Weighted integral formulas on manifolds

We present a method of finding weighted Koppelman formulas for $(p,q)$-forms on $n$-dimensional complex manifolds $X$ which admit a vector bundle of rank $n$ over $X \times X$, such that the diagonal of $X \times X$ has a defining section. We apply the method to \Pn and find weighted Koppelman formulas for $(p,q)$-forms with values in a line bundle over \Pn. As an application, we look at the cohomology groups of $(p,q)$-forms over \Pn with values in various line bundles, and find explicit solutions to the \dbar-equation in some of the trivial groups. We also look at cohomology groups of $(0,q)$-forms over \Pn \times \Pm with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds.Comment: 25 page

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems

We give here some negative results in Sturm-Liouville inverse theory, meaning that we cannot approach any of the potentials with $m+1$ integrable derivatives on $\mathbb{R}^+$ by an $\omega$-parametric analytic family better than order of $(\omega\ln\omega)^{-(m+1)}$. Next, we prove an estimation of the eigenvalues and characteristic values of a Sturm-Liouville operator and some properties of the solution of a certain integral equation. This allows us to deduce from [Henkin-Novikova] some positive results about the best reconstruction formula by giving an almost optimal formula of order of $\omega^{-m}$.Comment: 40 page

On an inverse problem for anisotropic conductivity in the plane

Let $\hat \Omega \subset \mathbb R^2$ be a bounded domain with smooth boundary and $\hat \sigma$ a smooth anisotropic conductivity on $\hat \Omega$. Starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on $\partial \hat \Omega$, we give an explicit procedure to find a unique domain $\Omega$, an isotropic conductivity $\sigma$ on $\Omega$ and the boundary values of a quasiconformal diffeomorphism $F:\hat \Omega \to \Omega$ which transforms $\hat \sigma$ into $\sigma$.Comment: 9 pages, no figur

Going beyond Visualization. Verbalization as Complementary Medium to Explain Machine Learning Models

In this position paper, we argue that a combination of visualization and verbalization techniques is beneficial for creating broad and versatile insights into the structure and decision-making processes of machine learning models. Explainability of machine learning models is emerging as an important area of research. Hence, insights into the inner workings of a trained model allow users and analysts, alike, to understand the models, develop justifications, and gain trust in the systems they inform. Explanations can be generated through different types of media, such as visualization and verbalization. Both are powerful tools that enable model interpretability. However, while their combination is arguably more powerful than each medium separately, they are currently applied and researched independently. To support our position that the combination of the two techniques is beneficial to explain machine learning models, we describe the design space of such a combination and discuss arising research questions, gaps, and opportunities

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

A logic road from special relativity to general relativity

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist

Ronald V. Dellums v. George Bush (D.D.C. 1990): Memorandum Amicus Curiae of Law Professors

This joint memorandum is submitted to the court hearing Dellums v. Bush. This amicus brief advocates that the President may not order American armed forces to make war without consultation with and approval by Congress. The brief also argues that the case is justiciable

Evidence for protein-mediated fatty acid efflux by adipocytes

Abstract Aim: The hormonally controlled mobilization and release of fatty acids from adipocytes into the circulation is an important physiological process required for energy homeostasis. While uptake of fatty acids by adipocytes has been suggested to be predominantly protein-mediated, it is unclear whether the efflux of fatty acids also requires membrane proteins. Methods: We used fluorescent fatty acid efflux assays and colorimetric assays for free fatty acids and glycerol to identify inhibitors with effects on fatty acid efflux, but not lipolysis, in 3T3-L1 adipocytes. We assessed the effect of these inhibitors on a fibroblast-based cell line expressing fatty acid transport protein 1, hormone-sensitive lipase and perilipin, which presumably lacks adipocyte-specific proteins for fatty acid efflux. Results: We identified 4,4¢-diisothiocyanatostilbene-2,2¢-disulfonic acid (DIDS) as an inhibitor of fatty acid efflux that did not impair lipolysis or the cellular exit of glycerol but lead to an accumulation of intracellular fatty acids. In contrast, fatty acid efflux by the reconstituted cellular model for fatty acid efflux was responsive to lipolytic stimuli, but insensitive to DIDS inhibition. Conclusion: We propose that adipocytes specifically express an as yet unidentified DIDS-sensitive protein that enhances the efflux of fatty acids and therefore may lead to novel treatment approaches for obesity-related disorders characterized by abnormal lipid fluxes and ectopic triglyceride accumulation

\u3cem\u3eRonald V. Dellums v. George Bush\u3c/em\u3e (D.D.C. 1990): Memorandum \u3cem\u3eAmicus Curiae\u3c/em\u3e of Law Professors

This joint memorandum is submitted to the court hearing Dellums v. Bush. This amicus brief advocates that the President may not order American armed forces to make war without consultation with and approval by Congress. The brief also argues that the case is justiciable