Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $\mu_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of measures on a space \cG of maps from $\P^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $\mu_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of \fg-valued three-forms on $M.$ We show that these measures are positive, and that the measures \mu_\cG^{s,t} are Borel probability measures. As an application we show that formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $\mu_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$Comment: Minor correction

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Summation of connectivity strengths in the visual cortex reveals stability of neuronal microcircuits after plasticity

Abstract : Background: Within sensory systems, neurons are continuously affected by environmental stimulation. Recently, we showed that, on cell-pair basis, visual adaptation modulates the connectivity strength between similarly tuned neurons to orientation and we suggested that, on a larger scale, the connectivity strength between neurons forming sub-networks could be maintained after adaptation-induced-plasticity. In the present paper, based on the summation of the connectivity strengths, we sought to examine how, within cell-assemblies, functional connectivity is regulated during an exposure-based adaptation. Results: Using intrinsic optical imaging combined with electrophysiological recordings following the reconfiguration of the maps of the primary visual cortex by long stimulus exposure, we found that within functionally connected cells, the summed connectivity strengths remain almost equal although connections among individual pairs are modified. Neuronal selectivity appears to be strongly associated with neuronal connectivity in a “homeodynamic” manner which maintains the stability of cortical functional relationships after experience-dependent plasticity. Conclusions: Our results support the “homeostatic plasticity concept” giving new perspectives on how the summation in visual cortex leads to the stability within labile neuronal ensembles, depending on the newly acquired properties by neurons

Caveolin-1-Enhanced Motility and Focal Adhesion Turnover Require Tyrosine-14 but Not Accumulation to the Rear in Metastatic Cancer Cells

Caveolin-1 is known to promote cell migration, and increased caveolin-1 expression is associated with tumor progression and metastasis. In fibroblasts, caveolin-1 polarization and phosphorylation of tyrosine-14 are essential to promote migration. However, the role of caveolin-1 in migration of metastatic cells remains poorly defined. Here, caveolin-1 participation in metastatic cell migration was evaluated by shRNA targeting of endogenous caveolin-1 in MDA-MB-231 human breast cancer cells and ectopic expression in B16-F10 mouse melanoma cells. Depletion of caveolin-1 in MDA-MB-231 cells reduced, while expression in B16-F10 cells promoted migration, polarization and focal adhesion turnover in a sequence of events that involved phosphorylation of tyrosine-14 and Rac-1 activation. In B16-F10 cells, expression of a non-phosphorylatable tyrosine-14 to phenylalanine mutant failed to recapitulate the effects observed with wild-type caveolin-1. Alternatively, treatment of MDA-MB-231 cells with the Src family kinase inhibitor PP2 reduced caveolin-1 phosphorylation on tyrosine-14 and cell migration. Surprisingly, unlike for fibroblasts, caveolin-1 polarization and re-localization to the trailing edge were not observed in migrating metastatic cells. Thus, expression and phosphorylation, but not polarization of caveolin-1 favor the highly mobile phenotype of metastatic cells

Neurons are MHC Class I-Dependent Targets for CD8 T Cells upon Neurotropic Viral Infection

Following infection of the central nervous system (CNS), the immune system is faced with the challenge of eliminating the pathogen without causing significant damage to neurons, which have limited capacities of renewal. In particular, it was thought that neurons were protected from direct attack by cytotoxic T lymphocytes (CTL) because they do not express major histocompatibility class I (MHC I) molecules, at least at steady state. To date, most of our current knowledge on the specifics of neuron-CTL interaction is based on studies artificially inducing MHC I expression on neurons, loading them with exogenous peptide and applying CTL clones or lines often differentiated in culture. Thus, much remains to be uncovered regarding the modalities of the interaction between infected neurons and antiviral CD8 T cells in the course of a natural disease. Here, we used the model of neuroinflammation caused by neurotropic Borna disease virus (BDV), in which virus-specific CTL have been demonstrated as the main immune effectors triggering disease. We tested the pathogenic properties of brain-isolated CD8 T cells against pure neuronal cultures infected with BDV. We observed that BDV infection of cortical neurons triggered a significant up regulation of MHC I molecules, rendering them susceptible to recognition by antiviral CTL, freshly isolated from the brains of acutely infected rats. Using real-time imaging, we analyzed the spatio-temporal relationships between neurons and CTL. Brain-isolated CTL exhibited a reduced mobility and established stable contacts with BDV-infected neurons, in an antigen- and MHC-dependent manner. This interaction induced rapid morphological changes of the neurons, without immediate killing or impairment of electrical activity. Early signs of neuronal apoptosis were detected only hours after this initial contact. Thus, our results show that infected neurons can be recognized efficiently by brain-isolated antiviral CD8 T cells and uncover the unusual modalities of CTL-induced neuronal damage

On the Origin of the Functional Architecture of the Cortex

The basic structure of receptive fields and functional maps in primary visual cortex is established without exposure to normal sensory experience and before the onset of the critical period. How the brain wires these circuits in the early stages of development remains unknown. Possible explanations include activity-dependent mechanisms driven by spontaneous activity in the retina and thalamus, and molecular guidance orchestrating thalamo-cortical connections on a fine spatial scale. Here I propose an alternative hypothesis: the blueprint for receptive fields, feature maps, and their inter-relationships may reside in the layout of the retinal ganglion cell mosaics along with a simple statistical connectivity scheme dictating the wiring between thalamus and cortex. The model is shown to account for a number of experimental findings, including the relationship between retinotopy, orientation maps, spatial frequency maps and cytochrome oxidase patches. The theory's simplicity, explanatory and predictive power makes it a serious candidate for the origin of the functional architecture of primary visual cortex

The Toll-Like Receptor Gene Family Is Integrated into Human DNA Damage and p53 Networks

In recent years the functions that the p53 tumor suppressor plays in human biology have been greatly extended beyond “guardian of the genome.” Our studies of promoter response element sequences targeted by the p53 master regulatory transcription factor suggest a general role for this DNA damage and stress-responsive regulator in the control of human Toll-like receptor (TLR) gene expression. The TLR gene family mediates innate immunity to a wide variety of pathogenic threats through recognition of conserved pathogen-associated molecular motifs. Using primary human immune cells, we have examined expression of the entire TLR gene family following exposure to anti-cancer agents that induce the p53 network. Expression of all TLR genes, TLR1 to TLR10, in blood lymphocytes and alveolar macrophages from healthy volunteers can be induced by DNA metabolic stressors. However, there is considerable inter-individual variability. Most of the TLR genes respond to p53 via canonical as well as noncanonical promoter binding sites. Importantly, the integration of the TLR gene family into the p53 network is unique to primates, a recurrent theme raised for other gene families in our previous studies. Furthermore, a polymorphism in a TLR8 response element provides the first human example of a p53 target sequence specifically responsible for endogenous gene induction. These findings—demonstrating that the human innate immune system, including downstream induction of cytokines, can be modulated by DNA metabolic stress—have many implications for health and disease, as well as for understanding the evolution of damage and p53 responsive networks

Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

We investigate the matter rogue wave in Bose-Einstein Condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; Rogue wave is unstable and the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein Condensates

Memory-experience gap in early adolescents' happiness reports

Studies among adult populations show that estimates of how happy one has felt in the past tend to be more positive than average happiness as assessed using time sampling techniques. This ‘memory-experience gap’ is attributed to cognitive biases, among which fading affect bias. In this paper we report a study among 352 pupils of a secondary school in the Netherlands. These youngsters reported subsequently: 1) how happy they had felt yesterday, 2) how happy they had felt during the last month, 3) what they had done the previous day and 4) how the