Symmetries of the finite Heisenberg group for composite systems

Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsystems - qudits - with arbitrary dimensions n and m. In this paper we present detailed descriptions - in the group of inner automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated by tensor products of generalized Pauli matrices of orders n and m. The symmetry group is then given by the quotient group of the normalizer.Comment: Submitted to J. Phys. A: Math. Theo

Symmetries of finite Heisenberg groups for k-partite systems

Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems comprised of k subsystems which are described with position and momentum variables in Z_{n_i}, i=1,...,k. Their Hilbert spaces are given by k-fold tensor products of Hilbert spaces of dimensions n_1,...,n_k. Symmetry group of the corresponding finite Heisenberg group is given by the quotient group of a certain normalizer. We provide the description of the symmetry groups for arbitrary multipartite cases. The new class of symmetry groups represents very specific generalization of finite symplectic groups over modular rings.Comment: 6 pages, to appear in Proceedings of QTS7 "Quantum Theory and Symmetries 7", Prague, August 7-13, 201

Analysis of Composition and Structure of Coastal to Mesopelagic Bacterioplankton Communities in the Northern Gulf of Mexico

16S rRNA gene amplicons were pyrosequenced to assess bacterioplankton community composition, diversity, and phylogenetic community structure for 17 stations in the northern Gulf of Mexico (nGoM) sampled in March 2010. Statistical analyses showed that samples from depths ≤100 m differed distinctly from deeper samples. SAR 11 α-Proteobacteria and Bacteroidetes dominated communities at depths ≤100 m, which were characterized by high α-Proteobacteria/γ-Proteobacteria ratios (α/γ > 1.7). Thaumarchaeota, Firmicutes, and δ-Proteobacteria were relatively abundant in deeper waters, and α/γ ratios were low (<1). Canonical correlation analysis indicated that δ- and γ-Proteobacteria, Thaumarchaeota, and Firmicutes correlated positively with depth; α-Proteobacteria and Bacteroidetes correlated positively with temperature and dissolved oxygen; Actinobacteria, β-Proteobacteria, and Verrucomicrobia correlated positively with a measure of suspended particles. Diversity indices did not vary with depth or other factors, which indicated that richness and evenness elements of bacterioplankton communities might develop independently of nGoM physical-chemical variables. Phylogenetic community structure as measured by the net relatedness (NRI) and nearest taxon (NTI) indices also did not vary with depth. NRI values indicated that most of the communities were comprised of OTUs more distantly related to each other in whole community comparisons than expected by chance. NTI values derived from phylogenetic distances of the closest neighbor for each OTU in a given community indicated that OTUs tended to occur in clusters to a greater extent than expected by chance. This indicates that “habitat filtering” might play an important role in nGoM bacterioplankton species assembly, and that such filtering occurs throughout the water column

Feynman's path integral and mutually unbiased bases

Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases. We confirm the corresponding property of the short-time propagator by using a specially devised N x N -approximation of quantum mechanics in L^2(R) applied to our finite-dimensional analogue of a free quantum particle.Comment: 12 pages, submitted to Journal of Physics A: Math. Theor., minor correction

Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?

We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$, containing a square, into its factors. Illustrative low dimensional examples are the quartit ($q=4$) and two-qubit ($q=2^2$) systems, the octit ($q=8$), qubit/quartit ($q=2\times 4$) and three-qubit ($q=2^3$) systems, and so on. In the single qudit case, e.g. $q=4,8,12,...$, one defines a bijection between the $\sigma (q)$ maximal commuting sets [with $\sigma[q)$ the sum of divisors of $q$] of Pauli observables and the maximal submodules of the modular ring $\mathbb{Z}_q^2$, that arrange into the projective line $P_1(\mathbb{Z}_q)$ and a independent set of size $\sigma (q)-\psi(q)$ [with $\psi(q)$ the Dedekind psi function]. In the multiple qudit case, e.g. $q=2^2, 2^3, 3^2,...$, the Pauli graphs rely on symplectic polar spaces such as the generalized quadrangles GQ(2,2) (if $q=2^2$) and GQ(3,3) (if $q=3^2$). More precisely, in dimension $p^n$ ($p$ a prime) of the Hilbert space, the observables of the Pauli group (modulo the center) are seen as the elements of the $2n$-dimensional vector space over the field $\mathbb{F}_p$. In this space, one makes use of the commutator to define a symplectic polar space $W_{2n-1}(p)$ of cardinality $\sigma(p^{2n-1})$, that encodes the maximal commuting sets of the Pauli group by its totally isotropic subspaces. Building blocks of $W_{2n-1}(p)$ are punctured polar spaces (i.e. a observable and all maximum cliques passing to it are removed) of size given by the Dedekind psi function $\psi(p^{2n-1})$. For multiple qudit mixtures (e.g. qubit/quartit, qubit/octit and so on), one finds multiple copies of polar spaces, ponctured polar spaces, hypercube geometries and other intricate structures. Such structures play a role in the science of quantum information.Comment: 18 pages, version submiited to J. Phys. A: Math. Theo

Clinical trial of laronidase in Hurler syndrome after hematopoietic cell transplantation.

BackgroundMucopolysaccharidosis I (MPS IH) is a lysosomal storage disease treated with hematopoietic cell transplantation (HCT) because it stabilizes cognitive deterioration, but is insufficient to alleviate all somatic manifestations. Intravenous laronidase improves somatic burden in attenuated MPS I. It is unknown whether laronidase can improve somatic disease following HCT in MPS IH. The objective of this study was to evaluate the effects of laronidase on somatic outcomes of patients with MPS IH previously treated with HCT.MethodsThis 2-year open-label pilot study of laronidase included ten patients (age 5-13 years) who were at least 2 years post-HCT and donor engrafted. Outcomes were assessed semi-annually and compared to historic controls.ResultsThe two youngest participants had a statistically significant improvement in growth compared to controls. Development of persistent high-titer anti-drug antibodies (ADA) was associated with poorer 6-min walk test (6MWT) performance; when patients with high ADA titers were excluded, there was a significant improvement in the 6MWT in the remaining seven patients.ConclusionsLaronidase seemed to improve growth in participants &lt;8 years old, and 6MWT performance in participants without ADA. Given the small number of patients treated in this pilot study, additional study is needed before definitive conclusions can be made

Weak mutually unbiased bases

Quantum systems with variables in ${\mathbb Z}(d)$ are considered. The properties of lines in the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space of these systems, are studied. Weak mutually unbiased bases in these systems are defined as bases for which the overlap of any two vectors in two different bases, is equal to $d^{-1/2}$ or alternatively to one of the $d_i^{-1/2},0$ (where $d_i$ is a divisor of $d$ apart from $d,1$). They are designed for the geometry of the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space, in the sense that there is a duality between the weak mutually unbiased bases and the maximal lines through the origin. In the special case of prime $d$, there are no divisors of $d$ apart from $1,d$ and the weak mutually unbiased bases are mutually unbiased bases

Understanding Writing Challenges of Rural MSW Students: Preparing Students for Ethical Practice

This study explores the attitudes and reflections of rural MSW students regarding writing. Twenty-seven students completed the modified Writing-to-learn Attitudes Survey (WTLAS). Fourteen completed an open-ended reflection where they were asked to assess their strengths and challenges in writing, as well as strategies for improvement. Results of WTLAS indicated students were anxious about writing, had difficulty organizing their thoughts, presenting their ideas clearly, and had little confidence in their writing. Results of the writing reflection indicated students were able to identify multiple challenges and strengths as well as means to remedy shortcomings. Qualitative analysis indicated the most frequent challenges were: clear and concise writing, time management, and APA style and format. The researchers review interventions implemented with an MSW cohort to enhance writing abilities and discuss the link between effective writing and ethical practice