Automata on linear orderings generalize the notions of finite-word and infinite-word automata. They recognize words indexed by linear orderings, defined as mappings from the elements of such orderings to a finite alphabet. The reachability problem has already been solved for automata on scattered linear orderings, i.e., those that do not involve density, as well as for automata over all linear orderings. The main contribution of this work is to provide a polynomial algorithm that decides reachability over the specific linear orderings R and Q. Given an automaton on linear orderings and a pair (p, q) of its states, this procedure decides in polynomial time whether this automaton admits a path from p to q labeled by a word indexed by R or Q. This also solves the non-emptiness problem for the language accepted by these automata restricted to the orderings of the reals and rationals. This algorithm constitutes an essential step towards designing an automata-based decision procedure for the first-order monadic theory of order interpreted over R or Q.

The SMT-LIB benchmark collection is a large set of problems for SMT solvers. It has been continuously maintained and expanded since its creation in the early 2000s by the SMT-LIB initiative. It has been used since 2005 by the annual SMT solver competition to compare the performance of SMT solvers, and by researchers to study novel solving techniques. Effective use of the collection often requires access to benchmark metadata (e.g., date, source, satisfiability status, theory symbol count, and so on). Furthermore, this metadata and the past competition results contain a wealth of historical information about the development of SMT solving. In this paper, we report on our efforts to collect and curate all metadata from the SMT-LIB benchmarks together with the results of all past SMT-COMP competitions in a single SQLite database. We also present tools to explore this database and extract relevant insights. Since APIs for SQLite databases are available for all major programming languages, the database makes it easy to add features using SMT benchmark metadata to SMT development tools. To illustrate the structure of the collected data we perform multiple case studies. In particular, we present a comparison of SMT solvers that is independent of the changing hardware and benchmarks used by the competition. The database is released annually on Zenodo, and serves as an archive of the state of SMT-LIB and, by extension, of the state of the art in SMT.

We consider the first-order theory of order over real numbers extended with monadic uninterpreted predicates. It has long been established that this theory is decidable, by different approaches such as a reduction to linear-time temporal logic over the reals, expressing the problem as a particular case of deciding the first-order theory of all linear orderings, or reasoning about restrictions of the monadic second-order theory of order. The main contribution of this work is to provide a complete self-contained proof of decidability for this logic. Additionally, our proof develops a symbolic notation system for models of satisfiable formulas, which can be seen as a first step towards an actual implementation of a decision procedure for the theory of order over the reals.

The aim of this study was to examine the possibility of consecutive spawning of the first domesticated generation (F1) of pikeperch ( Sander lucioperca). Fingerlings of pikeperch, produced in controlled reproduction from wild fish, were grown in captive conditions to sexual maturity for 2 years in concrete tanks. Histological observations revealed that the fish were in the peripheral nucleoli stage at 20-month old and ready to spawn at 2-year-old (129.3 +/- 12.9 g) with an increase in water temperature. They were injected with 200 IU of human chorionic gonadotropin per kilogram of body weight and put in to the rectangular concrete tanks with an artificial bed for each pair to spawn. The results throughout the 4 years of propagation of domesticated pikeperch showed the readiness of fish in response to spawning induction and the nest quality (surface of the nest covered by the eggs) was fairly affected by the age of fish, while no significant changes were found in fertilization and hatching rates among different ages. In conclusion, this study demonstrated that domesticated pikeperch can be spawned at 2year old and still capable of producing eggs for further years in captive conditions. This can help the fish farmers to distinguish the best age classes of domesticated pikeperch to achieve higher quantity and quality of controlled reproduction and offspring production.

Automata have been defined to recognize languages of words indexed by linear orderings, which generalize the usual notions of finite, infinite, and ordinal words. The reachability problem for these automata has already been solved for scattered linear orderings. In this paper, we design an analogous procedure that solves reachability over the specific domains ℝ and ℚ . Given an automaton on linear orderings, this procedure decides in polynomial time whether this automaton accepts at least one word indexed by ℝ or by ℚ . We claim that this algorithm constitutes an essential step to designing effective decision procedures for the first-order monadic theory of order interpreted over ℝ or ℚ .

This paper describes the TPTP format for representing interpretations. It provides a background survey that helped ensure that the representation format is adequate for different types of interpretations: Tarskian, Herbrand, and Kripke interpretations. The needs of applications that use models are considered. The syntax and semantics of the format are expounded in detail, with multiple examples. Verification of models is discussed. Some tools that support processing the format are noted. The properties of interpretations represented in the format are discussed.

Deciding formulas that mix arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set of models of the formula under analysis, and then testing whether this automaton accepts a non-empty language. A drawback is that universal quantification is usually handled by a reduction to existential quantification and complementation. For logical formalisms in which models are encoded as infinite words, this hinders the practical use of this method due to the difficulty of complementing infinite-word automata. The contribution of this paper is to introduce an algorithm for directly computing the effect of universal first-order quantifiers on automata recognizing sets of models, for formulas involving natural numbers encoded in unary notation. This paves the way to implementable decision procedures for various arithmetic theories.

To improve the quality of reproduction in Eurasian perch, Perca fluviatilis L., which is a promising candidate for Eurasian freshwater aquaculture that is currently cultivated in recirculating aquaculture systems (RAS), investigating the hormones that mediate and affect reproduction in this species is indispensable. The literature defines a group of four major corticosteroids (11-deoxycorticosterone, 11-deoxycortisol, corticosterone and cortisol) that might mediate critical stages of reproduction in female perch. Unfortunately, neither the basic roles nor the kinetics of these four corticosteroids throughout the reproductive cycle of female perch have been well defined to date. In this study, we therefore elucidated the plasma kinetics of these four corticosteroids during the reproductive cycle of domesticated female perch while monitoring the expression of the different receptors and enzymes that mediate their production and possible functions. Additionally, we performed an in vitro experiment during late vitellogenesis to investigate the possible direct roles of these steroids during that stage. Our results revealed that these four corticosteroids were detectable throughout the reproductive cycle, and the levels of most of them (11-deoxycorticosterone, 11-deoxycortisol, and cortisol) fluctuated significantly depending on the stage of reproduction. 11-Deoxycorticosterone and 11-deoxycortisol exhibited their highest levels, 1.8 ng/ml and 58 ng/ml, respectively, at the beginning of the reproductive cycle. By the end of the reproductive cycle, 11-deoxycortisol and cortisol plasma levels exhibited a surge, reaching 58 ng/ml and 150 ng/ml, respectively. During the perch reproductive cycle, the corticosteroid receptor complex is not regulated only at the hormone level, as the expression levels of all corticosteroid receptor genes showed a progressive and similar decline. In vitro exposure of vitellogenic oocytes to some of these corticosteroids (11-deoxycorticosterone and 11-deoxycortisol) induced an increase in yolk globule diameter and a decrease in the density of yolk globules, which indicates the involvement of both of these hormones in yolk globule coalescence. Taken together, these results implicate corticosteroids in the reproductive cycle, although the related cellular mechanisms remain to be investigated.

Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set of models of the formula under analysis, and then testing whether this automaton accepts a non-empty language. A drawback is that universal quantification is usually handled by a reduction to existential quantification and complementation. For logical formalisms in which models are encoded as infinite words, this hinders the practical use of this method due to the difficulty of complementing infinite-word automata. The contribution of this paper is to introduce an algorithm for directly computing the effect of universal first-order quantifiers on automata recognizing sets of models, for formulas involving natural numbers encoded in unary notation. This makes it possible to apply the automata-based approach to obtain implementable decision procedures for various arithmetic theories.

First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are often undecidable, as is, for instance, Presburger arithmetic extended with a single uninterpreted unary predicate. In the SMT world, difference logic is a quite popular fragment of linear arithmetic which is less expressive than Presburger arithmetic. Difference logic on integers with uninterpreted unary predicates is known to be decidable, even in the presence of quantifiers. We here show that (quantified) difference logic on real numbers with a single uninterpreted unary predicate is undecidable, quite surprisingly. Moreover, we prove that difference logic on integers, together with order on reals, combined with uninterpreted unary predicates, remains decidable.

Optimizing production in aquaponics requires in-depth knowledge of the plant, fish and microbial compartments. This opinion paper is focused on root-released organic compounds and their implication in aquaponics, an area that has received little to no direct research to date. Key scientific literature from two distinct fields of study-phytochemicals in aquaculture science and root exudates in plant science-reveals possible pathways and effects. Root exudates, passively or actively released by plants as a stress response, protection or signalling, have the potential to influence the systems microbiome and the cultured fish, as similar phytochemicals have been found to affect bacterial abundance and diversity and fish health and behaviour. These are key aspects to run aquaponics successfully, which shows the need for further investigation to better understand sources and mechanisms of such molecules and possible ways to harness beneficial effects that can guide new research directions as the role of aquaponics grows in recirculating aquaculture.

Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its latest stable version, the SMT-LIB standard defines a theory of algebraic datatypes, which is currently supported by several mainstream SMT solvers. In this paper, we study this particular theory of datatypes and prove that it is strongly polite, showing how it can be combined with other arbitrary disjoint theories using polite combination. The combination method uses a new, simple, and natural notion of additivity that enables deducing strong politeness from (weak) politeness.

Polyculture offers an alternative to monoculture in recirculated aquaculture systems (RAS). Nevertheless, RAS polyculture can potentially result in beneficial as well as detrimental consequences. This places a premium on assessing consequences of a particular polyculture prior to its implementation in farming production. In fish aquaculture, most of previous assessments of polyculture consequences have been carried out through multi-trait approach by analysing independently species traits related to a single biological function. Yet, polyculture can impact many biological functions and the overall consequences are the result of multiple interactions from different functions. Therefore, an integrative analysis is required to synthesise the polyculture consequences at the multi-trait levels. Here we propose a multi-trait evaluation framework (i.e. considering traits related to multiple functions), for the polyculture consequence assessment. We analyse this framework through multi-variate analysis prior integrating results for each trait. As test case, we used pikeperch (Sander lucioperca), reared in monoculture and in polyculture with European perch (Perca fluviatilis), common carp (Cyprinus carpio) and black-bass (Micropterus salmoides). Our results revealed the importance of applying multi-trait framework to obtain a reliable assessment of fish polycultures. The divergence that might occur in the expression of some traits in the same polyculture has been highlighted to support this argument. Through the integration method, it was possible to find the suitable combination(s) of fish and to exclude the unsuitable ones. For future researches, we suggest to support the multi-trait assessment by weighting the traits involved in the multivariate analysis.

In the context of global change, the aim of this study was to investigate the effects of temperature on the survival rate and various variables (development time, morphometric measures, energy values) for both embryos and post-hatch stages until first food intake of northern pike (Esox lucius). We applied five constant temperatures (8, 10, 12, 14 and 16 °C) and their effects were analyzed during the entire endogenous feeding period at three stages: hatching, emergence and first food intake. Around 80,000 eggs from five females and five males were used. As expected, the development time was three times longer at 8 than at 16 °C. The survival rate of well-formed post-hatch stages at the end of the endogenous feeding period was similar between temperatures: 76% (10 °C), 73% (12 °C), 72% (14 °C), 72% (16 °C), except at 8 °C (70%). Also at 16 °C, post-hatch stages were larger and had the highest energy value when starting feeding exogenously. These results are in accordance with current models that predict an increase of the distribution area of northern pike in France in coming decades associated with climate change projections (1 to 5 °C increase by 2100 for France).

The pikeperch is a freshwater/brackish water fish species with growing interest for European aquaculture. Wild populations show signs of decline in many areas of the species natural range due to human activities. The comparative evaluation of genetic status in wild and domesticated populations is extremely useful for the future establishment of genetic breeding programs. The main objective of the present study was to assess and compare the genetic variability of 13 domesticated populations from commercial farms and 8 wild populations, developing an efficient microsatellite multiplex tool for genotyping. Partial cytochrome b gene sequences were also used to infer phylogeographic relationships. Results show that on average, the domesticated populations do not exhibit significantly lower levels of genetic diversity compared to the wild ones and do not suffer from inbreeding. Nuclear data provide evidence that pikeperch populations in Europe belong to at least two genetically differentiated groups: the first one is predominantly present in Northern Europe and around the Baltic Sea, while the second one comprises populations from Central Europe. In this second group, Hungarian origin populations constitute a differentiated stock that needs special consideration. Aquaculture broodstocks analyzed appear to contain fish of a single origin with only a few exceptions.

In European aquaculture, Eurasian perch, Perca fluviatilis L., is perceived as one of the most highly valuable freshwater fish species and a strong candidate for the development of freshwater aquaculture. In the pursuit of improving the quality of reproduction in this domesticated species, investigating the hormones mediating the final oocyte maturation (FOM) is therefore indispensable. But, the exact nature of the maturation-inducing hormone (MIH) in Eurasian perch is unknown. To further validate the existence of a maturation-inducing activity behind potential hormonal candidates in this species, we in vitro tested a group of nine hormones: cortisol (Co), 11-deoxycortisol (11-D), corticosterone (coS), 11-deoxycorticosterone (DOC), 17α,20βdihydroxy-4-pregnen-3-one (DHP) and 17α,20β,21 trihydroxy-4-pregnen-3-one (THP), prostaglandin E2 (PGE2), estradiol-17β (E2) and testosterone (T), in their ability to trigger FOM advancement and the production of sex steroids potentially involved in FOM. Using mature female perch, two in vitro experiments were conducted with oocytes at the start of the FOM. The follicles were incubated for 62 h in Cortland media with and without human chorionic gonadotropin (hCG). By the end of the incubation, only DHP and THP triggered the full advancement in FOM even at low doses with the effect of DHP being in vivo validated. However, the de novo productions of E2 and DHP were not shown to be regulated by either of the MIH candidates. Progestagens are hence more credible candidates as MIH than corticosteroids in Eurasian perch. Our in vitro study also revealed that both PGE2 and DHP are strongly associated with ovulation and that PGE2 might have slightly contributed to such DHP activity.