3,796 research outputs found
Music Expectation by Cognitive Rule-Mapping
Iterative rules appear everywhere in music cognition, creating strong expectations. Consequently, denial of rule projection becomes an important compositional strategy, generating numerous possibilities for musical affect. Other rules enter the musical aesthetic through reflexive game playing. Still other kinds are completely constructivist in nature and may be uncongenial to cognition, requiring much training to be recognized, if at all. Cognitive rules are frequently found in contexts of varied repetition (AA), but they are not necessarily bounded by stylistic similarity. Indeed, rules may be especially relevant in the processing of unfamiliar contexts (AB), where only abstract coding is available. There are many kinds of deduction in music cognition. Typical examples include melodic sequence, partial melodic sequence, and alternating melodic sequence (which produces streaming). These types may coexist in the musical fabric, involving the invocation of both simultaneous and nested rules. Intervallic expansion and reduction in melody also involve higherorder abstractions. Various mirrored forms in music entail rule-mapping as well, although these may be more difficult to perceive than their analogous visual symmetries. Listeners can likewise deduce additivity and subtractivity at work in harmony, tempo, texture, pace, and dynamics. Rhythmic augmentation and diminution, by contrast, rely on multiplication and division. The examples suggest numerous hypotheses for experimental research
One-dimensional models of disordered quantum wires: general formalism
In this work we describe, compile and generalize a set of tools that can be
used to analyse the electronic properties (distribution of states, nature of
states, ...) of one-dimensional disordered compositions of potentials. In
particular, we derive an ensemble of universal functional equations which
characterize the thermodynamic limit of all one-dimensional models and which
only depend formally on the distributions that define the disorder. The
equations are useful to obtain relevant quantities of the system such as
density of states or localization length in the thermodynamic limit
A Gaussian Model for Simulated Geomagnetic Field Reversals
Field reversals are the most spectacular changes in the geomagnetic field but
remain little understood. Paleomagnetic data primarily constrain the reversal
rate and provide few additional clues. Reversals and excursions are
characterized by a low in dipole moment that can last for some 10kyr. Some
paleomagnetic records also suggest that the field decreases much slower before
an reversals than it recovers afterwards and that the recovery phase may show
an overshoot in field intensity. Here we study the dipole moment variations in
several extremely long dynamo simulation to statistically explored the reversal
and excursion properties. The numerical reversals are characterized by a switch
from a high axial dipole moment state to a low axial dipole moment state. When
analysing the respective transitions we find that decay and growth have very
similar time scales and that there is no overshoot. Other properties are
generally similar to paleomagnetic findings. The dipole moment has to decrease
to about 30% of its mean to allow for reversals. Grand excursions during which
the field intensity drops by a comparable margin are very similar to reversals
and likely have the same internal origin. The simulations suggest that both are
simply triggered by particularly large axial dipole fluctuations while other
field components remain largely unaffected. A model at a particularly large
Ekman number shows a second but little Earth-like type of reversals where the
total field decays and recovers after some time
A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
Interval Temporal Logic (ITL) is an established temporal formalism for
reasoning about time periods. For over 25 years, it has been applied in a
number of ways and several ITL variants, axiom systems and tools have been
investigated. We solve the longstanding open problem of finding a complete
axiom system for basic quantifier-free propositional ITL (PITL) with infinite
time for analysing nonterminating computational systems. Our completeness proof
uses a reduction to completeness for PITL with finite time and conventional
propositional linear-time temporal logic. Unlike completeness proofs of equally
expressive logics with nonelementary computational complexity, our semantic
approach does not use tableaux, subformula closures or explicit deductions
involving encodings of omega automata and nontrivial techniques for
complementing them. We believe that our result also provides evidence of the
naturalness of interval-based reasoning
IST Austria Thesis
This dissertation concerns the automatic verification of probabilistic systems and programs with arrays by statistical and logical methods. Although statistical and logical methods are different in nature, we show that they can be successfully combined for system analysis. In the first part of the dissertation we present a new statistical algorithm for the verification of probabilistic systems with respect to unbounded properties, including linear temporal logic. Our algorithm often performs faster than the previous approaches, and at the same time requires less information about the system. In addition, our method can be generalized to unbounded quantitative properties such as mean-payoff bounds. In the second part, we introduce two techniques for comparing probabilistic systems. Probabilistic systems are typically compared using the notion of equivalence, which requires the systems to have the equal probability of all behaviors. However, this notion is often too strict, since probabilities are typically only empirically estimated, and any imprecision may break the relation between processes. On the one hand, we propose to replace the Boolean notion of equivalence by a quantitative distance of similarity. For this purpose, we introduce a statistical framework for estimating distances between Markov chains based on their simulation runs, and we investigate which distances can be approximated in our framework. On the other hand, we propose to compare systems with respect to a new qualitative logic, which expresses that behaviors occur with probability one or a positive probability. This qualitative analysis is robust with respect to modeling errors and applicable to many domains. In the last part, we present a new quantifier-free logic for integer arrays, which allows us to express counting. Counting properties are prevalent in array-manipulating programs, however they cannot be expressed in the quantified fragments of the theory of arrays. We present a decision procedure for our logic, and provide several complexity results
- …