104,059 research outputs found
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
Constant amplitude and post-overload fatigue crack growth behavior in PM aluminum alloy AA 8009
A recently developed, rapidly solidified, powder metallurgy, dispersion strengthened aluminum alloy, AA 8009, was fatigue tested at room temperature in lab air. Constant amplitude/constant delta kappa and single spike overload conditions were examined. High fatigue crack growth rates and low crack closure levels compared to typical ingot metallurgy aluminum alloys were observed. It was proposed that minimal crack roughness, crack path deflection, and limited slip reversibility, resulting from ultra-fine microstructure, were responsible for the relatively poor da/dN-delta kappa performance of AA 8009 as compared to that of typical IM aluminum alloys
Forbidden triads and Creative Success in Jazz: The Miles Davis Factor
This article argues for the importance of forbidden triads - open triads with
high-weight edges - in predicting success in creative fields. Forbidden triads
had been treated as a residual category beyond closed and open triads, yet I
argue that these structures provide opportunities to combine socially evolved
styles in new ways. Using data on the entire history of recorded jazz from 1896
to 2010, I show that observed collaborations have tolerated the openness of
high weight triads more than expected, observed jazz sessions had more
forbidden triads than expected, and the density of forbidden triads contributed
to the success of recording sessions, measured by the number of record releases
of session material. The article also shows that the sessions of Miles Davis
had received an especially high boost from forbidden triads
The relation between degrees of belief and binary beliefs: A general impossibility theorem
Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take
On the existence of -thresholds and related limits
The -thresholds are important numerical invariants in prime
characteristic, whose existence had been established only under certain
assumptions. We show the existence of -thresholds in full generality. We
study properties of standard graded algebras over a field for which -pure
threshold and -threshold at the irrelevant maximal ideal agree. We also
exhibit explicit bounds for the -invariants and Castelnuovo-Mumford
regularity of Frobenius powers of ideals in terms of -thresholds and
-pure thresholds, obtaining existence of related limits in certain cases.Comment: 21 page
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