A new Fortran 90 program to compute regular and irregular associated Legendre functions

We present a modern Fortran 90 code to compute the regular and irregular associated Legendre functions for all x∈(−1,+1) (on the cut) and |x|>1 and integer degree (l) and order (m). The code applies either forward or backward recursion in (l) and (m) in the stable direction, starting with analytically known values for forward recursion and considering both a Wronskian based and a modified Miller's method for backward recursion. While some Fortran 77 codes existed for computing the functions off the cut, no Fortran 90 code was available for accurately computing the functions for all real values of x different from x=±1 where the irregular functions are not defined.

Program summary

Program title: Associated Legendre FunctionsCatalogue identifier: AEHE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 6722No. of bytes in distributed program, including test data, etc.: 310 210Distribution format: tar.gzProgramming language: Fortran 90Computer: Linux systemsOperating system: LinuxRAM: bytesClassification: 4.7Nature of problem: Compute the regular and irregular associated Legendre functions for integer values of the degree and order and for all real arguments. The computation of the interaction of two electrons, 1/|r₁−r₂|, in prolate spheroidal coordinates is used as one example where these functions are required for all values of the argument and we are able to easily compare the series expansion in associated Legendre functions and the exact value.Solution method: The code evaluates the regular and irregular associated Legendre functions using forward recursion when |x|<1 starting the recursion with the analytically known values of the first two members of the sequence. For values of the argument |x|<1, the upward recursion over the degree for the regular functions is numerically stable. For the irregular functions, backward recursion must be applied and a suitable method of starting the recursion is required. The program has two options; a modified version of Miller's algorithm and the use of the Wronskian relation between the regular and irregular functions, which was the method considered in [1]. Both approaches require the computation of a continued fraction to begin the recursion. The Wronskian method (which can also be described as a modified Miller's method) is a convenient method of computations when both the regular and irregular functions are needed.Running time: The example tests provided take a few seconds to run.References:

• [1] 

  A. Gil, J. Segura, A code to evaluate prolate and oblate spheroidal harmonics, Comput. Phys. Commun. 108 (1998) 267–278.

     

Maximal Pairs of Computably Enumerable Sets in the Computably Lipschitz Degrees

A set A is computably Lipschitz or cl-reducible, for short, to a set B if A is Turing reducible to B by an oracle Turing machine with use function ? such that ? is bounded by the identity function up to an additive constant, i.e., ?(n)??n+O(1). In this paper we study maximal pairs of computably enumerable (c.e.) cl-degrees or maximal pairs, for short, i.e., pairs of c.e. cl-degrees such that there is no c.e. cl-degree that is above both cl-degrees in this pair. Our main results are as follows. (1) A c.e. Turing degree contains a c.e. cl-degree that is half of a maximal pair if and only if this Turing degree contains a maximal pair if and only if this Turing degree is array noncomputable. (2) The cl-degrees of all weak truth-table complete sets are halves of maximal pairs while there is a Turing complete set A such that the cl-degree of A is not half of any maximal pair. In fact, any high c.e. Turing degree contains a c.e. cl-degree that is not half of a maximal pair. (3) Above any c.e. cl-degree there is a maximal pair. (4) There is a maximal pair which at the same time is a minimal pair. (5) There is a pair of c.e. cl-degrees that is not maximal and does not possess a least upper bound. Moreover, we make some observations on the structure of the c.e. cl-degrees in general. For instance, we give a very simple proof of the fact that there are no maximal c.e. cl-degrees.     

The Oncolytic Adenovirus XVir-N-31, in Combination with the Blockade of the PD-1/PD-L1 Axis,Conveys Abscopal Effects in a Humanized Glioblastoma Mouse Model

Glioblastoma (GBM) is an obligatory lethal brain tumor with a median survival, even with the best standard of care therapy, of less than 20 months. In light of this fact, the evaluation of new GBM treatment approaches such as oncolytic virotherapy (OVT) is urgently needed. Based on our preliminary preclinical data, the YB-1 dependent oncolytic adenovirus (OAV) XVir-N-31 represents a promising therapeutic agent to treat, in particular, therapy resistant GBM. Preclinical studies have shown that XVir-N-31 prolonged the survival of GBM bearing mice. Now using an immunohumanized mouse model, we examined the immunostimulatory effects of XVir-N-31 in comparison to the wildtype adenovirus (Ad-WT). Additionally, we combined OVT with the inhibition of immune checkpoint proteins by using XVir-N-31 in combination with nivolumab, or by using a derivate of XVir-N-31 that expresses a PD-L1 neutralizing antibody. Although in vitro cell killing was higher for Ad-WT, XVir-N-31 induced a much stronger immunogenic cell death that was further elevated by blocking PD-1 or PD-L1. In vivo, an intratumoral injection of XVir-N-31 increased tumor infiltrating lymphocytes (TILs) and NK cells significantly more than Ad-WT not only in the virus-injected tumors, but also in the untreated tumors growing in the contralateral hemisphere. This suggests that for an effective treatment of GBM, immune activating properties by OAVs seem to be of greater importance than their oncolytic capacity. Furthermore, the addition of immune checkpoint inhibition (ICI) to OVT further induced lymphocyte infiltration. Consequently, a significant reduction in contralateral non-virus-injected tumors was only visible if OVT was combined with ICI. This strongly indicates that for an effective eradication of GBM cells that cannot be directly targeted by an intratumoral OV injection, additional ICI therapy is required.     

ADAM10 and ADAM17—Novel Players in Retinoblastoma Carcinogenesis

A disintegrin and metalloproteinase (ADAM) family proteins, acting as sheddases, are important factors in a number of pathologies, including cancer, and have been suggested as promising therapeutic targets. The study presented focuses on the involvement of ADAM10 and ADAM17 in retinoblastoma (RB), the most common malignant intraocular childhood tumor. A significant correlation between ADAM17 expression levels and RB laterality and RB staging was observed. Levels of ADAM10 or ADAM17 regulating miRNAs miR-145, -152, and -365 were significantly downregulated in RB cell lines, and reduced miR levels with simultaneously upregulated ADAM10 and ADAM17 expression were found in RB patients. The involvement of both ADAMs analyzed in ectodomain shedding of the neuronal cell adhesion molecule L1 (L1CAM), shown to induce pro-tumorigenic effects in RB, was confirmed. Lentiviral ADAM10 and ADAM17 single or ADAM10/17 double knockdown (KD) induced caspase-dependent apoptosis and reduced cell viability, proliferation, growth, and colony formation capacity of RB cells. Moreover, differential phosphorylation of the serine/threonine kinase AKT was observed following ADAM17 KD in RB cells. Chicken chorioallantoic membrane (CAM) assays revealed that ADAM17 and ADAM10/17 depletion decreases the tumorigenic and migration potential of RB cells in vivo. Thus, ADAMs are potential novel targets for future therapeutic RB approaches.     

Absolute characterization of high numerical aperture microscope objectives utilizing a dipole scatterer

Measuring the aberrations of optical systems is an essential step in the fabrication of high precision optical components. Such a characterization is usually ba...     

Assessment of noise attenuating powertrain components

Forschung im Ingenieurwesen - Wind turbine noise used to be dominated by aerodynamic blade noise, effectively masking mechanical noise, originating from the drivetrain. Successful blade noise...     

Bericht über neue ferromagnetische Werkstoffe

Ohne ZusammenfassungMit 5 Textabbildungen.     

MS-Based Screening of 5-Substituted Nipecotic Acid Derived Hydrazone Libraries as Ligands of the GABA Transporter 1

A screening of compound libraries based on nipecotic acid derivatives with lipophilic residues attached to the scarcely explored 5-position of the core structure was used for the search of new inhibitors of the γ-aminobutyric acid (GABA) transporter 1 (mGAT1). The generated compound libraries, which were based on hydrazone chemistry commonly used in dynamic combinatorial chemistry but rendered pseudostatic, were screened for their binding affinities toward mGAT1 by means of MS Binding Assays. With nipecotic acid derived hydrazone rac- 16 h [rac-(3R,5S)-{5-[(E)-2-{[5-(2-phenylethynyl)thiophen-2-yl]methylidene}hydrazin-1-yl]piperidine-3-carboxylic acid}-sodium chloride (1/2)], one hit was found and evaluated displaying sub-micromolar potency (pK_i=6.62±0.04) and a noncompetitive interaction mode at mGAT1. By bearing a 5-(2-phenylethynyl)thiophen-2-yl residue attached to the 5-position of nipecotic acid via a three-atom spacer, compound rac- 16 h contains a structural moiety so far unprecedented for these kinds of bioactive molecules, and complements novel 5-substituted nipecotic acid derived ligands of mGAT1 revealed in a recently published screening campaign. This new class of ligands, with an inhibition mode distinct from that of benchmark mGAT1 inhibitors, could serve as research tools for investigations of mGAT1-mediated GABA transport.