On a class of second-order PDEs admitting partner symmetries

Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs with four variables, that possess partner symmetries and contain only second derivatives of the unknown. We present a general form of such a PDE together with recursion relations between partner symmetries. This general PDE is transformed to several simplest canonical forms containing the two heavenly equations of Plebanski among them and two other nonlinear equations which we call mixed heavenly equation and asymmetric heavenly equation. On an example of the mixed heavenly equation, we show how to use partner symmetries for obtaining noninvariant solutions of PDEs by a lift from invariant solutions. Finally, we present Ricci-flat self-dual metrics governed by solutions of the mixed heavenly equation and its Legendre transform.Comment: LaTeX2e, 26 pages. The contents change: Exact noninvariant solutions of the Legendre transformed mixed heavenly equation and Ricci-flat metrics governed by solutions of this equation are added. Eq. (6.10) on p. 14 is correcte

Translation, cross-cultural adaptation, and validation of a Dutch version of the actions and feelings questionnaire in autistic and neurotypical adult

The actions and feelings questionnaire (AFQ) provides a short, self-report measure of how well someone uses and understands visual communicative signals such as gestures. The objective of this study was to translate and cross-culturally adapt the AFQ into Dutch (AFQ-NL) and validate this new version in neurotypical and autistic populations. Translation and adaptation of the AFQ consisted of forward translation, synthesis, back translation, and expert review. In order to validate the AFQ-NL, we assessed convergent and divergent validity. We additionally assessed internal consistency using Cronbach’s alpha. Validation and reliability outcomes were all satisfactory. The AFQ-NL is a valid adaptation that can be used for both autistic and neurotypical populations in the Netherlands

Differences in the production and perception of communicative kinematics in autism

In human communication, social intentions and meaning are often revealed in the way we move. In this study, we investigate the flexibility of human communication in terms of kinematic modulation in a clinical population, namely, autistic individuals. The aim of this study was twofold: to assess (a) whether communicatively relevant kinematic features of gestures differ between autistic and neurotypical individuals, and (b) if autistic individuals use communicative kinematic modulation to support gesture recognition. We tested autistic and neurotypical individuals on a silent gesture production task and a gesture comprehension task. We measured movement during the gesture production task using a Kinect motion tracking device in order to determine if autistic individuals differed from neurotypical individuals in their gesture kinematics. For the gesture comprehension task, we assessed whether autistic individuals used communicatively relevant kinematic cues to support recognition. This was done by using stick-light figures as stimuli and testing for a correlation between the kinematics of these videos and recognition performance. We found that (a) silent gestures produced by autistic and neurotypical individuals differ in communicatively relevant kinematic features, such as the number of meaningful holds between movements, and (b) while autistic individuals are overall unimpaired at recognizing gestures, they processed repetition and complexity, measured as the amount of submovements perceived, differently than neurotypicals do. These findings highlight how subtle aspects of neurotypical behavior can be experienced differently by autistic individuals. They further demonstrate the relationship between movement kinematics and social interaction in high-functioning autistic individuals

Differences in functional brain organization during gesture recognition between autistic and neurotypical individuals

Persons with and without autism process sensory information differently. Differences in sensory processing are directly relevant to social functioning and communicative abilities, which are known to be hampered in persons with autism. We collected functional magnetic resonance imaging (fMRI) data from 25 autistic individuals and 25 neurotypical individuals while they performed a silent gesture recognition task. We exploited brain network topology, a holistic quantification of how networks within the brain are organized to provide new insights into how visual communicative signals are processed in autistic and neurotypical individuals. Performing graph theoretical analysis, we calculated two network properties of the action observation network: local efficiency, as a measure of network segregation, and global efficiency, as a measure of network integration. We found that persons with autism and neurotypical persons differ in how the action observation network is organized. Persons with autism utilize a more clustered, local-processing-oriented network configuration (i.e., higher local efficiency), rather than the more integrative network organization seen in neurotypicals (i.e., higher global efficiency). These results shed new light on the complex interplay between social and sensory processing in autism

Solutions of the sDiff(2)Toda equation with SU(2) Symmetry

We present the general solution to the Plebanski equation for an H-space that admits Killing vectors for an entire SU(2) of symmetries, which is therefore also the general solution of the sDiff(2)Toda equation that allows these symmetries. Desiring these solutions as a bridge toward the future for yet more general solutions of the sDiff(2)Toda equation, we generalize the earlier work of Olivier, on the Atiyah-Hitchin metric, and re-formulate work of Babich and Korotkin, and Tod, on the Bianchi IX approach to a metric with an SU(2) of symmetries. We also give careful delineations of the conformal transformations required to ensure that a metric of Bianchi IX type has zero Ricci tensor, so that it is a self-dual, vacuum solution of the complex-valued version of Einstein's equations, as appropriate for the original Plebanski equation.Comment: 27 page

Lorentz and Galilei Invariance on Lattices

We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations on regular lattices is the umbral calculus.Comment: 5 page

On the water-bag model of dispersionless KP hierarchy

We investigate the bi-Hamiltonian structure of the waterbag model of dKP for two component case. One can establish the third-order and first-order Hamiltonian operator associated with the waterbag model. Also, the dispersive corrections are discussed.Comment: 19 page

Bi-Hamiltonian representation, symmetries and integrals of mixed heavenly and Husain systems

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries (J. Phys. A: Math. Theor. Vol. 42 (2009) 395202 (20pp)), mixed heavenly equation and Husain equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain equation, formulated in a two-component form, we present recursion operators, Lax pairs of Olver-Ibragimov-Shabat type and discover their Lagrangians, symplectic and bi-Hamiltonian structure. We obtain all point and second-order symmetries, integrals and bi-Hamiltonian representations of these systems and their symmetry flows together with infinite hierarchies of nonlocal higher symmetries.Comment: LaTeX2e source, 43 pages, 23 references, title modified, errors corrected, study of recursions of symmetries and integrals adde

Modulation of Wnt/β-catenin signaling and proliferation by a ferrous iron chelator with therapeutic efficacy in genetically engineered mouse models of cancer

Using a screen for Wnt/β-catenin inhibitors, a family of 8-hydroxyquinolone derivatives with in vivo anti-cancer properties was identified. Analysis of microarray data for the lead compound N-((8-hydroxy-7-quinolinyl) (4-methylphenyl)methyl)benzamide (HQBA) using the Connectivity Map database suggested that it is an iron chelator that mimics the hypoxic response. HQBA chelates Fe2+ with a dissociation constant of ∼10−19 , with much weaker binding to Fe3+ and other transition metals. HQBA inhibited proliferation of multiple cell lines in culture, and blocked the progression of established spontaneous cancers in two distinct genetically engineered mouse models of mammary cancer, MMTV-Wnt1 and MMTV-PyMT mice, without overt toxicity. HQBA may inhibit an iron-dependent factor that regulates cell-type-specific β-catenin-driven transcription. It inhibits cancer cell proliferation independently of its effect on β-catenin signaling, as it works equally well in MMTV-PyMT tumors and diverse β-catenin-independent cell lines. HQBA is a promising specific intracellular Fe2+ chelator with activity against spontaneous mouse mammary cancers

DJ-1 Null Dopaminergic Neuronal Cells Exhibit Defects in Mitochondrial Function and Structure: Involvement of Mitochondrial Complex I Assembly

DJ-1 is a Parkinson's disease-associated gene whose protein product has a protective role in cellular homeostasis by removing cytosolic reactive oxygen species and maintaining mitochondrial function. However, it is not clear how DJ-1 regulates mitochondrial function and why mitochondrial dysfunction is induced by DJ-1 deficiency. In a previous study we showed that DJ-1 null dopaminergic neuronal cells exhibit defective mitochondrial respiratory chain complex I activity. In the present article we investigated the role of DJ-1 in complex I formation by using blue native-polyacrylamide gel electrophoresis and 2-dimensional gel analysis to assess native complex status. On the basis of these experiments, we concluded that DJ-1 null cells have a defect in the assembly of complex I. Concomitant with abnormal complex I formation, DJ-1 null cells show defective supercomplex formation. It is known that aberrant formation of the supercomplex impairs the flow of electrons through the channels between respiratory chain complexes, resulting in mitochondrial dysfunction. We took two approaches to study these mitochondrial defects. The first approach assessed the structural defect by using both confocal microscopy with MitoTracker staining and electron microscopy. The second approach assessed the functional defect by measuring ATP production, O2 consumption, and mitochondrial membrane potential. Finally, we showed that the assembly defect as well as the structural and functional abnormalities in DJ-1 null cells could be reversed by adenovirus-mediated overexpression of DJ-1, demonstrating the specificity of DJ-1 on these mitochondrial properties. These mitochondrial defects induced by DJ-1mutation may be a pathological mechanism for the degeneration of dopaminergic neurons in Parkinson's disease