In vivo stability of ester- and ether-linked phospholipid-containing liposomes as measured by perturbed angular correlation spectroscopy

To evaluate liposome formulations for use as intracellular sustained-release drug depots, we have compared the uptake and degradation in rat liver and spleen of liposomes of various compositions, containing as their bulk phospholipid an ether-linked phospholipid or one of several ester-linked phospholipids, by perturbed angular correlation spectroscopy. Multilamellar and small unilamellar vesicles (MLVs and SUVs), composed of egg phosphatidylcholine, sphingomyelin, distearoyl phosphatidylcholine (DSPC), dipalmitoyl phosphatidylcholine (DPPC) or its analog dihexadecylglycerophosphorylcholine (DHPC), and cholesterol plus phosphatidylserine, and containing (111)In complexed to nitrilotriacetic acid, were injected intravenously in rats. Recovery of (111)In-labeled liposomes in blood, liver, and spleen was assessed at specific time points after injection and the percentage of liposomes still intact in liver and spleen was determined by measurement of the time-integrated angular perturbation factor ([G22(∞)] of the (111)In label. We found that MLVs but not SUVs, having DHPC as their bulk phospholipid, showed an increased resistance against lysosomal degradation as compared to other phospholipid-containing liposomes. The use of diacyl phospholipids with a high gel/liquid-crystalline phase-transition temperature, such as DPPC and DSPC, also retarded degradation of MLV, but not of SUV in the dose range tested, while the rate of uptake of these liposomes by the liver was lower

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

On the generalized Davenport constant and the Noether number

Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.Comment: 14 page

Semi-invariants of symmetric quivers of finite type

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall call the representation orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover we can define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. For symmetric quivers of finite type, we prove that the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, in the case when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$

Effects of pumping on entomopathogenic nematodes and temperature increase within a spray system

Exposure to hydrodynamic stresses and increased temperature during hydraulic agitation within a spray system could cause permanent damage to biological pesticides during spray application. Damage to a benchmark biopesticide, entomopathogenic nematodes (EPNs), was measured after a single passage through three different pump types (centrifugal, diaphragm, and roller) at operating pressures up to 828 kPa. No mechanical damage to the EPNs due to passage through the pumps was observed. Separate tests evaluated the effect of pump recirculation on temperature increase of water within a laboratory spray system (56.8-L spray tank) and a conventional-scale spray system (1136-L spray tank). A constant volume of water (45.4 L) was recirculated through each pump at 15.1 L/min within the laboratory spray system. After 2 h, the temperature increase for the centrifugal pump was 33.6 degrees C, and for the diaphragm and roller pumps was 8.5 degrees C and 11.2 degrees C, respectively. The centrifugal pump was also evaluated within the conventional spray system, under both a constant (757 L) and reducing volume scenario, resulting in an average temperature increase of 3.2 degrees C and 6.5 degrees C, respectively, during the 3-h test period. When comparing the number of recirculations for each test, the rate of temperature increase was the same for the conventional spray, system (for both the constant and reducing volume scenarios), while for the laboratory spray system the temperature increased at a greater rate, suggesting that the volume capacity of the spray tank is the primary factor influencing the temperature increase. Results from this study indicate that thermal influences during pump recirculation could be more detrimental to EPNs than mechanical stress. Results show that extensive recirculation of the tank mix can cause considerable increases in the liquid temperature. Diaphragm and roller pumps (low-capacity pumps) are better suited for use with biopesticides compared to the centrifugal pump, which was found to contribute significant heat to the spray system

Invariants and separating morphisms for algebraic group actions

The first part of this paper is a refinement of Winkelmann’s work on invariant rings and quotients of algebraic group actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient X//G given by the possibly not finitely generated ring of invariants is “almost” an algebraic variety, and that the quotient morphism π: X → X//G has a number of nice properties. One of the main difficulties comes from the fact that the quotient morphism is not necessarily surjective. These general results are then refined for actions of the additive group Ga, where we can say much more. We get a rather explicit description of the so-called plinth variety and of the separating variety, which measures how much orbits are separated by invariants. The most complete results are obtained for representations. We also give a complete and detailed analysis of Roberts’ famous example of a an action of Ga on 7-dimensional affine space with a non-finitely generated ring of invariants

Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Screening and assessment for post-acute COVID-19 syndrome (PACS), guidance by personal pilots and support with individual digital trainings within intersectoral care: a study protocol of a randomized controlled trial.

BACKGROUND: Because the clinical patterns and symptoms that persist after a COVID-19 infection are diverse, a diagnosis of post-acute COVID-19 syndrome (PACS) is difficult to implement. The current research project therefore aims to evaluate the feasibility and the practicability of a comprehensive, interdisciplinary, and cross-sectoral treatment program consisting of a low-threshold online screening and holistic assessment for PACS. Furthermore, it aims to evaluate digital interventions and the use of so-called personal guides that may help to facilitate the recovery of PACS. METHODS: This German study consists of a low-threshold online screening for PACS where positively screened participants will be supported throughout by personal pilots. The personal pilots are aimed at empowering patients and helping them to navigate through the study and different treatment options. Patients will then be randomly assigned either to an intervention group (IG) or an active control group (ACG). The IG will receive a comprehensive assessment of physiological and psychological functioning to inform future treatment. The ACG does not receive the assessment but both groups will receive a treatment consisting of an individual digital treatment program (digital intervention platform and an intervention via a chatbot). This digital intervention is based on the needs identified during the assessment for participants in the IG. Compared to that, the ACG will receive a more common digital treatment program aiming to reduce PACS symptoms. Importantly, a third comparison group (CompG) will be recruited that does not receive any treatment. A propensity score matching will take place, ensuring comparability between the participants. Primary endpoints of the study are symptom reduction and return to work. Secondary outcomes comprise, for example, social participation and activities in daily life. Furthermore, the feasibility and applicability of the online screening tool, the holistic assessment, digital trainings, and personal pilots will be evaluated. DISCUSSION: This is one of the first large-scale studies to improve the diagnosis and the care of patients with PACS by means of empowerment. It is to be evaluated whether the methods utilized can be used for the German and international population. Trial registration ClinicalTrials.gov Identifier: NCT05238415; date of registration: February 14, 2022

Categorification of skew-symmetrizable cluster algebras

We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with the action of a finite group G, we construct a G-equivariant mutation on the set of maximal rigid G-invariant objects of C. Using an appropriate cluster character, we can then attach to these data an explicit skew-symmetrizable cluster algebra. As an application we prove the linear independence of the cluster monomials in this setting. Finally, we illustrate our construction with examples associated with partial flag varieties and unipotent subgroups of Kac-Moody groups, generalizing to the non simply-laced case several results of Gei\ss-Leclerc-Schr\"oer.Comment: 64 page