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

Generating Permutations with Restricted Containers

We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-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 $\mathcal{C}$-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