Function Of Omega Research Articles

From Understanding the Population Dynamics of the NSGA-II to the First Proven Lower Bounds

Due to the more complicated population dynamics of the NSGA-II, none of the existing runtime guarantees for this algorithm is accompanied by a non-trivial lower bound. Via a first mathematical understanding of the population dynamics of the NSGA-II, that is, by estimating the expected number of individuals having a certain objective value, we prove that the NSGA-II with suitable population size needs Omega(Nn log n) function evaluations to find the Pareto front of the OneMinMax problem and Omega(Nn^k) evaluations on the OneJumpZeroJump problem with jump size k. These bounds are asymptotically tight (that is, they match previously shown upper bounds) and show that the NSGA-II here does not even in terms of the parallel runtime (number of iterations) profit from larger population sizes. For the OneJumpZeroJump problem and when the same sorting is used for the computation of the crowding distance contributions of the two objectives, we even obtain a runtime estimate that is tight including the leading constant.

Skeleton for the one-dimensional aggregation equation

For the aggregation equation in mathbb {R}, we consider the evolution of an initial density corresponding to the characteristic function of some set Omega _0. We study the limit measure at the blow up time 1 for Omega _0 open or compact and we inspect the limit set (skeleton) where this measure is supported.

The Upregulation of GSTO2 is Associated with Colon Cancer Progression and a Poor Prognosis.

Colorectal cancer is the second-leading cause of cancer-related mortality in the United States. Glutathione S-transferase can affect the development of cancer. Glutathione S-transferase omega 2, a member of the GST family, plays an important role in many tumors. However, the role of Glutathione S-transferase omega 2 in the development of colon cancer remains unclear. Herein, our study aimed to investigate the exact role of Glutathione S-transferase omega 2 in colon cancer. We used RNA sequencing data from The Cancer Genome Atlas and the Genotype-Tissue Expression database to analyze Glutathione S-transferase omega 2 expressions. Then, we explore the protein information of Glutathione S-transferase omega 2 in the Human Protein Atlas, GeneCards, and String database. In addition, western blot and immunohistochemistry were performed to evaluate the protein levels of Glutathione S-transferase omega 2 in colon cancer tissues. We acquire data from the Gene Expression Omnibus and The Cancer Genome Atlas databases. Also, we performed relevant prognostic analyses of these data. In addition, we performed a statistical analysis of the clinical data from The Cancer Genome Atlas database and the expression level of Glutathione S-transferase omega 2. Then, we performed Cox regression analysis and found independent risk factors for prognosis in patients with colon cancer. The Kyoto Encyclopedia of Genes and Genomes and Gene Ontology enrichment analyses were used to explore the potential biological functions of Glutathione S-transferase omega 2. The infiltration of colon cancer-immune cells was evaluated by the CIBERSORT method. RNA silencing was performed using siRNA constructs in HCT-116 and HT-29 cell lines. Cell Counting Kit-8 and EdU assays were performed to determine cell proliferation. Transwell experiments and scratch tests were used to determine cell migration. As for the mRNA and protein expression levels of cells, we used quantitative real-time PCR and western blot to detect them. Our research shows that Glutathione S-transferase omega 2 is overexpressed in colon cancer patients, and this overexpression is associated with a poor prognosis. The high expression of Glutathione S-transferase omega 2 is significantly correlated stage with stage, M, and N classification progression in colon cancer by statistical analysis. Univariate and multivariate Cox regression analyses showed that Glutathione S-transferase omega 2 was an independent risk factor for poor prognosis in colon cancer. In addition, we also found that Glutathione S-transferase omega 2 expression levels can affect the immune microenvironment of colon cancer cells. Gene silencing of Glutathione S-transferase omega 2 in HT-29 and HCT-116 cells significantly inhibited tumor growth and migration. In summary, we found that Glutathione S-transferase omega 2 can be used as a molecular indicator of colon cancer prognosis. In vitro, gene silencing of Glutathione S-transferase omega 2 inhibited colon cancer cells' growth and migration.

Additive averages of multiplicative correlation sequences and applications

We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ>0, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(an+b)1/(cn+d)ℓ: n ∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.

Optimization Criteria and Efficiency of a Thermoelectric Generator.

The efficiency of a thermoelectric generator model under maximum conditions is presented for two optimization criteria proposed under the context of finite-time thermodynamics, namely, the efficient power criterion and the Omega function, where this last function represents a trade-off between useful and lost energy. The results are compared with the performance of the device at maximum power output. A macroscopic thermoelectric generator (TEG) model with three possible sources of irreversibilities is considered: (i) the electric resistance R for the Joule heating, (ii) the thermal conductances Kh and Kc of the heat exchangers between the thermal baths and the TEG, and (iii) the internal thermal conductance K for heat leakage. In particular, two configurations of the macroscopic TEG are studied: the so-called exoreversible case and the endoreversible limit. It shows that for both TEG configurations, the efficiency at maximum Omega function is always greater than that obtained in conditions of maximum efficient power, and this in turn is greater than that of the maximum power regime.

The Generalized Omega Function and Its Connection with Some Probability Distributions

In this paper, we present a generator function-based mapping called the generalized omega function. We show that a particular class of exponential functions is the asymptotic generalized omega function class. Owing to this property of the new function, it can be utilized for constructing bounded alternatives to cumulative distribution functions and density functions of some well-known random variables, including the Weibull, exponential and standard normal.

A State-of-the-Art Fund Performance Index: Higher-Order Omega and Its Consistency with Almost Stochastic Dominance

This paper provides a mathematical proof and theoretical analysis of the one-to-one consistency between higher-order Omega and Almost Stochastic Dominance rules when evaluating fund performance. The consistency between higher-order Omega and Almost Nth-degree Stochastic Dominance reinforces the effectiveness of applying the higher-order Omega function in fund performance measurement, as the Almost Stochastic Dominance rules are more likely to be observed in real life. This study also clarifies that the higher-order Omega decreases when threshold L increases. The ranking of funds based on higher-order Omega changes at different thresholds. Hence, it is critical to specify the L so that the consistency holds. Through evaluating the performance of eleven U.S. funds between 2010 and 2020, we demonstrate the applications of the Nth-order Omega in the concept of Almost Stochastic Dominance rules. Furthermore, the empirical results also show the superiority of the Nth-order Omega over the traditional fund performance measure, i.e., Sharpe ratio and the lower-order Omega. The ranking of fund performance based on higher-order Omega is consistent with Almost Stochastic Dominance rules.

Extension of Mathieu series and alternating Mathieu series involving the Neumann function Y_nu

The main objective of this paper is to present a new extension of the familiar Mathieu series and the alternating Mathieu series S(r) and {{widetilde{S}}}(r) which are denoted by {mathbb {S}}_{mu ,nu }(r) and widetilde{{mathbb {S}}}_{mu ,nu }(r), respectively. The computable series expansions of their related integral representations are obtained in terms of the exponential integral E_1, and convergence rate discussion is provided for the associated series expansions. Further, for the series {mathbb {S}}_{mu ,nu }(r) and widetilde{{mathbb {S}}}_{mu ,nu }(r), related expansions are presented in terms of the Riemann Zeta function and the Dirichlet Eta function, also their series built in Gauss’ {}_2F_1 functions and the associated Legendre function of the second kind Q_mu ^nu are given. Our discussion also includes the extended versions of the complete Butzer–Flocke–Hauss Omega functions. Finally, functional bounding inequalities are derived for the investigated extensions of Mathieu-type series.

The Number Theoretic Omega Function and Summations Involving the Exponents of Prime Numbers in the Factorization of Factorials

The Number Theoretic Omega Function and Summations Involving the Exponents of Prime Numbers in the Factorization of Factorials

Additive arithmetic functions meet the inclusion–exclusion principle: Asymptotic formulas concerning the GCD and LCM of several integers

We obtain asymptotic formulas for the sums {sum}_{n_1,dots, {n}_kleqslant x} f((n1, . , nk)) and {sum}_{n_1,dots, {n}_kleqslant x} f([n1, . , nk]), involving the GCD and LCM of the integers n1, . , nk, where f belongs to certain classes of additive arithmetic functions. In particular, we consider the generalized omega function Ωℓ(n) = {sum}_{p^{nu}BigVert {n}^{v^{ell }}}mathrm{investigated} by Duncan (1962) and Hassani (2018), and the functions A(n) = {sum}_{p^{nu}BigVert n} vp, A∗(n) = ∑p ∣ np, B(n) = A(n) − A∗(n) studied by Alladi and Erdős (1977). As a key auxiliary result, we use an inclusion–exclusion-type identity.

Factorization invariants of the additive structure of exponential Puiseux semirings

Exponential Puiseux semirings are additive submonoids of [Formula: see text] generated by almost all of the nonnegative powers of a positive rational number, and they are natural generalizations of rational cyclic semirings. In this paper, we investigate some of the factorization invariants of exponential Puiseux semirings and briefly explore the connections of these properties with semigroup-theoretical invariants. Specifically, we provide exact formulas to compute the catenary degrees of these monoids and show that minima and maxima of their sets of distances are always attained at Betti elements. Additionally, we prove that sets of lengths of atomic exponential Puiseux semirings are almost arithmetic progressions with a common bound, while unions of sets of lengths are arithmetic progressions. We conclude by providing various characterizations of the atomic exponential Puiseux semirings with finite omega functions; in particular, we completely describe them in terms of their presentations.

Povezanost polimorfizma glutation transferaza omega sa laboratorijskim pokazateljima zapaljenja u KOVIDU-19

In a view of important functions of glutathione transferase omega (GSTO) class in redox homeostasis and innate immunity, it was proposed that interindividual differences in COVID-19 clinical manifestations might be affected by GSTO1 (rs4925) and GSTO2 (rs156697) polymorphisms. To assess the potential association of these polymorphisms with biochemical, coagulation and inflammatory laboratory parameters in the group of mild and severe COVID-19 patients. GSTO1 and GSTO2 single nucleotide polymorphisms were determined by qPCR in 251 samples of COVID-19 patients. Biochemical, coagulation and inflammatory laboratory parameters of COVID-19 participants were procured from routine laboratory practice on the day of admission. Polymorphisms of GSTO1 and GSTO2 affect laboratory biochemical profile of COVID-19 patients. GSTO1*C allele was associated with increased levels of C-reactive protein (CRP) (p=0.035), interleukin-6 (IL-6) (p=0.047), D-dimer (p=0.014) and lactate dehydrogenase LDH (p=0.002), whereas GSTO2*G allele was associated with CRP (p=0.033). COVID-19 patients homozygous for variant GSTO1*A allele and GSTO2*G had the highest levels of serum Fe (p=0.019, p=0.052, respectively). Our findings regarding the influence of GSTO1 and GSTO2 polymorphisms on inflammation and coagulation parameters might be of clinical importance. In future, these findings could aid in a more personalized approach for better recognition of patients prone to thrombosis and excessive immune response.

Upper bounds for the ground state energy of the Laplacian with zero magnetic field on planar domains

We obtain upper bounds for the first eigenvalue of the magnetic Laplacian associated to a closed potential 1-form (hence, with zero magnetic field) acting on complex functions of a planar domain Omega , with magnetic Neumann boundary conditions. It is well known that the first eigenvalue is positive whenever the potential admits at least one non-integral flux. By gauge invariance, the lowest eigenvalue is simply zero if the domain is simply connected; then, we obtain an upper bound of the ground state energy depending only on the ratio between the number of holes and the area; modulo a numerical constant the upper bound is sharp and we show that in fact equality is attained (modulo a constant) for Aharonov-Bohm-type operators acting on domains punctured at a maximal epsilon -net. In the last part, we show that the upper bound can be refined, provided that one can transform the given domain in a simply connected one by performing a number of cuts with sufficiently small total length; we thus obtain an upper bound of the lowest eigenvalue by the ratio between the number of holes and the area, multiplied by a Cheeger-type constant, which tends to zero when the domain is metrically close to a simply connected one.

Parameters identification of PV model using improved slime mould optimizer and Lambert W-function

The characterization of PV unit can be made using one-, two-, and triple-diode electrical model. Each model has its own merits in terms of number of unknown parameters to be extracted and burden of calculation, and etc. In most applications, one-diode model (1-DM) is sufficed for the purpose of simulation and analysis in steady-state and dynamic conditions. This paper cares of extracting the unknown five parameters of the 1-DM exploiting the real I-V dataset points. New effort of employing the slime mould algorithm (SMA) and its improved version (ImSMA) is addressed to attain the same goal. Lambert W-function or omega function is used for accurate calculus of PV current. Two benchmarking test cases widely used in the literature are demonstrated and analysed to appraise the performance of SMA/ImSMA complete with subsequent analysis and discussions. The best ImSMA’s results of root mean squared current errors are 7.73006e−4 A and 1.3798e−2 A for RTC solar cell and STP6-120/36; respectively. Various scenarios under varied conditions are demonstrated utilizing the cropped best values of the model’s parameters In addition to that, performance measures are made to validate the cropped results along with comparisons to other recent competing algorithms. It can be concluded that the validations in consort with established outcomes signify the ImSMA in recognizing the PV unidentified 1-DM parameters.

Isotropic exact solutions in F(R,Y,phi ) gravity via Noether symmetries

The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely f(R,Y,phi ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by Y=R_{alpha beta }R^{alpha beta }, while phi represents scalar field. For this purpose, we assume different general cases of generic f(R,Y,phi ) function and explore its possible forms along with field potential V(phi ) by taking constant and variable coupling function of scalar field omega (phi ). In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

Counting Restricted Partitions of Integers Into Fractions: Symmetry and Modes of the Generating Function and a Connection to ω(t)

Motivated by the study of integer partitions, we consider partitions of integers into fractions of a particular form, namely with constant denominators and distinct odd or even numerators. When numerators are odd, the numbers of partitions for integers smaller than the denominator form symmetric patterns. Such properties can be applied to a particular class of nonlinear Diophantine equations. Most importantly, we find that our restrictions enable an elementary proof of the unimodality of the nonzero terms of the generating function, which in general is quite hard. We also examine partitions with even numerators. We prove that there are 2ω(t) − 2 partitions of an integer t into fractions with the first x consecutive even integers for numerators and equal denominators of y, where 0 < y < x < t. We then use this to produce corollaries such as a series identity and an extension of the prime omega function to the complex plane.

Thermoluminescence glow-curve deconvolution using analytical expressions: A unified presentation

This study provides a unified presentation of thermoluminescence (TL) glow-curve deconvolution within the framework of the open source R package “tgcd”, according to various analytical expressions that describe first-, second-, general-, and mixed-order kinetics as well as the recently developed semi-analytical expressions that derive from the one trap-one recombination center (OTOR) model that utilizes the Lambert W function or the Wright Omega function. We provide a comprehensive, flexible, convenient, and openly accessible program to analyze TL glow curves according to different models and expressions. The consistency of kinetic parameters determined using different model expressions was assessed using measured TL glow curve of CaF2:Dy. The performance of the computerized glow curve deconvolution (CGCD) method was also tested using simulated glow curves. Results revealed the benefits of comparing kinetic parameters determined from different model expressions and those obtained using experimental TL evaluation methods to assess the reliability of deconvolution results. The accuracy of the CGCD method is dependent upon both the model expressions used and the intrinsic trapping parameters of the TL material.

Thermodynamic optimization subsumed in stability phenomena

In the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. This feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. Furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. Endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the Pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the Omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

Energy efficient power control for device to device communication in 5G networks

Next generation cellular networks require high capacity, enhanced energy efficiency and guaranteed quality of service (QoS). In order to meet these targets, device-to device (D2D) communication is being considered for future 5th generation especially for certain applications that require the proximity gain, the reuse gain, and the hop gain. In this paper, we investigate energy efficient power control for the uplink of an OFDMA (orthogonal frequency-division multiple access) single-cell communication system composed of both regular cellular users and device to device (D2D) pairs. Firstly, we analyze and mathematically model the actual requirements forD2D communications and traditional cellular links in terms of minimum rate and maximum power requirement. Secondly, we use fractional programming in order to transform the original problem into an equivalent concave one and we use the non-cooperative Game theory in order to characterize the equilibrium. Then, the solution of the game is given as a water-filling power allocation. Furthermore, we implement a distributed power allocation scheme using three ways: a) Fractional programming techniques b) Closed form expression (the novelty is the use of wright omega function). c) Inverse water filling. Finally, simulations in both static and dynamic channel setting are presented to illustrate the improved performance in term of EE, SE (spectral efficiency) and time of execution of the iterative algorithm (Dinkelbach) than the closed form algorithms.

Chirped Lambert W-kink solitons of the complex cubic-quintic Ginzburg-Landau equation with intrapulse Raman scattering

In this paper, an exact explicit solution for the complex cubic-quintic Ginzburg-Landau equation is obtained, by using Lambert W function or omega function. More pertinently, we term them as Lambert W-kink-type solitons, begotten under the influence of intrapulse Raman scattering. Parameter domains are delineated in which these optical solitons exit in the ensuing model. We report the effect of model coefficients on the amplitude of Lambert W-kink solitons, which enables us to control efficiently the pulse intensity and hence their subsequent evolution. Also, moving fronts or optical shock-type solitons are obtained as a byproduct of this model. We explicate the mechanism to control the intensity of these fronts, by fine tuning the spectral filtering or gain parameter. It is exhibited that the frequency chirp associated with these optical solitons depends on the intensity of the wave and saturates to a constant value as the retarded time approaches its asymptotic value.