Some results on injectivity and multistationarity in chemical reaction networks

The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic results also mentioned. Several results appear in, or are close to, results in the literature. Here, we emphasise the connections between the results, and where possible, present elementary proofs which rely solely on basic linear algebra and calculus. A number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analysed in the paper

The inheritance of nondegenerate multistationarity in chemical reaction networks

We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction networks (CRNs). Specifically, when is it that we can deduce that a CRN admits MPNE or MPSE based on analysis of its subnetworks? Using basic techniques from analysis we are able to identify a number of situations where MPNE and MPSE are inherited as we build up a network. Some of these modifications are known while others are new, but all results are proved using the same basic framework, which we believe will yield further results. The results are presented primarily for mass action kinetics, although with natural, and in some cases immediate, generalisation to other classes of kinetics

Combinatorial approaches to Hopf bifurcations in systems of interacting elements

We describe combinatorial approaches to the question of whether families of real matrices admit pairs of nonreal eigenvalues passing through the imaginary axis. When the matrices arise as Jacobian matrices in the study of dynamical systems, these conditions provide necessary conditions for Hopf bifurcations to occur in parameterised families of such systems. The techniques depend on the spectral properties of additive compound matrices: in particular, we associate with a product of matrices a signed, labelled digraph termed a DSR^[2] graph, which encodes information about the second additive compound of this product. A condition on the cycle structure of this digraph is shown to rule out the possibility of nonreal eigenvalues with positive real part. The techniques developed are applied to systems of interacting elements termed “interaction networks”, of which networks of chemical reactions are a special case

Dislocation density and graphitization of diamond crystals

Two sets of diamond specimens compressed at 2 GPa at temperatures varying between 1060 K and 1760 K were prepared; one in which graphitization was promoted by the presence of water and another in which graphitization of diamond was practically absent. X-ray diffraction peak profiles of both sets were analyzed for the microstructure by using the modified Williamson-Hall method and by fitting the Fourier coefficients of the measured profiles by theoretical functions for crystallite size and lattice strain. The procedures determined mean size and size distribution of crystallites as well as the density and the character of the dislocations. The same experimental conditions resulted in different microstructures for the two sets of samples. They were explained in terms of hydrostatic conditions present in the graphitized samples

Pheochromocytoma – clinical manifestations, diagnosis and current perioperative management

Pheochromocytoma is a neuroendocrine tumor characterized by the excessive production of catecholamines (epinephrine, norepinephrine, and dopamine). The diagnosis is suspected due to hypertensive paroxysms, associated with vegetative phenomena, due to the catecholaminergic hypersecretion. Diagnosis involves biochemical tests that reveal elevated levels of catecholamine metabolites (metanephrine and normetanephrine). Functional imaging, such as 123I-metaiodobenzylguanidine scintigraphy (123I-MIBG), has increased specificity in identifying the catecholamine-producing tumor and its metastases. The gold-standard treatment for patients with pheochromocytoma is represented by the surgical removal of the tumor. Before surgical resection, it is important to optimize blood pressure and intravascular volume in order to avoid negative hemodynamic events

Microstructure of nanocrystalline diamond powders studied by powder diffractometry

High resolution x-ray diffraction peaks of diamond nanosize powders of nominal sizes ranging from 5 to 250 nm were analyzed and provided information on grain structure, average size of crystallites, and concentration of dislocations. Selected samples were heat treated at 1670 K at pressures 2.0 and 5.5 GPa or had surface modified by outgassing, heat treatment at vacuum conditions, and by controlled adsorption of gases. The apparent lattice parameter method was applied to characterize the structure of a shell-core model of nanosize particles. The multiple whole profile fitting provided information on crystallite sizes and density of dislocations. Population of dislocations increased with applied pressure, while strain and interplanar distances in the surface layers decreased. Adsorption of foreign gases on the grain surface modified the structure of the surface layers but did not affect dislocations near the center of the grains

The importance of early arthritis in patients with rheumatoid arthritis

Rheumatoid arthritis (RA) is a systemic inflammatory disorder that manifests predominantly in the synovial joint, where it causes a chronic inflammatory process, leading to early osteoarticular destructions. These destructions are progressive and irreversible, generating a significant functional deficiency. During the last years, the diagnostic approach of RA has focused on early arthritis. Early arthritis can develop into established RA or another established arthropathy, like systemic lupus erythematosus or psoriatic arthritis. It can have a spontaneous resolution or may remain undifferentiated for indefinite periods of time. The management of early arthritis has changed considerably in the past few years, under the influence of new concepts of diagnosis and new effective therapies. The treatment goal of early arthritis should now be the clinical remission and prevention of joint destruction. Methotrexate is the first line of therapy, used to treat early arthralgia and to reverse or limit impending exacerbation to RA. Biological treatment is used as a second line therapy in patients with severe disease who do not respond or have a contraindication to disease-modifying antirheumatic drugs (DMARDs). Patients with early arthritis should usually be identified and directed to rheumatologists to confirm the presence of arthritis, and to establish the correct diagnosis plus to initiate the proper treatment strategies

Cardio metabolic risk factors for atrial fibrillation in type 2 diabetes mellitus: Focus on hypertension, metabolic syndrome and obesity

Objective. Atrial fibrillation (AF) in type 2 diabetes mellitus (T2DM) has been little explored so far. However, there are several cardio metabolic risk factors for AF in T2DM patients, such as arterial hypertension, obesity or the metabolic syndrome. Our objective was to evaluate cardio metabolic risk factors for AF in T2DM patients. Methods. We studied the medical records of T2DM patients hospitalized in the Internal Medicine department of an emergency referral hospital in Bucharest, Romania. The study was observational, retrospective and carried out between January-June 2018. Results. The study group included 221 T2DM patients (with a mean age of 68.65 ± 10.64, ranging between 37-93 years): 116 women (52.49%; with a mean age of 70.53 ± 10.69, ranging between 37-93 years) and 105 men (47.51%; with a mean age of 66.57 ± 10.23, ranging between 38-91 years). 92 patients had AF (41.63%): 40 women (34.48%) and 52 men (49.52%). 180 patients (81.45%) were hypertensive: 103 women (88.79%) and 77 men (73.33%). 113 patients (51.13%) had metabolic syndrome: 58 women (50.00%) and 55 men (52.38%). 77 patients (34.84%) were obese: 45 women (38.79%) and 32 men (30.48%). AF patients associated obesity in 26 cases (28.26%), hypertension in 73 cases (79.35%) and metabolic syndrome in 56 cases (60.87%). Conclusions. Out of the study group, 92 T2DM patients (41.63%) had AF, men being more likely to suffer from AF than women (p=0.0288). Hypertension affected 180 patients (81.45%) and in greater proportion women vs. men (p=0.0051). The metabolic syndrome and obesity were discovered in 113 patients (51.13%) and 77 patients (34.84%), respectively, with no significant differences in terms of gender. In our research, the highest cardio metabolic risk factors for AF in T2DM were hypertension (OR = 3.6675) and the metabolic syndrome (OR = 3.3388)