LIPIcs

A regular language L of finite words is composite if there are regular languages L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced and studied in [O. Kupferman and J. Mosheiff, 2015], where the complexity of deciding the primality of the language of a given DFA was left open, with a doubly-exponential gap between the upper and lower bounds. We study primality for unary regular languages, namely regular languages with a singleton alphabet. A unary language corresponds to a subset of ℕ, making the study of unary prime languages closer to that of primality in number theory. We show that the setting of languages is richer. In particular, while every composite number is the product of two smaller numbers, the number t of languages necessary to decompose a composite unary language induces a strict hierarchy. In addition, a primality witness for a unary language L, namely a word that is not in L but is in all products of languages that contain L and have an index smaller than L’s, may be of exponential length. Still, we are able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs

LIPIcs

A deterministic finite automaton (DFA) is composite if its language L() can be decomposed into an intersection ⋂_{i = 1}^k L(_i) of languages of smaller DFAs. Otherwise, is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those for which the transition monoid is a group. We provide an NP algorithm to decide whether a permutation DFA is composite, and show that the difficulty of this problem comes from the number of non-accepting states of the instance: we give a fixed-parameter tractable algorithm with the number of rejecting states as the parameter. Moreover, we investigate the class of commutative permutation DFAs. Their structural properties allow us to decide compositionality in NL, and even in LOGSPACE if the alphabet size is fixed. Despite this low complexity, we show that complex behaviors still arise in this class: we provide a family of composite DFAs each requiring polynomially many factors with respect to its size. We also consider the variant of the problem that asks whether a DFA is k-factor composite, that is, decomposable into k smaller DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete. Finally, we show that in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton alphabet

Prioritising CAP intervention needs: An improved cumulative voting approach

The process to define the 2023–2027 Common Agricultural Policy (CAP) is underway. The implementation model governing the process requires each EU Member State to design a National Strategic Plan to deliver operational actions exploiting the synergies under the two pillars of the policy. Each Plan must be built from an evidence-based needs assessment that undergoes rigorous prioritisation and planning to create comprehensive, integrated, and achievable interventions. In Italy, the success of this planning process requires all interested stakeholders to generate options for the regional authorities who plan, manage, and legislate agricultural activities. This research proposes a decision-making technique, based on the cumulative voting approach, that can be used effectively when multiple persons from different backgrounds and perspectives are engaged in problem-solving and needs prioritisation. The results indicate that the model can be applied both theoretically and practically to prioritise Strategic Plan needs that involve national and regional authorities. Validation of the model allows it to be used in the next consultative processes and for expansion to socioeconomic stakeholders

Land rent values determinants: a Hedonic Pricing approach at local scale

Farmland values are driven by a complex set of factors. Starting from the idea that land rent values may reflect several characteristics both internal and external to agricultural sector, the paper has implemented a hedonic model based on land rent values in the metropolitan area of Milan, Northern Italy, assessing the influence of climate, soil, territorial and farm variables on a sample of farms. The model is based on data at rent contract level, matched with data at farm and municipal scale retrieved from different sources. Results confirm that land rent prices are affected by some climate variables, along with territorial and farm characteristics

Spontaneous heavy cluster emission rates using microscopic potentials

The nuclear cluster radioactivities have been studied theoretically in the framework of a microscopic superasymmetric fission model (MSAFM). The nuclear interaction potentials required for binary cold fission processes are calculated by folding in the density distribution functions of the two fragments with a realistic effective interaction. The microscopic nuclear potential thus obtained has been used to calculate the action integral within the WKB approximation. The calculated half lives of the present MSAFM calculations are found to be in good agreement over a wide range of observed experimental data.Comment: 4 pages, 4 figure

Beta decay of 71,73Co; probing single particle states approaching doubly magic 78Ni

Low-energy excited states in 71,73Ni populated via the {\beta} decay of 71,73Co were investigated in an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU). Detailed analysis led to the construction of level schemes of 71,73Ni, which are interpreted using systematics and analyzed using shell model calculations. The 5/2- states attributed to the the f5/2 orbital and positive parity 5/2+ and 7/2+ states from the g9/2 orbital have been identified in both 71,73Ni. In 71Ni the location of a 1/2- {\beta}-decaying isomer is proposed and limits are suggested as to the location of the isomer in 73Ni. The location of positive parity cluster states are also identified in 71,73Ni. Beta-delayed neutron branching ratios obtained from this data are given for both 71,73Co.Comment: Accepted for publication in PR

Folding model analysis of alpha radioactivity

Radioactive decay of nuclei via emission of $\alpha$ particles has been studied theoretically in the framework of a superasymmetric fission model using the double folding (DF) procedure for obtaining the $\alpha$-nucleus interaction potential. The DF nuclear potential has been obtained by folding in the density distribution functions of the $\alpha$ nucleus and the daughter nucleus with a realistic effective interaction. The M3Y effective interaction has been used for calculating the nuclear interaction potential which has been supplemented by a zero-range pseudo-potential for exchange along with the density dependence. The nuclear microscopic $\alpha$-nucleus potential thus obtained has been used along with the Coulomb interaction potential to calculate the action integral within the WKB approximation. This subsequently yields microscopic calculations for the half lives of $\alpha$ decays of nuclei. The density dependence and the exchange effects have not been found to be very significant. These calculations provide reasonable estimates for the lifetimes of $\alpha$ radioactivity of nuclei.Comment: 7 pages including 1 figur

"Growing through relationship" - the Engagement of the Health Professional Students in the Internship Experience: a Grounded Theory Research

BACKGROUND AND AIM: Little is known about the students' engagement in the training experience and how it is lived by the health professional students. We aim at building a theoretical model of the engagement process starting from their lived experiences with Grounded Theory approach. METHODS: In-depth qualitative interviews are conducted with 12 students from the Master Degree Courses in Nursing, Physiotherapy and Prevention Techniques in the environment and in the workplace, who had carried out and/or were doing internships in the same territory (2nd and 3rd year). Results The health professions' student engagement in the training program is developed in three main phases: initial phase, central phase and final phase, where emotions, behaviours, awareness contribute to the development of the entire engagement process with different relevance. The intertwining of these different components that develop along the stages of the experience gives life to the core category: growing through relationship, which expressed the crucial role of the relational network built during the internship experience in shaping students' engagement. CONCLUSIONS: The results of this study underline the crucial role of students' engagement in the internship experience in favouring both better learning outcomes and perspective professional success and wellbeing. (www.actabiomedica.it)