Analytical Condition Research Articles

Learning with uncertain inflation target

This paper studies the effects of a temporary increase in the inflation target in a model with adaptive learning and imperfect credibility of the central bank. In such a setup the private sector has to learn the model governing the economy and assess if the change in the interest rate is due to a standard interest rate shock or to a persistent shock to the inflation target. We find that the analytical condition that guarantees asymptotical E-stability under full credibility is the same that we obtain for the calibrated version of our model under imperfect credibility. Under full credibility the transition to the long-run equilibrium is faster and the variance of inflation is lower. Our results are consistent with the view that increasing the inflation target can be used as a policy instrument without unanchoring expectations.

Toroidal anapole with point magnetic dipoles

The role of multipolar expansion of the localized current is significant in a broad range of disciplines in the physics of nowadays. It is actively used in such problems as the design of nanoantennas in photonics or the description of exotic states of matter. The toroidal multipoles are the third group of multipoles which complements the electric and magnetic multipolar families. The investigation of toroidal multipoles is important because of their role in the formation of so-called anapole states, non-radiating sources. The further study showed that there are also exist the higher-order toroidal dipoles or mean-square radii, which are equivalent. Here we suggest the structure which consists of point magnetic dipoles and supports the toroidal anapole state, which is obtained with the destructive interference of electric toroidal dipole with the first mean-square radius of the electric toroidal dipole. We also present an analytical condition for toroidal anapole with this system of point magnetic dipoles placed in two circles.

Dynamical behaviour of single photobioreactor with variable yield coefficient

Scholars studied chemostat model with variable yield coefficient and a growth rate in Monod expression for the existence of natural oscillations in a bioreactor. This article explores dynamical properties of a similar simple model, analytically and numerically, in which the growth rate is a modified Haldane expression. Study includes determination of analytic conditions for existence of steady-state washout and no washout solutions, optimization of the performance of the bioreactor when no washout solution occurs, stability of the optimized steady state solution, and the ranges of the parameter values for which natural oscillations (Hopf Bifurcation) take place. Investigation shows that it is possible to gain natural oscillations for much smaller values of the substrate concentration compared to Monod-based earlier works.

Cherenkov radiation and scattering of external dispersive waves by two-color solitons

For waveguides with two separate regions of anomalous dispersion, it is possible to create a quasistable two-color solitary wave. In this paper, we consider how those waves interact with dispersive radiation, i.e., both the generation of Cherenkov radiation and the scattering of incident dispersive waves. We derive the analytic resonance conditions and verify them through numeric experiments. We also report incident radiation driving the internal oscillations of the soliton during the scattering process in the case of an intense incident radiation. We generalize the resonance conditions for the case of an oscillating soliton and demonstrate how one can use the scattering process to probe and excite an internal mode of two-color soliton molecules.

Aspects of univalence in holographic axion models

Univalent functions are complex, analytic (holomorphic) and injective functions that have been widely discussed in complex analysis. It was recently proposed that the stringent constraints that univalence imposes on the growth of functions combined with sufficient analyticity conditions could be used to derive rigorous lower and upper bounds on hydrodynamic dispersion relation, i.e., on all terms appearing in their convergent series representations. The results are exact bounds on physical quantities such as the diffusivity and the speed of sound. The purpose of this paper is to further explore these ideas, investigate them in concrete holographic examples, and work towards a better intuitive understanding of the role of univalence in physics. More concretely, we study diffusive and sound modes in a family of holographic axion models and offer a set of observations, arguments and tests that support the applicability of univalence methods for bounding physical observables described in terms of effective field theories. Our work provides insight into expected ‘typical’ regions of univalence, comparisons between the tightness of bounds and the corresponding exact values of certain quantities characterising transport, tests of relations between diffusion and bounds that involve chaotic pole-skipping, as well as tests of a condition that implies the conformal bound on the speed of sound and a complementary condition that implies its violation.

Existence Conditions and Stability for the Power-Flow of DC Micro-Grids With CPLs

The power flow equation of the DC micro-grid with distributed generations (DGs) under MPPT control (MPPT-DGs) and constant power loads (CPLs) is a strongly coupled nonlinear equation, which is difficult to solve. Moreover, the negative impedance of CPL tends to make the system unstable. This paper analyzes the existence conditions and stability of the power-flow of DC micro-grids, which contain distributed generations (DGs) under droop control (Droop-DGs), MPPT-DGs, and constant power loads (CPLs). To begin with, the power-flow equation of the DC micro-grid is derived. Next, by constructing a contraction mapping, the analytic solvability condition of the nonlinear power-flow equation is obtained based on Banach’s fixed-point theorem. Under the proposed solvability condition, an equivalent linearized model around the equilibrium is developed to analyze the stability of the DC micro-grid. By analyzing the eigenvalues of the Jacobian matrix, we have obtained a robust stability condition of the equilibrium. Finally, simulation results verify the presented results.

Optimal Secondary Frequency Regulation With ON-OFF Loads in Power Networks

Load-side participation can provide support to the power network by appropriately adapting the demand when required. In addition, it enables an economically improved power allocation. In this study, we consider the problem of providing an optimal power allocation among generation and ON-OFF loads within the secondary frequency control timeframe. In particular, we consider a mixed-integer optimization problem, which ensures that the secondary frequency control objectives (i.e., generation–demand balance and the frequency attaining its nominal value at steady state) are satisfied. We present analytic conditions on the generation and ON-OFF load profiles such that an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -optimality interpretation of the steady-state power allocation is obtained, providing a nonconservative value for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> . Moreover, we develop a hierarchical control scheme that provides ON-OFF load values that satisfy the proposed conditions. We study the interaction of the proposed control scheme with the physical dynamics of the power network and provide analytic stability guarantees. Our results are verified with numerical simulations on the Western System Coordinating Council (WSCC) 9-bus system and the Northeast Power Coordinating Council (NPCC) 140-bus system, where it is demonstrated that the proposed algorithm yields a close to optimal power allocation.

An introduction to model implied instrumental variables using two stage least squares (MIIV-2SLS) in structural equation models (SEMs).

Structural equation models (SEMs) are widely used to handle multiequation systems that involve latent variables, multiple indicators, and measurement error. Maximum likelihood (ML) and diagonally weighted least squares (DWLS) dominate the estimation of SEMs with continuous or categorical endogenous variables, respectively. When a model is correctly specified, ML and DWLS function well. But, in the face of incorrect structures or nonconvergence, their performance can seriously deteriorate. Model implied instrumental variable, two stage least squares (MIIV-2SLS) estimates and tests individual equations, is more robust to misspecifications, and is noniterative, thus avoiding nonconvergence. This article is an overview and tutorial on MIIV-2SLS. It reviews the six major steps in using MIIV-2SLS: (a) model specification; (b) model identification; (c) latent to observed (L2O) variable transformation; (d) finding MIIVs; (e) using 2SLS; and (f) tests of overidentified equations. Each step is illustrated using a running empirical example from Reisenzein's (1986) randomized experiment on helping behavior. We also explain and illustrate the analytic conditions under which an equation estimated with MIIV-2SLS is robust to structural misspecifications. We include additional sections on MIIV approaches using a covariance matrix and mean vector as data input, conducting multilevel SEM, analyzing categorical endogenous variables, causal inference, and extensions and applications. Online supplemental material illustrates input code for all examples and simulations using the R package MIIVsem. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Frequency Regulation With Thermostatically Controlled Loads: Aggregation of Dynamics and Synchronization

Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency-control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior, which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e., simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this article, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions, which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared with existing implementations.

Neo-Fisherian Policies and Liquidity Traps

Liquidity traps can be either fundamental or confidence-driven. In a simple, unified New Keynesian framework, I provide the analytical condition for the latter’s prevalence: enough shock persistence and endogenous intertemporal amplification of future (“news”) shocks, making income effects dominate substitution effects. The same condition allows neo-Fisherian effects (expansionary-inflationary interest rate increases), which are thus inherent in confidence traps. Several monetary and fiscal policies (forward guidance, interest rate increases, public spending, labor tax cuts) have diametrically opposed effects according to the trap variety. This duality provides testable implications to disentangle between trap types; that is essential, for optimal policies are also conflicting across trap varieties. (JEL E12, E31, E32, E43, E52, E62)

Quantitative determination of plant hormones and derivatives in biogas slurry using on-line solid phase extraction with high performance liquid chromatography (On-Line SPE HPLC)

A novel method using on-line solid phase extraction coupled with high performance liquid chromatography (On-line SPE HPLC) was developed to measure three important plant hormones and two indole derivatives in the biogas slurry. These measured substances include abscisic acid (ABA), gibberellins (GA), indoleacetic acid (IAA), tryptophan (TRP) and skatole (IMD), respectively. This method could continuously perform extraction of ABA, GA, IAA, TRP and IMD from different concentrations of biogas slurry samples without complicated pretreatment avoiding lost, and then the extracts were analyzed by high performance liquid chromatography (HPLC). After optimized the analytical condition, a baseline separation of three plant hormones and two indole derivatives was accomplished within 35 mins. The results showed excellent linearity (R2 values of 0.9930-0.9999) and intra- and inter-day precisions (in the range of 3.8-7.2% and 3.9-7.5%), respectively. The limits of detection and quantification were in the range of 0.16-0.47 μg·mL-1 and 0.53-1.57 μg·mL-1, respectively. The determination performance was satisfactory with the proposed method. The results showed that the developed method was suitable for analysis of trace plant hormones in the biogas slurry.

Quantitative determination of plant hormones and derivatives in biogas slurry using on-line solid phase extraction with high performance liquid chromatography (On-Line SPE HPLC)

A novel method using on-line solid phase extraction coupled with high performance liquid chromatography (On-line SPE HPLC) was developed to measure three important plant hormones and two indole derivatives in the biogas slurry. These measured substances include abscisic acid (ABA), gibberellins (GA), indoleacetic acid (IAA), tryptophan (TRP) and skatole (IMD), respectively. This method could continuously perform extraction of ABA, GA, IAA, TRP and IMD from different concentrations of biogas slurry samples without complicated pretreatment avoiding lost, and then the extracts were analyzed by high performance liquid chromatography (HPLC). After optimized the analytical condition, a baseline separation of three plant hormones and two indole derivatives was accomplished within 35 mins. The results showed excellent linearity (R2 values of 0.9930-0.9999) and intra- and inter-day precisions (in the range of 3.8-7.2% and 3.9-7.5%), respectively. The limits of detection and quantification were in the range of 0.16-0.47 μg·mL-1 and 0.53-1.57 μg·mL-1, respectively. The determination performance was satisfactory with the proposed method. The results showed that the developed method was suitable for analysis of trace plant hormones in the biogas slurry.

Copositivity for a Class of Fourth-Order Symmetric Tensors Given by Scalar Dark Matter

The mathematical model of general scalar potentials may be written as a fourth-order symmetric tensor with a particular structure in particle physics. In this paper, we mainly discuss the copositivity of a class of tensors defined by the scalar dark matter with the Higgs doublet and an inert doublet and a complex singlet. With the help of its structure, we obtain the necessary and sufficient conditions, which attains the analytic conditions required by the physical problems. At the same time, this work presents how to determine a unique solution of the tensor complementarity problem with a parameter.

Bubbles in discrete-time models

We introduce a new definition of bubbles in discrete-time models based on the discounted stock price losing mass under an equivalent martingale measure at some finite drawdown. We provide equivalent probabilistic characterisations of this definition and give examples of discrete-time martingales that are bubbles and others that are not. In the Markovian case, we provide sufficient analytic conditions for the presence of bubbles. We also show that the existence of bubbles is directly linked to the existence of a non-trivial solution to a linear Volterra integral equation of the second kind involving the Markov kernel. Finally, we show that our definition of bubbles in discrete time is consistent with the strict local martingale definition of bubbles in continuous time in the sense that a properly discretised strict local martingale in continuous time is a bubble in discrete time.

Extension of the Observability Rank Condition to Time-Varying Nonlinear Systems

This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors.

Applicable Condition of the Approximate Parameter Estimation Method of the Generalized Gamma Distribution

The generalized Gamma distribution ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{G}\Gamma \text{D}$ </tex-math></inline-formula> ) has been found accurate for modeling synthetic aperture radar (SAR) data. To facilitate the practical applications of this model, an approximate method for estimating the parameters in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{G}\Gamma \text{D}$ </tex-math></inline-formula> was recently given by Stacy (1962) and discussed by Krylov et al. (2013) and Abramowitz and Stegun (1972), in which the applicable condition of the method is restrictive and incorrect. This article further derives the analytical condition of the applicability of the method. Examples of theoretical analysis and simulations verify the correctness of the derivations.

Conditions for global minimum in the A_4 symmetric 3HDM

There has been a great interest in three Higgs doublet models (3HDM) symmetric under an exact A_4 symmetry. We provide the complete analytic necessary and sufficient conditions for a point to be the global minimum along the neutral directions in such models, discussing many of the subtleties involved. We also present a number of numerical examples, to highlight those issues. We then turn to the directions which break electric charge, presenting a safe analytical sufficient condition for bounded from below (BFB) potentials. Based on extensive numerical simulations, we discuss one conjecture on BFB along charge breaking directions.

Polarity-driven laminar pattern formation by lateral-inhibition in 2D and 3D bilayer geometries

Abstract Fine-grain patterns produced by juxtacrine signalling have previously been studied using static monolayers as cellular domains. However, analytic results are usually restricted to a few cells due to the algebraic complexity of non-linear dynamical systems. Motivated by concentric patterning of Notch expression observed in the mammary gland, we combine concepts from graph and control theory to represent cellular connectivity and behaviour. The resulting theoretical framework allows us to exploit the symmetry of multicellular bilayer structures in 2D and 3D, thereby deriving analytical conditions that drive the dynamical system to form laminar patterns, consistent with the formation of cell polarity by activator localization. Critically, the patterning conditions are independent of the precise dynamical details, thus the framework allows for generality in understanding the influence of cellular geometry and signal polarity on patterning using lateral-inhibition systems. Applying the analytic conditions to mammary organoids suggests that intense cell signalling polarity is required for the maintenance of stratified cell types within a static bilayer using a lateral-inhibition mechanism. Furthermore, by employing 2D and 3D cell-based models, we highlight that the cellular polarity conditions derived from static domains can generate laminar patterning in dynamic environments. However, they are insufficient for the maintenance of patterning when subjected to substantial morphological perturbations. In agreement with the mathematical implications of strict signalling polarity induced on the cells, we propose an adhesion-dependent Notch-Delta biological process that has the potential to initiate bilayer stratification in a developing mammary organoid.

Understanding lipase assays in the diagnosis of pancreatitis in veterinary medicine.

Pancreatitis commonly occurs in humans, dogs, and cats. For both veterinary and human health-care professionals, measurement of serum pancreatic lipase concentration or activity provides useful support for a diagnosis of pancreatitis. In this Currents in One Health manuscript, we will discuss commonly used lipase assays in veterinary medicine, namely catalytic colorimetric and immunological lipase assays. We highlight potential diagnostic pitfalls associated with analytical specificity, assay validation, and sample condition interferences. Catalytic lipase assays may detect extrapancreatic lipases. In addition, we propose a decision tree for interpretation of lipase assays in the context of a clinical patient.

Effects of Different Extraction Methods on Vanilla Aroma.

To establish the analytic conditions for examining the aroma quality of vanilla pods, we compared different extraction methods and identified a suitable option. We utilized headspace solid-phase microextraction (HS-SPME), steam distillation (SD), simultaneous steam distillation (SDE) and alcoholic extraction combined with gas chromatography (GC) and gas chromatography–mass spectrometry (GC-MS) to identify volatile components of vanilla pods. A total of 84 volatile compounds were identified in this experiment, of which SDE could identify the most volatile compounds, with a total of 51 species, followed by HS-SPME, with a total of 28 species. Ten volatile compounds were identified by extraction with a minimum of 35% alcohol. HS-SPME extraction provided the highest total aroma peak areas, and the peak areas of aldehydes, furans, alcohols, monoterpenes and phenols compounds were several times higher than those of the other extraction methods. The results showed that the two technologies, SDE and HS-SPME, could be used together to facilitate analysis of vanilla pod aroma.