Linear Order Research Articles

How Competitive Is the Agriculture in European Union Member States? An Assessment of Changes over the Past Decade

The need to monitor changes in the level of agricultural competitiveness of EU member states necessitates the development of an appropriate set of indicators to answer the question of whether a country is improving its competitive position. This paper proposes a synthetic measure for assessing the agricultural competitiveness in the member states of the European Union (EU) from 2012 to 2021. Statistics on the respective indicators were derived from the Eurostat database and Agri-Food Data Portal. The survey was based on linear ordering using a standardised sums approach. This implies that member states vary in competitiveness in the agricultural sector. From 2012 to 2021, the most competitive countries were Denmark, the Netherlands, and Belgium. Simultaneously, the rankings of agricultural competitiveness changed over the 10 years under review. The highest improvement rates were recorded in Finland, Slovakia, and Ireland. However, the differences between the old and new member states are still explicit. None of the new member states of the EU were in the top ten with regard to their agricultural competitiveness. Many areas associated with agriculture in these countries require considerable improvement. We also carried out a principal component analysis (PCA), which allowed us to identify the parameters conveying relevant information on the analysed phenomenon and unveil the hidden structures in the primary data set. We discovered that the share of the EU’s agricultural output in the EU exports of agricultural products explained variations in the agricultural competitiveness within member states.

Parametric factorization of non linear second order differential equations

In this paper the factorization method introduced by Rosu & Cornejo-Pérez for second order non linear differential equations is generalized by adding a parameter in order to obtain the general solutions for the mixed quadratic and linear Liénard type equation. The new parametric factorization is used to obtain complete analytic solutions for nonlinear second order differential equations. The parametric factorization introduced in this article reduces to the standard factorization scheme when the parameter goes to zero. As an example, we apply the parametric factorization approach to solve the generalized Fisher equation and the Israel-Stewart cosmological model. The parametric factorization presented in this paper can be used in other non linear mixed Liénard type equations.

Design of fractional MOIF and MOPIF controller using PSO algorithm for the stabilization of an inverted pendulum‐cart system

AbstractThe topic of this paper is the design of two fractional order schemes, based on a state feedback for linear integer order system. In the first one of the state feedback is associated with a fractional order integral () controller. In the second structure the state feedback is associated with a fractional order proportional integral () controller. With such controllers, the closed loop system with state feedback described by the state equations splits in n‐subsystems with different fractional orders derivatives of the state variable. In order to find the optimal parameters value of both controllers () and (), a multi‐objective particle swarm optimization algorithm is used, with the integral of absolute error, the overshoot , the Buslowicz stability criterion are considered as objective functions. The multi‐objective integral fractional order controller and the multi‐objective proportional integral fractional order controller are applied to stabilize the inverted pendulum‐cart system (IP‐C), and their performance is compared to the fractional order controller. The simulation results of these innovative controllers are also compared with those obtained by conventional proportional–integral–derivative and fractional order proportional–integral–derivative controllers. The robustness of the proposed controllers against disturbances is investigated through simulation runs, considering the non‐linear model of the IP‐C system. The obtained results demonstrate that our approach not only leads to high effectiveness but also showcases remarkable robustness, supported by both simulation and experimental results.

Confidence intervals for odds ratio from multistage randomized phase II trials.

A multi-stage randomized trial design can significantly improve efficiency by allowing early termination of the trial when the experimental arm exhibits either low or high efficacy compared to the control arm during the study. However, proper inference methods are necessary because the underlying distribution of the target statistic changes due to the multi-stage structure. This article focuses on multi-stage randomized phase II trials with a dichotomous outcome, such as treatment response, and proposes exact conditional confidence intervals for the odds ratio. The usual single-stage confidence intervals are invalid when used in multi-stage trials. To address this issue, we propose a linear ordering of all possible outcomes. This ordering is conditioned on the total number of responders in each stage and utilizes the exact conditional distribution function of the outcomes. This approach enables the estimation of an exact confidence interval accounting for the multi-stage designs.

Scrutinizing coupled vector dark energy in light of data

Since current challenges faced by ΛCDM might be hinting at new unravelled physics, here we investigate a plausible cosmological model where a vector field acts as source of dark energy. In particular, we examine whether an energy-momentum exchange between dark energy and dark matter could provide an explanation for current discrepancies in cosmological parameters. We carefully work out equations governing background and linear order perturbations and implement them in a Boltzmann code. We found that a negative coupling makes the dark energy equation of state less negative and closer to a cosmological constant during the matter dominated epoch than an uncoupled vector dark energy model. While the effect of the coupling is hardly noticeable through its effect on matter density perturbations, matter velocity perturbations and gravitational potentials are enhanced at late-times when dark energy dominates. Therefore, data of redshift space distortions help to narrow down these kinds of couplings in the dark sector. We computed cosmological constraints and found common parameters also present in ΛCDM are in good agreement with the Planck collaboration baseline result. Our best fit for a negatively coupled vector field predicts a higher growth rate of matter perturbations at low redshift, thus exacerbating the disagreement with redshift space distortions data. While a positively coupled vector field can lead to power suppression of P m(k,z = 0) on small scales as well as a lower growth rate of matter perturbations than the standard model, it might compromise the goodness of fit to the CMB angular power spectrum on small scales. We conclude that our negatively coupled vector dark energy model does not solve current tensions (i.e., H 0 and σ 8). Moreover, having three additional parameters with respect to ΛCDM, the negatively coupled vector dark energy model is heavily disfavoured by Bayesian evidence.

Novel Approaches to the Formulation of Scheduling Problems

This paper presents two novel formulations for scheduling problems, namely order-position hybrid formulation (OPH) and order-disjunctive hybrid formulation (ODH), which extend and combine parts of existing formulation strategies. The first strategy (OPH) is based on sequence position and linear ordering formulations, adding relationships between constraints that allow relaxing some decision variables. The second approach (ODH) is based on linear ordering and disjunctive formulations. In this work, we prove ODH to be the most efficient formulation known so far. The experiments have been carried out with a large set of problems, which consider single machines and identical parallel machines. Computational results show that OPH is better than the rest of the existing formulations for the case of weighted completion objectives, while ODH turns out to be the best approach for most scenarios studied.

ON THE STRUCTURE OF PUNCTUAL LINEAR ORDERS ISOMORPHIC TO THE LEAST LIMIT ORDINAL

The algorithmic complexity of presentations for various structures receives significant attention in modern literature. The main tool for determining such complexities is reducibility. It is a mapping that preserves relations of signature (for example, equivalence relation, orders, and so on). This work is dedicated to the study of punctual representations of the least limit ordinal with respect to primitive recursive reducibility. We denote this structure as PR(ω). In particular, the paper examines the properties of structures Ω, consisting of computable copies of the least limit ordinal with respect to computable reducibility, and Peq, consisting of punctual equivalence relations with respect to primitive recursive reducibility. We say that the linear order L is reducible to the linear order R, if there exists a total function ρ such that (χ, γ) Є L if and only if (ρ(χ), ρ(γ)) Є R. Reducibility is called computable (primitive recursive) if the function that performs the reducibility is computable (primitive recursive). It is shown that the degree of ω is not the least degree in PR(ω), as it was in Ω. The structure PR(ω) does not contain maximal degrees, and this structure is not dense. Also, an example of an incomparable pair that has the least upper bound is given.

Low scattered linear orders

Abstract In 1998 R. Downey formulated a problem: to describe a property $P$ of classical order types, which guarantees that if $\mathcal{L}$ is a low linear order and $P$ holds for the order type of $\mathcal{L}$ then $\mathcal{L}$ is isomorphic to a computable linear order. We find a new such property $P$. Also, we give an upper bound on a complexity of an isomorphism between computable and low copies and show that this bound is sharp.

Big Ramsey degrees in ultraproducts of finite structures

We develop a transfer principle of structural Ramsey theory from finite structures to ultraproducts. We show that under certain mild conditions, when a class of finite structures has finite small Ramsey degrees, under the (Generalized) Continuum Hypothesis the ultraproduct has finite big Ramsey degrees for internal colorings. The necessity of restricting to internal colorings is demonstrated by the example of the ultraproduct of finite linear orders. Under CH, this ultraproduct L⁎ has, as a spine, η1, an uncountable analogue of the order type of rationals η. Finite big Ramsey degrees for η were exactly calculated by Devlin in [5]. It is immediate from [39] that η1 fails to have finite big Ramsey degrees. Moreover, we extend Devlin's coloring to η1 to show that it witnesses big Ramsey degrees of finite tuples in η on every copy of η in η1, and consequently in L⁎. This work gives additional confirmation that ultraproducts are a suitable environment for studying Ramsey properties of finite and infinite structures.

Weight distribution of random linear codes and Krawtchouk polynomials

AbstractFor and pick uniformly at random vectors in and let be the orthogonal complement of their span. Given with , let be the random variable that counts the number of words in of Hamming weight (where is assumed to be an even integer). Linial and Mosheiff [Random Struct. Algorithms. 62 (2023), 68Ű‐130] determined the asymptotics of the moments of of all orders . In this paper we extend their estimates up to moments of linear order. Our key observation is that the behavior of the suitably normalized moment of is essentially determined by the norm of the Krawtchouk polynomial .

A systematic approach to obtain the analytical solution for linear second order ordinary differential equations: part I

A systematic approach to obtain the analytical solution for linear second order ordinary differential equations: part I

A reactive molecular dynamics model for uranium/hydrogen containing systems.

Uranium-based materials are valuable assets in the energy, medical, and military industries. However, understanding their sensitivity to hydrogen embrittlement is particularly challenging due to the toxicity of uranium and the computationally expensive nature of quantum-based methods generally required to study such processes. In this regard, we have developed a Chebyshev Interaction Model for Efficient Simulation (ChIMES) that can be employed to compute energies and forces of U and UH3 bulk structures with vacancies and hydrogen interstitials with accuracy similar to that of Density Functional Theory (DFT) while yielding linear scaling and orders of magnitude improvement in computational efficiency. We show that the bulk structural parameters, uranium and hydrogen vacancy formation energies, and diffusion barriers predicted by the ChIMES potential are in strong agreement with the reference DFT data. We then use ChIMES to conduct molecular dynamics simulations of the temperature-dependent diffusion of a hydrogen interstitial and determine the corresponding diffusion activation energy. Our model has particular significance in studies of actinides and other high-Z materials, where there is a strong need for computationally efficient methods to bridge length and time scales between experiments and quantum theory.

Development of a continuous reheating furnace state-space model based on the finite volume method

This study developed a modeling approach of a continuous steel slab reheating furnace process as a particular case of spatially distributed parameter systems involving radiative heat transfer. The aim of the resulting mathematical model, which is both detailed and computationally tractable, is to serve in prospective advanced process control (APC) and model-based optimization. The two-dimensional state-space model is introduced to accurately simulate the temperature distribution and dynamics, using the finite volume method (FVM) to incorporate essential heat transfer phenomena, including radiation, conduction, convection, advection, and simple combustion. The study presents a novel furnace measurement model that interprets temperature sensor readings (useful for state estimation), a benefit of the FVM treatment of radiative heat transfer. Strategies for linearization and model order reduction, such as balanced truncation, are proposed to facilitate real-time control. The simulation case study demonstrates the targeted capabilities of the model. The accuracy of the model is verified through comparisons with more complex computational fluid dynamics (CFD) software models. The study prioritizes theoretical modeling over empirical validation of a specific furnace unit, omitting experimental validation at this stage.

First-Order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications

Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces , have been used for temporal specification in automated planning, process modelling, (runtime) verification and synthesis of programs, as well as in knowledge representation and reasoning. In this paper, we focus on first-order temporal logic on finite traces . We first investigate preservation of equivalences and satisfiability of formulas between finite and infinite traces, by providing a set of semantic and syntactic conditions to guarantee when the distinction between reasoning in the two cases can be blurred. Moreover, we show that the satisfiability problem on finite traces for several decidable fragments of first-order temporal logic is ExpSpace -complete, as in the infinite trace case, while it decreases to NExpTime when finite traces bounded in the number of instants are considered. This leads also to new complexity results for temporal description logics over finite traces. Finally, we investigate applications to planning and verification, in particular by establishing connections with the notions of insensitivity to infiniteness and safety from the literature. Linear temporal logic over finite traces is used as a formalism for temporal specification in automated planning, process modelling and (runtime) verification. In this paper, we investigate first-order temporal logic over finite traces, lifting some known results to a more expressive setting. Satisfiability in the two-variable monodic fragment is shown to be ExpSpace -complete, as for the infinite trace case, while it decreases to NExpTime when we consider finite traces bounded in the number of instants. This leads to new complexity results for temporal description logics over finite traces. We further investigate satisfiability and equivalences of formulas under a model-theoretic perspective, providing a set of semantic conditions that characterise when the distinction between reasoning over finite and infinite traces can be blurred. Finally, we apply these conditions to planning and verification.

Estimation of the Impact of Vaccination Intervention on Recovered Coronavirus Patients

This work estimated the impact of vaccination intervention on coronavirus patients who have recovered from the disease and the vulnerability index of the recovered population due to the impact of vaccine was also investigated. This work adopted a numerical solution to study the continuous dynamical system of linear first order differential equations describing a SEIR (Susceptible, Exposed, Infected, Recovered) model on the spread of Coronavirus Disease – 2019 (COVID-19). To tackle this problem, MATLAB ordinary differential equation of order 45 (ODE45) numerical method was adopted for the analysis. The vulnerability index of the recovered population was low due to the impact of vaccine meaning that the recovered population will gain immunity and they will not be re-infected. The study recommended that coronavirus patients who have recovered from the disease should ensure that they have vaccination administered to them to avoid re-occurrence of the virus attack as an intervention strategy. 

Analysis of the chemical diffusion master equation for creation and mutual annihilation reactions

We propose an infinite dimensional generating function method for finding the analytical solution of the so-called chemical diffusion master equation (CDME) for creation and mutual annihilation chemical reactions. CDMEs model by means of an infinite system of coupled Fokker–Planck equations the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles; here, we focus an creation and mutual annihilation chemical reactions combined with Brownian diffusion of the single particles. Using our method we are able to link certain finite dimensional projections of the solution of the CDME to the solution of a single linear fourth order partial differential equation containing as many variables as the dimension of the aforementioned projection space. Our technique extends the one presented in Lanconelli [J. Math. Anal. Appl. 526, 127352 (2023)] and Lanconelli et al. [arXiv:2302.10700 [math.PR] (2023)] which allowed for an explicit representation for the solution of birth-death type CDMEs.

Design strategy of microbially produced semiconductor maquettes of Cu2Se4SnZn8+ crystal alloy for enhanced harmonic generations

During present study, we have attempted to present few nanosized maquettes of a semiconductor alloy which can be designed under the action of microbes to be utilize for their high-tech applications like their nonlinear optical (NLO) applications. All the designed maquettes are studied for their geometrical, optical, electronic transitions and bonding interactions. It was found that inclusion of late transition metals is more effective in tuning them as NLO switches. Also, the last three maquettes presented both electronegative and electropositive regions to display them as non-sized magnets. Their linear polarizability (<α0 > ), first hyper-polarizability (β0) and second order hyperpolarizability (γ0) values were found as: 0.08–11.42 × 10-24, 0.08.71–11.42 × 10-24, 1.42–71.30 × 10-24 esu respectively. These values were significantly higher than the one presented in literature The intention of this investigation was to investigate the NLO properties of Cu2Se4SnZn8+ crystals for future high-tech applications.

Effect of R&D activity on level of innovation of EU countries in 2014 and 2020.

Research and development carried out by companies are pivotal for innovative economies of countries, especially in the unpredictable and changing social, economic and political environment. In this context, it is very important to answer, which factors identify the effectiveness of measures in relation to R&D activity and innovativeness in EU countries and how should the degree of development of a country be assessed in terms of R&D activity? The purpose of this article is to verify level of innovativeness and degree of research and development (R&D) activity in EU countries in the years 2014 and 2020 using Hellwig's measure of development. To achieve this, qualitative and quantitative analysis, synthesis, deduction and induction, comparative analysis, and reasoning by analogy of phenomena were employed. The research was conducted on the basis of the expertly selected variables for their relation to R&D activity from a number of sources, such as Eurostat, World Bank Data, etc.. The indicated variables were analysed using statistical methods and then subjected to a linear ordering procedure based on the Hellwig development pattern method. Thanks to the research results, it is possible to indicate areas in which the initiation of activities would have the greatest degree of influence on development of R&D activity, thus influencing the increase in the level of innovativeness of a country. Indicators relating to R&D activity were selected and then used as variables to study the effect of the degree of R&D activity in EU countries in the years 2014 and 2020 on the level of innovativeness of these countries. The conducted research coincides with the results presented in the European Innovation Scoreboard. There is a significant correlation between the development of R&D activities and innovation performance.

Nothing to it: a reply to Wheeler's "much ado about nothing".

Wheeler (Cladistics 2023, 39, 475) recently suggested that the issues with inapplicable characters in phylogenetic analysis can be dealt with directly by treating observed absences of a feature not in a separate absence/presence character but as insertion/deletion events in a complex character that describes the feature in all its variation; and that this dynamic homology view can be achieved by imposing a sequence or linear order on a set of characters and by analysing the resulting sequence character using custom alphabet tree alignment algorithms. As Wheeler observed, this approach can lead to considering inappropriate character states (such as a head state and a foot state) homologous. We show that it is also sensitive to the specific ordering assumption used and that such different character orders can lead to a preference for different trees. We present a simple four-taxon dataset with observations of absence, but no inapplicable characters or other kinds of character dependence, for which the dynamic homology framework gives different results to classic algorithms for independent characters, including an optimal tree with biologically impossible reconstructions at inner nodes (every terminal has a head but the inner nodes are headless). We show how these issues can be solved by removing the character ordering assumption that the approach requires. Doing so, the dynamic homology framework reduces in general to Maddison's (Syst. Biol. 1993, 42, 576) well-known proposal to deal with inapplicability using step matrix analysis of complex characters. If in addition costs are interpreted in terms of homology, it reduces to Goloboff et al.'s (Cladistics 2021, 37, 596) step matrix implementation for maximization of homology as applied to inapplicable characters. However, if used with homogeneous costs, as Wheeler suggested, it reduces to unordered analysis of such complex characters, which is known to treat tails that may share many observed features as irrelevant for establishing kinship when they differ in just one feature, e.g. colour.

Early humans out of Africa had only base-initial numerals

The vast majority of languages have numerals involving multiplication. Cross-linguistically, a numeral that involves a multiplier and a numeral base can be base-final, e.g., three hundred [three × hundred] in English, or base-initial, e.g., ikie ita [hundred × three] in Ibibio (Niger-Congo). A worldwide survey of 4099 languages reveals that 39% of the languages are base-initial, 48% are base-final, 4% use both orders, and 8% are without numeral bases. As the first step towards explaining this diversity and worldwide distribution, we offer convergent evidence to support the hypothesis that the languages of early humans in Africa had base-initial numerals. From a linguistic point of view, linearization is necessary for the verbal expression of multiplicative numerals. Between the two linear orders of multiplication, we demonstrate that the base-initial order has an initial advantage in communicative efficiency. We also offer typological evidence from the dominant head-initial word order in present-day numeral systems and nominal phrases in African languages. Finally, results from a phylogenetic analysis based on a global tree of human languages show that the base-initial order is more stable diachronically and more likely to be at the root of the reconstructed tree of languages in Africa between 100 and 150 thousand years ago. The dominant base-final order in non-African languages of modernity is thus likely to be a development after the Out-of-Africa exodus between 60 and 80 thousand years ago.