812 research outputs found
A d-Step Approach for Distinct Squares in Strings
We present an approach to the problem of maximum number of distinct squares in a string which underlines the importance of considering as key variables both the length n and n − d where d is the size of the alphabet. We conjecture that a string of length n and containing d distinct symbols has no more than n − d distinct squares, show the critical role played by strings satisfying n = 2d, and present some properties satisfied by strings of length bounded by a constant times the size of the alphabet
A simple algorithm for computing the Lempel-Ziv factorization
We give a space-efficient simple algorithm for computing the Lempel?Ziv factorization ofa string. For a string of length n over an integer alphabet, it runs in O(n) time independentlyof alphabet size and uses o(n) additional space
A civil society perspective on inequalities: the COVID-19 revision
This paper re-examines the ‘civil society perspective’ on engaging in strategy that can
respond to the current rapidly changing context by unpacking the roles of civil society
organisations throughout the pandemic. The evidence collected through this research
shows the need to recognize civil society’s efforts and contributions to the wellbeing of
their communities
A numerical study of the correspondence between paths in a causal set and geodesics in the continuum
This paper presents the results of a computational study related to the
path-geodesic correspondence in causal sets. For intervals in flat spacetimes,
and in selected curved spacetimes, we present evidence that the longest maximal
chains (the longest paths) in the corresponding causal set intervals
statistically approach the geodesic for that interval in the appropriate
continuum limit.Comment: To the celebration of the 60th birthday of Rafael D. Sorki
Quasidecoupled state for dark matter in nonstandard thermal histories
Dark matter drops out of kinetic equilibrium with standard model particles
when the momentum-transfer rate equals the expansion rate. In a
radiation-dominated universe, this occurs at essentially the same time as dark
matter kinetically decouples from the plasma. Dark matter may also fall out of
kinetic equilibrium with standard model particles during an early
matter-dominated era (EMDE), which occurs when the energy content of the
Universe is dominated by either a decaying oscillating scalar field or a
semistable massive particle before big bang nucleosynthesis. Until now, it has
been assumed that kinetic decoupling during an EMDE happens similarly to the
way it does in a radiation-dominated era. We show that this is not the case. By
studying the evolution of the dark matter temperature, we establish a
quasidecoupled state for dark matter in an EMDE, during which the dark matter
temperature cools faster than the plasma temperature but slower than it would
cool if the dark matter were fully decoupled. The dark matter does not fully
decouple until the EMDE ends and the Universe becomes radiation dominated. We
also extend the criteria for quasidecoupling to other nonstandard thermal
histories and consider how quasidecoupling affects the free-streaming length of
dark matter.Comment: 8 pages, 2 figures: expanded discussion; updated to match published
versio
Force and energy dissipation variations in non-contact atomic force spectroscopy on composite carbon nanotube systems
UHV dynamic force and energy dissipation spectroscopy in non-contact atomic
force microscopy were used to probe specific interactions with composite
systems formed by encapsulating inorganic compounds inside single-walled carbon
nanotubes. It is found that forces due to nano-scale van der Waals interaction
can be made to decrease by combining an Ag core and a carbon nanotube shell in
the Ag@SWNT system. This specific behaviour was attributed to a significantly
different effective dielectric function compared to the individual
constituents, evaluated using a simple core-shell optical model. Energy
dissipation measurements showed that by filling dissipation increases,
explained here by softening of C-C bonds resulting in a more deformable
nanotube cage. Thus, filled and unfilled nanotubes can be discriminated based
on force and dissipation measurements. These findings have two different
implications for potential applications: tuning the effective optical
properties and tuning the interaction force for molecular absorption by
appropriately choosing the filling with respect to the nanotube.Comment: 22 pages, 6 figure
On the maximal number of cubic subwords in a string
We investigate the problem of the maximum number of cubic subwords (of the
form ) in a given word. We also consider square subwords (of the form
). The problem of the maximum number of squares in a word is not well
understood. Several new results related to this problem are produced in the
paper. We consider two simple problems related to the maximum number of
subwords which are squares or which are highly repetitive; then we provide a
nontrivial estimation for the number of cubes. We show that the maximum number
of squares such that is not a primitive word (nonprimitive squares) in
a word of length is exactly , and the
maximum number of subwords of the form , for , is exactly .
In particular, the maximum number of cubes in a word is not greater than
either. Using very technical properties of occurrences of cubes, we improve
this bound significantly. We show that the maximum number of cubes in a word of
length is between and . (In particular, we improve the
lower bound from the conference version of the paper.)Comment: 14 page
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