Error bounds for PDE-regularized learning

In this work we consider the regularization of a supervised learning problem by partial differential equations (PDEs) and derive error bounds for the obtained approximation in terms of a PDE error term and a data error term. Assuming that the target function satisfies an unknown PDE, the PDE error term quantifies how well this PDE is approximated by the auxiliary PDE used for regularization. It is shown that this error term decreases if more data is provided. The data error term quantifies the accuracy of the given data. Furthermore, the PDE-regularized learning problem is discretized by generalized Galerkin discretizations solving the associated minimization problem in subsets of the infinite dimensional functions space, which are not necessarily subspaces. For such discretizations an error bound in terms of the PDE error, the data error, and a best approximation error is derived

The structure of coevolving infection networks

Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with constant infected node density in which the interplay of disease dynamics and link rewiring prompts the convergence towards a well defined degree distribution, irrespective of the initial network topology. We develop a method to study this dynamic equilibrium and give an analytic description of the structure of the characteristic degree distributions and other network measures. The method applies to a broad class of systems and can be used to determine the steady-state topology of many other adaptive networks.Comment: Typo corrected in the last term of Eq.(2). Definition of P_S(x,y,t|x_0,y_0) changed to allow for correct normalization in Eq.(5), consequently \hat{P}_I=r*P_I instead of \hat{P}_I=P_I. All subsequent formulae, results and conclusions in the original paper remain unaffecte

Theoretical and experimental investigation of performance characteristics and design aspects of cross-spring pivots

Cross-spring pivots have been widely employed over the last decades in a broad variety of precision engineering applications due to the high motion repeatability achieved thanks to the absence of stick slip and clearance. In this paper, the non-linear effect of the anticlastic curvature of the leaf-springs is considered for the accurate analytical modeling of the elasto-kinematic behavior of cross-spring pivots. Finite element analyses (FEA), based on a non-linear thin-shell model, are carried out in order to compare them with the analytical results for the main performance parameters of this type of device, i.e. center-shift, rotational stiffness and stress in the leaf-springs. Furthermore, an experimental setup is built to assess the applicability limits of both models. Finally, remarkable performance aspects of cross-spring pivots are discussed aiming for design improvements

New insights in dermatophyte research

Dermatophyte research has renewed interest because of changing human floras with changing socioeconomic conditions, and because of severe chronic infections in patients with congenital immune disorders. Main taxonomic traits at the generic level have changed considerably, and now fine-tuning at the species level with state-of-the-art technology has become urgent. Research on virulence factors focuses on secreted proteases now has support in genome data. It is speculated that most protease families are used for degrading hard keratin during nitrogen recycling in the environment, while others, such as Sub6 may have emerged as a result of ancestral gene duplication, and are likely to have specific roles during infection. Virulence may differ between mating partners of the same species and concepts of zoo- and anthropophily may require revision in some recently redefined species. Many of these questions benefit from international cooperation and exchange of materials. The aim of the ISHAM Working Group Dermatophytes aims to stimulate and coordinate international networking on these fungi

Toward a Novel Multilocus Phylogenetic Taxonomy for the Dermatophytes.

Type and reference strains of members of the onygenalean family Arthrodermataceae have been sequenced for rDNA ITS and partial LSU, the ribosomal 60S protein, and fragments of β-tubulin and translation elongation factor 3. The resulting phylogenetic trees showed a large degree of correspondence, and topologies matched those of earlier published phylogenies demonstrating that the phylogenetic representation of dermatophytes and dermatophyte-like fungi has reached an acceptable level of stability. All trees showed Trichophyton to be polyphyletic. In the present paper, Trichophyton is restricted to mainly the derived clade, resulting in classification of nearly all anthropophilic dermatophytes in Trichophyton and Epidermophyton, along with some zoophilic species that regularly infect humans. Microsporum is restricted to some species around M. canis, while the geophilic species and zoophilic species that are more remote from the human sphere are divided over Arthroderma, Lophophyton and Nannizzia. A new genus Guarromyces is proposed for Keratinomyces ceretanicus. Thirteen new combinations are proposed; in an overview of all described species it is noted that the largest number of novelties was introduced during the decades 1920-1940, when morphological characters were used in addition to clinical features. Species are neo- or epi-typified where necessary, which was the case in Arthroderma curreyi, Epidermophyton floccosum, Lophophyton gallinae, Trichophyton equinum, T. mentagrophytes, T. quinckeanum, T. schoenleinii, T. soudanense, and T. verrucosum. In the newly proposed taxonomy, Trichophyton contains 16 species, Epidermophyton one species, Nannizzia 9 species, Microsporum 3 species, Lophophyton 1 species, Arthroderma 21 species and Ctenomyces 1 species, but more detailed studies remain needed to establish species borderlines. Each species now has a single valid name. Two new genera are introduced: Guarromyces and Paraphyton. The number of genera has increased, but species that are relevant to routine diagnostics now belong to smaller groups, which enhances their identification

Different reactions to adverse neighborhoods in games of cooperation

In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods. Here we consider two different types of reaction to adverse neighborhoods, and all possible mixtures between these reactions. When faced with a gloomy outlook, players can either choose to cut and rewire some of their links to other individuals, or they can migrate to another location and establish new links in the new local neighborhood. We find that in general local rewiring is more favorable for the evolution of cooperation than emigration from adverse neighborhoods. Rewiring helps to maintain the diversity in the degree distribution of players and favors the spontaneous emergence of cooperative clusters. Both properties are known to favor the evolution of cooperation on networks. Interestingly, a mixture of migration and rewiring is even more favorable for the evolution of cooperation than rewiring on its own. While most models only consider a single type of reaction to adverse neighborhoods, the coexistence of several such reactions may actually be an optimal setting for the evolution of cooperation.Comment: 12 pages, 5 figures; accepted for publication in PLoS ON

Network Economics and the Environment: Insights and Perspectives

Local interactions and network structures appear to be a prominent feature of many environmental problems. This paper discusses a wide range of issues and potential areas of application, including the role of relational networks in the pattern of adoption of green technologies, common pool resource problems characterized by a multiplicity of sources, the role of social networks in multi-level environmental governance, infrastructural networks in the access to and use of natural resources such as oil and natural gas, the use of networks to describe the internal structure of inter-country relations in international agreements, and the formation of bilateral "links" in the process of building up an environmental coalition. For each of these areas, we examine why and how network economics would be an effective conceptual and analytical tool, and discuss the main insights that we can foresee