Cutoff Function Research Articles

Electro-characteristics of Myocardial Pouches and Reduction of the Frequency of Steam Pops During Radiofrequency Ablation.

Background: Radiofrequency ablation (RFA) effectively treats arrhythmia. Steam pop (SP) is a dangerous complication of RFA, which can lead to pericardial tamponade or even death.Objective: This study aimed to explore the electro-characteristics of myocardial pouches, and the relationship between SP, pouch, and impedance.Methods: Swine myocardium was divided into the pouch group and smooth myocardium group. Continuous RFA at 50 W was applied. The initial impedance reduction within the first 3 s of ablation and the time from the start of ablation to SP were recorded. After enabling the delta impedance cutoff function, RFA was performed at different percentage of delta impedance (PDI) cutoff thresholds.Results: The impedance was higher for the pouch myocardium compared to the smooth myocardium (123.22 ± 8.63 Ω and 95.75 ± 4.75 Ω, respectively; p < 0.001). The RFA duration before SPs was shorter in the pouch group compared to the smooth myocardium group [9 s (interquartile range, IQR: 6.25–13 s) and 33 s (IQR: 26.25–40.75 s), respectively; p < 0.001]. Within the first 3 s of RFA, impedance reduction (24.65 ± 6.57 Ω and 12.78 ± 3.35 Ω, respectively; p < 0.001) and PDI [19.18% (IQR: 16.39–24.20%) and 12.96% (IQR: 11.17–14.39%), respectively; p < 0.001] were greater in the pouch group compared to the smooth myocardium group. A PDI of 15% and delta time of 3 s effectively reduced the frequency of SPs without seriously affecting RFA use.Conclusion: SPs occur more frequently in the pouch area during RFA. Appropriate delta impedance cutoff settings (PDI: 15%; delta time: 3 s) can reduce the frequency of SPs and improve the RFA safety.

Massive Cerebral Air Embolism Due to Aortography

Though rare, air embolism as a serious complication may occur in patients undergoing coronary angiography and aortography. If gas embolism is diagnosed, hyperbaric oxygen therapy should be initiated immediately after the air source is cutoff and vital functions are stabilized. In this case presentation, a patient went into a coma after a massive iatrogenic cerebral air embolism that developed during the aortography procedure. The patient was discharged with hyperbaric oxygen therapy without any sequelae.

A first principle study of electronic structure and magnetic properties of TlFe2Se2

Here we have studied about TlFe2Se2, which belongs to the 122 type (Ternary Iron Selenides) of the iron chalcogenide group and calculated its electronic structure and magnetic properties. This compound has a superconducting property with a transition temperature around 35 K. By Density Functional Theory (DFT) approach we have tried to describe various superconducting properties of the TlFe2Se2 material. Here Quantum Espresso approach of DFT is used to calculate the following properties of TlFe2Se2 (i) The Self Consistent field (SCF) and the prediction of cut-off wave function from it and (ii) the description of Band Diagram and Density of states (DOS).

Spectrum of the semi-relativistic Pauli–Fierz model II

We consider the ground state of the semi-relativistic Pauli–Fierz Hamiltonian $$ H = |\textbf{p} - \textbf{A(x)}| + H\_f + V\textbf{(x)}. $$ Here $\textbf{A(x)}$ denotes the quantized radiation field with an ultraviolet cutoff function and $H\_f$ the free field Hamiltonian with dispersion relation $|\textbf{k}|$. The Hamiltonian $H$ describes the dynamics of a massless and semi-relativistic charged particle interacting with the quantized radiation field with an ultraviolet cutoff function. In 2016, the first two authors proved the existence of the ground state $\Phi\_m$ of the massive Hamiltonian $H\_m$ is proven. Here, the massive Hamiltonian $H\_m$ is defined by $H$ with dispersion relation $\sqrt{\textbf{k}^2+m^2}$ $(m>0)$. In this paper, the existence of the ground state of $H$ is proven. To this aim, we estimate a singular and non-local pull-through formula and show the equicontinuity of ${a(k)\Phi\_m}{0\<m\<m\_0}$ with some $m\_0$, where $a(k)$ denotes the formal kernel of the annihilation operator. Showing the compactness of the set ${\Phi\_m}{0\<m\<m\_0}$, the existence of the ground state of $H$ is shown.

Gradient flow and holography from a local Wilsonian cutoff

We consider the vacuum partition function of a 4d scalar QFT in a curved background as function of bare marginal and relevant couplings. A local UV cutoff Lambda (x) transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms including Wilsonian cutoff functions. The local cutoff can be absorbed completely by a rescaling of the metric and the bare couplings. The vacuum partition function satisfies consistency conditions which follow from the Abelian nature of local redefinitions of the cutoff, and which differ from Weyl rescalings. These imply a gradient flow for beta functions describing the cutoff dependence of rescaled bare couplings. The consistency conditions allow to satisfy all but one Hamiltonian constraints required for a holographic description of the flow of bare couplings with the cutoff.

Fermionic Condensate in de Sitter Spacetime

Fermionic condensate is investigated in $(D+1)$-dimensional de Sitter spacetime by using the cutoff function regularization. In order to fix the renormalization ambiguity for massive fields an additional condition is imposed, requiring the condensate to vanish in the infinite mass limit. For large values of the field mass the condensate decays exponentially in odd dimensional spacetimes and follows a power law decay in even dimensional spacetimes. For a massless field the fermionic condensate vanishes for odd values of the spatial dimension $D$ and is nonzero for even $D$. Depending on the spatial dimension the fermionic condensate can be either positive or negative. The change in the sign of the condensate may lead to instabilities in interacting field theories.

The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term

Abstract In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.

Simulating the complexity of the dark matter sheet – II. Halo and subhalo mass functions for non-cold dark matter models

ABSTRACT We present ‘sheet + release’ simulations that reliably follow the evolution of dark matter structure at and below the dark matter free-streaming scale, where instabilities in traditional N-body simulations create a large population of spurious artificial haloes. Our simulations sample a large range of power-spectrum cutoff functions, parameterized through the half-mode scale khm and a slope parameter β. This parameter space can represent many non-cold dark matter (NCDM) models, including thermal relic warm dark matter, sterile-neutrinos, fuzzy dark matter, and a significant fraction of ETHOS models. Combining these simulations with additional N-body simulations, we find the following results. (1) Even after eliminating spurious haloes, the halo mass function in the strongly suppressed regime ($n_{\rm {X}}/n_{\rm {CDM}} \lt 5 \ \mathrm{ per \, cent}$) remains uncertain because it depends strongly on the definition of a halo. At these mass scales traditional halo finders primarily identify overdensities that are unbound, highly elongated, dominated by tidal fields, or far from virialized. (2) The regime where the suppression is smaller than a factor of 20 is quite robust to these uncertainties, however, and can be inferred reliably from suitable N-body simulations. (3) Parameterizing the suppression in the halo- and subhalo mass functions through the scales where the suppression reaches $20 \ \mathrm{ per \, cent}$, 50 per cent, and $80 \ \mathrm{ per \, cent}$, we provide simple formulae which enable predictions for many NCDM models. (4) The halo mass–concentration relations in our sheet + release simulations agree well with previous results based on N-body simulations. (5) In general, we confirm the validity of previous N-body studies of warm dark matter models, largely eliminating concerns about the effects of artificial haloes.

Profit-based credit models with lender’s attitude towards risk and loss

Profit scoring represents a shift from default risk modeling. Here, lenders align their lending strategies to reflect their profitability objective. This paper proposes models that address the lender’s profit maximization objective. We develop varying cutoff functions that inform lending decisions while considering a lender’s attitude towards risk and loss. We derive two propositions about the properties of the variable cutoff functions for risk-averse and loss-averse lenders. Using a proprietary consumer loan data set, we show the effect of cutoff functions in lending decisions and find that both risk-averse and loss-averse lenders are profitable if they use parameter estimators that support their profitability objective.

Existence and Convergence of Solutions to Fractional Pure Critical Exponent Problems

Abstract We study existence and convergence properties of least-energy symmetric solutions (l.e.s.s.) to the pure critical exponent problem ( - Δ ) s ⁢ u s = | u s | 2 s ⋆ - 2 ⁢ u s , u s ∈ D 0 s ⁢ ( Ω ) , 2 s ⋆ := 2 ⁢ N N - 2 ⁢ s , (-\Delta)^{s}u_{s}=\lvert u_{s}\rvert^{2_{s}^{\star}-2}u_{s},\quad u_{s}\in D^% {s}_{0}(\Omega),\,2^{\star}_{s}:=\frac{2N}{N-2s}, where s is any positive number, Ω is either ℝ N {\mathbb{R}^{N}} or a smooth symmetric bounded domain, and D 0 s ⁢ ( Ω ) {D^{s}_{0}(\Omega)} is the homogeneous Sobolev space. Depending on the kind of symmetry considered, solutions can be sign-changing. We show that, up to a subsequence, a l.e.s.s. u s {u_{s}} converges to a l.e.s.s. u t {u_{t}} as s goes to any t &gt; 0 {t&gt;0} . In bounded domains, this convergence can be characterized in terms of an homogeneous fractional norm of order t - ε {t-\varepsilon} . A similar characterization is no longer possible in unbounded domains due to scaling invariance and an incompatibility with the functional spaces; to circumvent these difficulties, we use a suitable rescaling and characterize the convergence via cut-off functions. If t is an integer, then these results describe in a precise way the nonlocal-to-local transition. Finally, we also include a nonexistence result of nontrivial nonnegative solutions in a ball for any s &gt; 1 {s&gt;1} .

Non-Markovianity measure of Gaussian channels based on fidelity of teleportation

The non-monotonic behavior of certain quantities under indivisible CPTP maps is a method for probing and quantifying non-Markovianity of a quantum operation. Fidelity of teleportation refers to the measurement of the efficiency of teleportation protocol, it displays non-monotonic behavior due to the interaction between the channel of teleportation and a non-Markovian environment. Considering this behavior, we offer a non-Markovianity measure for the Gaussian channels. We consider a two-mode squeezed vacuum state as the channel of teleportation and the quantum Brownian channel and also its generalization as the environment. Assuming an Ohmic environment with exponential and also Lorentz-Drude cutoff functions, we investigate the effect of temperature and also cutoff functions on the dynamics of non-Markovianity.

Improved description of atomic environments using low-cost polynomial functions with compact support

The prediction of chemical properties using machine learning techniques calls for a set of appropriate descriptors that accurately describe atomic and, on a larger scale, molecular environments. A mapping of conformational information on a space spanned by atom-centred symmetry functions (SF) has become a standard technique for energy and force predictions using high-dimensional neural network potentials (HDNNP). An appropriate choice of SFs is particularly crucial for accurate force predictions. Established atom-centred SFs, however, are limited in their flexibility, since their functional form restricts the angular domain that can be sampled without introducing problematic derivative discontinuities. Here, we introduce a class of atom-centred SFs based on polynomials with compact support called polynomial symmetry functions (PSF), which enable a free choice of both, the angular and the radial domain covered. We demonstrate that the accuracy of PSFs is either on par or considerably better than that of conventional, atom-centred SFs. In particular, a generic set of PSFs with an intuitive choice of the angular domain inspired by organic chemistry considerably improves prediction accuracy for organic molecules in the gaseous and liquid phase, with reductions in force prediction errors over a test set approaching 50% for certain systems. Contrary to established atom-centred SFs, computation of PSF does not involve any exponentials, and their intrinsic compact support supersedes use of separate cutoff functions, facilitating the choice of their free parameters. Most importantly, the number of floating point operations required to compute polynomial SFs introduced here is considerably lower than that of other state-of-the-art SFs, enabling their efficient implementation without the need of highly optimised code structures or caching, with speedups with respect to other state-of-the-art SFs reaching a factor of 4.5 to 5. This low-effort performance benefit substantially simplifies their use in new programs and emerging platforms such as graphical processing units. Overall, polynomial SFs with compact support improve accuracy of both, energy and force predictions with HDNNPs while enabling significant speedups compared to their well-established counterparts.

Fully decoupled, linear and positivity-preserving scheme for the chemotaxis–Stokes equations

In this article, we develop a fully decoupled, linear and positivity-preserving finite element scheme for solving the chemotaxis–Stokes equations, which describe the biological chemotaxis phenomenon in the fluid environment. To deal with the strong coupling of the problem, we first consider a fully decoupled and linear semi-discrete scheme, in which we only need to solve several linearized sub-problems at each time step for the velocity, pressure, oxygen concentration and cell density, respectively. Then, based on the linear finite element method for the spatial discretization, the flux-corrected transport algorithm is extended to the oxygen concentration and cell density sub-problems to preserve their positivity. Finally, we show a series of numerical examples to verify its efficiency. We also find that better simulation can be obtained by regularizing the cut-off function and setting a random initial cell density in the equations.

Uniform a priori estimates for solutions of higher critical order fractional equations

In this paper, we establish uniform a priori estimates for positive solutions to higher critical order fractional Lame-Emden equations for all large exponents by adopting a new idea of using the combination of Green’s representations with suitable cut-off functions. We obtain two key ingredients needed in the estimates. One is the monotonicity of solutions in the inward normal direction near the boundary by using the method of moving planes in a local way, and the other is the integration by parts formula for higher order fractional operators. Both of them will become useful tools in the analysis of higher order fractional equations. It is well-known that, with such a priori estimate, one will be able to obtain the existence of solutions via topological degree or continuation arguments.

Weyl consistency conditions from a local Wilsonian cutoff

A local UV cutoff Lambda (x) transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms for scalar fields including Wilsonian cutoff functions. First we consider scalar fields in curved space-time with local bare couplings of any canonical dimension, and anomalous dimensions which describe their dependence on the UV cutoff. The local component of the UV cutoff plays the role of an additional coupling, albeit with a trivial constant beta function. This approach allows to derive Weyl consistency conditions for the corresponding anomalous dimensions which assume the form of an exact gradient flow. For renormalizable theories the Weyl consistency conditions are initially of the form of an approximate gradient flow for the beta functions, and we derive conditions under which it becomes the form of an exact gradient flow.

On a class of $p(x)$-Laplacian equations without any growth and Ambrosetti-Rabinowitz conditions

The aim of this paper is to establish the existence of nontrivial solutions for $p(x)$-Laplacian equations without any growth and Ambrosetti-Rabinowitz conditions. Employing the cutoff function approach, we show that auxiliary problem has at least one nontrivial solution. Furthermore, we obtain nontrivial solutions for original problems using De Giorgi iteration. The results presented here extend some recent contributions obtained for problems driven by the $p(x)$-Laplacian or even to more general differential operators.

Long time behavior of solutions to the damped forced generalized Ostrovsky equation below the energy space

In this paper, we investigate the long time behavior of the damped forced generalized Ostrovsky equation below the energy space. First, by using Fourier restriction norm method and Tao’s [ k , Z ] [k,Z] - multiplier method, we establish the multi-linear estimates, including the bilinear and trilinear estimates on the Bourgain space X s , b . X_{s,b}. Then, combining the multi-linear estimates with the contraction mapping principle as well as L ~ 2 \widetilde {L}^{2} energy method, we establish the global well-posedness and existence of the bounded absorbing sets in L ~ 2 . \widetilde {L}^{2}. Finally, we show the existence of global attractor in L ~ 2 \widetilde {L}^{2} and its compactness in H ~ 5 \widetilde {H}^{5} by means of the high-low frequency decomposition method, cut-off function, tail estimate together with Kuratowski α \alpha -measure in order to overcome the non-compactness of the classical Sobolev embedding. This result improves earlier ones in the literatures, such as Goubet and Rosa [J. Differential Equations 185 (2002), no. 1, 25–53], Moise and Rosa [Adv. Differential Equations 2 (1997), no. 2, 251–296], Wang et al. [J. Math. Anal. Appl. 390 (2012), no. 1, 136–150], Wang [Discrete Contin. Dyn. Syst. 35 (2015), no. 8, 3799–3825], and Guo and Huo [J. Math. Anal. App. 329 (2007), no. 1, 392–407].

A general way to confined stationary Vlasov-Poisson plasma configurations

We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $\Omega\subset\mathbb{R}^3$ describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of $\Omega$. In a first part we provide such an existence result for a generalized system of Vlasov-Poisson type and investigate the relation between the strength of the external magnetic field, the sharpness of the confinement and the amount of plasma that is confined measured in terms of the total charges. The key tools here are the method of sub-/supersolutions and the use of first integrals in combination with cutoff functions. In a second part we apply these general results to the usual Vlasov-Poisson equation in three different settings: the infinite and finite cylinder, as well as domains with toroidal symmetry. This way we prove the existence of stationary solutions corresponding to a two-component plasma confined in a Mirror trap, as well as a Tokamak.

The renormalization group and the diffusion equation

Abstract We study the relationship between the renormalization group and the diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

Spectroscopic proprieties of the ground and the higher excited states of the KCs

Potential energy curves, spectroscopic parameters, electric dipole moments (PEDM and TEDM) and vibrational levels’ spacing for 141Σ+, 133Σ+, 81,3Π, and 31,3Δ electronic states, including the ionic limit K−Cs+, are highly computed and presented in adiabatic representation. These properties are determined by the use of an ab initio method involving non-empirical pseudo-potentials, the core polarization potentials, the l-dependent cut-off functions, and the full valence configuration interaction. An important shape where an ionic state behaving as (−1/R), has been clearly pointed out in the 1Σ+ symmetry. This irregularity has been made due to the ionic charge transfer state (K−Cs+), which induces a series of avoided crossings at intermediate and long internuclear ranges. It is interesting to note that the ionic character linked to the ionic charge transfer K−Cs+ state has been clearly illustrated in the PEDM. The current calculations on the KCs molecule are complementary to the published theoretical works, including recently observed electronic states that had not been calculated previously. For the low-lying electric states, spectroscopic constants, PEDM, as well as TEDM are in good agreement with the available experimental data. The relevant data of the KCs molecule are meaningful and useful in several prospective experiments such as photo-association experiments or the manipulation of ultra-cold molecules.