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Background: Bacterial growth rate, commonly reported in terms of doubling time, is frequently determined by one of two techniques: either by measuring optical absorption of a growing culture or by taking samples at different times during their growth phase, diluting them, spreading them on agar plates, incubating them, and counting the colonies that form. Both techniques require measurements of multiple repeats, as well careful assessment of reproducibility and consistency. Existing literature using either technique gives a wide range of growth rate values for even the most extensively studied species of bacteria, such as Escherichia coli, Pseudomonas aeruginosa, and Staphylococcus aureus. This work aims to apply several methods to reliably determine the growth rate of a recently identified species of Enterobacteriaceae, called Enterobacter sp. SM3, and to compare that rate with that of a well-known wildtype E. coli strain KP437. Results: We extend conventional optical density (OD) measurements to determine the growth rate of Enterobacter sp. SM3. To assess the reliability of this technique, we compare growth rates obtained by fitting the OD data to exponential growth, applying a relative density method, and measuring shifts in OD curves following set factors of dilution. The main source of error in applying the OD technique is due to the reliance on an exponential growth phase with a short span. With proper choice of parameter range, however, we show that these three methods yield consistent results. We also measured the SM3 division rate by counting colony-forming units (CFU) versus time, yielding results consistent with the OD measurements. In lysogeny broth at 37oC, SM3 divides every 21 ± 3 min, notably faster than the RP437 strain of E. coli, which divides every 29 ± 2 min. Conclusion: The main conclusion of this report is that conventional optical density (OD) measurements and the colony-forming units (CFU) method can yield consistent values of bacterial growth rate. However, to ensure the reproducibility and reliability of the measured growth rate of each bacterial strain, different methods ought to be applied in close comparison. The effort of checking for consistency among multiple techniques, as we have done in this study, is necessary to avoid reporting variable values of doubling time for particular species or strains of bacteria, as seen in the literature. [ABSTRACT FROM AUTHOR]

An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T = (V , E) with the natural distance d defined on graphs and a weighted measure μ of exponential growth, the authors introduce the variable Lebesgue space L p (·) (μ) over (V , d , μ) and investigate it under the global Hölder continuity condition for p (·) . As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on L p (·) (μ) is obtained, and an unbounded example is presented. [ABSTRACT FROM AUTHOR]

A nonlinear viscoelastic Kirchhoff-type equation with a logarithmic nonlinearity, delay and Balakrishnan-Taylor damping terms is studied. We prove the exponential growth and the blow-up of solutions with positive initial-energy under suitable hypotheses. [ABSTRACT FROM AUTHOR]

This study focuses on investigating a problem involving a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. We aim to demonstrate, under appropriate conditions, the exponential growth of solutions with positive initial-energy. [ABSTRACT FROM AUTHOR]

Given a group G acting by isometries on a metric space X, we consider a preferred collection of paths of the space X, a path system, and study the spectrum of relative exponential growth rates and quotient exponential growth rates of the infinite index subgroups of G that are quasi-convex with respect to this path system. If G contains a constricting element with respect to the same path system, we are able to determine when the growth rates of the first kind are strictly smaller than the growth rate of G, and when the growth rates of the second kind coincide with the growth rate of G. Examples of applications include relatively hyperbolic groups, CAT.0/ groups, and hierarchically hyperbolic groups containing a Morse element. [ABSTRACT FROM AUTHOR]

We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schrödinger equation driven by a weighted N$N$‐Laplace operator and without the mass term, and a higher‐order fractional Poisson equation. Since the system is set in RN$\mathbb {R}^N$, the limiting case for the Sobolev embedding, we consider nonlinearities with exponential growth. Existence is proved relying on the study of a corresponding Choquard equation in which the Riesz kernel is a logarithm, hence sign‐changing and unbounded from above and below. This is in turn solved by means of a variational approximating procedure for an auxiliary Choquard equation, where the logarithm is uniformly approximated by polynomial kernels. Our results are new even in the planar case N=2$N=2$. [ABSTRACT FROM AUTHOR]

BACKGROUND: Polycystic Ovary Syndrome (PCOS) is a medical condition that causes hormonal disorders in women in their childbearing years. The hormonal imbalance leads to a delayed or even absent menstrual cycle. Women with PCOS mainly suffer from extreme weight gain, facial hair growth, acne, hair loss, skin darkening, and irregular periods, leading to infertility in rare cases. Doctors usually examine ultrasound images and conclude the affected ovary but are incapable of deciding whether it is a normal cyst, PCOS, or cancer cyst manually. OBJECTIVE: To have access to the high-risk crucial PCOS and to detect the condition and the treatment aimed at mitigating health hazards such as endometrial hyperplasia/cancer, infertility, pregnancy complications, and the long-term burden of chronic diseases such as cardiometabolic disorders linked with PCOS. METHODS: The proposed Self-Defined Convolution Neural Network method (SD_CNN) is used to extract the features and machine learning models such as SVM, Random Forest, and Logistic Regression are used to classify PCOS images. The parameter tuning is done with lesser parameters in order to overcome over-fitting issues. The self-defined model predicts the occurrence of the cyst based on the analyzed features and classifies the class labels effectively. RESULTS: The Random Forest Classifier was found to be the most reliable and accurate among Support Vector Machine (SVM) and Logistic Regression (LR), with accuracy being 96.43%. CONCLUSION: The proposed model establishes better trade-off compared to various other approaches and works effectually for PCOS prediction. [ABSTRACT FROM AUTHOR]

This article deals with the following fractional N s -Laplace Kichhoff equation involving exponential growth of the form: ε N K [ u ] s , N s N s (- Δ) N / s s u + Z (x) | u | N s - 2 u = f (u) in R N , where ε > 0 is a parameter, s ∈ (0 , 1) and (- Δ) p s is the fractional p-Laplace operator with p = N s ≥ 2 , K is a Kirchhoff function, f is a continuous function with exponential growth and Z is a potential function possessing a local minimum. Under some suitable conditions, we obtain the existence, multiplicity and concentration of solutions to the above problem via penalization methods and Lyusternik-Schnirelmann theory. [ABSTRACT FROM AUTHOR]

We prove that for each p ∈ (1 , ∞) the energy functional associated with the Dirichlet system - div (ϕ p (∇ u) ∇ u) = ∂ 1 F (u , v) in Ω , - div (ϕ p (∇ v) ∇ v) = ∂ 2 F (u , v) in Ω , u = v = 0 on ∂ Ω , admits at least one global, nonnegative minimizer (u p , v p) ∈ W 0 Φ p (Ω) × W 0 Φ p (Ω) which converges uniformly on Ω ¯ to (d Ω , d Ω) , as p → ∞ . Here Φ p (t) : = ∫ 0 t s ϕ p (s) d s and d Ω stands for the distance function to the boundary ∂ Ω . [ABSTRACT FROM AUTHOR]

Abstract Background Bacterial growth rate, commonly reported in terms of doubling time, is frequently determined by one of two techniques: either by measuring optical absorption of a growing culture or by taking samples at different times during their growth phase, diluting them, spreading them on agar plates, incubating them, and counting the colonies that form. Both techniques require measurements of multiple repeats, as well careful assessment of reproducibility and consistency. Existing literature using either technique gives a wide range of growth rate values for even the most extensively studied species of bacteria, such as Escherichia coli, Pseudomonas aeruginosa, and Staphylococcus aureus. This work aims to apply several methods to reliably determine the growth rate of a recently identified species of Enterobacteriaceae, called Enterobacter sp. SM3, and to compare that rate with that of a well-known wildtype E. coli strain KP437. Results We extend conventional optical density (OD) measurements to determine the growth rate of Enterobacter sp. SM3. To assess the reliability of this technique, we compare growth rates obtained by fitting the OD data to exponential growth, applying a relative density method, and measuring shifts in OD curves following set factors of dilution. The main source of error in applying the OD technique is due to the reliance on an exponential growth phase with a short span. With proper choice of parameter range, however, we show that these three methods yield consistent results. We also measured the SM3 division rate by counting colony-forming units (CFU) versus time, yielding results consistent with the OD measurements. In lysogeny broth at 37oC, SM3 divides every 21 ± 3 min, notably faster than the RP437 strain of E. coli, which divides every 29 ± 2 min. Conclusion The main conclusion of this report is that conventional optical density (OD) measurements and the colony-forming units (CFU) method can yield consistent values of bacterial growth rate. However, to ensure the reproducibility and reliability of the measured growth rate of each bacterial strain, different methods ought to be applied in close comparison. The effort of checking for consistency among multiple techniques, as we have done in this study, is necessary to avoid reporting variable values of doubling time for particular species or strains of bacteria, as seen in the literature.

This paper is concerned with the existence of normalized solutions for the following class of Choquard elliptic problems: - Δ u + λ u = (I α ∗ F (u)) f (u) + μ (I α ∗ | u | q ) | u | q - 2 u , in R 2 , ∫ R 2 | u | 2 = a , where a > 0 , I α is the Riesz potential, ∗ represents the convolution operator, f has exponential critical growth in R 2 , F (t) = ∫ 0 t f (s) d s , and 1 + α 2 < q < 2 + α 2 . By variational methods, we prove the existence of two normalized solutions: one with negative energy and one with positive energy. [ABSTRACT FROM AUTHOR]

We investigate Choquard equations in $ \mathbb R^N $ driven by a weighted $ N $-Laplace operator with polynomial kernel and zero mass. Since the setting is limiting for the Sobolev embedding, we work with nonlinearities which may grow up to the critical exponential. We establish the existence of a positive solution by variational methods, complementing the analysis in [32], where the case of a logarithmic kernel was considered.

Abstract This paper uses the Galerkin method to investigate the existence of positive solution to a class of singular elliptic problems given by { − Δ u = λ 0 u β 0 + Λ 0 | ∇ u | γ 0 + f 0 ( u ) | x | α 0 + h 0 ( x ) , u > 0 in Ω , u = 0 on ∂ Ω , $$\begin{aligned} \textstyle\begin{cases} -\Delta u= \displaystyle \frac {\lambda _{0}}{u^{\beta _{0}}} + \Lambda _{0} |\nabla u|^{\gamma _{0}}+ \frac{f_{0}(u)}{|x|^{\alpha _{0}}}+ h_{0}(x), \ \ u>0 \ \ \text{in} \ \Omega , \\ u=0 \ \text{on} \ \ \partial \Omega , \end{cases}\displaystyle \end{aligned}$$ where Ω ⊂ R 2 $\Omega \subset \mathbb{R}^{2}$ is a bounded smooth domain, 0 < β 0 $0 0 $\overline{\Upsilon}>0$ .

The Schrödinger–Poisson system describes standing waves for the nonlinear Schrödinger equation interacting with the electrostatic field. In this paper, we are concerned with the existence of positive ground states to the planar Schrödinger–Poisson system with a nonlinearity having either a subcritical or a critical exponential growth in the sense of Trudinger–Moser. A feature of this paper is that neither the finite steep potential nor the reaction satisfies any symmetry or periodicity hypotheses. The analysis developed in this paper seems to be the first attempt in the study of planar Schrödinger–Poisson systems with lack of symmetry. [ABSTRACT FROM AUTHOR]

We investigate Choquard equations in RN driven by a weighted RN-Laplace operator with polynomial kernel and zero mass. Since the setting is limiting for the Sobolev embedding, we work with nonlinearities which may grow up to the critical exponential. We establish the existence of a positive solution by variational methods, complementing the analysis in [32], where the case of a logarithmic kernel was considered. [ABSTRACT FROM AUTHOR]

This paper uses the Galerkin method to investigate the existence of positive solution to a class of singular elliptic problems given by { − Δ u = λ 0 u β 0 + Λ 0 | ∇ u | γ 0 + f 0 (u) | x | α 0 + h 0 (x) , u > 0 in Ω , u = 0 on ∂ Ω , where Ω ⊂ R 2 is a bounded smooth domain, 0 < β 0 , γ 0 ≤ 1 , α 0 ∈ [ 0 , 2) , h 0 (x) ≥ 0 , h 0 ≠ 0 , h 0 ∈ L ∞ (Ω) , 0 < ∥ h 0 ∥ ∞ < λ 0 < Λ 0 , and f 0 are continuous functions. More precisely, f 0 has a critical exponential growth, that is, the nonlinearity behaves like exp (ϒ ‾ s 2) as | s | → ∞ , for some ϒ ‾ > 0 . [ABSTRACT FROM AUTHOR]

We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes constructed using relatively coarse numerical meshes enable accurate estimation of several major optical modes, which are essential in practical applications. [ABSTRACT FROM AUTHOR]

In the present paper, we study the existence of ground state sign-changing solutions for a class of Kirchhoff type problem - a + b ∫ Ω | ∇ u | 2 d x Δ u = f (u) , x ∈ Ω ; u = 0 , x ∈ ∂ Ω , where a , b > 0 , f ∈ C (R , R) satisfies subcritical exponential growth or critical exponential growth in a bounded domain Ω ∈ R 2 with a smooth boundary ∂ Ω . In combination with Trudinger-Moser inequality, we prove the existence of least energy sign-changing solution by variational method and obtain its concentration behaviors as b ↘ 0 in both subcritical case and critical case. [ABSTRACT FROM AUTHOR]

Abstract In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.

Introduction: It is unlikely that the population growth rate has stayed steady in recent years, given the present situation in Iran. There has been a slight rise in population growth over the past 60 years, according to birth, mortality, and census results from 1956 to 2016. Material & Methods: Mathematical modeling is a common element of computer programs used to predict population growth. This model was applied as a useful and instructive tool in the present research to predict Iran's population until 2041. Results: The standard mathematical modeling approach predicted the total population using the data from Iran's 1956–2016 census using different mathematical modeling methods. The descriptive population growth prediction model (exponential) outperformed the other techniques in terms of compatibility with historical population data. Furthermore, it proved to be highly effective and appropriate for projecting Iran's population in the future. For the year 2041, the following population estimates were projected: A total population of 113,215,189, a male population of 57,366,315, a female population of 55,848,874, an urban population of 83,786,814, a rural population of 29,428,375, and a total population of Iran exceeding 100 million people during the year 2031. Discussion & Conclusion: Combining the exponential and hyperbolic extrapolation models allows for the prediction that Iran's population will increase to 159,852,540 people by the year 2075, which is twice as many as that of the 2016 census. Moreover, it is also feasible to calculate the approximate total population that lived 100,000 years before the 1956 census using mathematical modeling.

Abstract In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 $f_{1}=f_{2}=0$ .

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term. [ABSTRACT FROM AUTHOR]

In this work, we study the existence of the least energy sign-changing solution for the following degenerate Kirchhoff-type problem involving the fractional N/s-Laplacian with logarithmic and both subcritical and critical exponential nonlinearities: \[ \begin{cases} \displaystyle M\left(\int_{\mathbb R^{2N}}\frac{|u(x) - u(y)|^{\frac{N}{s}}}{|x - y|^{2N}}\,{\rm d}x\,{\rm d}y \right)(-\Delta)_{N/s}^s u \\ \quad = |u|^{q-2}u\ln |u|^2 + \mu f(u), & {\rm in}\ \Omega,\\ u=0, & {\rm in}\ \mathbb R^N\setminus \Omega, \end{cases} \] { M (∫ R 2 N | u (x) − u (y) | N s | x − y | 2 N d x d y) (− Δ) N / s s u = | u | q − 2 uln ⁡ | u | 2 + μf (u) , in Ω , u = 0 , in R N ∖ Ω , where $ \Omega \subset \mathbb {R}^N $ Ω ⊂ R N is a bounded domain. The proof is based on constrained variational method, fractional Trudinger–Moser inequality, quantitative deformation lemma and Brouwer's degree theory in Nehari sets. To be more precise, the least energy sign-changing solution is obtained by minimizing the energy functional on the sign-changing Nehari manifold. [ABSTRACT FROM AUTHOR]

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 . [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of least energy sign-changing solutions for the following N-Laplacian Kirchhoff-type problem with logarithmic and exponential nonlinearities: - a + b ∫ Ω | ∇ u | N d x Δ N u = | u | p - 2 u ln | u | 2 + λ f (u) , in Ω , u = 0 , on ∂ Ω , where f(t) behaves like e x p α | t | N N - 1 . Combining constrained variational method, topological degree theory and quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution u b with precisely two nodal domains. Moreover, we show that the energy of u b is strictly larger than two times of the ground state energy and analyze the convergence property of u b as b ↘ 0 . [ABSTRACT FROM AUTHOR]

Introduction: It is unlikely that the population growth rate has stayed steady in recent years, given the present situation in Iran. There has been a slight rise in population growth over the past 60 years, according to birth, mortality, and census results from 1956 to 2016. Material & Methods: Mathematical modeling is a common element of computer programs used to predict population growth. This model was applied as a useful and instructive tool in the present research to predict Iran's population until 2041. Results: The standard mathematical modeling approach predicted the total population using the data from Iran's 1956–2016 census using different mathematical modeling methods. The descriptive population growth prediction model (exponential) outperformed the other techniques in terms of compatibility with historical population data. Furthermore, it proved to be highly effective and appropriate for projecting Iran's population in the future. For the year 2041, the following population estimates were projected: A total population of 113,215,189, a male population of 57,366,315, a female population of 55,848,874, an urban population of 83,786,814, a rural population of 29,428,375, and a total population of Iran exceeding 100 million people during the year 2031. Discussion & Conclusion: Combining the exponential and hyperbolic extrapolation models allows for the prediction that Iran's population will increase to 159,852,540 people by the year 2075, which is twice as many as that of the 2016 census. Moreover, it is also feasible to calculate the approximate total population that lived 100,000 years before the 1956 census using mathematical modeling. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp - Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp (Rd) and a time weighted Lr (Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space. [ABSTRACT FROM AUTHOR]

We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes constructed using relatively coarse numerical meshes enable accurate estimation of several major optical modes, which are essential in practical applications.

An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure μ of exponential growth, the authors introduce the variable Lebesgue space Lp(·)(μ) over (V,d,μ) and investigate it under the global Hölder continuity condition for p(·). As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on Lp(·)(μ) is obtained, and an unbounded example is presented.

We study the nonlinear Schrödinger equation for the s -fractional p -Laplacian strongly coupled with the Poisson equation in dimension two and with p = 2 s , which is the limiting case for the embedding of the fractional Sobolev space W s , p (R 2). We prove existence of solutions by means of a variational approximating procedure for an auxiliary Choquard equation in which the uniformly approximated sign-changing logarithmic kernel competes with the exponential nonlinearity. Qualitative properties of solutions such as symmetry and decay are also established by exploiting a suitable moving planes technique. [ABSTRACT FROM AUTHOR]

Copyright of HMD: Praxis der Wirtschaftsinformatik is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We show the existence of a positive solution u p for a Dirichlet p-Laplacian problem with nonlinearity involving an exponential term that can be supercritical. We determine the asymptotic behavior of u p as p → 1 + and p → + ∞ , which are related to the Cheeger constant and the distance function to the boundary, respectively. Furthermore, we also prove a nonexistence result concerning the range of the parameter λ . [ABSTRACT FROM AUTHOR]

Copyright of Biology Teaching is the property of East China Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we propose a gradient type term for the k-Hessian equation that extends for k > 1 the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan–Kramer change of variables. As applications, we ensure the existence of solutions for a new class of k-Hessian equation in the sublinear and superlinear cases for Sobolev type growth. The threshold for existence is obtained in some particular cases. In addition, for the Trudinger–Moser type growth regime, we also prove the existence of solutions under either subcritical or critical conditions. [ABSTRACT FROM AUTHOR]

Floyd showed that if a sequence of compact hyperbolic Coxeter polygons converges, then so does the sequence of the growth rates of the Coxeter groups associated with the polygons. For the case of the hyperbolic 3-space, Kolpakov discovered the same phenomena for specific convergent sequences of hyperbolic Coxeter polyhedra. In this paper, we show that the growth rate is a continuous function on the space of Coxeter systems. This is an extension of the results due to Floyd and Kolpakov since the convergent sequences of Coxeter polyhedra give rise to that of Coxeter systems in the space of marked groups. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem for a space-time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space. [ABSTRACT FROM AUTHOR]

Environmental and climatic changes are inducing population declines in numerous species. However, certain species demonstrate remarkable resilience, exhibiting both population growth and range expansion. This longitudinal study in Sweden carried out over two decades (2004–2023) examines the noctuid moths Mythimna albipuncta and Hoplodrina ambigua. Abundance and phenology data were gathered from three light traps in southeastern Sweden and integrated with distribution and phenology data from the Global Biodiversity Information Facility. In M. albipuncta, the distribution area expanded from 7 to 76 occupied grids (60 km2) and the abundance increased from 7 to 6136 individuals, while in H. ambigua, the distribution area expanded from 1 to 87 occupied grids and the abundance increased from 0 to 6937 individuals, during the course of the study. Furthermore, a positive yearly association was observed between the number of occupied grids and light trap abundance for each species. We also found significant extensions in the adult flight periods of more than 100 days in both species. Light traps emerged as an effective monitoring tool, with light trap abundance as a reliable proxy for distribution changes. Our findings demonstrate that the studied species cope very well with environmental and climatic changes. Given their role as dominant links between primary producers and higher trophic levels, abundance and distribution shifts of these ecological engineers have the potential to cascade up and down in the ecosystem. [ABSTRACT FROM AUTHOR]