183,621 research outputs found
Repetitions in infinite palindrome-rich words
Rich words are characterized by containing the maximum possible number of
distinct palindromes. Several characteristic properties of rich words have been
studied; yet the analysis of repetitions in rich words still involves some
interesting open problems. We address lower bounds on the repetition threshold
of infinite rich words over 2 and 3-letter alphabets, and construct a candidate
infinite rich word over the alphabet with a small critical
exponent of . This represents the first progress on an open
problem of Vesti from 2017.Comment: 12 page
Fingerprint for Network Topologies
A network's topology information can be given as an adjacency matrix. The
bitmap of sorted adjacency matrix(BOSAM) is a network visualisation tool which
can emphasise different network structures by just looking at reordered
adjacent matrixes. A BOSAM picture resembles the shape of a flower and is
characterised by a series of 'leaves'. Here we show and mathematically prove
that for most networks, there is a self-similar relation between the envelope
of the BOSAM leaves. This self-similar property allows us to use a single
envelope to predict all other envelopes and therefore reconstruct the outline
of a network's BOSAM picture. We analogise the BOSAM envelope to human's
fingerprint as they share a number of common features, e.g. both are simple,
easy to obtain, and strongly characteristic encoding essential information for
identification.Comment: 12papes, 3 figures, in pres
The variable containment problem
The essentially free variables of a term in some -calculus, FV , form the set ( FV}. This set is significant once we consider equivalence classes of -terms rather than -terms themselves, as for instance in higher-order rewriting. An important problem for (generalised) higher-order rewrite systems is the variable containment problem: given two terms and , do we have for all substitutions and contexts [] that FV FV?
This property is important when we want to consider as a rewrite rule and keep -step rewriting decidable. Variable containment is in general not implied by FV FV. We give a decision procedure for the variable containment problem of the second-order fragment of . For full we show the equivalence of variable containment to an open problem in the theory of PCF; this equivalence also shows that the problem is decidable in the third-order case
What words mean and express: semantics and pragmatics of kind terms and verbs
For many years, it has been common-ground in semantics and in philosophy of language that semantics is in the business of providing a full explanation about how propositional meanings are obtained. This orthodox picture seems to be in trouble these days, as an increasing number of authors now hold that semantics does not deal with thought-contents. Some of these authors have embraced a “thin meanings” view, according to which lexical meanings are too schematic to enter propositional contents. I will suggest that it is plausible to adopt thin semantics for a class of words. However, I’ll also hold that some classes of words, like kind terms, plausibly have richer lexical meanings, and so that an adequate theory of word meaning may have to combine thin and rich semantics
Construction Of A Rich Word Containing Given Two Factors
A finite word with contains at most distinct
palindromic factors. If the bound is attained, the word is called
\emph{rich}. Let \Factor(w) be the set of factors of the word . It is
known that there are pairs of rich words that cannot be factors of a common
rich word. However it is an open question how to decide for a given pair of
rich words if there is a rich word such that \{u,v\}\subseteq
\Factor(w). We present a response to this open question:\\ If are
rich words, , and
\{w_1,w_2\}\subseteq \Factor(w) then there exists also a rich word
such that \{w_1,w_2\}\subseteq \Factor(\bar w) and , where and is the size
of the alphabet. Hence it is enough to check all rich words of length equal or
lower to in order to decide if there is a rich word containing
factors
The Freiheitssatz for generic Poisson algebras
We prove the Freiheitssatz for the variety of generic Poisson algebras
Network-Configurations of Dynamic Friction Patterns
The complex configurations of dynamic friction patterns-regarding real time
contact areas- are transformed into appropriate networks. With this
transformation of a system to network space, many properties can be inferred
about the structure and dynamics of the system. Here, we analyze the dynamics
of static friction, i.e. nucleation processes, with respect to "friction
networks". We show that networks can successfully capture the crack-like shear
ruptures and possible corresponding acoustic features. We found that the
fraction of triangles remarkably scales with the detachment fronts. There is a
universal power law between nodes' degree and motifs frequency (for triangles,
it reads T(k)\proptok{\beta} ({\beta} \approx2\pm0.4)). We confirmed the
obtained universality in aperture-based friction networks. Based on the
achieved results, we extracted a possible friction law in terms of network
parameters and compared it with the rate and state friction laws. In
particular, the evolutions of loops are scaled with power law, indicating the
aggregation of cycles around hub nodes. Also, the transition to slow rupture is
scaled with the fast variation of local heterogeneity. Furthermore, the motif
distributions and modularity space of networks -in terms of withinmodule degree
and participation coefficient-show non-uniform general trends, indicating a
universal aspect of energy flow in shear ruptures
- …