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

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

Cryomicroscopy reveals the structural basis for a flexible hinge motion in the immunoglobulin M pentamer

Immunoglobulin M (IgM) is the most ancient of the five isotypes of immunoglobulin (Ig) molecules and serves as the first line of defence against pathogens. Here, we use cryo-EM to image the structure of the human full-length IgM pentamer, revealing antigen binding domains flexibly attached to the asymmetric and rigid core formed by the Cμ4 and Cμ3 constant regions and the J-chain. A hinge is located at the Cμ3/Cμ2 domain interface, allowing Fabs and Cμ2 to pivot as a unit both in-plane and out-of-plane. This motion is different from that observed in IgG and IgA, where the two Fab arms are able to swing independently. A biased orientation of one pair of Fab arms results from asymmetry in the constant domain (Cμ3) at the IgM subunit interacting most extensively with the J-chain. This may influence the multi-valent binding to surface-associated antigens and complement pathway activation. By comparison, the structure of the Fc fragment in the IgM monomer is similar to that of the pentamer, but is more dynamic in the Cμ4 domain

Intrathecal enzyme replacement for Hurler syndrome: biomarker association with neurocognitive outcomes.

PurposeAbnormalities in cerebrospinal fluid (CSF) have been reported in Hurler syndrome, a fatal neurodegenerative lysosomal disorder. While no biomarker has predicted neurocognitive response to treatment, one of these abnormalities, glycosaminoglycan nonreducing ends (NREs), holds promise to monitor therapeutic efficacy. A trial of intrathecal enzyme replacement therapy (ERT) added to standard treatment enabled tracking of CSF abnormalities, including NREs. We evaluated safety, biomarker response, and neurocognitive correlates of change.MethodsIn addition to intravenous ERT and hematopoietic cell transplantation, patients (N = 24) received intrathecal ERT at four peritransplant time points; CSF was evaluated at each point. Neurocognitive functioning was quantified at baseline, 1 year, and 2 years posttransplant. Changes in CSF biomarkers and neurocognitive function were evaluated for an association.ResultsOver treatment, there were significant decreases in CSF opening pressure, biomarkers of disease activity, and markers of inflammation. Percent decrease in NRE from pretreatment to final intrathecal dose posttransplant was positively associated with percent change in neurocognitive score from pretreatment to 2 years posttransplant.ConclusionIntrathecal ERT was safe and, in combination with standard treatment, was associated with reductions in CSF abnormalities. Critically, we report evidence of a link between a biomarker treatment response and neurocognitive outcome in Hurler syndrome

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