Dynamic Consistency of Conditional Simple Temporal Networks via Mean Payoff Games: a Singly-Exponential Time DC-Checking

Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. It offers a more flexible formalism than the equivalent CSTP model of Tsamardinos, Vidal and Pollack, from which it was derived mainly as a sound formalization. Three notions of consistency arise for CSTNs and CSTPs: weak, strong, and dynamic. Dynamic consistency is the most interesting notion, but it is also the most challenging and it was conjectured to be hard to assess. Tsamardinos, Vidal and Pollack gave a doubly-exponential time algorithm for deciding whether a CSTN is dynamically-consistent and to produce, in the positive case, a dynamic execution strategy of exponential size. In the present work we offer a proof that deciding whether a CSTN is dynamically-consistent is coNP-hard and provide the first singly-exponential time algorithm for this problem, also producing a dynamic execution strategy whenever the input CSTN is dynamically-consistent. The algorithm is based on a novel connection with Mean Payoff Games, a family of two-player combinatorial games on graphs well known for having applications in model-checking and formal verification. The presentation of such connection is mediated by the Hyper Temporal Network model, a tractable generalization of Simple Temporal Networks whose consistency checking is equivalent to determining Mean Payoff Games. In order to analyze the algorithm we introduce a refined notion of dynamic-consistency, named \epsilon-dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction time \hat{\varepsilon} where the CSTN transits from being, to not being, dynamically-consistent. The proof technique introduced in this analysis of \hat{\varepsilon} is applicable more in general when dealing with linear difference constraints which include strict inequalities

Checking Dynamic Consistency of Conditional Hyper Temporal Networks via Mean Payoff Games (Hardness and (pseudo) Singly-Exponential Time Algorithm)

In this work we introduce the \emph{Conditional Hyper Temporal Network (CHyTN)} model, which is a natural extension and generalization of both the \CSTN and the \HTN model. Our contribution goes as follows. We show that deciding whether a given \CSTN or CHyTN is dynamically consistent is \coNP-hard. Then, we offer a proof that deciding whether a given CHyTN is dynamically consistent is \PSPACE-hard, provided that the input instances are allowed to include both multi-head and multi-tail hyperarcs. In light of this, we continue our study by focusing on CHyTNs that allow only multi-head or only multi-tail hyperarcs, and we offer the first deterministic (pseudo) singly-exponential time algorithm for the problem of checking the dynamic-consistency of such CHyTNs, also producing a dynamic execution strategy whenever the input CHyTN is dynamically consistent. Since \CSTN{s} are a special case of CHyTNs, this provides as a byproduct the first sound-and-complete (pseudo) singly-exponential time algorithm for checking dynamic-consistency in CSTNs. The proposed algorithm is based on a novel connection between CSTN{s}/CHyTN{s} and Mean Payoff Games. The presentation of the connection between \CSTN{s}/CHyTNs and \MPG{s} is mediated by the \HTN model. In order to analyze the algorithm, we introduce a refined notion of dynamic-consistency, named $\epsilon$-dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction time $\hat{\varepsilon}$ where a \CSTN/CHyTN transits from being, to not being, dynamically consistent. The proof technique introduced in this analysis of $\hat{\varepsilon}$ is applicable more generally when dealing with linear difference constraints which include strict inequalities.Comment: arXiv admin note: text overlap with arXiv:1505.0082

Hybrid SAT-Based Consistency Checking Algorithms for Simple Temporal Networks with Decisions

A Simple Temporal Network (STN) consists of time points modeling temporal events and constraints modeling the minimal and maximal temporal distance between them. A Simple Temporal Network with Decisions (STND) extends an STN by adding decision time points to model temporal plans with decisions. A decision time point is a special kind of time point that once executed allows for deciding a truth value for an associated Boolean proposition. Furthermore, STNDs label time points and constraints by conjunctions of literals saying for which scenarios (i.e., complete truth value assignments to the propositions) they are relevant. Thus, an STND models a family of STNs each obtained as a projection of the initial STND onto a scenario. An STND is consistent if there exists a consistent scenario (i.e., a scenario such that the corresponding STN projection is consistent). Recently, a hybrid SAT-based consistency checking algorithm (HSCC) was proposed to check the consistency of an STND. Unfortunately, that approach lacks experimental evaluation and does not allow for the synthesis of all consistent scenarios. In this paper, we propose an incremental HSCC algorithm for STNDs that (i) is faster than the previous one and (ii) allows for the synthesis of all consistent scenarios and related early execution schedules (offline temporal planning). Then, we carry out an experimental evaluation with KAPPA, a tool that we developed for STNDs. Finally, we prove that STNDs and disjunctive temporal networks (DTNs) are equivalent

On Restricted Disjunctive Temporal Problems: Faster Algorithms and Tractability Frontier

In 2005 T.K.S. Kumar studied the Restricted Disjunctive Temporal Problem (RDTP), a restricted but very expressive class of Disjunctive Temporal Problems (DTPs). An RDTP comes with a finite set of temporal variables, and a finite set of temporal constraints each of which can be either one of the following three types: (t_1) two-variable linear-difference simple constraint; (t_2) single-variable disjunction of many interval constraints; (t_3) two-variable disjunction of two interval constraints only. Kumar showed that RDTPs are solvable in deterministic strongly polynomial time by reducing them to the Connected Row-Convex (CRC) constraints satisfaction problem, also devising a faster randomized algorithm. Instead, the most general form of DTPs allows for multi-variable disjunctions of many interval constraints and it is NP-complete. This work offers a deeper comprehension on the tractability of RDTPs, leading to an elementary deterministic strongly polynomial time algorithm for them, significantly improving the asymptotic running times of all the previous deterministic and randomized solutions. The result is obtained by reducing RDTPs to the Single-Source Shortest Paths (SSSP) and the 2-SAT problem (jointly), instead of reducing to CRCs. In passing, we obtain a faster (quadratic time) algorithm for RDTPs having only {t_1, t_2}-constraints and no t_3-constraint. As a second main contribution, we study the tractability frontier of solving RDTPs blended with Hyper Temporal Networks (HyTNs), a disjunctive strict generalization of Simple Temporal Networks (STNs) based on hypergraphs: we prove that solving temporal problems having only t_2-constraints and either only multi-tail or only multi-head hyperarc-constraints lies in NP cap co-NP and admits deterministic pseudo-polynomial time algorithms; on the other hand, problems having only t_3-constraints and either only multi-tail or only multi-head hyperarc-constraints turns out strongly NP-complete

A phytosociological analysis of abandoned olive-grove grasslands of Ausoni mountains (Tyrrhenian district of Central Italy)

Over the last fifty years, about 80% of Olea europea L. cultivations in the submediterranean belt of Central Italy have been abandoned and they are now subjected to new colonizations from surrounding wild vegetation. A phytosociological study of the main types of grassland communities occurring in this «vanishing» typically mediterranean landscape is presented here. The Ausoni Mountains, a Tyrrhenian coastal chain of central Italy were selected as a study area. Distribution of secondary grassland communities is influenced by the combined action of many factors, such as bioclimatic parameters, soil characteristics, time since abandonment, land use pattern. In the warmest sites, the early successional stages are characterized by Hyparrhenia hirta open dry grasslands. This community is gradually replaced by dense steppe-like grasslands very poor in species, dominated by Ampelodesmos mauritanicus (Psoraleo-Ampelodesmetum or less frequently by Hyparrhenia hirta again. Both the inland areas and the north facing slopes are characterized by Festuco-Brometea communities. Perennial grasses, in particular Brachypodium rupestre (Galio-Brachypodietum) dominate these environments, and annual species are confined to restricted areas, such as trampled sites or terrace boundaries (Crucianello-Hypochoeridetum). Two new associations (Galio lucidi-Brachypodietum rupestris and Thymo vulgaris-Hyparrhenietum hirtae ) are presented in this paper

The main plant community types of the alpine belt of the Apennine chain

This paper deals with the occurrence of the main plant community types occurring within the alpine bioclimatic belt in the Central Apennines. The study area was represented by three mountain groups, the Gran Sasso, Maiella and Laga mountains. These three mountain chains are those in which, out of the entire Apennine area, alpine vegetation is best expressed. The vegetation has been investigated following the Braun-Blanquet phytosociological approach. During the field work 135 releves were collected. The raw data were further treated with multivariate analysis procedures to find objective clusters on a statistical basis. Several plant community types, belonging to different phytosociological classes, such as Elyno-Seslerietea, Salicetea herbaceae, Thlaspietea rotundifolii, Asplenietea trichomanis, were identified. In particular two new phytosociological associations, Galio-Silenetum acaulis and Potentillo-Festucetum alfredianae, and several new sub-associations are described in this paper. In order to express the occurrence and autonomy of the Apennine alpine bioclimatic belt also in coenological terms, a new Seslerion apenninae sub-alliance, named Leontopodio-Elynenion, is here proposed

Current therapeutic approaches for plantar fasciitis

Nicolò Martinelli, Carlo Bonifacini, Giovanni RomeoDepartment of Ankle and Foot Surgery, IRCCS Galeazzi Orthopaedic Institute, Milan, ItalyAbstract: Almost 1 million Americans are affected by plantar fasciitis (PF), which is the commonest cause of chronic heel pain. This condition is often managed conservatively, and many rehabilitation protocols, some with the aid of orthoses, have been adopted, with good-to-excellent clinical results. Although most cases of chronic PF can be successfully managed with a conservative approach, alternative treatments, including high-energy shock wave therapy and corticosteroid injections, are commonly accepted as second-line treatment when traditional conservative therapy fails. However, surgery is still an important mode of treatment. Recently, new minimally invasive surgical techniques that offer numerous advantages (faster recovery time, early weight-bearing, lower postoperative pain) over standard surgical approaches have been proposed, with good results and low complication rates. The purpose of this review is to report new conservative and surgical techniques for the treatment of PF. A literature search for articles about plantar fasciitis was conducted on the PubMed database in order to identify publications addressing the treatments of PF. The literature suggests that, initially, traditional conservative treatments consisting of rest, oral nonsteroidal anti-inflammatory drugs, foot orthotics, and stretching exercises can be tried for several weeks. In patients with chronic recalcitrant PF, extracorporeal shock wave therapy or corticosteroid injection can be considered. Surgery (minimally invasive techniques) should be considered only after failure of the conservative treatments.Keywords: heel pain, surgery, plantar fasciosi

On the Implementation of an Innovative Energy/Financial Optimization Tool and its Application for Technology Screening within the EU-project School of the Future☆

Abstract A tool for the energy & financial optimization of the renovation of school buildings was developed based on an existing tool - ASCOT. The tool combines an energy calculation with a LCC-analysis, which are calculated simultaneously. The tool was then used for the screening of energy saving measures in school buildings in four European countries: Denmark, Germany, Italy and Norway. For Italy, the screening was carried out for three climates