1,394 research outputs found
On the Multi-Interval Ulam-R\'enyi Game: for 3 lies 4 intervals suffice
We study the problem of identifying an initially unknown -bit number by
using yes-no questions when up to a fixed number of the answers can be
erroneous. In the variant we consider here questions are restricted to be the
union of up to a fixed number of intervals. For any let be the
minimum such that for all sufficiently large , there exists a strategy
matching the information theoretic lower bound and only using -interval
questions. It is known that . However, it has been conjectured
that the This linearity conjecture is supported by the known
results for small values of . For we have We extend
these results to the case . We show improving upon the
previously known bound Comment: 31 pages, 5 figures, extension of the result to non-asymptotic
strategie
Chirality transitions in frustrated -valued spin systems
We study the discrete-to-continuum limit of the helical XY -spin
system on the lattice . We scale the interaction parameters in
order to reduce the model to a spin chain in the vicinity of the
Landau-Lifschitz point and we prove that at the same energy scaling under which
the -model presents scalar chirality transitions, the cost of every
vectorial chirality transition is now zero. In addition we show that if the
energy of the system is modified penalizing the distance of the field
from a finite number of copies of , it is still possible to prove the
emergence of nontrivial (possibly trace dependent) chirality transitions
Bubble-Flip---A New Generation Algorithm for Prefix Normal Words
We present a new recursive generation algorithm for prefix normal words.
These are binary strings with the property that no substring has more 1s than
the prefix of the same length. The new algorithm uses two operations on binary
strings, which exploit certain properties of prefix normal words in a smart
way. We introduce infinite prefix normal words and show that one of the
operations used by the algorithm, if applied repeatedly to extend the string,
produces an ultimately periodic infinite word, which is prefix normal.
Moreover, based on the original finite word, we can predict both the length and
the density of an ultimate period of this infinite word.Comment: 30 pages, 3 figures, accepted in Theoret. Comp. Sc.. This is the
journal version of the paper with the same title at LATA 2018 (12th
International Conference on Language and Automata Theory and Applications,
Tel Aviv, April 9-11, 2018
Hemihelical local minimizers in prestrained elastic bi-strips
We consider a double layered prestrained elastic rod in the limit of
vanishing cross section. For the resulting limit Kirchoff-rod model with
intrinsic curvature we prove a supercritical bifurcation result, rigorously
showing the emergence of a branch of hemihelical local minimizers from the
straight configuration, at a critical force and under clamping at both ends. As
a consequence we obtain the existence of nontrivial local minimizers of the
-d system.Comment: 16 pages, 2 figure
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