Contextuality: A Philosophical Paradigm, with Applications to Philosophy of Cognitive Science

We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem obvious, has several important consequences. This paper first presents ideas on Contextuality, for then applying them to problems in philosophy of cognitive science. Because of space limitations, for the second part we will assume that the reader is familiar with the literature of philosophy of cognitive science, but if this is not the case, it would not be a limitation for understanding the main ideas of this paper. We do not argue that Contextuality is a panaceic answer for explaining everything, but we do argue that everything is inside a context. And because this is always, we sometimes ignore it, but we believe that many problems are dissolved with a contextual approach, noticing things we ignore because of their obviousity. We first give a notion of context. We present the idea that errors are just incongruencies inside a context. We also present previous ideas of absolute being, relative being, and lessincompleteness. We state that all logics, and also truth judgements, are contextdependent, and we develop a “Context-dependant Logic”. We apply ideas of Contextuality to problems in semantics, the problem of “where is the mind”, and the study of consciousness

Calibration by correlation using metric embedding from non-metric similarities

This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?) and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature) as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case, on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional), and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm performs as theoretically predicted for all corner cases of the observability analysis

A machine learning route between band mapping and band structure

The electronic band structure (BS) of solid state materials imprints the multidimensional and multi-valued functional relations between energy and momenta of periodically confined electrons. Photoemission spectroscopy is a powerful tool for its comprehensive characterization. A common task in photoemission band mapping is to recover the underlying quasiparticle dispersion, which we call band structure reconstruction. Traditional methods often focus on specific regions of interests yet require extensive human oversight. To cope with the growing size and scale of photoemission data, we develop a generic machine-learning approach leveraging the information within electronic structure calculations for this task. We demonstrate its capability by reconstructing all fourteen valence bands of tungsten diselenide and validate the accuracy on various synthetic data. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales in conjunction with theory, while realizing a path towards integrating band mapping data into materials science databases

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study