A fine-grained computational interpretation of Girard’s intuitionistic proof-nets

This paper introduces a functional term calculus, called pn, that captures the essence of the operational semantics of Intuitionistic Linear Logic Proof-Nets with a faithful degree of granularity, both statically and dynamically. On the static side, we identify an equivalence relation on pn-terms which is sound and complete with respect to the classical notion of structural equivalence for proof-nets. On the dynamic side, we show that every single (exponential) step in the term calculus translates to a different single (exponential) step in the graphical formalism, thus capturing the original Girard’s granularity of proof-nets but on the level of terms. We also show some fundamental properties of the calculus such as confluence, strong normalization, preservation of β-strong normalization and the existence of a strong bisimulation that captures pairs of pn-terms having the same graph reduction.

An application of parallel cut elimination in multiplicative linear logic to the Taylor expansion of proof nets

We examine some combinatorial properties of parallel cut elimination in multiplicative linear logic (MLL) proof nets. We show that, provided we impose a constraint on some paths, we can bound the size of all the nets satisfying this constraint and reducing to a fixed resultant net. This result gives a sufficient condition for an infinite weighted sum of nets to reduce into another sum of nets, while keeping coefficients finite. We moreover show that our constraints are stable under reduction. Our approach is motivated by the quantitative semantics of linear logic: many models have been proposed, whose structure reflect the Taylor expansion of multiplicative exponential linear logic (MELL) proof nets into infinite sums of differential nets. In order to simulate one cut elimination step in MELL, it is necessary to reduce an arbitrary number of cuts in the differential nets of its Taylor expansion. It turns out our results apply to differential nets, because their cut elimination is essentially multiplicative. We moreover show that the set of differential nets that occur in the Taylor expansion of an MELL net automatically satisfies our constraints. Interestingly, our nets are untyped: we only rely on the sequentiality of linear logic nets and the dynamics of cut elimination. The paths on which we impose bounds are the switching paths involved in the Danos--Regnier criterion for sequentiality. In order to accommodate multiplicative units and weakenings, our nets come equipped with jumps: each weakening node is connected to some other node. Our constraint can then be summed up as a bound on both the length of switching paths, and the number of weakenings that jump to a common node.

An Insect- and Rain-Proof Net Raises the Production and Quality of Chinese Bayberry by Preventing Damage From Insects and Altering Bacterial Communities

Chinese bayberry (Myrica rubra) is a popular, nutrient- and antioxidant-rich fruit in Asia. However, it is susceptible to Drosophila during ripening, which disrupts production and causes economic loss. This study compared the effects of insecticides, insect-proof nets (IPNs), and insect- and rain-proof nets (IRPNs) on Chinese bayberry production and quality. Drosophila was absent in fruits from IPN- or IRPN-treated trees but only significantly reduced by insecticides. IPNs and IRPNs significantly increased fruit diameter, weight, edible rate and the Brix/acid ratio, and IRPNs had the strongest effect. Analysis of 16S rDNA showed that fruits collected from differently treated trees had unique bacterial communities. In IRPN fruits, Acetobacter and Gluconobacter were significantly decreased, reducing sugar consumption and disease; in addition, PICRUSt analysis predicted imputed functional profiles related to carbohydrate and nitrogen metabolism and mineral transport for fruit growth and development. This study proposed the use of IRPNs for improving Chinese bayberry production and quality.

Evaluation of Silica-Coated Insect Proof Nets for the Control of Aphis fabae, Sitophilus oryzae, and Tribolium confusum

Insect proof nets are widely used in agriculture as mechanical and physical barriers to regulate pest populations in a greenhouse. However, their integration in the greenhouse ventilation openings is highly associated with the decrease of air flow and the adequate ventilation. Thus, there is need for alternative pest management tools that do not impair adequate ventilation. In the present study, we tested four net formulations of relatively large mesh size coated with SiO2 nanoparticles, namely, ED3, ED3-P, ED5, and ED5-P to evaluate their insecticidal properties against adults of Aphis fabae and Sitophilus oryzae and larvae of Tribolium confusum. ED3 and ED5 nets were coated with SiO2 nanoparticles of different diameter, while in the case of ED3-P and ED5-P, paraffin was added to increase the mass of the deposited particles on the net’s surface. In the first series of bioassays, the knockdown and mortality rates of these species were evaluated after exposure to the aforementioned net formulations for 5, 10, 15, 20, 25, 30, 60, 90, and 180 min. In the second series of bioassays, knockdown and mortality of these species were recorded after 1, 7, and 10 days of post-exposure to the nets for different time intervals (15, 30, and 60 min). Based on our results, all nets significantly affected A. fabae, since all insects were dead at the 1-day post-exposure period to the silica-treated nets. Conversely, at the same interval, no effect on either S. oryzae adults or T. confusum larvae was observed. However, in the case of S. oryzae, the efficacy of all nets reached 100% 7 days after the exposure, even for adults that had been initially exposed for 15 min to the treated nets. Among the species tested, T. confusum larvae exhibited the lowest mortality rate, which did not exceed 34% at the 10 days of post-exposure interval. Our work underlines the efficacy of treated nets in pest management programs, under different application scenarios, at the pre- and post-harvest stages of agricultural commodities.

Mitigation of climatic conditions and pest protection provided by insect-proof nets for cabbage cultivation in East Africa

SummaryAlthough several studies have underlined the advantages of using insect-proof nets to improve yields while reducing the use of pesticides, one obstacle to the diffusion of this technique in tropical conditions is the associated increase in temperature in the tunnel. The aim of this work was to assess the interest of combining the physical protection provided by nets against insect pests with the beneficial impacts of using shade nets to grow cabbages. A two-season experiment was set up to compare temperature conditions, insect pest populations, yields, and the quality of cabbage crops grown in the open field and in low tunnels covered with nets providing different degrees of shading, 17.2% by white and 50.1% by silver nets. During the day, the temperature under the white and silver nets was 10.4 °C and 6.3 °C higher, respectively, than in the open field in the first season, and 6.5 °C and 5.9 °C higher in the second season. Both insect-proof nets significantly reduced insect pest populations and hence the need for insecticide treatments. The white nets increased marketable yield by 45.4% in the first season and by 16.4% in the second compared to yields in the open field, whereas silver nets reduced yield by 18.6% and 15.0%, respectively. The reduction in yield under silver nets was attributed to excessive shading that prevented the light requirements of cabbage crops from being fulfilled. Economic analysis raised some concerns about the profitability of the use of netting to grow cabbage due to investment costs and the lack of premium prices for vegetables produced with fewer pesticides in local markets.