Abstract. Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce “multivariable” manifold calculus of functors which is a generalization of this theory to functors whose domain is a product of categories of open sets. We construct multivariable Taylor approximations to such functors, classify multivariable homogeneous functors, apply this classification to compute the derivatives of a functor, and show what this gives for the space of link maps. We also relate Taylor approximations in single variable calculus to our multivariable ones.

New antibiotics against multidrug-resistant bacteria are urgently needed, but rapid acquisition of resistance limits their usefulness. Endogenous antimicrobial peptides (AMPs) with moderate selectivity, but multimodal mechanism of action, have remained effective against bacteria for millions of years. Their therapeutic application, however, requires optimizing the balance between antibacterial activity and selectivity, so that rational design methods for increasing selectivity are highly desirable. We have created training (n=36) and testing (n=37) sets from frog-derived AMPs with determined therapeutic index (TI). The 'sequence moments' concept then enabled us to find a one-parameter linear model resulting in a good correlation between measured and predicted TI (r2=0.83 and 0.64 for each set, respectively). The concept was then used in the AMP-Designer algorithm to propose primary structures for highly selective AMPs against Gram-negative bacteria. Testing the activity of one such peptide produced a TI>200 as compared to the best AMP in the data-base, with TI=125.

The study of the present literature for pharmacognostical identification has shown that there is not enough information for the clear differentiation of Mentha species. There exist some data about chemical compounds and morphological aspects [1, 2] but proper anatomical descriptions are missing (except M. × piperita).

Houseleek is one of the 150 plant species belonging to the Crassulaceae family which authentically grow in Mexico. It has been cultivated in Europe since IX century as decorative plant as well as medicinal plant. Due to the fact that it has not been enough investigated from a chemical point of view, its usage today is limited to folk medicine.

Maximal-ratio combiner (MRC) performances in fading channels have been of interest for a long time, which can be seen by a number of papers concerning this topic. In this paper we treat bit error probability (BEP), symbol error probability (SEP) and outage probability of MRC in presence of 𝜅-𝜇 fading. We will present 𝜅-𝜇 fading model, probability density function (PDF), and cumulative distribution function (CDF). We will also present PDF, CDF, and outage probability of the L-branch MRC output. BEP/SEP will be evaluated for broad class of modulation types and for coherent and noncoherent types of detection. BEP/SEP and outage performances of the MRC will be evaluated for different number of branches via Monte Carlo simulations and theoretical expressions.