Realism and Knowledge First. Interview with Timothy Williamson

The renowned British philosopher Timothy Williamson talks about his philosophical views and main lines of research. Williamson is a metaphysical realist in a broad sense. Fir him there are true or false answers to questions about all aspects of reality. Classical logic is a universal true theory. Knowledge-first epistemology is an alternative to the traditional belief-first epistemology. The former takes the concept of knowledge as a basic concept, explaining other epistemic concepts, including belief, in its terms, whereas the latter does the opposite. Knowledge, not truth, is the fundamental epistemic good. The Gettier problem and the skeptical problem that arise within traditional epistemology are ill posed and therefore cannot be solved. Hybrid epistemological theories do not satisfy the principles of simplicity and beauty and are refuted by counter-examples. Epistemic contextualism is problematic, and relativism violates the semantics of the phenomena being explained. Knowledge does not entail knowledge about knowledge. Knowledge-how is a kind of knowledge-that. The distinction between a priori and a posteriori is superficial, and there are no analytical truths. The concept of qualia is unhelpful for solving the problems related to consciousness. The so-called “hard problem” of consciousness points to an area of conceptual confusions in which we do not know how to reason properly. Speculative metaphysics is quite a respectable enterprise. But progress in metaphysics is not automatic; it requires the right methodology.

The ill-posedness of (non-)periodic travelling wave solution for deformed continuous Heisenberg spin equation

Based on an equivalent derivative nonlinear Schr\”{o}inger equation, some periodic and non-periodic two-parameter solutions of the deformed continuous Heisenberg spin equation are obtained. These solutions are all proved to be ill-posed by the estimates of Fourier integral in ${H}^{s}_{\mathrm{S}^{2}}$ (periodic solution in ${H}^{s}_{\mathrm{S}^{2}}(\mathbb{T})$ and non-periodic solution in ${H}^{s}_{\mathrm{S}^{2}}(\mathbb{R})$ respectively). If $\alpha \neq 0$, the range of the weak ill-posedness index is $1

Industry-Oriented Method for Dynamic Force Identification in Peripheral Milling Based on FSC-LSQR Using Acceleration Signals

Online measurement of milling force play a vital role in enabling machining process monitoring and control. In practice, the milling force is difficult to be measured directly with the dynamometer. This paper develops a novel method for milling force identification called least square QR-factorization with fast stopping criterion (FSC-LSQR) method, and the queue buffer structure (QBS) is employed for the online identification of milling force using acceleration signals. The convolution integral of milling force and acceleration signals is discretized, which turns the problem of milling force identification into a linear discrete ill-posed problem. The FSC-LSQR algorithm is adopted for milling force identification because of its high efficiency and accuracy, which handles the linear discrete ill-posed problem effectively. The online identification of milling force can be realized using the acceleration signal enqueue and the milling force dequeue operations of the QBS. Finally, the effectiveness of the method is verified by experiments. The experimental results show that the FSC-LSQR algorithm running time is within \((0.05s)\) and the calculation error is less than \((10\%)\). The proposed method can make the sampling frequency of the milling force reach 10240Hz by employing QBS, which satisfy the industry requirements of milling force measurement.

Estimating adsorption isotherm parameters in chromatography via a virtual injection promoting double feed-forward neural network

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve a nonlinear inverse problem in a partial differential equation so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the uniqueness of adsorption isotherms cannot be guaranteed, and moreover, the small noise in the measured response can lead to a large fluctuation in the traditional estimation of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method – the virtual injection promoting double feed-forward neural network (VIP-DFNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model – a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-DFNN is an efficient and robust algorithm.

Dealing with artefacts In JET iterative bolometric tomography using masks

Bolometric tomography is a widely applied technique to infer important indirect quantities in magnetically confined plasmas, such as the total radiated power. However, being an inverse and ill-posed problem, the tomographic algorithms have to be carefully steered to converge on the most approriate solutions and often specialists have to balance the quality of the obtained reconstructions between the core and the edge of the plasma. Given the topology of the emission and the layout of the diagnostics in practically all devices, the tomographic inversions of bolometry are often affected by artefacts, which can influence derived quantities and specific studies based on the reproduced tomograms, such as power balance studies and benchmarching of gyrokinetic simulations. This article deals with the introduction of a simple, but very efficient methodology. It is based on constraining the solution of the tomographic inversions by using a specific estimate of the initial solution, built with the data from specific combinations of detectors (called ‘masks’). It has been tested with phantoms and with real data, using the Maximum Likelihood approach at JET. Results show how the obtained tomograms improve sensibly both in the core and at the edge of the device when compared with those obtained without the use of masks as initial guess. The correction for the main artefacts can have a significant impact on the interpretation of both the core (electron transport, alpha heating) and the edge physics (detachment , SOL). The method is completely general and can be applied by any iterative algorithm starting from an initial guess for the emission profile to be reconstructed.

Secant-type iteration for nonlinear ill-posed equations in Banach space

In this paper, we study secant-type iteration for nonlinear ill-posed equations involving 𝑚-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

Mass Transfer Characteristics of Haemofiltration Modules—Experiments and Modeling

Reliable mathematical models are important tools for design/optimization of haemo-filtration modules. For a specific module, such a model requires knowledge of fluid- mechanical and mass transfer parameters, which have to be determined through experimental data representative of the usual countercurrent operation. Attempting to determine all these parameters, through measured/external flow-rates and pressures, combined with the inherent inaccuracies of pressure measurements, creates an ill-posed problem (as recently shown). The novel systematic methodology followed herein, demonstrated for Newtonian fluids, involves specially designed experiments, allowing first the independent reliable determination of fluid-mechanical parameters. In this paper, the method is further developed, to determine the complete mass transfer module-characteristics; i.e., the mass transfer problem is modelled/solved, employing the already fully-described flow field. Furthermore, the model is validated using new/detailed experimental data on concentration profiles of a typical solute (urea) in counter-current flow. A single intrinsic-parameter value (i.e., the unknown effective solute-diffusivity in the membrane) satisfactorily fits all data. Significant insights are also obtained regarding the relative contributions of convective and diffusive mass-transfer. This study completes the method for reliable module simulation in Newtonian-liquid flow and provides the basis for extension to plasma/blood haemofiltration, where account should be also taken of oncotic-pressure and membrane-fouling effects.