On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered

The XY Model and the Three-state Antiferromagnetic Potts model in Three Dimensions: Critical Properties from Fluctuating Boundary Conditions

We present the results of a Monte Carlo study of the three-dimensional XY model and the three-dimensional antiferromagnetic three-state Potts model. In both cases we compute the difference in the free energies of a system with periodic and a system with antiperiodic boundary conditions in the neighbourhood of the critical coupling. From the finite-size scaling behaviour of this quantity we extract values for the critical temperature and the critical exponent nu that are compatible with recent high statistics Monte Carlo studies of the models. The results for the free energy difference at the critical temperature and for the exponent nu confirm that both models belong to the same universality class.Comment: 13 pages, latex-file+2 ps-files KL-TH-94/8 and CERN-TH.7290/9

The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

Size and Treewidth Bounds for Conjunctive Queries

This paper provides new worst-case bounds for the size and treewith of the result Q(D) of a conjunctive query Q to a database D. We derive bounds for the result size |Q(D) | in terms of structural properties of Q, both in the absence and in the presence of keys and functional dependencies. These bounds are based on a novel “coloring ” of the query variables that associates a coloring number C(Q) to each query Q. Using this coloring number, we derive tight bounds for the size of Q(D) in case (i) no functional dependencies or keys are specified, and (ii) simple (one-attribute) keys are given. These results generalize recent size-bounds for join queries obtained by Atserias, Grohe, and Marx (FOCS 2008). An extension of our coloring technique also gives a lower bound for |Q(D) | in the general setting of a query with arbitrary functional dependencies. Our new coloring scheme also allows us to precisely characterize (both in the absence of keys and with simple keys) the treewidth-preserving queries— the queries for which the output treewidth is bounded by a function of the input treewidth. Finally we characterize the queries that preserve the sparsity of the input in the general setting with arbitrary functional dependencies

Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

Quantum phase transitions in the J-J' Heisenberg and XY spin-1/2 antiferromagnets on square lattice: Finite-size scaling analysis

We investigate the critical parameters of an order-disorder quantum phase transitions in the spin-1/2 $J-J'$ Heisenberg and XY antiferromagnets on square lattice. Basing on the excitation gaps calculated by exact diagonalization technique for systems up to 32 spins and finite-size scaling analysis we estimate the critical couplings and exponents of the correlation length for both models. Our analysis confirms the universal critical behavior of these quantum phase transitions: They belong to 3D O(3) and 3D O(2) universality classes, respectively.Comment: 7 pages, 3 figure

Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape

The Role of FRMD7 in Idiopathic Infantile Nystagmus

Idiopathic infantile nystagmus (IIN) is an inherited disorder in which the nystagmus arises independently of any other symptoms, leading to the speculation that the disorder represents a primary defect in the area of the brain responsible for ocular motor control. The inheritance patterns are heterogeneous, however the most common form is X-linked. FRMD7 resides at Xq26-27 and approximately 50% of X-linked IIN families map to this region. Currently 45 mutations within FRMD7 have been associated with IIN, confirming the importance of FRMD7 in the pathogenesis of the disease. Although mutations in FRMD7 are known to cause IIN, very little is known about the function of the protein. FRMD7 contains a conserved N-terminal FERM domain suggesting that it may provide a link between the plasma membrane and actin cytoskeleton. Limited studies together with the knowledge of the function of other FERM domain containing proteins, suggest that FRMD7 may play a role in membrane extension during neuronal development through remodeling of the actin cytoskeleton

Application strategy for an anthraquinonebased repellent and the protection of soybeans from Canada goose depredation

Agricultural crops can sustain extensive damage caused by Canada geese (Branta canadensis) when these crops are planted near wetlands or brood-rearing sites. From 2000 to 2015, South Dakota Game, Fish and Parks spent \u3e$5.6 million to manage damages caused by Canada geese to agricultural crops (primarily soybeans) in South Dakota, USA. For the purpose of developing a repellent application strategy for nonlethal goose damage management, we comparatively evaluated the width of anthraquinone applications (i.e., 9.4 L Flight Control® Plus goose repellent/ha [active ingredient: 50% 9,10-anthraquinone] at 0–36 m versus 0–73 m perpendicular to the edge of wetlands in 2014), the timing of the first repellent application (i.e., 9.4 L Flight Control Plus goose repellent/ha at 50% versus 75% seedling emergence in 2015), the yield of soybeans (Glycine max) within repellent-treated and untreated subplots, and anthraquinone chemical residues in Day County, South Dakota. Soybean yield was greater in subplots 73 m from the water’s edge than that in the 36-m subplots (P \u3c 0.02). Among subplots first sprayed at 50% seedling emergence, soybean yield was greater at 73 m and 82 m than that at 36 m (P \u3c 0.005). In contrast, we observed no difference in yield at 36 m, 73 m, or 82 m in the subplots first sprayed at 72% seedling emergence (P \u3e 0.09). We therefore conclude that goose damages were effectively managed in subplots first sprayed at 72% seedling emergence. Anthraquinone residues averaged 674 and 629 ppm anthraquinone upon the first application of the repellent (June to July), 22 and 35 ppm anthraquinone in the mid-season hay (August to September), and 36 and 28 ppb anthraquinone in the harvested seed (October to November) in 2014 and 2015, respectively. Our results suggest that a 73-m bandwidth of anthraquinone-based repellents first applied at approximately 72% or 65–85% seedling emergence can protect soybeans from Canada goose depredation

Application Strategy for an Anthraquinone-Based Repellent and the Protection of Soybeans from Canada Goose Depredation

Agricultural crops can sustain extensive damage caused by Canada geese (Branta canadensis) when these crops are planted near wetlands or brood-rearing sites. From 2000 to 2015, South Dakota Game, Fish and Parks spent \u3e$5.6 million to manage damages caused by Canada geese to agricultural crops (primarily soybeans) in South Dakota, USA. For the purpose of developing a repellent application strategy for nonlethal goose damage management, we comparatively evaluated the width of anthraquinone applications (i.e., 9.4 L Flight Control® Plus goose repellent/ha [active ingredient: 50% 9,10-anthraquinone] at 0–36 m versus 0–73 m perpendicular to the edge of wetlands in 2014), the timing of the first repellent application (i.e., 9.4 L Flight Control Plus goose repellent/ha at 50% versus 75% seedling emergence in 2015), the yield of soybeans (Glycine max) within repellent-treated and untreated subplots, and anthraquinone chemical residues in Day County, South Dakota. Soybean yield was greater in subplots 73 m from the water’s edge than that in the 36-m subplots (P \u3c 0.02). Among subplots first sprayed at 50% seedling emergence, soybean yield was greater at 73 m and 82 m than that at 36 m (P \u3c 0.005). In contrast, we observed no difference in yield at 36 m, 73 m, or 82 m in the subplots first sprayed at 72% seedling emergence (P \u3e 0.09). We therefore conclude that goose damages were effectively managed in subplots first sprayed at 72% seedling emergence. Anthraquinone residues averaged 674 and 629 ppm anthraquinone upon the first application of the repellent (June to July), 22 and 35 ppm anthraquinone in the mid-season hay (August to September), and 36 and 28 ppb anthraquinone in the harvested seed (October to November) in 2014 and 2015, respectively. Our results suggest that a 73-m bandwidth of anthraquinone-based repellents first applied at approximately 72% or 65–85% seedling emergence can protect soybeans from Canada goose depredation