scholarly journals Joint Fluctuation Theorems for Sequential Heat Exchange

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 763 ◽  
Author(s):  
Jader Santos ◽  
André Timpanaro ◽  
Gabriel Landi
Keyword(s):  
Heat Exchange ◽  
Joint Distribution ◽  
Bubble Chamber ◽  
Joint Probability ◽  
Fluctuation Theorem ◽  
Joint Probability Distribution ◽  
Fluctuation Theorems ◽  
Natural Tendency ◽  
Multiple Collisions ◽  
Heat Exchanges

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the joint probability distribution that heat Q 1 is exchanged with ancilla 1, heat Q 2 is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski–Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.

scholarly journals Surface Temperature Gradients as Diagnostic Indicators of Midlatitude Circulation Dynamics

2012 ◽  
Vol 25 (12) ◽  
pp. 4154-4171 ◽  
Author(s):  
Christina Karamperidou ◽  
Francesco Cioffi ◽  
Upmanu Lall
Keyword(s):  
Surface Temperature ◽  
Joint Distribution ◽  
Large Scale ◽  
Joint Probability ◽  
Temperature Gradients ◽  
Joint Probability Distribution ◽  
Jet Stream ◽  
Climate Conditions ◽  
Atmospheric Circulation Patterns ◽  
Circulation Patterns

Abstract Zonal and meridional surface temperature gradients are considered to be determinants of large-scale atmospheric circulation patterns. However, there has been limited investigation of these gradients as diagnostic aids. Here, the twentieth-century variability in the Northern Hemisphere equator-to-pole temperature gradient (EPG) and the ocean–land temperature contrast (OLC) is explored. A secular trend in decreasing EPG and OLC is noted. Decadal and interannual (ENSO-related) variations in the joint distribution of EPG and OLC are identified, hinting at multistable climate states that may be indigenous to the climate or due to changing boundary forcings. The NH circulation patterns for cases in the tails of the joint distribution of EPG and OLC are also seen to be different. Given this context, this paper extends past efforts to develop insights into jet stream dynamics using the Lorenz-1984 model, which is forced directly and only by EPG and OLC. The joint probability distribution of jet stream and eddy energy, conditional on EPG and OLC scenarios, is investigated. The scenarios correspond to (i) warmer versus colder climate conditions and (ii) polarized ENSO phases. The latter scenario involves the use of a heuristic ENSO model to drive the Lorenz-1984 model via a modulation of the EPG or the OLC. As with GCMs, the low-order model reveals that the response to El Niño forcing is not similar to an anthropogenic warming signature. The potential uses of EPG and OLC as macro-level indicators of climate change and variability and for comparing results across GCMs and observations are indicated.

scholarly journals On the distribution of an arbitrary subset of the eigenvalues for some finite dimensional random matrices

2019 ◽  
Vol 09 (01) ◽  
pp. 2040004
Author(s):  
Marco Chiani ◽  
Alberto Zanella
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Random Matrices ◽  
Probability Distribution Function ◽  
Joint Distribution ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Arbitrary Subset ◽  
Finite Dimensional ◽  
Joint Probability Distribution Function

We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues.

JOINT DISTRIBUTIONS OF PORTFOLIO LOSSES AND EXOTIC PORTFOLIO PRODUCTS

2007 ◽  
Vol 10 (04) ◽  
pp. 733-748 ◽  
Author(s):  
FRIEDEL EPPLE ◽  
SAM MORGAN ◽  
LUTZ SCHLOEGL
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Market Prices ◽  
Joint Distributions ◽  
Time Horizons ◽  
Path Dependent

The pricing of exotic portfolio products, e.g. path-dependent CDO tranches, relies on the joint probability distribution of portfolio losses at different time horizons. We discuss a range of methods to construct the joint distribution in a way that is consistent with market prices of vanilla CDO tranches. As an example, we show how our loss-linking methods provide estimates for the breakeven spreads of forward-starting tranches. .

scholarly journals Graphical Model Market Maker for Combinatorial Prediction Markets

2018 ◽  
Vol 63 ◽  
pp. 421-460
Author(s):  
Kathryn Blackmond Laskey ◽  
Wei Sun ◽  
Robin Hanson ◽  
Charles Twardy ◽  
Shou Matsumoto ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Prediction Markets ◽  
Probability Models ◽  
Prediction Market ◽  
Market Mechanisms ◽  
Inference Algorithms

We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

On the Maximization of Information Flow Between Spiking Neurons

2009 ◽  
Vol 21 (11) ◽  
pp. 2991-3009 ◽  
Author(s):  
Lucas C. Parra ◽  
Jeffrey M. Beck ◽  
Anthony J. Bell
Keyword(s):  
Joint Distribution ◽  
Point Processes ◽  
Joint Probability ◽  
Learning Rule ◽  
Spike Trains ◽  
Spiking Neurons ◽  
Joint Probability Distribution ◽  
Statistical Structure ◽  
Spiking Network ◽  
Efficient Representation

A feedforward spiking network represents a nonlinear transformation that maps a set of input spikes to a set of output spikes. This mapping transforms the joint probability distribution of incoming spikes into a joint distribution of output spikes. We present an algorithm for synaptic adaptation that aims to maximize the entropy of this output distribution, thereby creating a model for the joint distribution of the incoming point processes. The learning rule that is derived depends on the precise pre- and postsynaptic spike timings. When trained on correlated spike trains, the network learns to extract independent spike trains, thereby uncovering the underlying statistical structure and creating a more efficient representation of the incoming spike trains.

scholarly journals Age-dependence and aging-dependence: The case of neuronal loss and lifespan in a C. elegans model of Parkinson’s disease

2017 ◽  
Author(s):  
Javier Apfeld ◽  
Walter Fontana
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Joint Distribution ◽  
Disease Onset ◽  
Joint Probability ◽  
Neuronal Loss ◽  
Joint Probability Distribution ◽  
Age Dependence ◽  
C Elegans ◽  
Age Dependent

It is often assumed, but not established, that the major neurodegenerative diseases, such as Parkinson’s disease, are not just age-dependent (their incidence changes with time) but actually aging-dependent (their incidence is coupled to the process that determines lifespan). To determine a dependence on the aging process requires the joint probability distribution of disease onset and lifespan. For human Parkinson’s disease, such a joint distribution is not available because the disease cuts lifespan short. To acquire a joint distribution, we resorted to an established C. elegans model of Parkinson’s disease in which the loss of dopaminergic neurons is not fatal. We find that lifespan is not correlated with the loss of neurons and that a lifespan-extending intervention into insulin/IGF1 signaling accelerates neuronal loss, while leaving death and neuronal loss times uncorrelated. This suggests that distinct and compartmentalized instances of the same genetically encoded insulin/IGF1 signaling machinery act independently to control neurodegeneration and lifespan in C. elegans. Although the human context might well be different, our study calls attention to maintaining a rigorous distinction between age-dependence and aging-dependence.

scholarly journals Probability elicitation using geostatistics in hydrocarbon exploration

2021 ◽  
Author(s):  
André Luís Morosov ◽  
Reidar Brumer Bratvold
Keyword(s):  
Value Creation ◽  
Decision Process ◽  
Conceptual Models ◽  
Joint Probability ◽  
Decision Makers ◽  
Hydrocarbon Exploration ◽  
Joint Probability Distribution ◽  
Proof Of Concept ◽  
Geological Information ◽  
Decision Supporting

AbstractThe exploratory phase of a hydrocarbon field is a period when decision-supporting information is scarce while the drilling stakes are high. Each new prospect drilled brings more knowledge about the area and might reveal reserves, hence choosing such prospect is essential for value creation. Drilling decisions must be made under uncertainty as the available geological information is limited and probability elicitation from geoscience experts is key in this process. This work proposes a novel use of geostatistics to help experts elicit geological probabilities more objectively, especially useful during the exploratory phase. The approach is simpler, more consistent with geologic knowledge, more comfortable for geoscientists to use and, more comprehensive for decision-makers to follow when compared to traditional methods. It is also flexible by working with any amount and type of information available. The workflow takes as input conceptual models describing the geology and uses geostatistics to generate spatial variability of geological properties in the vicinity of potential drilling prospects. The output is stochastic realizations which are processed into a joint probability distribution (JPD) containing all conditional probabilities of the process. Input models are interactively changed until the JPD satisfactory represents the expert’s beliefs. A 2D, yet realistic, implementation of the workflow is used as a proof of concept, demonstrating that even simple modeling might suffice for decision-making support. Derivative versions of the JPD are created and their effect on the decision process of selecting the drilling sequence is assessed. The findings from the method application suggest ways to define the input parameters by observing how they affect the JPD and the decision process.

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