Symmetric Toda, gradient flows, and tridiagonalization

The Toda lattice (1967) is a Hamiltonian system given by $n$ points on a line governed by an exponential potential. Flaschka (1974) showed that the Toda lattice is integrable by interpreting it as a flow on the space of symmetric tridiagonal $n\times n$ matrices, while Moser (1975) showed that it is a gradient flow on a projective space. The symmetric Toda flow of Deift, Li, Nanda, and Tomei (1986) generalizes the Toda lattice flow from tridiagonal to all symmetric matrices. They showed the flow is integrable, in the classical sense of having $d$ integrals in involution on its $2d$-dimensional phase space. The system may be viewed as integrable in other ways as well. Firstly, Symes (1980, 1982) solved it explicitly via $QR$-factorization and conjugation. Secondly, Deift, Li, Nanda, and Tomei (1986) 'tridiagonalized' the system into a family of tridiagonal Toda lattices which are solvable and integrable. In this paper we derive their tridiagonalization procedure in a natural way using the fact that the symmetric Toda flow is diffeomorphic to a twisted gradient flow on a flag variety, which may then be decomposed into flows on a product of Grassmannians. These flows may in turn be embedded into projective spaces via Pl\"ucker embeddings, and mapped back to tridiagonal Toda lattice flows using Moser's construction. In addition, we study the tridiagonalized flows projected onto a product of permutohedra, using the twisted moment map of Bloch, Flaschka, and Ratiu (1990). These ideas are facilitated in a natural way by the theory of total positivity, building on our previous work (2023).Comment: 21 page

Gestion clinique et réhabilitation du patient souffrant de schizophrénie et réfractaire au traitement : fondements conceptuels et résultats (première partie)

Malgré les percées importantes en psychopharmacologie dans le traitement des personnes souffrant de schizophrénie, plusieurs patients demeurent trop handicapés pour obtenir leur congé des établissements psychiatriques publics. Cet article décrit le développement d’un partenariat entre les secteurs public et privé qui a mené à la création d’un programme spécialisé et intensif de réhabilitation behaviorale, dans les hôpitaux publics, à l’intention des patients souffrant de schizophrénie, et considérés réfractaires aux traitements. Les éléments essentiels de ce programme et ses fondements philosophiques y sont décrits. Des données sur les résultats sont discutées afin de souligner le fait que lorsque des traitements basés sur des données probantes sont dispensés à cette population, les résultats peuvent être positifs dans la plupart des cas. Et le nombre de patients « réfractaires aux traitements » devient moindre lorsque son estimation n’est pas seulement basée sur la réponse aux médicaments.Despite advances in psychopharmacology for people with schizophrenia, many patients remain too disabled to be discharged from public psychiatric facilities. This paper decribes the development of a public-private partnership which led to the creation of a specialized, intensive behavioral rehabilitation program for schizophrenia patients who were considered to be treatment-refractory at public hospitals. The essential elements of this treatment program are described, along with the philosophical bases of its treatment. Outcome data are discussed to emphasize the point that when evidence-based treatment is implemented with this population, outcomes can be positive in most cases, and therefore, the number of « treatment-refractory » patients is actually less than is estimated based on response to medication alone.A pesar de los avances importantes de la psicofarmacología en el tratamiento de las personas con esquizofrenia, muchos pacientes siguen estando demasiado discapacitados para obtener sus incapacidades en los establecimientos psiquiátricos públicos. Este artículo describe el desarrollo de una asociación entre el sector público y privado, que ha conducido a la creación de un programa especializado e intensivo de rehabilitación conductista, en los hospitales públicos, para los pacientes que sufren de esquizofrenia y que son considerados como refractarios a los tratamientos. Los elementos esenciales de este programa y sus fundamentos filosóficos son descritos en este artículo. También se discuten los datos de los resultados con el fin de subrayar el hecho de que cuando los tratamientos basados en los datos probantes son presentados a esta población, los resultados pueden ser positivos en la mayoría de los casos y el número de pacientes “refractarios a los tratamientos” disminuye cuando su estimación no se basa sólo en su respuesta a los medicamentos.Apesar das descobertas importantes em psicofarmacologia no tratamento de pessoas que sofrem de esquizofrenia, vários pacientes continuam debilitados demais para obter sua alta dos estabelecimentos psiquiátricos públicos. Este artigo descreve o desenvolvimento de uma parceria entre os setores público e privado que levou à criação de um programa especializado e intensivo de reabilitação behaviorista, nos hospitais públicos, para pacientes que sofrem de esquizofrenia, considerados refratários aos tratamentos. Os elementos essenciais deste programa e seus fundamentos filosóficos são descritos no artigo. São discutidos dados sobre os resultados para ressaltar o fato de que, quando tratamentos baseados nos dados probatórios são dispensados a esta população, os resultados podem ser positivos na maior parte dos casos. O número de pacientes “refratários aos tratamentos” diminui quando sua estimativa não é somente baseada na resposta aos medicamentos

Double Lorentzian Atomic Prism

We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal, and idler beams resulting from a four-wave mixing process. Due to the high transparency possible between the resonances, these results have applications in the filtering of narrow-band entangled photons and interaction-free measurements

The Excitation Ladder of Cavity Polaritons

Multidimensional coherent spectroscopy directly unravels multiply excited states that overlap in a linear spectrum. We report multidimensional coherent optical photocurrent spectroscopy in a semiconductor polariton diode and explore the excitation ladder of cavity polaritons. We measure doubly and triply avoided crossings for pairs and triplets of exciton-polaritons, demonstrating the strong coupling between light and dressed doublet and triplet semiconductor excitations. These results demonstrate that multiply excited excitonic states strongly coupled to a microcavity can be described as two coupled quantum-anharmonic ladders

Excitation Ladder of Cavity Polaritons

Multidimensional coherent spectroscopy directly unravels multiply excited states that overlap in a linear spectrum. We report multidimensional coherent optical photocurrent spectroscopy in a semiconductor polariton diode and explore the excitation ladder of cavity polaritons. We measure doubly and triply avoided crossings for pairs and triplets of exciton polaritons, demonstrating the strong coupling between light and dressed doublet and triplet semiconductor excitations. These results demonstrate that multiply excited excitonic states strongly coupled to a microcavity can be described as two coupled quantum-anharmonic ladders

Fermion correlators in non-abelian holographic superconductors

We consider fermion correlators in non-abelian holographic superconductors. The spectral function of the fermions exhibits several interesting features such as support in displaced Dirac cones and an asymmetric distribution of normal modes. These features are compared to similar ones observed in angle resolved photoemission experiments on high T_c superconductors. Along the way we elucidate some properties of p-wave superconductors in AdS_4 and discuss the construction of SO(4) superconductors.Comment: 49 pages, 11 figure

Structural basis of GM-CSF and IL-2 sequestration by the viral decoy receptor GIF.

Subversion of the host immune system by viruses is often mediated by molecular decoys that sequester host proteins pivotal to mounting effective immune responses. The widespread mammalian pathogen parapox Orf virus deploys GIF, a member of the poxvirus immune evasion superfamily, to antagonize GM-CSF (granulocyte macrophage colony-stimulating factor) and IL-2 (interleukin-2), two pleiotropic cytokines of the mammalian immune system. However, structural and mechanistic insights into the unprecedented functional duality of GIF have remained elusive. Here we reveal that GIF employs a dimeric binding platform that sequesters two copies of its target cytokines with high affinity and slow dissociation kinetics to yield distinct complexes featuring mutually exclusive interaction footprints. We illustrate how GIF serves as a competitive decoy receptor by leveraging binding hotspots underlying the cognate receptor interactions of GM-CSF and IL-2, without sharing any structural similarity with the cytokine receptors. Our findings contribute to the tracing of novel molecular mimicry mechanisms employed by pathogenic viruses

Tropical metacommunities along elevational gradients: effects of forest type and other environmental factors.

Elevational gradients provide a natural experiment for assessing the extent to which the structure of animal metacommunities is molded by biotic and abiotic characteristics that change gradually, or is molded by aspects of plant community composition and physiognomy that change in a more discrete fashion. We used a metacommunity framework to integrate species-specifi c responses to environmental gradients as an approach to detect emergent patterns at the mesoscale in the Luquillo Mountains of Puerto Rico. Elements of metacommunity structure (coherence, species turnover and range boundary clumping) formed the basis for distinguishing among random, checkerboard, Gleasonian, Clementsian, evenly spaced and nested patterns. Paired elevational transects (300 -1000 m a.s.l.) were sampled at 50 m intervals to decouple underlying environmental mechanisms: a mixed forest transect refl ected changes in abiotic and biotic conditions, including forest type (i.e. tabonuco, palo colorado and elfi n forests), whereas another transect refl ected changes in environmental conditions but not forest type, as its constituent plots were located within palm forest. Based on distributional data (presence versus absence of species), the mixed forest transect exhibited Clementsian structure, whereas the palm forest transect exhibited quasi-Gleasonian structure. In contrast, the distribution of modes in species abundance was random with respect to the latent environmental gradient in the mixed forest transect and clumped with respect to the latent environmental gradient in the palm forest transect. Such contrasts suggest that the environmental factors aff ecting abundance diff ered in form or type from those aff ecting distributional boundaries. Variation among elevational strata with respect to the fi rst axis of correspondence from reciprocal averaging was highly correlated with elevation along each transect, even though axis scores were not correlated between mixed forest and palm forest transects. Th is suggests that the identity of the environmental characteristics, or the form of response by the fauna to those characteristics, diff ered between the two elevational transects. Despite the proximity of the transects, the patchy confi guration of palm forest, and the pervasive distribution of the dominant palm species, the relative importance of abiotic variables and habitat in structuring gastropod metacommunities diff ered between transects, which is remarkable and attests to the sensitivity of metacommunity structure to environmental variation

Tropical metacommunities along elevational gradients: effects of forest type and other environmental factors.

Elevational gradients provide a natural experiment for assessing the extent to which the structure of animal metacommunities is molded by biotic and abiotic characteristics that change gradually, or is molded by aspects of plant community composition and physiognomy that change in a more discrete fashion. We used a metacommunity framework to integrate species-specific responses to environmental gradients as an approach to detect emergent patterns at the mesoscale in the Luquillo Mountains of Puerto Rico. Elements of metacommunity structure (coherence, species turnover and range boundary clumping) formed the basis for distinguishing among random, checkerboard, Gleasonian, Clementsian, evenly spaced and nested patterns. Paired elevational transects (300-1000 m a.s.l.) were sampled at 50 m intervals to decouple underlying environmental mechanisms: a mixed forest transect reflected changes in abiotic and biotic conditions, including forest type (i.e. tabonuco, palo colorado and elfin forests), whereas another transect reflected changes in environmental conditions but not forest type, as its constituent plots were located within palm forest. Based on distributional data (presence versus absence of species), the mixed forest transect exhibited Clementsian structure, whereas the palm forest transect exhibited quasi-Gleasonian structure. In contrast, the distribution of modes in species abundance was random with respect to the latent environmental gradient in the mixed forest transect and clumped with respect to the latent environmental gradient in the palm forest transect. Such contrasts suggest that the environmental factors affecting abundance differed in form or type from those affecting distributional boundaries. Variation among elevational strata with respect to the first axis of correspondence from reciprocal averaging was highly correlated with elevation along each transect, even though axis scores were not correlated between mixed forest and palm forest transects. This suggests that the identity of the environmental characteristics, or the form of response by the fauna to those characteristics, differed between the two elevational transects. Despite the proximity of the transects, the patchy configuration of palm forest, and the pervasive distribution of the dominant palm species, the relative importance of abiotic variables and habitat in structuring gastropod metacommunities differed between transects, which is remarkable and attests to the sensitivity of metacommunity structure to environmental variation

The genomes of two key bumblebee species with primitive eusocial organization

Background: The shift from solitary to social behavior is one of the major evolutionary transitions. Primitively eusocial bumblebees are uniquely placed to illuminate the evolution of highly eusocial insect societies. Bumblebees are also invaluable natural and agricultural pollinators, and there is widespread concern over recent population declines in some species. High-quality genomic data will inform key aspects of bumblebee biology, including susceptibility to implicated population viability threats. Results: We report the high quality draft genome sequences of Bombus terrestris and Bombus impatiens, two ecologically dominant bumblebees and widely utilized study species. Comparing these new genomes to those of the highly eusocial honeybee Apis mellifera and other Hymenoptera, we identify deeply conserved similarities, as well as novelties key to the biology of these organisms. Some honeybee genome features thought to underpin advanced eusociality are also present in bumblebees, indicating an earlier evolution in the bee lineage. Xenobiotic detoxification and immune genes are similarly depauperate in bumblebees and honeybees, and multiple categories of genes linked to social organization, including development and behavior, show high conservation. Key differences identified include a bias in bumblebee chemoreception towards gustation from olfaction, and striking differences in microRNAs, potentially responsible for gene regulation underlying social and other traits. Conclusions: These two bumblebee genomes provide a foundation for post-genomic research on these key pollinators and insect societies. Overall, gene repertoires suggest that the route to advanced eusociality in bees was mediated by many small changes in many genes and processes, and not by notable expansion or depauperation