Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) sub-structure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.Comment: 28 pages, LaTeX 12pt article styl

Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.Comment: 5 pages, RevTe

Deformations of the Boson sp(4,R)sp(4,R) Representation and its Subalgebras

The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space. One of the deformed representation is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and three representations of the noncompact u(1,1) are also deformed and are contained in this deformed algebra. They are reducible in the action spaces of sp(4,R) and decompose into irreducible representations. The other deformed representation, is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the standard deformed su(2). All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, an other deformation of su(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation is reducible and decomposes into irreducible ones that yields a complete description of the same

Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications

A multi-shell generalization of a fermion representation of the q-deformed compact symplectic sp_q(4) algebra is introduced. An analytic form for the action of two or more generators of the Sp_q(4) symmetry on the basis states is determined and the result used to derive formulae for the overlap between number preserving states as well as for matrix elements of a model Hamiltonian. A second-order operator in the generators of Sp_q(4) is identified that is diagonal in the basis set and that reduces to the Casimir invariant of the sp(4) algebra in the non-deformed limit of the theory. The results can be used in nuclear structure applications to calculate beta-decay transition probabilities and to provide for a description of pairing and higher-order interactions in systems with nucleons occupying more than a single-j orbital.Comment: 10 page

An Algebraic Pairing Model with Sp(4) Symmetry and its Deformation

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0^+ ground states, they also have a large effect on the energies of excited states, including especially excited 0^+ states. In this article we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp_{(q)}(4) to different realizations of u_{(q)}(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0^{+} states of even-even and odd-odd nuclei in the 1d_{3/2}, 1f_{7/2}, and 1f_{5/2}2p_{1/2}2p_{3/2}1g_{9/2} shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Sp_{q}(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with non-linear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0^{+} energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking, and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher-order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.Comment: 19 pages, 5 figures minor changes; improvements to achieve a better and clearer presentation of our messages and idea

Post-traumatic anxiety associates with failure of the innate immune receptor TLR9 to evade the pro-inflammatory NFκB pathway

Post-traumatic anxiety notably involves inflammation, but its causes and functional significance are yet unclear. Here, we report that failure of the innate immune system Toll-like receptor 9 (TLR9) to limit inflammation is causally involved with anxiety-associated inflammation and that peripheral administration of specific oligonucleotide activators of TLR9 may prevent post-traumatic consequences in stressed mice. Suggesting involvement of NFκB-mediated enhancement of inflammatory reactions in the post-traumatic phenotype, we found association of serum interleukin-1β increases with symptoms severity and volumetric brain changes in post-traumatic stress disorder patients. In predator scent-stressed mice, the moderate NFκB-activating oligonucleotides mEN101 and its human ortholog BL-7040, but not the canonic NFκB activator oligonucleotide ODN1826, induced anxiolytic effects. In stressed mice, peripherally administered mEN101 prevented delayed stress-inducible serum interleukin-1β increases while limiting stress-characteristic hippocampal transcript modifications and the anxiety-induced EGR1-mediated neuronal activation. Attesting to the TLR9 specificity of this response, BL-7040 suppressed NFκB-mediated luciferase in transfected cells co-expressing TLR9, but not other TLRs. Furthermore, TLR9−/− mice were mEN101 and BL-7040 resistant and presented unprovoked anxiety-like behavior and anxiety-characteristic hippocampal transcripts. Our findings demonstrate functional relevance of TLR9 in protecting stressed mammals from overreacting to traumatic experiences and suggest using oligonucleotide-mediated peripheral TLR9 activation to potentiate the innate immune system and prevent post-traumatic inflammation and anxiety

A role of 18F-fluorodeoxyglucose positron emission/computed tomography in a strategy for abdominal wall metastasis of colorectal mucinous adenocarcinoma developed after laparoscopic surgery

Metastasis to the abdominal wall including port sites after laparoscopic surgery for colorectal cancer is rare. Resection of metastatic lesions may lead to greater survival benefit if the abdominal wall metastasis is the only manifestation of recurrent disease. A 57-year-old man, who underwent laparoscopic surgery for advanced mucinous adenocarcinoma of the cecum 6 years prior, developed a nodule in the surgical wound at the lower right abdomen. Although tumor markers were within normal limits, the metastasis to the abdominal wall and abdominal cavity from the previous cecal cancer was suspected. An abdominal computed tomography scan did not provide detective evidence of metastasis. 18F-fluorodeoxyglucose positron emission/computed tomography (18F-FDG PET/CT) was therefore performed, which demonstrated increased 18F-fluorodeoxyglucose uptake (maximum standardized uptake value: 3.1) in the small abdominal wall nodule alone. Histopathological examination of the resected nodule confirmed the diagnosis of metastatic mucinous adenocarcinoma. Prognosis of intestinal mucinous adenocarcinoma is reported to be poorer than that of non-mucinous adenocarcinoma. In conclusion, this case suggests an important role of 18F-FDG PET/CT in early diagnosis and decision-making regarding therapy for recurrent disease in cases where a firm diagnosis of recurrent colorectal cancer is difficult to make

Optogenetic stimulation of a hippocampal engram activates fear memory recall

A specific memory is thought to be encoded by a sparse population of neurons. These neurons can be tagged during learning for subsequent identification3 and manipulation. Moreover, their ablation or inactivation results in reduced memory expression, suggesting their necessity in mnemonic processes. However, the question of sufficiency remains: it is unclear whether it is possible to elicit the behavioural output of a specific memory by directly activating a population of neurons that was active during learning. Here we show in mice that optogenetic reactivation of hippocampal neurons activated during fear conditioning is sufficient to induce freezing behaviour. We labelled a population of hippocampal dentate gyrus neurons activated during fear learning with channelrhodopsin-2 (ChR2) and later optically reactivated these neurons in a different context. The mice showed increased freezing only upon light stimulation, indicating light-induced fear memory recall. This freezing was not detected in non-fear-conditioned mice expressing ChR2 in a similar proportion of cells, nor in fear-conditioned mice with cells labelled by enhanced yellow fluorescent protein instead of ChR2. Finally, activation of cells labelled in a context not associated with fear did not evoke freezing in mice that were previously fear conditioned in a different context, suggesting that light-induced fear memory recall is context specific. Together, our findings indicate that activating a sparse but specific ensemble of hippocampal neurons that contribute to a memory engram is sufficient for the recall of that memory. Moreover, our experimental approach offers a general method of mapping cellular populations bearing memory engrams.RIKEN Brain Science InstituteNational Institutes of Health (U.S.) (Grant R01-MH078821)National Institutes of Health (U.S.) (Grant P50-MH58880

A hippocampal circuit linking dorsal CA2 to ventral CA1 critical for social memory dynamics

Recent results suggest that social memory requires the dorsal hippocampal CA2 region as well as a subset of ventral CA1 neurons. However, it is unclear whether dorsal CA2 and ventral CA1 represent parallel or sequential circuits. Moreover, because evidence implicating CA2 in social memory comes largely from long-term inactivation experiments, the dynamic role of CA2 in social memory remains unclear. Here, we use pharmacogenetics and optogenetics in mice to acutely and reversibly silence dorsal CA2 and its projections to ventral hippocampus. We show that dorsal CA2 activity is critical for encoding, consolidation, and recall phases of social memory. Moreover, dorsal CA2 contributes to social memory by providing strong excitatory input to the same subregion of ventral CA1 that contains the subset of neurons implicated in social memory. Thus, our studies provide new insights into a dorsal CA2 to ventral CA1 circuit whose dynamic activity is necessary for social memory.We thank David H. Brann and the other members of the Siegelbaum laboratory for helpful discussions and João Cerqueira for critical input. This work was supported by R01 MH104602 and R01 MH106629 from the NIH (S.A.S.), by PD/BD/113700/2015 from the Portuguese Foundation for Science and Technology (T.M.) and by the European Molecular Biology Organization (A.O.)