相关论文: The Visual Decoding of the Wheel of Duality in Con…
This is an essay in what might be called ``mathematical metaphysics.'' There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of…
Production theory, defined as the study of the economic process of transforming inputs into outputs, consists of two simultaneous economic forces: cost minimization and profit maximization. The cost minimization problem involves deriving…
The goal of this paper is to investigate the importance of providing visual "big pictures" in the teaching of economics. The plurality and variety of concepts, variables, diagrams, and models involved in economics can be a source of…
A generalized view of Duality is offered as a bridge between physical sciences and the more abstract philosophical dimensions bordering on mysticism. To that end several examples of duality are first cited from from conventional physics…
This monograph discusses dualities in physics: what dualities are, their main examples--from quantum mechanics and electrodynamics to statistical mechanics, quantum field theory and string theory--and the philosophical questions they raise.…
This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to…
Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses…
Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance in applications to high-dimensional systems, such…
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…
Economies are complex man-made systems where organisms and markets interact according to motivations and principles not entirely understood yet. The increasing dissatisfaction with the postulates of traditional economics i.e. perfectly…
The indirect transactions between sectors of an economic system has been a long-standing open problem. There have been numerous attempts to conceptually define and mathematically formulate this notion in various other scientific fields in…
By dimensional reduction of a self dual p-form theory on some compact space, we determine the duality generators of the gauge theory in 4 dimensions. In this picture duality is seen as a consequence of the geometry of the compact space. We…
Duality between estimation and control is a foundational concept in Control Theory. Most students learn about the elementary duality -- between observability and controllability -- in their first graduate course in linear systems theory.…
The primary tasks of a cognitive system is to survive and to maximize a life-long utility function, like the number of offsprings. A direct computational maximization of life-long utility is however not possible in complex environments,…
We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was…
We interpret multi-product supply chains (SCs) as coordinated markets; under this interpretation, a SC optimization problem is a market clearing problem that allocates resources and associated economic values (prices) to different…
The scientific and practical needs of the twenty-first century lead humankind to convergence of the specialized and diverse branches of science and technology. This convergence reveals the need for new mathematical theories capable of…
A literacy-targeted approach to economic instruction draws on insights from cognitive science. It highlights that students process complex economic information by constructing and modifying schemas that represent economic material.…
Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics. Systems that are mapped onto themselves by a duality transformation are called…
Duality, not monism, constitutes the hermeneutic lens that characterizes the original Copenhagen interpretation of Quantum Mechanics. Therefore, evoking the principles of correspondence and complementarity, in this work we re-assert a…