The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2

The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in solition theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.Comment: 10 page

Implicit relevance feedback from electroencephalography and eye tracking in image search

Objective. Methods from brain–computer interfacing (BCI) open a direct access to the mental processes of computer users, which offers particular benefits in comparison to standard methods for inferring user-related information. The signals can be recorded unobtrusively in the background, which circumvents the time-consuming and distracting need for the users to give explicit feedback to questions concerning the individual interest. The obtained implicit information makes it possible to create dynamic user interest profiles in real-time, that can be taken into account by novel types of adaptive, personalised software. In the present study, the potential of implicit relevance feedback from electroencephalography (EEG) and eye tracking was explored with a demonstrator application that simulated an image search engine. Approach. The participants of the study queried for ambiguous search terms, having in mind one of the two possible interpretations of the respective term. Subsequently, they viewed different images arranged in a grid that were related to the query. The ambiguity of the underspecified search term was resolved with implicit information present in the recorded signals. For this purpose, feature vectors were extracted from the signals and used by multivariate classifiers that estimated the intended interpretation of the ambiguous query. Main result. The intended interpretation was inferred correctly from a combination of EEG and eye tracking signals in 86% of the cases on average. Information provided by the two measurement modalities turned out to be complementary. Significance. It was demonstrated that BCI methods can extract implicit user-related information in a setting of human-computer interaction. Novelties of the study are the implicit online feedback from EEG and eye tracking, the approximation to a realistic use case in a simulation, and the presentation of a large set of photographies that had to be interpreted with respect to the content.EC/FP7/611570/EU/Symbiotic Mind Computer Interaction for Information Seeking/MindSeeBMBF, 01GQ0850, Bernstein Fokus Neurotechnologie - Nichtinvasive Neurotechnologie für Mensch-Maschine Interaktio

A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation

An approach based on the spectral and Lie - algebraic techniques for constructing vertex operator representation for solutions to a Riemann type Gurevicz-Zybin hydrodynamical hierarchy is devised. A functional representation generating an infinite hirerachy of dispersive Lax type integrable flows is obtaned.Comment: 6 page

The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities

In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive relation, we explicitly generate infinitely many higher order conserved densities dependent on arbitrary parameters. We find three Nijenhuis recursion operators resulting from Hamiltonian pairs, of which two are new. They generate three hierarchies of commuting local symmetries. Finally, we give a local recursion operator depending on an arbitrary parameter. As a by-product, we classify all anti-symmetric operators of a definite form that are compatible with the Hamiltonian operator $D_x^{-1}$

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the related gradient identity is stated. The integrability of a discrete nonlinear Schredinger type dynamical system is treated in detail.Comment: 20 page

Methodological challenges and biases in the field of cognitive function among patients with chronic kidney disease

Chronic kidney disease (CKD) affects approximately 850 million people globally and is associated with an increased risk of cognitive impairment. The prevalence of cognitive impairment among CKD patients ranges from 30 to 60%, and the link between CKD and cognitive impairment is partially understood. Methodological challenges and biases in studying cognitive function in CKD patients need to be addressed to improve diagnosis, treatment, and management of cognitive impairment in this population. Here, we review the methodological challenges and study design issues, including observational studies’ limitations, internal validity, and different types of bias that can impact the validity of research findings. Understanding the unique challenges and biases associated with studying cognitive function in CKD patients can help to identify potential sources of error and improve the quality of future research, leading to more accurate diagnoses and better treatment plans for CKD patients.</p

fac-Tris(pyridine-2-carboxyl­ato-κ2 N,O)cobalt(III)

In the title compound, [Co(C6H4NO2)3], the CoIII ion lies on a threefold rotation axis and is in a distorted octa­hedral environment defined by three N and three O donor atoms from three fac-disposed pyridine-2-carboxyl­ate ligands. The ligands are coordinated in a chelate fashion, forming three five-membered rings. In the crystal, translationally related complex molecules are organized into columns along [001] via C—H⋯O hydrogen bonds

Polyploidization for the Genetic Improvement of Cannabis sativa

Cannabis sativa L. is a diploid species, cultivated throughout the ages as a source of fiber, food, and secondary metabolites with therapeutic and recreational properties. Polyploidization is considered as a valuable tool in the genetic improvement of crop plants. Although this method has been used in hemp-type Cannabis, it has never been applied to drug-type strains. Here, we describe the development of tetraploid drug-type Cannabis lines and test whether this transformation alters yield or the profile of important secondary metabolites: Δ9-tetrahydrocannabinol (THC), cannabidiol (CBD), or terpenes. The mitotic spindle inhibitor oryzalin was used to induce polyploids in a THC/CBD balanced drug-type strain of Cannabis sativa. Cultured axillary bud explants were exposed to a range of oryzalin concentrations for 24 h. Flow cytometry was used to assess the ploidy of regenerated shoots. Treatment with 20–40 μM oryzalin produced the highest number of tetraploids. Tetraploid clones were assessed for changes in morphology and chemical profile compared to diploid control plants. Tetraploid fan leaves were larger, with stomata about 30% larger and about half as dense compared to diploids. Trichome density was increased by about 40% on tetraploid sugar leaves, coupled with significant changes in the terpene profile and a 9% increase in CBD that was significant in buds. No significant increase in yield of dried bud or THC content was observed. This research lays important groundwork for the breeding and development of new Cannabis strains with diverse chemical profiles, of benefit to medical and recreational users