The Random Feature Model for Input-Output Maps between Banach Spaces

Well known to the machine learning community, the random feature model, originally introduced by Rahimi and Recht in 2008, is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to the real line. In this paper, we instead propose a methodology for use of the random feature model as a data-driven surrogate for operators that map an input Banach space to an output Banach space. Although the methodology is quite general, we consider operators defined by partial differential equations (PDEs); here, the inputs and outputs are themselves functions, with the input parameters being functions required to specify the problem, such as initial data or coefficients, and the outputs being solutions of the problem. Upon discretization, the model inherits several desirable attributes from this infinite-dimensional, function space viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions. We view the random feature model as a non-intrusive data-driven emulator, provide a mathematical framework for its interpretation, and demonstrate its ability to efficiently and accurately approximate the nonlinear parameter-to-solution maps of two prototypical PDEs arising in physical science and engineering applications: viscous Burgers' equation and a variable coefficient elliptic equation

The Random Feature Model for Input-Output Maps between Banach Spaces

Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to the real line. In this paper, we instead propose a methodology for use of the random feature model as a data-driven surrogate for operators that map an input Banach space to an output Banach space. Although the methodology is quite general, we consider operators defined by partial differential equations (PDEs); here, the inputs and outputs are themselves functions, with the input parameters being functions required to specify the problem, such as initial data or coefficients, and the outputs being solutions of the problem. Upon discretization, the model inherits several desirable attributes from this infinite-dimensional viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions. We view the random feature model as a non-intrusive data-driven emulator, provide a mathematical framework for its interpretation, and demonstrate its ability to efficiently and accurately approximate the nonlinear parameter-to-solution maps of two prototypical PDEs arising in physical science and engineering applications: viscous Burgers' equation and a variable coefficient elliptic equation.Comment: To appear in SIAM Journal on Scientific Computing; 32 pages, 9 figure

Convergence Rates for Learning Linear Operators from Noisy Data

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known basis, this work solves the equivalent inverse problem of estimating the operator's eigenvalues given the data. Adopting a Bayesian approach, the theoretical analysis establishes posterior contraction rates in the infinite data limit with Gaussian priors that are not directly linked to the forward map of the inverse problem. The main results also include learning-theoretic generalization error guarantees for a wide range of distribution shifts. These convergence rates quantify the effects of data smoothness and true eigenvalue decay or growth, for compact or unbounded operators, respectively, on sample complexity. Numerical evidence supports the theory in diagonal and non-diagonal settings.Comment: To appear in SIAM/ASA Journal on Uncertainty Quantification (JUQ); 34 pages, 5 figures, 2 table

the impact of delayed treatment on 6 minute walk distance test in patients with pulmonary arterial hypertension a meta analysis

Abstract Background The impact of treatment delay in stable patients with pulmonary arterial hypertension (PAH) remains unaddressed. Methods This meta-analysis included six datasets of PAH therapies with randomized-controlled trials (RCT) and corresponding open-label extension (OLE) studies. We evaluated the change in 6MWD at 1year in the OLE studies by active treatment versus ex-placebo group. The ex-placebo group (i.e., the patients randomized to placebo in the RCT and ultimately treated with active therapy in the OLE) represented the "delay-in-treatment" population. Results Patients with a treatment delay of 12–16weeks in PAH targeted therapy had an improvement in 6-minute walk distance (6MWD) test at 1year, but this improvement did not amount to the same degree of improvement as their initially treated counterparts. The difference in 6MWD was 15m to 20m at 1year. Conclusion A short-term delay in PAH targeted therapy may adversely affect functional capacity in patients with PAH. This meta-analysis provides some insight as to whether earlier treatment would benefit stable patients with PAH

Interpersonal relationship and human resources management in public organization: A study of securities and exchange commission of Nigeria

In Human Resource Management, emphasis is greatly placed on the pattern of role relationship to the neglect of the interpersonal relationship among workgroups by managers. Scholars are also guilty of this as they tend to devout greatly their literary work on other workgroup relationship contexts. The study Interpersonal Relationship and Human Resource Management in Public Organisations: A Study of Securities and Exchange Commission, is a cross-sectional survey research that is aimed at determining the extent to which interpersonal relationship has effected the role relationships within workgroups in public organizations and how it can be managed toward Human Resource Management. The study utilized a structured questionnaire to obtain primary data and was analyzed using simple percentage statistical method as presented. Hypothesis was formulated and tested, using the Chi-Square Method and conclusions reached based on the findings of the study; that workgroups with good interpersonal relationship perform better as a team in public organisations in Nigeria. The study recommends that the socio psychological environment of members should be a determinant for workgroup selection, relationship management and development in public organizations in Nigeria

FungalTraits:A user-friendly traits database of fungi and fungus-like stramenopiles

The cryptic lifestyle of most fungi necessitates molecular identification of the guild in environmental studies. Over the past decades, rapid development and affordability of molecular tools have tremendously improved insights of the fungal diversity in all ecosystems and habitats. Yet, in spite of the progress of molecular methods, knowledge about functional properties of the fungal taxa is vague and interpretation of environmental studies in an ecologically meaningful manner remains challenging. In order to facilitate functional assignments and ecological interpretation of environmental studies we introduce a user friendly traits and character database FungalTraits operating at genus and species hypothesis levels. Combining the information from previous efforts such as FUNGuild and Fun(Fun) together with involvement of expert knowledge, we reannotated 10,210 and 151 fungal and Stramenopila genera, respectively. This resulted in a stand-alone spreadsheet dataset covering 17 lifestyle related traits of fungal and Stramenopila genera, designed for rapid functional assignments of environmental studies. In order to assign the trait states to fungal species hypotheses, the scientific community of experts manually categorised and assigned available trait information to 697,413 fungal ITS sequences. On the basis of those sequences we were able to summarise trait and host information into 92,623 fungal species hypotheses at 1% dissimilarity threshold

Ευρετικές προσεγγίσεις του μοναδιάστατου προβλήματος πακετοποίησης

Article 59.1, of the International Code of Nomenclature for Algae, Fungi, and Plants (ICN; Melbourne Code), which addresses the nomenclature of pleomorphic fungi, became effective from 30 July 2011. Since that date, each fungal species can have one nomenclaturally correct name in a particular classification. All other previously used names for this species will be considered as synonyms. The older generic epithet takes priority over the younger name. Any widely used younger names proposed for use, must comply with Art. 57.2 and their usage should be approved by the Nomenclature Committee for Fungi (NCF). In this paper, we list all genera currently accepted by us in Dothideomycetes (belonging to 23 orders and 110 families), including pleomorphic and non-pleomorphic genera. In the case of pleomorphic genera, we follow the rulings of the current ICN and propose single generic names for future usage. The taxonomic placements of 1261 genera are listed as an outline. Protected names and suppressed names for 34 pleomorphic genera are listed separately. Notes and justifications are provided for possible proposed names after the list of genera. Notes are also provided on recent advances in our understanding of asexual and sexual morph linkages in Dothideomycetes. A phylogenetic tree based on four gene analyses supported 23 orders and 75 families, while 35 families still lack molecular data