. In a subgroup of 14 patients undertaking such a training protocol, a breakfast test with minimal model analysis of insulin secretion and insulin sensitivity and an exercise calorimetry were performed before and after 10 weeks of targeted training. Over 48 months patients had lost on the average −8.37 ± 1.74 kg, i.e. −9.42 ± 1.93% of the initial weight (P < 0.001). Between 36 and 48 months weight loss was still in progress (on the average −0.2 kg/month). The subgroup of 14 patients undertaking LIPOXmax training showed after the initial period of 10 weeks the expected modifications of body composition in only half of the subjects, while exercise calorimetry showed an improvement of the ability to oxidize lipids during exercise (P = 0.011) and an increase in first phase insulin secretion (P = 0.003). The expected increase in insulin sensitivity was found only in 4 subjects and changes in insulin sensitivity were negatively correlated to changes in fat mass (r = −0.608, P = 0.047) and also negatively correlated to changes in beta-cell sensitivity (a measurement of second-phase insulin release) (r = −0.710, P = 0.032). There was also a correlation between changes in waist circumference and total prehepatic insulin release (r = −0.763, P = 0.046). Exercise training performed in the zone of maximal lipid oxidation has a sustained weigh-reducing effect that persists more than 4 years. This study demonstrates also for the first time that there are early effects on metabolism that become significant even before any obvious change in body composition. Insulin sensitivity improves when fat mass decreases and is in turn correlated with a decrease in second phase insulin secretion. By contrast the ability to oxidize lipids during exercise improves earlier, as well as phase 1 insulin secretion. Therefore, LIPOXmax training rapidly improves lipid oxidation and first phase insulin secretion, and has long lasting weight-lowering effects that further improves insulin sensitivity and reverses the insulin resistance-related excess in insulin secretion. The latter effects are not fully obtained after 11 weeks. [ABSTRACT FROM AUTHOR]

The debate over the explanatory nature of cognitive models has been waged mostly between two factions: the mechanists and the dynamical systems theorists. The former hold that cognitive models are explanatory only if they satisfy a set of mapping criteria, particularly the 3M/3M* requirement. The latter have argued, pace the mechanists, that some cognitive models are both dynamical and constitute covering-law explanations. In this paper, I provide a minimal model interpretation of dynamical cognitive models, arguing that this both provides needed clarity to the mechanist versus dynamicist divide in cognitive science and also paves the way towards further insights about scientific explanation generally. [ABSTRACT FROM AUTHOR]

Type 2 diabetes is a disease characterized by impaired insulin secretion and defective glucagon suppression in the postprandial period. We examined the effect of impaired glucagon suppression on glucose concentrations and endogenous glucose production (EGP) at different degrees of insulin secretory impairment. The contribution of anthropometric characteristics, peripheral, and hepatic insulin action to this variability was also examined. To do so, we studied 54 nondiabetic subjects on two occasions in which endogenous hormone secretion was inhibited by somatostatin, with glucagon infused at a rate of 0.65 ng/kg/min, at 0 min to prevent a fall in glucagon (nonsuppressed day) or at 120 min to create a transient fall in glucagon (suppressed day). Subjects received glucose (labeled with [3-³H]-glucose) infused to mimic the systemic appearance of 50-g oral glucose. Insulin was infused to mimic a prandial insulin response in 18 subjects, another 18 received 80% of the dose, and the remaining 18 received 60%. EGP was measured using the tracer-dilution technique. Decreased prandial insulin resulted in greater % increase in peak glucose but not in integrated glucose concentrations attributable to nonsuppressed glucagon. The % change in integrated EGP was unaffected by insulin dose. Multivariate regression analysis, adjusted for age, sex, weight, and insulin dose, did not show a relationship between the EGP response to impaired suppression of glucagon and insulin action as measured at the time of screening by oral glucose tolerance. A similar analysis for hepatic insulin action also did not show a relationship with the EGP response. These data indicate that the effect of impaired glucagon suppression on EGP is independent of anthropometric characteristics and insulin action. [ABSTRACT FROM AUTHOR]

The authors’ perspective is described regarding modifications made in their clinic to glucose challenge protocols and mathematical models in order to estimate insulin secretion, insulin sensitivity and glucose effectiveness in patients living with Insulin-Requiring Diabetes and patients who received Pancreatic Islet Transplants to treat Type I diabetes (T1D) with Impaired Awareness of Hypoglycemia. The evolutions are described of protocols and models for use in T1D, and Insulin-Requiring Type 2 Diabetes (T2D) that were the basis for studies in the Islet Recipients. In each group, the need for modifications, and how the protocols and models were adapted is discussed. How the ongoing application of the adaptations is clarifying the Islet pathophysiology in the Islet Transplant Recipients is outlined.

The authors' perspective is described regarding modifications made in their clinic to glucose challenge protocols and mathematical models in order to estimate insulin secretion, insulin sensitivity and glucose effectiveness in patients living with Insulin-Requiring Diabetes and patients who received Pancreatic Islet Transplants to treat Type I diabetes (T1D) with Impaired Awareness of Hypoglycemia. The evolutions are described of protocols and models for use in T1D, and Insulin-Requiring Type 2 Diabetes (T2D) that were the basis for studies in the Islet Recipients. In each group, the need for modifications, and how the protocols and models were adapted is discussed. How the ongoing application of the adaptations is clarifying the Islet pathophysiology in the Islet Transplant Recipients is outlined. [ABSTRACT FROM AUTHOR]

We address a problem with the Bergman-Cobelli Minimal Model, which has been used for 40 years to estimate SI during an intravenous glucose tolerance test (IVGTT). During the IVGTT blood glucose and insulin concentrations are measured in response to an acute intravenous glucose load. Insulin secretion is often assessed by the area under the insulin curve during the first few minutes (Acute Insulin Response, AIR). The issue addressed here is that we have found in simulated IVGTTs, representing certain contexts, Minimal Model estimates of SI are inversely related to AIR, resulting in artifactually lower SI. This may apply to Minimal Model studies reporting lower SI in Blacks than in Whites, a putative explanation for increased risk of T2D in Blacks. The hyperinsulinemic euglycemic clamp (HIEC), the reference method for assessing insulin sensitivity, by contrast generally does not show differences in insulin sensitivity between these groups. The reason for this difficulty is that glucose rises rapidly at the start of the IVGTT and reaches levels independent of SI, whereas insulin during this time is determined by AIR. The minimal model in effect interprets this combination as low insulin sensitivity even when actual insulin sensitivity is unchanged. This happens in particular when high AIR results from increased number of readily releasable insulin granules, which may occur in Blacks. We conclude that caution should be taken when comparing estimates of SI between Blacks and Whites.

We address a problem with the Bergman-Cobelli Minimal Model, which has been used for 40 years to estimate S I during an intravenous glucose tolerance test (IVGTT). During the IVGTT blood glucose and insulin concentrations are measured in response to an acute intravenous glucose load. Insulin secretion is often assessed by the area under the insulin curve during the first few minutes (Acute Insulin Response, AIR). The issue addressed here is that we have found in simulated IVGTTs, representing certain contexts, Minimal Model estimates of S I are inversely related to AIR, resulting in artifactually lower S I . This may apply to Minimal Model studies reporting lower S I in Blacks than in Whites, a putative explanation for increased risk of T2D in Blacks. The hyperinsulinemic euglycemic clamp (HIEC), the reference method for assessing insulin sensitivity, by contrast generally does not show differences in insulin sensitivity between these groups. The reason for this difficulty is that glucose rises rapidly at the start of the IVGTT and reaches levels independent of S I , whereas insulin during this time is determined by AIR. The minimal model in effect interprets this combination as low insulin sensitivity even when actual insulin sensitivity is unchanged. This happens in particular when high AIR results from increased number of readily releasable insulin granules, which may occur in Blacks. We conclude that caution should be taken when comparing estimates of S I between Blacks and Whites. [ABSTRACT FROM AUTHOR]

Glucagon is secreted from the pancreatic alpha cells and plays an important role in the maintenance of glucose homeostasis, by interacting with insulin. The plasma glucose levels determine whether glucagon secretion or insulin secretion is activated or inhibited. Despite its relevance, some aspects of glucagon secretion and kinetics remain unclear. To gain insight into this, we aimed to develop a mathematical model of the glucagon kinetics during an oral glucose tolerance test, which is sufficiently simple to be used in the clinical practice. The proposed model included two first-order differential equations -one describing glucagon and the other describing C-peptide in a compartment remote from plasma - and yielded a parameter of possible clinical relevance (i.e., SGLUCA(t), glucagon-inhibition sensitivity to glucose-induced insulin secretion). Model was validated on mean glucagon data derived from the scientific literature, yielding values for SGLUCA(t) ranging from -15.03 to 2.75 (ng of glucagon·nmol of C-peptide-1). A further validation on a total of 100 virtual subjects provided reliable results (mean residuals between -1.5 and 1.5 ng·L-1) and a negative significant linear correlation (r = -0.74, p < 0.0001, 95% CI: -0.82 – -0.64) between SGLUCA(t) and the ratio between the areas under the curve of suprabasal remote C-peptide and glucagon. Model reliability was also proven by the ability to capture different patterns in glucagon kinetics. In conclusion, the proposed model reliably reproduces glucagon kinetics and is characterized by sufficient simplicity to be possibly used in the clinical practice, for the estimation in the single individual of some glucagon-related parameters.

Glucose effectiveness, defined as the ability of glucose itself to increase glucose utilization and inhibit hepatic glucose production, is an important mechanism maintaining normoglycemia. We conducted a minimal modeling analysis of glucose effectiveness at zero insulin (GEZI) using intravenous glucose tolerance test data from subjects with type 2 diabetes (T2D, n=154) and non-diabetic (ND) subjects (n=343). A hierarchical statistical analysis was performed, which provided a formal mechanism for pooling the data from all study subjects, to yield a single composite population model that quantifies the role of subject specific characteristics such as weight, height, age, sex, and glucose tolerance. Based on the resulting composite population model, GEZI was reduced from 0.021 min–1 (standard error – 0.00078 min–1) in the ND population to 0.011 min–1 (standard error – 0.00045 min–1) in T2D. The resulting model was also employed to calculate the proportion of the non–insulin-dependent net glucose uptake in each subject receiving an intravenous glucose load. Based on individual parameter estimates, the fraction of total glucose disposal independent of insulin was 72.8% ± 12.0% in the 238 ND subjects over the course of the experiment, indicating the major contribution to the whole-body glucose clearance under non-diabetic conditions. This fraction was significantly reduced to 48.8% ± 16.9% in the 30 T2D subjects, although still accounting for approximately half of the total in the T2D population based on our modeling analysis. Given the potential application of glucose effectiveness as a predictor of glucose intolerance and as a potential therapeutic target for treating diabetes, more investigations of glucose effectiveness in other disease conditions can be conducted using the hierarchical modeling framework reported herein.

Glucose effectiveness, defined as the ability of glucose itself to increase glucose utilization and inhibit hepatic glucose production, is an important mechanism maintaining normoglycemia. We conducted a minimal modeling analysis of glucose effectiveness at zero insulin (GEZI) using intravenous glucose tolerance test data from subjects with type 2 diabetes (T2D, n=154) and non-diabetic (ND) subjects (n=343). A hierarchical statistical analysis was performed, which provided a formal mechanism for pooling the data from all study subjects, to yield a single composite population model that quantifies the role of subject specific characteristics such as weight, height, age, sex, and glucose tolerance. Based on the resulting composite population model, GEZI was reduced from 0.021 min–1 (standard error – 0.00078 min–1) in the ND population to 0.011 min–1 (standard error – 0.00045 min–1) in T2D. The resulting model was also employed to calculate the proportion of the non–insulin-dependent net glucose uptake in each subject receiving an intravenous glucose load. Based on individual parameter estimates, the fraction of total glucose disposal independent of insulin was 72.8% ± 12.0% in the 238 ND subjects over the course of the experiment, indicating the major contribution to the whole-body glucose clearance under non-diabetic conditions. This fraction was significantly reduced to 48.8% ± 16.9% in the 30 T2D subjects, although still accounting for approximately half of the total in the T2D population based on our modeling analysis. Given the potential application of glucose effectiveness as a predictor of glucose intolerance and as a potential therapeutic target for treating diabetes, more investigations of glucose effectiveness in other disease conditions can be conducted using the hierarchical modeling framework reported herein. [ABSTRACT FROM AUTHOR]

Glucagon is secreted from the pancreatic alpha cells and plays an important role in the maintenance of glucose homeostasis, by interacting with insulin. The plasma glucose levels determine whether glucagon secretion or insulin secretion is activated or inhibited. Despite its relevance, some aspects of glucagon secretion and kinetics remain unclear. To gain insight into this, we aimed to develop a mathematical model of the glucagon kinetics during an oral glucose tolerance test, which is sufficiently simple to be used in the clinical practice. The proposed model included two first-order differential equations -one describing glucagon and the other describing C-peptide in a compartment remote from plasma - and yielded a parameter of possible clinical relevance (i.e., SGLUCA(t), glucagon-inhibition sensitivity to glucose-induced insulin secretion). Model was validated on mean glucagon data derived from the scientific literature, yielding values for SGLUCA(t) ranging from -15.03 to 2.75 (ng of glucagon·nmol of C-peptide-1). A further validation on a total of 100 virtual subjects provided reliable results (mean residuals between -1.5 and 1.5 ng·L-1) and a negative significant linear correlation (r = -0.74, p < 0.0001, 95% CI: -0.82 – -0.64) between SGLUCA(t) and the ratio between the areas under the curve of suprabasal remote C-peptide and glucagon. Model reliability was also proven by the ability to capture different patterns in glucagon kinetics. In conclusion, the proposed model reliably reproduces glucagon kinetics and is characterized by sufficient simplicity to be possibly used in the clinical practice, for the estimation in the single individual of some glucagon-related parameters. [ABSTRACT FROM AUTHOR]

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (SI) and glucose effectiveness (SG), from data of the insulin‐modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model‐based assessment of SI and SG. The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing SI and SG as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing SI and SG than the sparse standard design. [ABSTRACT FROM AUTHOR]

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.

Idealization is ubiquitous in human cognition, and so is the inclination to be puzzled by it: what to make of ideal gas, infinitely large populations, homo economicus, perfectly just society, known to violate matters of fact? This is apparent in social science theorizing (from J. H. von Thünen, J. S. Mill, and Max Weber to Milton Friedman and Thomas Schelling), recent philosophy of science analyzing scientific modeling, and the debate over ideal and non-ideal theory in political philosophy (since John Rawls). I will offer a set of concepts and principles to improve transparency about the precise contents of idealizations (in terms of negligibility, applicability, tractability, and early-step status) and their distinct functions (such as contributing to minimal modeling, benchmark modeling, and how-possibly modeling). [ABSTRACT FROM AUTHOR]

Let X be a simply connected space with finite-dimensional rational homotopy groups. Let p ∞ : U E → B aut 1 (X) be the universal fibration of simply connected spaces with fibre X. We give a DG Lie algebra model for the evaluation map ω : aut 1 (B aut 1 (X Q)) → B aut 1 (X Q) expressed in terms of derivations of the relative Sullivan model of p ∞ . We deduce formulas for the rational Gottlieb group and for the evaluation subgroups of the classifying space B aut 1 (X Q) as a consequence. We also prove that C P Q n cannot be realized as B aut 1 (X Q) for n ≤ 4 and X with finite-dimensional rational homotopy groups. [ABSTRACT FROM AUTHOR]

We construct examples of n -folds of general type with relatively small volumes with respect to p g (X). [ABSTRACT FROM AUTHOR]

A differential algebra with weight is an abstraction of both the derivation (weight zero) and the forward and backward difference operators (weight ±1). In 2010 Loday established the Koszul duality for the operad of differential algebras of weight zero. He did not treat the case of nonzero weight, noting that new techniques are needed since the operad is no longer quadratic. This paper continues Loday's work and establishes the Koszul duality in the case of nonzero weight. In the process, the minimal model and the Koszul dual homotopy cooperad of the operad governing differential algebras with weight are determined. As a consequence, a notion of homotopy differential algebras with weight is obtained and the deformation complex as well as its L ∞ -algebra structure for differential algebras with weight are deduced. [ABSTRACT FROM AUTHOR]

Background: Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship. Results: Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (sG) and insulin sensitivity (sI). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (sE) and glucagon sensitivity (δ). Conclusions: The models are used to investigate how different degrees of pax'tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted. [ABSTRACT FROM AUTHOR]

Aims/hypothesis: This study aimed to examine the metabolic health of young apparently healthy non-obese adults to better understand mechanisms of hyperinsulinaemia. Methods: Non-obese (BMI < 30 kg/m2) adults aged 18–35 years (N = 254) underwent a stable isotope-labelled OGTT. Insulin sensitivity, glucose effectiveness and beta cell function were determined using oral minimal models. Individuals were stratified into quartiles based on their insulin response during the OGTT, with quartile 1 having the lowest and quartile 4 the highest responses. Results: Thirteen per cent of individuals had impaired fasting glucose (IFG; n = 14) or impaired glucose tolerance (IGT; n = 19), allowing comparisons across the continuum of insulin responses within the spectrum of normoglycaemia and prediabetes. BMI (~24 kg/m2) was similar across insulin quartiles and in those with IFG and IGT. Despite similar glycaemic excursions, fasting insulin, triacylglycerols and cholesterol were elevated in quartile 4. Insulin sensitivity was lowest in quartile 4, and accompanied by increased insulin secretion and reduced insulin clearance. Individuals with IFG had similar insulin sensitivity and beta cell function to those in quartiles 2 and 3, but were more insulin sensitive than individuals in quartile 4. While individuals with IGT had a similar degree of insulin resistance to quartile 4, they exhibited a more severe defect in beta cell function. Plasma branched-chain amino acids were not elevated in quartile 4, IFG or IGT. Conclusions/interpretation: Hyperinsulinaemia within normoglycaemic young, non-obese adults manifests due to increased insulin secretion and reduced insulin clearance. Individual phenotypic characterisation revealed that the most hyperinsulinaemic were more similar to individuals with IGT than IFG, suggesting that hyperinsulinaemic individuals may be on the continuum toward IGT. Furthermore, plasma branched-chain amino acids may not be an effective biomarker in identifying hyperinsulinaemia and insulin resistance in young non-obese adults. [ABSTRACT FROM AUTHOR]

We explore the graded-formality and filtered-formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how these notions behave with respect to split injections, coproducts, direct products, as well as field extensions, and how they are inherited by solvable and nilpotent quotients. A key tool in this analysis is the 1-minimal model of the group, and the way this model relates to the aforementioned Lie algebras. We illustrate our approach with examples drawn from a variety of group-theoretic and topological contexts, such as finitely generated torsion-free nilpotent groups, link groups, and fundamental groups of Seifert fibered manifolds. [ABSTRACT FROM AUTHOR]

This paper describes the improved integrated minimal model for healthy subjects and patients with type 2 diabetes and the work leading up to this model. The original integrated minimal model characterizes simultaneously glucose and insulin following intravenous glucose tolerance test (IVGTT) in healthy subjects and provides apart from estimates of indices for insulin sensitivity (S i) and glucose effectiveness (S G), also full simulation capabilities. However, this model was developed using IVGTT data of total glucose and consequently, the model cannot separate hepatic glucose production from glucose disposal. By fitting the original integrated minimal model to IVGTT data of labelled and total glucose, we show that all parameter estimates of the glucose sub-model were significantly different between the fits, in particular, S G , which was ~3 fold higher with total, compared to labelled glucose. In addition, the time profiles of hepatic glucose production, obtained from the model, were unphysiological in most subjects. To correct these flaws, we developed the improved integrated minimal model based on the non-integrated, two-compartment minimal model. The improved integrated minimal model showed physiologically plausible dynamic time profiles of hepatic glucose production and all parameter estimates were compatible with those reported in original publication of the non-integrated minimal model. The integrated minimal model offers the benefits of the original integrated minimal model with simulation capabilities, in presence of endogenous insulin, combined with the benefits of the non-integrated minimal model, which accurately estimates the clinical indices of insulin sensitivity and glucose effectiveness. In addition, the improved integrated minimal model describes, apart from healthy subjects, also patients with type 2 diabetes. Unlabelled Image [ABSTRACT FROM AUTHOR]

We present homotopy classification of morphisms of differential graded algebras f : A → A ′ {f:A\to A^{\prime}} in terms of induced A ∞ {A_{\infty}} -algebra morphisms of corresponding minimal models { f i } : (H ⁢ (A) , { m i }) → (H ⁢ (A ′) , { m i ′ }) {\{f_{i}\}\kern-1.0pt:\kern-1.0pt(H(A),\{m_{i}\})\kern-1.0pt\to\kern-1.0pt(H(A% ^{\prime}),\{m^{\prime}_{i}\})}. [ABSTRACT FROM AUTHOR]