Minimisation of Multiplicity Tree Automata

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a polynomial bound in the standard Turing model would require a breakthrough in the complexity of polynomial identity testing by proving that the latter problem is logspace equivalent to the decision version of minimisation. The developed techniques also improve the state of the art in multiplicity word automata: we give an NC algorithm for minimising multiplicity word automata. Finally, we consider the minimal consistency problem: does there exist an automaton with $n$ states that is consistent with a given finite sample of weight-labelled words or trees? We show that this decision problem is complete for the existential theory of the rationals, both for words and for trees of a fixed alphabet rank.Comment: Paper to be published in Logical Methods in Computer Science. Minor editing changes from previous versio

Teacher Shocks and Student Learning: Evidence from Zambia

Following a tradition that relates household-level shocks to educational attainment, we examine the impact of teacher-level shocks on student learning. As a plausible measure for these shocks, we use teacher absenteeism during a 30-day recall period. A 5-percent increase in teacher absence rate reduced learning by 4 to 8 percent of average gains over the year, for both Mathematics and English. The estimated impacts are substantial and, in addition to the losses due to time away from class, likely reflect lower teaching quality when in class and less lesson-preparation when at home. Health problems-primarily their own illness and the illnesses of family members-account for more than 60 percent of teacher absenteeism. This suggests both that households are unable to substitute adequately for school-level teaching inputs and that, to support human capital formation, insurance at the school-level may be a policy priority that is worth exploring further

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops

In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. We determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.Comment: 42 pages, 6 figures, 8 tables; v2: minor corrections and improvement

Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata

We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata (without epsilon-transitions). We first show a general characterization of probabilistic bisimilarity in terms of two-player games, which naturally reduces checking bisimilarity of probabilistic labelled transition systems to checking bisimilarity of standard (non-deterministic) labelled transition systems. This reduction can be easily implemented in the framework of pPDA, allowing to use known results for standard (non-probabilistic) PDA and their subclasses. A direct use of the reduction incurs an exponential increase of complexity, which does not matter in deriving decidability of bisimilarity for pPDA due to the non-elementary complexity of the problem. In the cases of probabilistic one-counter automata (pOCA), of probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic process algebras (i.e., single-state pPDA) we show that an implicit use of the reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and 2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic versions. The bisimilarity problems for OCA and vPDA are known to have matching lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively); we show that these lower bounds also hold for fully probabilistic versions that do not use non-determinism

Are Antidumping Duties an Antidote for Predation?

Since price discrimination and selling below cost arise in the normal course of business and are usually legal for home firms, countering these practices by foreign firms provides a very weak rationale for antidumping duties. If antidumping duties were to provide a systematic defense against predation by foreign firms, however, a strong ''fair-trade'' justification would remain. This paper adapts the classic entry-deterrence analysis of Dixit (1979) and Brander and Spencer (1981) to provide a simple treatment of predation, which is applicable with price leadership as well as quantity leadership. Although situations of cross-border predation appear to be quite rare, foreign firms may sometimes find themselves in leadership positions if they have to make shipments and/or set prices before their home rivals. This paper shows that, in the context of such an international leadership game, predation ma y occur without dumping and vice versa. Further, when dumping and predation do coexist, a sophisticated form of antidumping duty would prevent predation, but the simple antidumping duties that are generally observed in practice will often be insufficient. Consequently, the paper challenges the ''fair-trade'' view of antidumping policy as an antidote for predation and strengthens the foundation of the counter-argument that antidumping constitutes a new insidious form of protectionism and trade harassment, which is of particularly serious concerns for small countries.trade, duopoly, Stackelberg, Cournot, antidumping, predation

The impact of lianas on tree regeneration in tropical forest canopy gaps: evidence for an alternative pathway of gap‐phase regeneration

1 Regeneration in forest canopy gaps is thought to lead invariably to the rapid recruitment and growth of trees and the redevelopment of the canopy. Our observations, however, suggest that an alternate successional pathway is also likely, whereby gap‐phase regeneration is dominated by lianas and stalled in a low‐canopy state for many years. We investigated gap‐phase regeneration in an old‐growth tropical forest on Barro Colorado Island (BCI) in Panama to test the following two hypotheses: (i) many gaps follow a pathway in which they remain at a low canopy height and are dominated by lianas and (ii) the paucity of trees in this pathway is a function of liana density. 2 We surveyed a total of 428 gaps of varying ages (c. 5, c. 10, and 13+ years old) and identified those which followed the conventional pathway of regeneration and others that remained stalled in a low‐canopy state for many years and were dominated by either lianas or palms. Each of these pathways will likely have different successional trajectories that will favour the growth of a distinct suite of mature species and ultimately result in contrasting species composition. 3 The successional pathway of liana‐dominated, stalled gaps is common throughout the forest. We estimate conservatively that 7.5% of the gaps that form each year will follow this pathway, probably due to the suppression of tree regeneration by lianas, and that many of these stalled gaps will persist for much longer than 13 years. Consequently, a high proportion of gaps in the forest at any given time will be stalled. Furthermore, liana tangles, which persist in the tropical forest understorey for extended periods of time, almost certainly originate in these gaps. 4 Liana abundance was positively correlated with pioneer tree abundance and diversity while negatively correlated with non‐pioneer tree abundance and diversity. Thus, lianas appear to inhibit non‐pioneer tree survival while indirectly enhancing that of pioneer trees. 5 Lianas are abundant in many types of tropical and temperate forests and a successional pathway involving liana‐dominated, stalled gaps may therefore be frequent and widespread