19,638 research outputs found
Statistical Entropy in General Equilibrium Theory
This essay seeks to develop an integrated account of the workings of statistical mechanics and thermodynamics as a theory of economic equilibrium. It begins with a probabilistic description of general systems (made out of numerous elements), based on the practice of statistical physics and the work of E. T. Jaynes, and a self-contained overview of the arguments that lead to the concept of statistical entropy as a measure of uncertainty or disorder and the maximum statistical entropy principle . This provides the conceptual setting for developing a statistical mechanical model of general equilibrium in pure exchange economies, inspired by the statistical theory of markets of Duncan K. Foley. Emphasis is placed in the derivation of the properties of the entropy function of an economy—the maximized statistical entropy as a function of the amounts of resources in that economy. We then show that the statistical equilibrium theory of pure exchange economies gives rise to a phenomenological or ‘macro’ theory of resource allocation in the image of classical thermodynamics (and the generalized thermodynamics of L. I. Rozonoer). We thus establish the fundamental principle of the phenomenological theory—the maximum entropy principle—and illustrate its use for the study of isolated and small open economies.statistical entropy, thermodynamics, general equilibrium, physics
Building Near-Real-Time Processing Pipelines with the Spark-MPI Platform
Advances in detectors and computational technologies provide new
opportunities for applied research and the fundamental sciences. Concurrently,
dramatic increases in the three Vs (Volume, Velocity, and Variety) of
experimental data and the scale of computational tasks produced the demand for
new real-time processing systems at experimental facilities. Recently, this
demand was addressed by the Spark-MPI approach connecting the Spark
data-intensive platform with the MPI high-performance framework. In contrast
with existing data management and analytics systems, Spark introduced a new
middleware based on resilient distributed datasets (RDDs), which decoupled
various data sources from high-level processing algorithms. The RDD middleware
significantly advanced the scope of data-intensive applications, spreading from
SQL queries to machine learning to graph processing. Spark-MPI further extended
the Spark ecosystem with the MPI applications using the Process Management
Interface. The paper explores this integrated platform within the context of
online ptychographic and tomographic reconstruction pipelines.Comment: New York Scientific Data Summit, August 6-9, 201
Agents, subsystems, and the conservation of information
Dividing the world into subsystems is an important component of the
scientific method. The choice of subsystems, however, is not defined a priori.
Typically, it is dictated by experimental capabilities, which may be different
for different agents. Here we propose a way to define subsystems in general
physical theories, including theories beyond quantum and classical mechanics.
Our construction associates every agent A with a subsystem SA, equipped with
its set of states and its set of transformations. In quantum theory, this
construction accommodates the notion of subsystems as factors of a tensor
product Hilbert space, as well as the notion of subsystems associated to a
subalgebra of operators. Classical systems can be interpreted as subsystems of
quantum systems in different ways, by applying our construction to agents who
have access to different sets of operations, including multiphase covariant
channels and certain sets of free operations arising in the resource theory of
quantum coherence. After illustrating the basic definitions, we restrict our
attention to closed systems, that is, systems where all physical
transformations act invertibly and where all states can be generated from a
fixed initial state. For closed systems, we propose a dynamical definition of
pure states, and show that all the states of all subsystems admit a canonical
purification. This result extends the purification principle to a broader
setting, in which coherent superpositions can be interpreted as purifications
of incoherent mixtures.Comment: 31+26 pages, updated version with new results, contribution to
Special Issue on Quantum Information and Foundations, Entropy, GM D'Ariano
and P Perinotti, ed
A Survey on Array Storage, Query Languages, and Systems
Since scientific investigation is one of the most important providers of
massive amounts of ordered data, there is a renewed interest in array data
processing in the context of Big Data. To the best of our knowledge, a unified
resource that summarizes and analyzes array processing research over its long
existence is currently missing. In this survey, we provide a guide for past,
present, and future research in array processing. The survey is organized along
three main topics. Array storage discusses all the aspects related to array
partitioning into chunks. The identification of a reduced set of array
operators to form the foundation for an array query language is analyzed across
multiple such proposals. Lastly, we survey real systems for array processing.
The result is a thorough survey on array data storage and processing that
should be consulted by anyone interested in this research topic, independent of
experience level. The survey is not complete though. We greatly appreciate
pointers towards any work we might have forgotten to mention.Comment: 44 page
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