Dihedral symmetry of periodic chain: quantization and coherent states

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian dihedral group D_n - is taken as its symmetry group. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.Comment: 13 pages; minor changes of the tex

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

The political economy of growing a rural university in the USA using online education: An examination of incentives for educational imperialism and academic capitalism

Rural colleges and universities in the USA struggle to recruit new students as their geographic region is depopulating and cost to attend classes on campus are increasing. Online education using the Internet is rapidly expanding as an effective growth strategy to reach new groups of students. In this paper we take the position that online education is a form of cultural imperialism and academic capitalism where curriculum developers and professors are motivated to enroll new students in order to maintain the credibility and strength of their programmes and host institutions. We argue that it is not our intent to be educational imperialists or capitalists. Rather these are unintended consequences of our actions. This argument is supported by political economy theory in that we are marketing a technical rational form of online education without awareness of its long‐term cultural, economic, or political ramifications. Even though we pride ourselves on developing a high quality programme that in our eyes meet the needs of our students, understanding the political economy of online education is essential if our programme that has access to the global market is to go beyond the individual needs of students and address social, cultural and political needs. We conclude that one way out of this malaise is to understand our role as instructors and course designers as a first step toward understanding the intended and unintended consequences of online education

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

Spin Path Integrals and Generations

The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman \emph{position} path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question "what happens when \emph{spin} path integrals are computed over products of MUBs?" Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons.Comment: 20 pages, 2 figures, accepted at Foundations of Physic

Germinal center B cells recognize antigen through a specialized immune synapse architecture

B cell activation is regulated by B cell antigen receptor (BCR) signaling and antigen internalization in immune synapses. Using large-scale imaging across B cell subsets, we show that in contrast to naive and memory B cells, which gathered antigen towards the synapse center before internalization, germinal center (GC) B cells extracted antigen by a distinct pathway using small peripheral clusters. Both naive and GC B cell synapses required proximal BCR signaling, but GC cells signaled less through the protein kinase C-β (PKC-β)–NF-κB pathway and produced stronger tugging forces on the BCR, thereby more stringently regulating antigen binding. Consequently, GC B cells extracted antigen with better affinity discrimination than naive B cells, suggesting that specialized biomechanical patterns in B cell synapses regulate T-cell dependent selection of high-affinity B cells in GCs