On the equivalence between radiance and retrieval assimilation

The need for consistent assimilation of satellite measurements for numerical weather prediction led operational meteorological centers to assimilate satellite radiances directly using variational data assimilation systems. More recently there has been a renewed interest in assimilating satellite retrievals (e.g., to avoid the use of relatively complicated radiative transfer models as observation operators for data assimilation). The aim of this paper is to provide a rigorous and comprehensive discussion of the conditions for the equivalence between radiance and retrieval assimilation. It is shown that two requirements need to be satisfied for the equivalence: (i) the radiance observation operator needs to be approximately linear in a region of the state space centered at the retrieval and with a radius of the order of the retrieval error; and (ii) any prior information used to constrain the retrieval should not underrepresent the variability of the state, so as to retain the information content of the measurements. Both these requirements can be tested in practice. When these requirements are met, retrievals can be transformed so as to represent only the portion of the state that is well constrained by the original radiance measurements and can be assimilated in a consistent and optimal way, by means of an appropriate observation operator and a unit matrix as error covariance. Finally, specific cases when retrieval assimilation can be more advantageous (e.g., when the estimate sought by the operational assimilation system depends on the first guess) are discussed

On the corrections to Strong-Stretching Theory for end-confined, charged polymers in a uniform electric field

We investigate the properties of a system of semi-diluted polymers in the presence of charged groups and counter-ions, by means of self-consistent field theory. We study a system of polyelectrolyte chains grafted to a similarly, as well as an oppositely charged surface, solving a set of saddle-point equations that couple the modified diffusion equation for the polymer partition function to the Poisson-Boltzmann equation describing the charge distribution in the system. A numerical study of this set of equations is presented and comparison is made with previous studies. We then consider the case of semi-diluted, grafted polymer chains in the presence of charge-end-groups. We study the problem with self-consistent field as well as strong-stretching theory. We derive the corrections to the Milner-Witten-Cates (MWC) theory for weakly charged chains and show that the monomer-density deviates from the parabolic profile expected in the uncharged case. The corresponding corrections are shown to be dictated by an Abel-Volterra integral equation of the second kind. The validity of our theoretical findings is confirmed comparing the predictions with the results obtained within numerical self-consistent field theory.Comment: 15 Pages, 12 figure

Eternal Immolation: could a Trinitarian coordinating-concept for Theistic Metaphysics solve the Problems of Theodicy?

The author contextualizes the Problem of Evil in Open Theism system, listing its main theses, primarily the logic-of- love-defense (and free-will-defense) connected to Trinitarian speculation. After evaluating the discussion in Analytic Philosophy of Religion, the focus is on the personal mystery of evil, claiming that, because of mystery and vagueness, the Problem of Evil is undecidable. Recalling other schools of thought (Pareyson: ontology of freedom; Moltmann: Dialectical theology; Kenotic theology; Original Sin hermeneutics), the author tries to grasp their common insights. One of them is the evident explanatory failure of theodicies, expressed in the antinomian statements ‘God is not innocent’. The author follows these insights, developing the concept of Eternal Immolation (Bulgakov), arguing that, without a proper understanding of its mystery (what is, and what is not), theistic theodicy could remain compromised. ‘Eternal Immolation’ is considered consequent – or already present – in recent speculations, it stands or falls when we accept that these reveal some unresolved points in Christian doctrine. Hence, ‘Eternal Immolation’ becomes a coordinating-concept, able to bring together their assumptions: several kinds of kenosis, the ontology of freedom with a logic-of-love defense, strongly linked to a libertarian human freedom, and the acknowledgement of the unresolved mystery of evil

Omniscience, Freedom, and Mystery

The text published below is the translation of a part of this published article: "Il Dio che rischia e che cambia: introduzione all’Open Theism". The issue of omniscience is one of the most debated in contemporary Analytical Philosophy of Religion. However, what is often lacking in this discussion is a deep understanding of the dilemma of omniscience and human freedom within a complete epistemological (what can we really say about the divine and the world), metaphysical and theological framework. For example, it is often forgotten to frame some issues within a clear definition of the notion of mystery

A support theorem for Hilbert schemes of planar curves

Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve encodes the cohomology of all Hilbert schemes of points on the curve. Globally, it follows that a family of such curves with smooth relative compactified Jacobian ("moduli space of D-branes") in an irreducible curve class on a Calabi-Yau threefold will contribute equally to the BPS invariants in the formulation of Pandharipande and Thomas, and in the formulation of Hosono, Saito, and Takahashi.Comment: 13 pages. (v2 updated to match published version.

Higher discriminants and the topology of algebraic maps

We show that the way in which Betti cohomology varies in a proper family of complex algebraic varieties is controlled by certain "higher discriminants" in the base. These discriminants are defined in terms of transversality conditions, which in the case of a morphism between smooth varieties can be checked by a tangent space calculation. They control the variation of cohomology in the following two senses: (1) the support of any summand of the pushforward of the IC sheaf along a projective map is a component of a higher discriminant, and (2) any component of the characteristic cycle of the proper pushforward of the constant function is a conormal variety to a component of a higher discriminant. The same would hold for the Whitney stratification of the family, but there are vastly fewer higher discriminants than Whitney strata. For example, in the case of the Hitchin fibration, the stratification by higher discriminants gives exactly the {\delta} stratification introduced by Ngo.Comment: v2: proofs rewritten in the language of microsupport, and added example of integrable system

Evaluation of sustainability: results from long term experimental arable systems in Tuscany

The research is aimed at implementing a methodology in order to estimate the sustainability of an agricultural system, through the use of Agro-ecological and Sustainability Indicators. The methodology is applied to three stockless, experimental agricultural systems, part of a long-term experiment (MOLTE) managed with diverse typologies (old organic, new organic vs conventional). The results derived from the three different management systems are estimated by considering crop rotation and efficiency in terms of energetic, macro-element (N, P, K) and organic matter flow. These are related to the landscape and biodiversity system, as well as the soil and the environmental system. The research shows that the agro-ecosystems managed with the organic agriculture method has succeeded to attain optimal levels of sustainability. Independently of time duration from conversion, the organic systems are better than the conventional system for all indicators, with the exception of the soil indicators that showed remarkable resilience

The Decomposition Theorem and the topology of algebraic maps

We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the Decomposition Theorem, indicate some important applications and examples.Comment: 117 pages. New title. Major structure changes. Final version of a survey to appear in the Bulletin of the AM