Adapted Downhill Simplex Method for Pricing Convertible Bonds

The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and min-max optimization. Stock prices (underlying asset) were modeled under the assumption of the geometric Brownian motion of their values. The Monte Carlo method was used for calculating the real payoff which is the objective function. The min-max optimization problem was solved using the derivative-free Downhill Simplex method. The performed numerical experiments allowed to formulate recommendations for the choice of appropriate size of the initial simplex in the Downhill Simplex Method, the number of generated trajectories of underlying asset, the size of the problem and initial trajectories of the behavior of investors and issuers.Comment: 18 pages, 8 figure

Strategies for recovering exact structure of neural circuits with broadly targeted fluorescent connectivity probes

We present a framework for reconstructing structure of complete neural circuits
in the brain using collections of independent measurements of connectivity
performed with existing anatomical or functional fluorescent probes, and
designed to provide complementary information about neural circuit’s structure
by targeting slightly different its parts either in deterministic or stochastic
succession. We discuss specific implementation of this procedure using
synaptic fluorescent marker GRASP and Cre/Lox system Brainbow to collect
ensemble of observations of the sets of synapses between stochastically labeled
samples of neurons. By representing such measurements mathematically as
weak constraints on circuit’s connectivity matrix and by solving a constrained
optimization problem, we are able to exactly deduce the wiring diagram in C.
Elegans in an in-silico experiment from only ~10,000 measurements. This
offers possibility for routinely reconstructing complete connectivity in smaller
organisms, such as C. Elegans, using exclusively light microscopy instruments
over the span of single weeks

Strategies for identifying exact structure of neural circuits with broad light microscopy connectivity probes

Dissecting the structure of neural circuits in the brain is one of the central problems of neuroscience. Until present day, the only way to obtain complete and detailed reconstructions of neural circuits was thought to be the serial section Electron Microscopy, which could take decades to complete a small circuit. In this paper, we develop a mathematical framework that allows performing such reconstructions much faster and cheaper with existing light microscopy and genetic tools. In this framework, a collection of genetically targeted light probes of connectivity is prepared from different animals and then used to systematically deduce the circuit's connectivity. Each measurement is represented as mathematical constraint on the circuit architecture. Such constraints are then computationally combined to identify the detailed connectivity matrix for the probed circuit. Connectivity here is understood broadly, such as that between different identifiable neurons or identifiable classes of neurons, etc. This paradigm may be applied with connectivity probes such as ChR2-assisted circuit mapping, GRASP or transsynaptic viruses, and genetic targeting techniques such as Brainbow, MARCM/MADM or UAS/Gal4, in model organisms such as C. Elegans, Drosophila, zerbafish, mouse, etc. In particular, we demonstrate how, by using this paradigm, the wiring diagram between all neurons in C. Elegans may be reconstructed with GRASP and Brainbow and off-the-shelf light microscopy tools in the time span of one week or less. Described approach allows recovering exact connectivity matrix even if neurons may not be targeted individually in ~Np*log(N) time (Np is the number of nonzero entries and N is the size of the connectivity matrix). For comparison, the minimal time that would be necessary to determine connectivity matrix directly by probing connections between individual neurons when one knows a-priory which pairs should be tested, e.g. with whole-cell patches, is ~Np

Structural organization of sacred landscapes

The article presents the results of scientific developments concerning the structural organization of sacred landscapes. The methodological basis of the study is the concept of constructive-geographic analysis, which is based on the approaches of the natural and the humanitarian sciences. The system approach to the study of sacred landscapes as a holistic organized territorial structure and a set of methods is used in this work, in particular: structural and logical generalization and system analysis, comparative and geographical, historical and geographical. The author considers the significance of the notion of sacral landscape more widely than religious, and considers it a natural, natural-anthropogenic, anthropogenic system associated with certain symbols of life, myths, significant events, religious feelings that are of great importance to a person or group of people and requires special respect and protection. The structural organization of all sacred landscapes is characterized by its properties and spatial structure and is closely connected with their social and functional purpose. As a result, such territorial systems can be divided into: confessional, taphal, actival, abnormal. The sacred landscape is characterized by polystructurenes, that is, the presence of spatial, temporal, morphological structure. In the spatial structure of the sacral landscape, the following components can be distinguished: a sacred object, anthropogenic and technogenic component, a landscape structure, a person with her spiritual experience. In addition, such a structure has a hierarchical structure, where individual, local, regional, national, global levels can be distinguished. The article presents the peculiarities of the temporal structure of sacral landscapes and outlines the external, internal, and the functioning time. Particular attention is paid to the characteristic of internal time, where one can distinguish the following phases of development: the formation of a natural, natural or anthropogenic landscape; the creation of a spiritual component; loss of sacred human perception of a natural, natural or anthropogenic landscape; the disappearance of the natural, natural anthropogenic landscape. Taking into account the morphological structure of the sacred landscape, it is substantiated that religious objects serving as markers of sacred landscapes can not correspond to one or another morphological unit of the landscape, that is, to completely repeat its outlines and boundaries. However, there is a correlation between the type of landscape landscape and the features of the sacred object that was formed there