Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

Magnification Control in Winner Relaxing Neural Gas

An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner relaxing approach for the neural gas network. Originally, winner relaxing learning is a slight modification of the self-organizing map learning rule that allows for adjustment of the magnification behavior by an a priori chosen control parameter. We transfer this approach to the neural gas algorithm. The magnification exponent can be calculated analytically for arbitrary dimension from a continuum theory, and the entropy of the resulting map is studied numerically conf irming the theoretical prediction. The influence of a diagonal term, which can be added without impacting the magnification, is studied numerically. This approach to maps of maximal mutual information is interesting for applications as the winner relaxing term only adds computational cost of same order and is easy to implement. In particular, it is not necessary to estimate the generally unknown data probability density as in other magnification control approaches.Comment: 14pages, 2 figure

ESG Due Diligence in a Share Purchase Transaction from an Investor’s Perspective

Abstract Faculty: Faculty of law Degree programme: Master’s degree programme Study track: Commercial law Author: Getter Villmann Title: ESG Due Diligence in a Share Purchase Transaction from an Investor’s Perspective Level: Master’s thesis Month and year: April 2021 Number of pages: XVIII + 79 Keywords: ESG, ESG due diligence, sustainable investing, mergers and acquisitions Where deposited: The Helsinki University Library Additional information: Supervisor: Jukka Mähönen Abstract: Sustainable or responsible investing has increased its popularity among investors throughout the last decade. Thus, nowadays, a growing amount of investors systematically include environmental, social and governance (ESG) factors as a part of their investment processes. In the context of a share purchase transaction, ESG integration during the investment phase is best achieved through a comprehensive ESG due diligence review performed by the purchaser to support its investment decision. This thesis aims to find answers to the following research questions: (i) what are the benefits and drivers for investors to perform an ESG due diligence review; (ii) how is ESG due diligence process conducted; and (iii) what are the effects of ESG due diligence findings to a share purchase agreement and the proposed transaction. Despite the accompanying financial and time costs, as a conclusion of this thesis, it was identified that performing an ESG due diligence review is beneficial for the investor in several ways. The main benefits of ESG due diligence review are risk mitigation and future ESG related opportunities, impacts on valuation, and higher return opportunities in the long-term perspective. Based on the ESG due diligence findings, an investor can make an informed decision whether to move forward with the share purchase transaction or not. These findings can also be reflected in the share purchase agreement through liability provisions and other terms to help the purchaser mitigate risks. The research suggests that in most cases the ESG integration benefits outweigh the cost issues and other ESG barriers. As indicated by this thesis, ESG due diligence is often performed with the help of external advisors as a desk review. As there is no clear standardisation concerning relevant ESG issues, the scope of ESG due diligence review depends on what is considered material in each particular case. The materiality of ESG issues depends on various circumstances, inter alia, the sector and location of the investment target, investor’s previous knowledge about the target and investor’s other preferences. The conclusions section of this thesis also includes suggestions on how ESG assessments could be developed in the future

The Intracellular Loop of the Glycine Receptor: It’s not all about the Size

The family of Cys-loop receptors (CLRs) shares a high degree of homology and sequence identity. The overall structural elements are highly conserved with a large extracellular domain (ECD) harboring an α-helix and 10 β-sheets. Following the ECD, four transmembrane domains (TMD) are connected by intracellular and extracellular loop structures. Except the TM3-4 loop, their length comprises 7-14 residues. The TM3-4 loop forms the largest part of the intracellular domain (ICD) and exhibits the most variable region between all CLRs. The ICD is defined by the TM3-4 loop together with the TM1-2 loop preceding the ion channel pore. During the last decade, crystallization approaches were successful for some members of the CLR family. To allow crystallization, the intracellular loop was in most structures replaced by a short linker present in prokaryotic CLRs. Therefore, no structural information about the large TM3-4 loop of CLRs including the glycine receptors (GlyRs) is available except for some basic stretches close to TM3 and TM4. The intracellular loop has been intensively studied with regard to functional aspects including desensitization, modulation of channel physiology by pharmacological substances, posttranslational modifications, and motifs important for trafficking. Furthermore, the ICD interacts with scaffold proteins enabling inhibitory synapse formation. This review focuses on attempts to define structural and functional elements within the ICD of GlyRs discussed with the background of protein-protein interactions and functional channel formation in the absence of the TM3-4 loop

Investigation of topographical stability of the concave and convex Self-Organizing Map variant

We investigate, by a systematic numerical study, the parameter dependence of the stability of the Kohonen Self-Organizing Map and the Zheng and Greenleaf concave and convex learning with respect to different input distributions, input and output dimensions

Batch and median neural gas

Neural Gas (NG) constitutes a very robust clustering algorithm given euclidian data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments.Comment: In Special Issue after WSOM 05 Conference, 5-8 september, 2005, Pari