Limit Synchronization in Markov Decision Processes

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing if the probability mass accumulates in a single state, possibly in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a probability distribution in the sequence assigns probability at least p to some state, and we distinguish three synchronization modes: (i) sure winning if there exists a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there exists a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there exists a strategy that produces a (1-epsilon)-synchronizing sequence. We consider the problem of deciding whether an MDP is sure, almost-sure, limit-sure winning, and we establish the decidability and optimal complexity for all modes, as well as the memory requirements for winning strategies. Our main contributions are as follows: (a) for each winning modes we present characterizations that give a PSPACE complexity for the decision problems, and we establish matching PSPACE lower bounds; (b) we show that for sure winning strategies, exponential memory is sufficient and may be necessary, and that in general infinite memory is necessary for almost-sure winning, and unbounded memory is necessary for limit-sure winning; (c) along with our results, we establish new complexity results for alternating finite automata over a one-letter alphabet

Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices

Pristine graphene is a semimetal and thus does not have a band gap. By making a nanometer scale periodic array of holes in the graphene sheet a band gap may form; the size of the gap is controllable by adjusting the parameters of the lattice. The hole diameter, hole geometry, lattice geometry and the separation of the holes are parameters that all play an important role in determining the size of the band gap, which, for technological applications, should be at least of the order of tenths of an eV. We investigate four different hole configurations: the rectangular, the triangular, the rotated triangular and the honeycomb lattice. It is found that the lattice geometry plays a crucial role for size of the band gap: the triangular arrangement displays always a sizable gap, while for the other types only particular hole separations lead to a large gap. This observation is explained using Clar sextet theory, and we find that a sufficient condition for a large gap is that the number of sextets exceeds one third of the total number of hexagons in the unit cell. Furthermore, we investigate non-isosceles triangular structures to probe the sensitivity of the gap in triangular lattices to small changes in geometry

Diversity and genetic structure of the native Brazil nut tree (Bertholletia excelsa Bonpl.) population.

The present study was carried out in a native Brazil nut tree population (Bertholletia excelsa Bonpl., Lecythidaceae) to assess its genetic diversity and structure. Ten microsatellite markers were used to genotype 198 adult trees (B. excelsa). The population presented high genetic diversity and inbreeding absence rates. The empirical Bayesian method showed three distinct groups in the structure of this population. Molecular analysis of variance showed 98% variability within groups, and 2% between groups. The genetic divergence (FST) indicated little difference between groups; thus, suggesting efficient gene flow between the analyzed B. excelsa adult trees

Clar's Theory, STM Images, and Geometry of Graphene Nanoribbons

We show that Clar's theory of the aromatic sextet is a simple and powerful tool to predict the stability, the \pi-electron distribution, the geometry, the electronic/magnetic structure of graphene nanoribbons with different hydrogen edge terminations. We use density functional theory to obtain the equilibrium atomic positions, simulated scanning tunneling microscopy (STM) images, edge energies, band gaps, and edge-induced strains of graphene ribbons that we analyze in terms of Clar formulas. Based on their Clar representation, we propose a classification scheme for graphene ribbons that groups configurations with similar bond length alternations, STM patterns, and Raman spectra. Our simulations show how STM images and Raman spectra can be used to identify the type of edge termination

Parametric Polyhedra with at least kk Lattice Points: Their Semigroup Structure and the k-Frobenius Problem

Given an integral $d \times n$ matrix $A$, the well-studied affine semigroup \mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\} can be stratified by the number of lattice points inside the parametric polyhedra $P_A(b)=\{x: Ax=b, x\geq0\}$. Such families of parametric polyhedra appear in many areas of combinatorics, convex geometry, algebra and number theory. The key themes of this paper are: (1) A structure theory that characterizes precisely the subset \mbox{ Sg}_{\geq k}(A) of all vectors b \in \mbox{ Sg}(A) such that $P_A(b) \cap {\mathbb Z}^n$ has at least $k$ solutions. We demonstrate that this set is finitely generated, it is a union of translated copies of a semigroup which can be computed explicitly via Hilbert bases computations. Related results can be derived for those right-hand-side vectors $b$ for which $P_A(b) \cap {\mathbb Z}^n$ has exactly $k$ solutions or fewer than $k$ solutions. (2) A computational complexity theory. We show that, when $n$, $k$ are fixed natural numbers, one can compute in polynomial time an encoding of \mbox{ Sg}_{\geq k}(A) as a multivariate generating function, using a short sum of rational functions. As a consequence, one can identify all right-hand-side vectors of bounded norm that have at least $k$ solutions. (3) Applications and computation for the $k$-Frobenius numbers. Using Generating functions we prove that for fixed $n,k$ the $k$-Frobenius number can be computed in polynomial time. This generalizes a well-known result for $k=1$ by R. Kannan. Using some adaptation of dynamic programming we show some practical computations of $k$-Frobenius numbers and their relatives

Immunolocalization of ricin accumulation during castor bean (Ricinus communis L.) seed development.

Ricin is a dimeric glycoprotein that accumulates in protein storage vacuoles of endosperm cells of Ricinus communis L. (castor bean). The proricin travels through the Golgi appar­atus and co-localizes throughout its route to the storage vacuoles of developing castor bean endosperm. We report here the pattern of seed morphological and ultrastructural changes during various stages of seed development, associated with ricin accumulation. ELISA was used to compare the ricin content in mature seeds of four Brazilian commercial cultivars. ELISA and immunoelectron microscopy anal­ysis were used to study ricin accumulation during seed development from 10 to 60 days after pollination (DAP). Results have shown that no ricin could be localized in the endosperm cells in the early development stages (before 20 DAP) and only a few localization points could be observed at 30 DAP. However, a significant ricin localization signal was observed at 40 DAP in the matrix of the protein storage vacuoles. The signal increased significantly from 50 to 60 DAP, when ricin was observed in both the matrix and crystalloids of the protein storage vacuoles. Understanding ricin expression at the cellular level is fundamental for the development of strategies for gene suppression using molecular breeding approaches

Typing Multi-Agent Systems via Commitments

Abstract. This work presents an agent typing system, that differently than most of other proposals relies on notions that are typical of agent systems instead of relying on a functional approach. Specifically, we use commitments to define types. The proposed typing includes a notion of compatibility, based on subtyping, which allows for the safe substitution of agents to roles along an interaction that is ruled by a commitment-based protocol. Type checking can be done dynamically when an agent enacts a role. The proposal is implemented in the 2COMM framework and exploits Java annotations. 2COMM is based on the Agent &amp; Artifact meta-model, exploit JADE and CArtAgO, by using CArtAgO artifacts in order to reify commitment protocols

Ecological patterns and conservation opportunities with carbon credits in Brazil nut groves: a study-case in the Southeast Amazon.

BACKGROUND: Brazil Nuts (BN) tree is a species of high importance in Amazon region. Their continuous use by traditional communities is often related to disturbances that lead to larger degraded areas where this species is commonly found ("BN groves"). Here we aimed to explore the ecological patterns of BN groves vegetation and its relationship with BN trees and evaluate their potential as a source of carbon credits. We sampled 15 circular plots, with Brazilian Nut trees as the center (focal trees) and collected morphometric data from the focal trees. Additionally, we evaluated fruit production for a period of 5 years to obtain annual measurements, which were used as a proxy of the anthropic impact associated with the collection process. Through analysis of the data, we: i) examined the effects of BN trees on the adjacent vegetation; ii) quantified the potential amount of carbon credits in the adjacent vegetation and in the focal trees by converting carbon stock to equivalent CO2. RESULTS: The adjacent vegetation structure was influenced by the size of BN trees (focal trees). No important effects of BN trees on the adjacent vegetation floristic composition and functional attributes were found. Additionally, we found that Brazilian Nut groves possess a significant potential for carbon credits that could be leveraged in the future carbon credit market. CONCLUSION: The study highlights the potential for carbon credit generation in Brazil nut groves in the Southeast Amazon as a means of supporting conservation and restoration efforts in these environments