7,703 research outputs found
Subclasses of the separable permutations
We prove that all subclasses of the separable permutations not containing
Av(231) or a symmetry of this class have rational generating functions. Our
principal tools are partial well-order, atomicity, and the theory of strongly
rational permutation classes introduced here for the first time
Inflations of Geometric Grid Classes: Three Case Studies
We enumerate three specific permutation classes defined by two forbidden
patterns of length four. The techniques involve inflations of geometric grid
classes
The Complexity of Pattern Matching for -Avoiding and Skew-Merged Permutations
The Permutation Pattern Matching problem, asking whether a pattern
permutation is contained in a permutation , is known to be
NP-complete. In this paper we present two polynomial time algorithms for
special cases. The first algorithm is applicable if both and are
-avoiding; the second is applicable if and are skew-merged.
Both algorithms have a runtime of , where is the length of and
the length of
Generating Permutations with Restricted Containers
We investigate a generalization of stacks that we call
-machines. We show how this viewpoint rapidly leads to functional
equations for the classes of permutations that -machines generate,
and how these systems of functional equations can frequently be solved by
either the kernel method or, much more easily, by guessing and checking.
General results about the rationality, algebraicity, and the existence of
Wilfian formulas for some classes generated by -machines are
given. We also draw attention to some relatively small permutation classes
which, although we can generate thousands of terms of their enumerations, seem
to not have D-finite generating functions
On the inverse image of pattern classes under bubble sort
Let B be the operation of re-ordering a sequence by one pass of bubble sort.
We completely answer the question of when the inverse image of a principal
pattern class under B is a pattern class.Comment: 11 page
Wiskott-Aldrich Syndrome (WAS) and Dedicator of Cytokinesis 8- (DOCK8) Deficiency
Both Wiskott-Aldrich syndrome (WAS) and dedicator of cytokinesis 8 (DOCK8) deficiency are primary immunodeficiency diseases caused by mutations in genes that result in defective organization of the cytoskeleton in hematopoietic tissues. They share some overlapping features such as a combined immunodeficiency, eczema and a predisposition to autoimmunity and malignancy, but also have some unique features that make them relatively easy to diagnose by clinical means. Both diseases can be cured by HSCT in a large proportion of patients. In WAS it is sometimes difficult to establish an indication for HSCT due to the large variability of disease severity, while HSCT is probably indicated in all patients affected by DOCK8 deficiency. There is considerably more published HSCT experience for WAS than for DOCK8 deficiency, but many open questions remain, which will be discussed in this review
Are there excellent service firms, and do they perform well?
While the construct of business excellence, as defined in the very successful hook by Peters and Waterman, had a marked influence on managers in the 1980s, and in all likelihood in the 1990s, it met with some scepticism in academic circles. This was because the construct as conceptualised did not meet the more rigorous requirements of reliability and validity established by critical researchers, and also because many of the so-called excellent firms later showed themselves to be rather ordinary performers at best. Recently, an apparently successful instrument to measure the original Peters and Waterman excellence construct named EXCEL has been developed by Shama et al., in the United States. In this article the authors describe the use of EXCEL in a sample of large UK service firms and comment on its reliability and validity. Links are also established between excellence and overrall business performance in these firms.peer-reviewe
New class of quantum error-correcting codes for a bosonic mode
We construct a new class of quantum error-correcting codes for a bosonic mode
which are advantageous for applications in quantum memories, communication, and
scalable computation. These 'binomial quantum codes' are formed from a finite
superposition of Fock states weighted with binomial coefficients. The binomial
codes can exactly correct errors that are polynomial up to a specific degree in
bosonic creation and annihilation operators, including amplitude damping and
displacement noise as well as boson addition and dephasing errors. For
realistic continuous-time dissipative evolution, the codes can perform
approximate quantum error correction to any given order in the timestep between
error detection measurements. We present an explicit approximate quantum error
recovery operation based on projective measurements and unitary operations. The
binomial codes are tailored for detecting boson loss and gain errors by means
of measurements of the generalized number parity. We discuss optimization of
the binomial codes and demonstrate that by relaxing the parity structure, codes
with even lower unrecoverable error rates can be achieved. The binomial codes
are related to existing two-mode bosonic codes but offer the advantage of
requiring only a single bosonic mode to correct amplitude damping as well as
the ability to correct other errors. Our codes are similar in spirit to 'cat
codes' based on superpositions of the coherent states, but offer several
advantages such as smaller mean number, exact rather than approximate
orthonormality of the code words, and an explicit unitary operation for
repumping energy into the bosonic mode. The binomial quantum codes are
realizable with current superconducting circuit technology and they should
prove useful in other quantum technologies, including bosonic quantum memories,
photonic quantum communication, and optical-to-microwave up- and
down-conversion.Comment: Published versio
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