Analytical Condition Research Articles

Quantifying the impact of the Si/O interface in CCSN explosions using the Force Explosion Condition

Abstract The explosion mechanism of a core-collapse supernova is a complex interplay between neutrino heating and cooling (including the effects of neutrino-driven convection), the gravitational potential, and the ram pressure of the infalling material. To analyze the post-bounce phase of a supernova, one can use the generalized Force Explosion Condition (FEC+), which succinctly formalizes the interplay among these four phenomena in an analytical condition, consistent with realistic simulations. In this paper, we use the FEC+ to study the post-bounce phase of 341 spherically symmetric simulations, where convection is included through a time-dependent mixing length approach. We find that the accretion of the Si/O interface through the expanding shock can significantly change the outcome of the supernova by driving the FEC+ above the explosion threshold. We systematically explore this by (i) artificially smoothing the pre-supernova density profile, and (ii) artificially varying the mixing length. In both cases, we find that large-enough density contrasts at the Si/O interface lead to successful shock revival only if the FEC+ is already close to the explosion threshold. Furthermore, we find that the accretion of the Si/O interface has a substantial effect on the critical condition for supernova explosions, contributing between 5 % and 15 %, depending on how pronounced the density contrast at the interface is. Earlier studies showed that convection affects the critical condition by 25–30 %, which demonstrates that the accretion of the Si/O interface through the shock can play a nearly comparable role in influencing shock dynamics.

Multichannel Bioelectronic Sensing: Binary Encoding of Environmental Contaminants

Environmental water contamination from natural and synthetic chemicals is a pressing global issue. Addressing this requires the development of portable, selective, and accurate sensors. Biosensors, particularly whole-cell bioelectronic sensors, are promising due to their ability to convert chemical signals into electrical signals via extracellular electron transfer (EET) pathways. However, these sensors typically employ a single electron transfer pathway as an electrochemical channel, limiting them to the detection of a single analyte (Atkinson et al. 2022).To expand the information content, we have developed a multichannel sensor where different chemicals regulate distinct EET pathways within a single Escherichia coli cell. One channel utilizes the flavin synthesis pathway from Bacillus subtilis (Yang Yun et al. 2017) and is controlled by a cadmium-responsive promoter (Hui et al. 2021). Another channel, the Mtr pathway from Shewanella oneidensis (Ross Daniel E. et al. 2007), is controlled by an arsenite-responsive promoter (Chen et al. 2019) through activation of cytochrome CymA expression. We exploit the differing redox potentials of these two EET pathways (Kracke, Vassilev, and Krömer 2015) to develop a redox-potential-dependent algorithm that efficiently converts analog current curves into 2-bit binary outputs. This enables our bioelectronic sensor to detect and differentiate heavy metals at EPA limits. When deployed in complex environmental water samples with lower electroactivities, our sensor effectively and accurately encodes 2-bit binary signals across various analyte conditions. Thus, our multichannel bioelectronic sensor advances the field through simultaneous detection of different chemicals by a single cell, significantly expanding information transmission from EET and helping to safeguard human and environmental health.

An optimization protocol of the volatile organic compounds analysis in earwax samples for untargeted volatilomics

Recent studies have highlighted the potential of earwax or cerumen, a non-conventional biomatrix, in volatilomics research as a valuable matrix for disease biomarker discovery. Despite that, there are still gaps in using non-conventional biomatrices in metabolomics research. In this sense, this study aimed to elucidate the main analytical factors involved in the extraction and analysis of volatile organic compounds (VOCs) in cerumen by headspace/gas chromatography-mass spectrometry (HS/GC–MS) using Design of Experiments (DoE) approaches. Furthermore, we present a repeatability study for the proposed method as a quality control process for cerumenomic assays. By applying factorial designs, it was possible to determine that the sample mass, splitless injector sampling time, headspace extraction time, headspace extraction temperature, injection volume, and vial volume were significant factors for the cerumen VOC analysis by HS/GC–MS. Throughout univariate and multivariate statistical approaches, we demonstrate that different analytical conditions lead to distinct chemical profiling of a sample. The most suitable analytical condition was determined after the optimization steps, and the proposed method's repeatability was evaluated by the metabolites coefficient variation (CV) calculation. Seventy-one earwax VOCs reached a CV considered adequate for untargeted metabolomics studies via GC–MS. In summary, this study describes a protocol for analysis optimization of a non-conventional biomatrix and also reports a quality control process in untargeted volatilomics assays using earwax. Our findings shed light on the potential of using earwax in volatolomic studies and establish analytical criteria to ensure quality in cerumenomic assays.

Dissipation of AGN Jets in a Clumpy Interstellar Medium

Accreting supermassive black holes frequently power jets that interact with the interstellar medium (ISM)/circumgalactic medium, regulating star formation in the galaxy. Highly supersonic jets launched by active galactic nuclei (AGN) power a cocoon that confines them and shocks the ambient medium. We build on the models of narrow conical jets interacting with a smooth ambient medium, including the effect of dense clouds, which are an essential ingredient of a multiphase ISM. The key physical ingredient of this model is that the clouds along the supersonic jet beam strongly decelerate the jet head but the subsonic cocoon easily moves around the clouds without much resistance. We propose scalings for important physical quantities—cocoon pressure, head and cocoon speed, and jet radius. For the first time, we obtain the analytic condition on the ambient medium’s clumpiness for the jet to dissipate within the cocoon and verify it with numerical simulations of conical jets interacting with a uniform ISM with embedded spherical clouds. A jet is defined to be dissipated when the cocoon speed exceeds the speed of the jet head. We compare our models with more sophisticated numerical simulations and direct observations of jet–ISM interaction (e.g., quasar J1316+1753), and we discuss implications for the Fermi/eROSITA bubbles. Our work also motivates effective subgrid models for AGN jet feedback in a clumpy ISM unresolved by the present generation of cosmological galaxy formation simulations.

Electrothermal filamentation of igniting plasmas.

Dense, hot plasmas are susceptible to the electrothermal instability: a collisional process which permits temperature perturbations in electron currents to grow. It is shown here that linearizing a system comprised of two opposing currents and a mobile ion background as three distinct fluids yields unstable modes with rapid growth rates (∼10^{13}s^{-1}) for wavenumbers below a threshold k_{th}. An analytical threshold condition is derived, this being surpassed for typical hot-spot and shell parameters. Particle-in-cell simulations successfully benchmark the predicted growth rates and threshold behavior. Electrothermal filamentation within the shell will impact the burn wave propagation into the cold fuel and resulting burn dynamics.

Canonical torsor bundles of prescribed rational functions on complex curves

The prescribed rational functions constitute a subset of rational functions satisfying certain symmetry and analyticity conditions. Over a smooth complex curve [Formula: see text], we construct explicitly a bundle [Formula: see text] with values in the prescribed rational functions. An intrinsic coordinate-independent formulation (the main result of the paper, Proposition 1) for such bundles is given. The construction presented in this paper is useful for studies of the canonical cosimplicial cohomology of infinite-dimensional Lie algebras on smooth manifolds, as well as for the purposes of conformal field theory and the theory of foliations.

Dynamics and bifurcations in genetic circuits with fibration symmetries.

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

A Novel Apparatus for the Fully Automated Extraction and Online Liquid Chromatographic Analysis of Solid Environmental Samples: Application to the Pressurized Hot Water Extraction of Pharmaceuticals in Soil.

A new self-assembled apparatus for the extraction of solid samples was designed and implemented to perform a recirculated pressurized hot water extraction (R-PHWE) directly coupled to liquid chromatography-tandem mass spectrometry. To investigate the potential of this new extraction apparatus, 34 target pharmaceutical compounds were analyzed in loam, silt-loam, and silty-clay-loam soils. The target analytes were characterized by heterogeneous physicochemical properties (e.g., -1.60 ≤ log D ≤ 5.91 at pH = 7.2, i.e., at the mean pH values of the three soils). Design of experiments (DoE) was used to identify the best extraction conditions for the target analytes by studying temperature, pressure, and number of extraction cycles. The results of DoE optimization pointed out the significant influence of the number of cycles on recovery. The application of DoE set point to the three reference soils provided recoveries ≥60% for 21-25 out the 34 target analytes, depending on soil. Good recovery precision (<25%) and moderate suppressive matrix effect (≤40%) were found for most target analytes, regardless of the soil considered. The optimized R-PHWE procedure evidenced statistically higher recoveries for 16 out of 34 target analytes when compared to conventional off-line dynamic PHWE.

On prime end distortion estimates of mappings with the Poletsky condition in domains with the Poincar´e inequality

This article is devoted to the study of mappings with bounded andfinite distortion defined in some domain of the Euclidean space. Weconsider mappings that satisfy some upper estimates for thedistortion of the modulus of families of paths, where the order ofthe modulus equals to $p,$ $n-1&lt;p\leqslant n.$ The main problemstudied in the manuscript is the investigation of the boundarybehavior of such mappings, more precisely, the distortion of thedistance under mappings near boundary points. The publication isprimarily devoted to definition domains with ``bad boundaries'', inwhich the mappings not even have a continuous extension to theboundary in the Euclidean sense. However, we introduce the conceptof a quasiconformal regular domain in which the specified continuousextension is valid and the corresponding distance distortionestimates are satisfied; however, both must be understood in thesense of the so-called prime ends. More precisely, such estimateshold in the case when the mapping acts from a quasiconformal regulardomain to an Ahlfors regular domain with the Poincar\'e inequality.The consideration of domains that are Ahlfors regular and satisfythe Poincar\'e inequality is due to the fact that, lower estimates forthe modulus of families of paths through the diameter of thecorresponding sets hold in these domains. (There are the so-calledLoewner-type estimates). We consider homeomorphisms and mappingswith branching separately. The main analytical condition under whichthe results of the paper were obtained is the finiteness of theintegral averages of some majorant involved in the defining modulusinequality under infinitesimal balls. This condition includes thesituation of quasiconformal and quasiregular mappings, because forthem the specified majorant is itself bounded in a definitiondomain. Also, the results of the article are valid for more generalclasses for which Poletsky-type upper moduli inequalities aresatisfied, for example, for mappings with finite length distortion.

Development and Validation of Ultra-Performance Liquid Chromatography (UPLC) Method for Simultaneous Quantification of Hydrochlorothiazide, Amlodipine Besylate, and Valsartan in Marketed Fixed-Dose Combination Tablet

Fixed-dose combination therapy is considered a practical approach in the treatment of various diseases, as it can simultaneously target different mechanisms of action that achieve the required therapeutic efficacy through a synergistic effect. A combination of hydrochlorothiazide (HTZ), amlodipine (AMD), and valsartan (VLS) has been created for the treatment of hypertension. Therefore, the aim of this study was to develop an optimized UPLC method for the simultaneous quantification of this combination. A DoE at a level of 32 was used to investigate the effects of column temperature (20, 30, and 40 °C) and formic acid concentration (0.05, 0.15, and 0.25%) on the retention time of each active pharmaceutical ingredient (API), the peak area, and the peak symmetry, as well as the resolution between HTZ-AMD and AMD-VLS peaks. The optimized analytical method was validated and used to extract the three APIs from the marketed product. The optimized analytical condition with a column temperature of 27.86 °C and a formic acid concentration of 0.172% showed good separation of the three APIs in 1.62 ± 0.006, 3.59 ± 0.002, and 3.94 ± 0.002 min for HTZ, AMD, and VST, respectively. The developed method was linear with the LOQ for a HTC, AMD, and VST of 0.028, 0.038, and 0.101 ppm, respectively. Moreover, the developed assay was sustainable and robust, with an RSD % of less than 2%. The application of this method in the extraction of HTZ, AMD, and VST from the Exforge® marketed product showed good separation with a measurable drug content of 23.5 ± 0.7, 9.68 ± 0.1, and 165.2 ± 5.2 mg compared to the label claims of 25/10/160 for HTZ, AMD, and VST, respectively.

Detangling the quantum tapestry of intrachannel interference in below-threshold nonsequential double ionization with few-cycle laser pulses

We perform a systematic analysis of single-channel quantum interference in laser-induced nonsequential double ionization with few-cycle pulses, using the strong-field approximation. We focus on a below-threshold intensity for which the recollision-excitation with subsequent ionization (RESI) mechanism is prevalent. We derive and classify several analytic interference conditions for single-channel RESI in arbitrary driving fields and address specific issues for few-cycle pulses. Since the cycles in a short pulse are no longer equivalent, there are several events whose dominance varies. We quantify this dominance for single excitation channels by proposing a dominance parameter. Moreover, there will be many types of superimposed interference fringes that must be taken into consideration. We find an intricate tapestry of patterns arising from phase differences related to symmetrization, temporal shifts and a combination of exchange and event interference. Published by the American Physical Society 2024

Fabric phase sorptive extraction increases the accuracy of liquid chromatography-fluorescence detection of zearalenone in food samples

ABSTRACT The accuracy of mycotoxins detection in the food samples has always been controversial and more sensitive methods help better regulatory activities and, therefore, the quality of final products. Zearalenone is a toxic substance from mycotoxins mainly produced by Fusarium fungi that has proven endocrine effects and is potentially carcinogenic. This research aimed to apply the fabric phase sorptive extraction (FPSE) technique to the liquid chromatography- fluorescence detection method to increase the sensitivity and accuracy of zearalenone extraction and determination in food samples. Applying graphene nanoparticles in the sol-gel process modifies the method depending on the amount of nanoparticles, volume and type of the back-extraction solvent, sample pH, ionic strength, and back-extraction time, which are all considered and investigated. At analytical conditions, the limit of quantification (LOQ) 16.57 and detection (LOD) of 4.97 ng/mL were observed. The method’s accuracy was determined by three spiking levels of 100, 150, and 200 ng/mL in the real samples. The mean recovery percentage in wheat were 61.69, 70.56, and 97.95%, and in the rice, 58.13, 66.00, and 102.59, respectively. The average percentages of the relative standard deviation of the instrument for intra-and inter-laboratory repeatability were less than 1.7%. This work provided a superior analytical condition to the conventional detection procedures in food safety laboratories.

Bohr–Sommerfeld quantization condition for self-adjoint Dirac operators

We study the eigenvalue problem for a self-adjoint 1D Dirac operator. It is known that, near an energy level where the square of the potential makes a simple well, the eigenvalues are approximated by a Bohr–Sommerfeld type quantization rule. A remarkable difference from the Schrödinger case appears in the Maslov correction term. This fact was recently found by Hirota [Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov–Shabat operator, J. Math. Phys. 58 (2017) 102–108] under the analyticity condition of the potential using a complex WKB method. In this paper, we approach this problem with a microlocal technique focusing on the asymptotic behavior of the eigenfunction along the characteristic set to generalize the result to [Formula: see text] potentials.

The Fourier spectrum and sumset type problems

AbstractWe introduce and study the Fourier spectrum which is a continuously parametrised family of dimensions living between the Fourier dimension and the Hausdorff dimension for both sets and measures. We establish some fundamental theory and motivate the concept via several applications, especially to sumset type problems. For example, we study dimensions of convolutions and sumsets, and solve the distance set problem for sets satisfying certain Fourier analytic conditions.

A mathematical model to study low-dose metronomic scheduling for chemotherapy

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient’s body.

Energy-Efficient Distributed Formation Control of Sampled-Data Multiagent Systems With Packet Losses.

This article investigates an energy-efficient formation control problem for multiagent systems with sampled data and random packet losses. A Bernoulli stochastic variable is used to describe packet losses, which is defined relative to the transmission energy consumed by antennas. A distributed sampled-data formation control law is designed and some analytic sufficient conditions on the formation control are derived. It is revealed that the sampling period, control parameters, network topology, as well as the transmission energy used by sensors impose inherent limitations in achieving the formation. Also, a method for searching the minimum allowable transmission energy is presented. Finally, numerical simulations are shown for illustration and verification.

Nonlinear spreading behavior across multi-platform social media universe.

Understanding how harmful content (mis/disinformation, hate, etc.) manages to spread among online communities within and across social media platforms represents an urgent societal challenge. We develop a non-linear dynamical model for such viral spreading, which accounts for the fact that online communities dynamically interconnect across multiple social media platforms. Our mean-field theory (Effective Medium Theory) compares well to detailed numerical simulations and provides a specific analytic condition for the onset of outbreaks (i.e., system-wide spreading). Even if the infection rate is significantly lower than the recovery rate, it predicts system-wide spreading if online communities create links between them at high rates and the loss of such links (e.g., due to moderator pressure) is low. Policymakers should, therefore, account for these multi-community dynamics when shaping policies against system-wide spreading.

Distributed Nash Equilibrium Seeking and Disturbance Rejection for High-Order Integrators Over Jointly Strongly Connected Switching Networks.

In this article, we study the problem of Nash equilibrium (NE) seeking of N -player games with high-order integrator agents over jointly strongly connected networks. The same problem was studied recently over static, undirected, and connected networks. Since a jointly strongly connected network can be directed and disconnected at every time instant, our result strictly includes the existing results as special cases. Moreover, in addition to some analytic conditions on the payoff functions, the existing results also rely on the satisfaction of an inequality involving some Lipschitz constant and the smallest nonzero eigenvalue of the Laplacian of the network graph. By adopting a different approach, our result does not rely on the satisfaction of this inequality. Furthermore, our result can also be extended to the case where the additive disturbances are imposed on the input of each agent. Our design is illustrated by two numerical examples.

Prefrontal engagement predicts the effect of museum visit on psychological well-being: an fNIRS exploration.

Recent research suggests that museum visits can benefit psychological well-being by reducing symptoms of stress and anxiety. However, these reported relaxing effects remain inconsistent between studies. Shedding light on the underlying cerebral mechanisms of museum visits might support a better understanding of how it affects psychological well-being. This study aimed to investigate the prefrontal engagement evoked by artwork analysis during a museum visit and to determine if these prefrontal substrates are associated with the museum's effect on psychological well-being in older adults. Nineteen adults aged between 65 and 79, toured a Baroque-style exhibit at the Montreal Museum of Fine Arts for approximately 20 minutes while equipped with a near-infrared spectroscopy system measuring the prefrontal cortex's hemodynamic activity. For each painting, participants received the instruction to either (1): analyze the painting and produce a personal interpretation of its signification (analytic condition) or (2) visualize the painting without any specific thoughts (visualization condition). Questionnaires measuring stress, anxiety, and well-being were administered before and after the visit. Sixteen older women (71.5 ± 4 years) were included in the analyses. Results showed that, at the group level, the analytic condition was associated with an increased activation pattern in the left ventrolateral prefrontal region, typically related to attentional processes (not observed in the visualization condition). The activation associated with the analytic condition predicted pre-/post-visit reductions in self-reported anxiety and stress in the sample of older women. These observations suggest that the level of engagement of attentional processes during artwork analysis may play a major role in the effect of a museum's visit on self-reported symptoms of anxiety.

Analytic States in Quantum Field Theory on Curved Spacetimes

We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh–Schlieder property hold with respect to states satisfying a weak form of microlocal analyticity condition. The former means the von Neumann algebra of observables of a spacelike tube equals the von Neumann algebra of observables of a significantly bigger region that is obtained by deforming the boundary of the tube in a timelike manner. This generalizes theorems by Araki (Helv Phys Acta 36:132–139, 1963) and Borchers (Nuovo Cim (10) 19:787–793, 1961) to curved spacetimes.