A New Oxygen Containing Pyclen-Type Ligand as a Manganese(II) Binder for MRI and 52Mn PET Applications: Equilibrium, Kinetic, Relaxometric, Structural and Radiochemical Studies

A new pyclen-3,9-diacetate derivative ligand (H23,9-OPC2A) was synthesized possessing an etheric O-atom opposite to the pyridine ring, to improve the dissociation kinetics of its Mn(II) complex (pyclen = 3,6,9,15-tetraazabicyclo(9.3.1)pentadeca-1(15),11,13-triene). The new ligand is less basic than the N-containing analogue (H23,9-PC2A) due to the non-protonable O-atom. In spite of its lower basicity, the conditional stability of the [Mn(3,9-OPC2A)] (pMn = −log(Mn(II)), cL = cMn(II) = 0.01 mM. pH = 7.4) remains unaffected (pMn = 8.69), compared to the [Mn(3,9-PC2A)] (pMn = 8.64). The [Mn(3,9-OPC2A)] possesses one water molecule, having a lower exchange rate with bulk solvents (kex298 = 5.3 ± 0.4 ´ 107 s−1) than [Mn(3,9-PC2A)] (kex298 = 1.26´108 s−1). These mild differences are rationalized by density-functional theory (DFT) calculations. The acid assisted dissociation of [Mn(3,9-OPC2A)] is considerably slower (k1 = 2.81 ± 0.07 M−1 s−1) than that of the complexes of diacetates or bisamides of various 12-membered macrocycles and the parent H23,9-PC2A. The [Mn(3,9-OPC2A)] is inert in rat/human serum as confirmed by 52Mn labeling (nM range), as well as by relaxometry (mM range). However, a 600-fold excess of EDTA (pH = 7.4) or a mixture of essential metal ions, propagated some transchelation/transmetalation in 7 days. The H23,9-OPC2A is labeled efficiently with 52Mn at elevated temperatures, yet at 37 °C the parent H23,9-PC2A performs slightly better. Ultimately, the H23,9-OPC2A shows advantageous features for further ligand designs for bifunctional chelators.

On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system

Consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types, namely a parabolic equation and a hyperbolic equation. To establish the conditional stability for such a coupling system in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. By means of these two Carleman estimates, we finally prove the conditional stability for our inverse problem, provided the source in the elastic equation be known near the boundary and the solution be in a prior bound set. Due to the lack of information about the time derivative of wave field at final moment, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.

Adaptive control to actively damp bistabilities in highly interrupted turning processes using a hardware-in-the-loop simulator

Interruptions in turning make the process forces non-smooth and nonlinear. Smooth nonlinear cutting forces result in the process of being stable for small perturbations and unstable for larger ones. Re-entry after interruptions acts as perturbations making the process exhibit bistabilities. Stability for such processes is characterized by Hopf bifurcations resulting in lobes and period-doubling bifurcations resulting in narrow unstable lenses. Interrupted turning remains an important technological problem, and since experimentation to investigate and mitigate instabilities are difficult, this paper instead emulates these phenomena on a controlled hardware-in-the-loop simulator. Emulated cutting on the simulator confirms that bistabilities persist with lobes and lenses. Cutting in bistable regimes should be avoided due to conditional stability. Hence, we demonstrate the use of active damping to stabilize cutting with interruptions/perturbations. To stabilize cutting with small/large perturbations, we successfully implement an adaptive gain tuning scheme that adapts the gain to the level of interruption/perturbation. To facilitate real-time detection of instabilities and their control, we characterize the efficacy of the updating scheme for its dependence on the time required to update the gain and for its dependence on the levels of gain increments. We observe that higher gain increments with shorter updating times result in the process being stabilized quicker. Such results are instructive for active damping of real processes exhibiting conditional instabilities prone to perturbations.

Landweber Iterative Regularization Method for Identifying the Initial Value Problem of the Rayleigh–Stokes Equation

In this paper, we study an inverse problem to identify the initial value problem of the homogeneous Rayleigh–Stokes equation for a generalized second-grade fluid with the Riemann–Liouville fractional derivative model. This problem is ill posed; that is, the solution (if it exists) does not depend continuously on the data. We use the Landweber iterative regularization method to solve the inverse problem. Based on a conditional stability result, the convergent error estimates between the exact solution and the regularization solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule are given. Some numerical experiments are performed to illustrate the effectiveness and stability of this method.

Scalable Microgrid Process Model: The Results of an Off-Grid Household Experiment

The security of national energy systems as well as the transition to a low-carbon future are two hot topics of discussion in the international political arena. Research on the stability of centralized energy systems is currently focused on distributed generation. Developing a scalable microgrid model enabling its massive adoption is one of the safest and feasible ways to solve such problem. The paper aims to fill an existing gap regarding the operation model of microgrids that is a barrier for the large-scale integration of those in the conventional grid network. In the proposed approach the authors identified key processes to be considered when operating microgrids, in the conditions shown through an experimental (simulation) campaign. A three-phase research was performed: (1) systematic literature review to explore the management models of a stand-alone microgrid design and management; (2) a household experiment; and (3) a computer simulation of energy balance for a selected household. We identified eight key processes constituting a scalable microgrid: five core processes, two supporting processes, and one management process. Subsequently, we developed a map of these processes obtaining a microgrid process model for massive adoption. The model of processes can be considered as a repeatable pattern of conduct in the creation and maintenance of microgrids, which their future owners can follow. To support our literature findings, we performed an experiment and a computer simulation of three sub-processes of the (re)design of the infrastructure process: (1) wind turbine selection, (2) photovoltaic power plant selection, and (3) energy-storage selection. Results confirm conditional stability of the analyzed microgrid and the need for cyclical simulation exercises until unconditional stability is achieved. In terms of sustainability, to keep the microgrid permanently in a positive energy balance will require the implementation of all key processes.

Inverse Problems and Artificial Intelligence

В данной работе приведен анализ взаимосвязей теории обратных и некорректных задач и математических аспектов искусственного интеллекта. Показано, что при анализе вычислительных алгоритмов, которые условно можно отнести к вычислительному искусственному интеллекту (машинное обучение, природоподобные алгоритмы, методы анализа и обработки данных), возможно, а подчас и необходимо, использовать результаты и подходы, развитые в теории и численных методах решения обратных и некорректных задач, такие как регуляризация, условная устойчивость и сходимость, использование априорной информации, идентифицируемость, чувствительность, усвоение данных. This paper analyzes the relationship between the theory of inverse and incorrect problems and the mathematical aspects of artificial intelligence. It is shown that computational algorithms that can be categorized as computational artificial intelligence (machine learning, nature-like algorithms, data analysis and processing) can or should be analyzed with the approaches developed for the theory and numerical methods for solving inverse and incorrect problems. They are regularization, conditional stability and convergence, the use of a priori information, identifiability, sensitivity, data assimilation.

ON COMPACT 4TH ORDER FINITE-DIFFERENCE SCHEMES FOR THE WAVE EQUATION

We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the n-dimensional nonhomogeneous wave equation, n≥ 1. Their construction is accomplished by both the classical Numerov approach and alternative technique based on averaging of the equation, together with further necessary improvements of the arising scheme for n≥ 2. The alternative technique is applicable to other types of PDEs including parabolic and time-dependent Schro¨dinger ones. The schemes are implicit and three-point in each spatial direction and time and include a scheme with a splitting operator for n≥ 2. For n = 1 and the mesh on characteristics, the 4th order scheme becomes explicit and close to an exact four-point scheme. We present a conditional stability theorem covering the cases of stability in strong and weak energy norms with respect to both initial functions and free term in the equation. Its corollary ensures the 4th order error bound in the case of smooth solutions to the IBVP. The main schemes are generalized for non-uniform rectangular meshes. We also give results of numerical experiments showing the sensitive dependence of the error orders in three norms on the weak smoothness order of the initial functions and free term and essential advantages over the 2nd approximation order schemes in the non-smooth case as well.

Zinc Trafficking 1. Probing the Roles of Proteome, Metallothionein, and Glutathione

The cellular trafficking pathways that conduct zinc to its sites of binding in functional proteins remain largely unspecified. In this study, the hypothesis was investigated that non-specific proteomic binding sites serve as intermediates in zinc trafficking. Proteome from pig kidney LLC-PK1 cells contains a large concentration of such sites, displaying an average conditional stability constant of 1010-11, that are dependent on sulfhydryl ligands to achieve high affinity binding of zinc. As a result, the proteome competes effectively with induced metallothionein for Zn2+ upon exposure of cells to extracellular Zn2+ or during in vitro direct competition. The reaction of added Zn2+ bound to proteome with apo-carbonic anhydrase was examined as a potential model for intracellular zinc trafficking. The extent of this reaction was inversely dependent upon proteome concentration and under cellular conditions thought to be negligible. The rate of reaction was strictly first order in both Zn2+ and apo-carbonic anhydrase and also considered to be insignificant in cells. Adding the low molecular weight fraction of cell supernatant to the proteome markedly enhanced the speed of this reaction, a phenomenon dependent on the presence of glutathione. In agreement, inclusion of glutathione accelerated the reaction in a concentration-dependent manner. The implications of abundant high affinity binding sites for Zn2+ within the proteome are considered in relation to their interaction with glutathione in the efficient delivery of Zn2+ to functional binding sites and in the operation of fluorescent zinc sensors as a tool to observe zinc trafficking.