Marrying the Merits of Nagelian Reduction and Functional Reduction

This paper points out the merit of Nagelian reduction, namely to propose a model of inter-theoretic reduction that retains the scientific quality of the reduced theory and the merit of functional reduction, namely to take multiple realization into account and to offer reductive explanations. By considering Lewis and Kim??s proposal for local reductions, we establish that functional reduction fails to achieve a theory reduction and cannot retain the scientific quality of the reduced theory. We improve on that proposal by showing how one can build functional sub-types that are coextensive with physical realizer types and thereby obtain a theory reduction that is explanatory and that vindicates the scientific quality of the special sciences.     

Constitution and Causation

I argue that the constitution relation transmits causal efficacy and thus is a suitable relation to deploy in many troubled areas of philosophy, such as the mind?Cbody problem. We need not demand identity.     

Tropes for Causation

Tropes, as distinguished from other possible kinds of entities such as universals, states of affairs, events and bare particulars, are best-suited to play the role of causal relata.     

On Anti Humeanism and Medical Singular Causation

In this paper I offer an anti-Humean interpretation of the causal interactions in somatic medicine. I focus on life-threatening pathological states and show how Nancy Cartwright??s capacities can offer a plausible epistemology for medical processes and the singular causal claims advanced in medical diagnoses. I argue that the capacities manifested in the emergence of symptoms and signs could be tracked down if healthy organisms are construed as nomological machines and suggest that the causal reasoning from current medical practice bears a tacit adherence to anti-Humean assumptions.     

Can Indirect Causation be Real?

Causal realists maintain that the causal relation consists in “something more” than its relata. Specifying this relation in nonreductive terms is however notoriously difficult. Michael Tooley has advanced a plausible account avoiding some of the relation’s most obvious difficulties, particularly where these concern the notion of a cross-temporal “connection.” His account distinguishes discrete from nondiscrete causation, where the latter is suitable to the continuity of cross-temporal causation. I argue, however, that such accounts face conceptual difficulties dating from Zeno’s time. A Bergsonian resolution of these difficulties appears to entail that, for the causal realist, there can be no indirect causal relations of the sort envisioned by Tooley. A consequence of this discussion is that the causal realist must conceive all causal relations as ultimately direct.     

Dimension Reduction and Optimality of the Uniform State in a Phase-Field-Crystal Model Involving a Higher-Order Functional

We study a phase-field-crystal model described by a free energy functional involving second-order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $$\Gamma $$-convergence result in an asymptotic thin-film regime leading to a reduced two-dimensional model. For the reduced model, we prove necessary and sufficient conditions for the global minimality of the uniform state. We also prove similar results for the Ohta–Kawasaki model.     

Optimal Control Problems with Integral Functional and Phase Constraints: Reduction to Optimal Consistency Parameter Problems

An iteration method to solve a class of optimal control problems with integral functional and phase constraints is developed in the paper.     

Backwards Causation, Time, and the Open Future

Here are some intuitions we have about the nature of space and time. There is something fundamentally different about the past, present, and future. What is definitive of the past is that the past events are fixed. What is definitive of the future is that future events are not fixed. What is definitive of the present is that it marks the objective ontological border between the past and the future and, by doing so, instantiates a particularly salient phenomenological property of “nowness.” Call the combination of these intuitions according to which there exists an objective present, a fixed past, and an open future, the intuitive view. I argue that, given the intuitive view, the possibility of backwards causation—and hence, for instance, backwards time travel—is problematic.     

Physical Intentionality,Extrinsicness, and the Direction of Causation

The Physical Intentionality Thesis claims that dispositions share the marks of psychological intentionality; therefore, intentionality is not exclusively a mental phenomenon. Beyond the standard five marks, Alexander Bird introduces two additional marks of intentionality that he argues dispositions do not satisfy: first, thoughts are extrinsic; second, the direction of causation is that objects cause thoughts, not vice versa. In response, this paper identifies two relevant conceptions of extrinsicness, arguing that dispositions show deep parallels to thoughts on both conceptions. Then, it shows that Bird’s discussion of direction of causation overlooks complexities of dispositionality and intentionality that problematize apparent differences between thoughts and dispositions. The paper ends with a discussion of why we find these parallels between thoughts and dispositions.     

Reduction and geometric quantization

A construction is created that makes it possible to geometrically quantize a reduced Hamiltonian system using the procedure of geometric quantization realized for a Hamiltonian system with symmetries (i.e., to find the discrete spectrum and the corresponding eigenfunctions, if these have been found for the initial system). The construction is used to geometrically quantize a system obtained by reduction of a Hamiltonian system that determines the geodesic flow on an n-dimensional sphere.Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1220–1228, September, 1992.     

Multiplicities and Reduction Numbers

Let (Rmbe a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.     

碳减排补贴与碳税下的供应链碳减排决策优化与协调

针考虑碳税政策和政府对制造商的碳减排技术创新投入补贴,构建了供应链博弈模型,根据协调条件给出了相应的契约形式及参数。通过对供应链模型的求解,得到了碳税和碳减排技术创新投入补贴下的最优碳减排量和最优订货量。数值分析结果表明:碳减排技术创新投入的补贴比例变化对供应链的最优碳减排量、订货量及期望利润的影响有较大影响,而且是成正向变化关系,而且在其他参数不变及供应链碳减排量一定的情况下,碳税与碳减排补贴比例呈反向变化关系,进而可为政府碳减排补贴政策制定及供应链碳减排优化提供科学的决策依据。     

Discovery of Functional and Approximate Functional Dependencies in Relational Databases

This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.     

Reduction numbers and initial ideals

The reduction number of a standard graded algebra is the least integer such that there exists a minimal reduction of the homogeneous maximal ideal of such that . Vasconcelos conjectured that where is the initial ideal of an ideal in a polynomial ring with respect to a term order. The goal of this note is to prove the conjecture.

     

Combined State and Parameter Reduction

This work demonstrates combined state and parameter space reduction for large-scale control systems. Two methods for combined reduction are briefly introduced and tested on two different models for brain connectivity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reduction and Minimality of Coexhausters

V.F. Demyanov introduced exhausters for the study of nonsmooth functions. These are families of convex compact sets that enable one to represent the main part of the increment of a considered function in a neighborhood of the studied point as MaxMin or MinMax of linear functions. Optimality conditions were described in terms of these objects. This provided a way for constructing new algorithms for solving nondifferentiable optimization problems. Exhausters are defined not uniquely. It is obvious that the smaller an exhauster, the less are the computational expenses when working with it. Thus, the problem of reduction of an available family arises. For the first time, this problem was considered by V.A. Roshchina. She proposed conditions for minimality and described some methods of reduction in the case when these conditions are not satisfied. However, it turned out that the exhauster mapping is not continuous in the Hausdorff metrics, which leads to the problems with convergence of numerical methods. To overcome this difficulty, Demyanov proposed the notion of coexhausters. These objects enable one to represent the main part of the increment of the considered function in a neighborhood of the studied point in the form of MaxMin or MinMax of affine functions. One can define a class of functions with the continuous coexhauster mapping. Optimality conditions can be stated in terms of these objects too. But coexhausters are also defined not uniquely. The problem of reduction of coexhausters is considered in this paper for the first time. Definitions of minimality proposed by Roshchina are used. In contrast to ideas proposed in the works of Roshchina, the minimality conditions and the technique of reduction developed in this paper have a clear and transparent geometric interpretation.     

Functional equations and martingales

Aequationes mathematicae - We consider functional equations (Cauchy’s, Abel’s and some other functional equations) and show that finding the general solution of these equations...