Statistical explanation of spontaneous freezing of water droplets
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WATER - DROPS↗
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Homodyning and heterodyning the quantum phase
The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.
Dariano, Giacomo M.↗
Architecture for Integrated Medical Model Dynamic Probabilistic Risk Assessment
Probabilistic Risk Assessment (PRA) is a modeling tool used to predict potential outcomes of a complex system based on a statistical understanding of many initiating events. Utilizing a Monte Carlo method, thousands of instances of the model are considered and outcomes are collected. PRA is considered static, utilizing probabilities alone to calculate outcomes. Dynamic Probabilistic Risk Assessment (dPRA) is an advanced concept where modeling predicts the outcomes of a complex system based not only on the probabilities of many initiating events, but also on a progression of dependencies brought about by progressing down a time line. Events are placed in a single time line, adding each event to a queue, as managed by a planner. Progression down the time line is guided by rules, as managed by a scheduler. The recently developed Integrated Medical Model (IMM) summarizes astronaut health as governed by the probabilities of medical events and mitigation strategies. Managing the software architecture process provides a systematic means of creating, documenting, and communicating a software design early in the development process. The software architecture process begins with establishing requirements and the design is then derived from the requirements.
Probability Theory↗
Design and Modeling of a Coded-Interleaving System in the Presence of Fading
Future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non linear effects (e.g. cloud coverage, atmospheric turbulence, scintillation, antenna mis-pointing, jitter, relative motion, etc.) that cause various degrees of fading loss over various time scales. We consider a channel experiencing block fading where the channel coherence time is a lot longer than the length of a codeword. As long as the fading duration is not excessive, an interleaver can be used in a coded-communication system that randomizes the fades among symbols of multiple codewords. This achieves an “averaging” effect that spreads the signal energy more evenly among the codewords, and improves the likelihood that each of them can be decoded correctly. For simplicity, we consider a block interleaver where adjacent symbols of a codeword have a fixed delay (or separation) with each other, and investigate the error-rate performance of a coded-interleaving system (with fixed and finite interleaving depth) in the presence of block fading. Unlike prior research which assumes theoretical channel coherence models, we aim to build upon our analysis using empirical spacecraft signal measurements obtained with the Deep Space Network, and to use the fundamental theories of probability and statistics (e.g. variations of Law of Large Numbers) to quantify the error-rate performance of the coded-interleaving system. We propose to utilize these results in the design of a two-dimensional coded-interleaving system for fading channels.
Sanchez-Net, Marc↗
Photon scattering cross sections of H2 and He measured with synchrotron radiation
Total (elastic + inelastic) differential photon scattering cross sections have been measured for H2 gas and He, using an X-ray beam. Absolute measured cross sections agree with theory within the probable errors. Relative cross sections (normalized to theory at large S) agree to better than one percent with theoretical values calculated from wave functions that include the effect of electron-electron Coulomb correlation, but the data deviate significantly from theoretical independent-particle (e.g., Hartree-Fock) results. The ratios of measured absolute He cross sections to those of H2, at any given S, also agree to better than one percent with theoretical He-to-H2 cross-section ratios computed from correlated wave functions. It appears that photon scattering constitutes a very promising tool for probing electron correlation in light atoms and molecules.
Ice, G. E.↗
Photon-scattering cross sections of H2 and He measured with synchrotron radiation
Total (elastic + inelastic) differential photon-scattering cross sections have been measured for H2 gas and for He, using an X-ray beam. Absolute measured cross sections agree with theory within the probable errors. Relative cross sections (normalized to theory at large S) agree to better than 1% with theoretical values calculated from wave functions that include the effect of electron-electron Coulomb correlation, but the data deviate significantly from theoretical independent-particle (e.g., Hartree-Fock) results. The ratios of measured absolute He cross sections to those of H2, at any given S, also agree to better than 1% with theoretical He-to-H2 cross-section ratios computed from correlated wave functions. It appears that photon scattering constitutes a very promising tool for probing electron correlation in light atoms and molecules. The degree of polarization of the synchrotron radiation beam has been measured by rotating the scattering plane about the beam axis; results are compared with theory.
Ice, G. E.↗
A model of human decisionmaking in multiple process monitoring situations
It is proposed that human decisionmaking performance in multiple process monitoring situations can be modeled in terms of the detection of process related events and the allocation of attention among processes once events are felt to have occurred. An elementary pattern recognition technique, discriminant analysis, is used to generate estimates of event occurrence probability. A queueing theory framework is then utilized to incorporate these probabilities as well as other task characteristics into the solution of the attention allocation problem. The performance of the model is compared with that of subjects in two experiments.
Greenstein, J. S.↗
A probability of encounter with interstellar comets and the likelihood of their existence
A theory of the probability of encounter of the sun with an interstellar comet at a distance comparable to the earth-sun distance is formulated, and a general expression is derived establishing the relationship among the influx rate of interstellar comets, the perihelion distance, the space density of the comets, the Maxwellian distribution of comet velocities in the interstellar cloud, and the cloud's systematic velocity relative to the sun. An upper limit of .0006 solar mass per cubic parsec is established for the space density of interstellar comets. The theoretical distribution of semimajor axes of interstellar comets shows that a strong hyperbolic excess must be present in the orbits of a majority of interstellar comets regardless of the dynamical characteristics of the comet cloud, except when the cloud is moving along with the sun and the distribution of individual velocities has a very low dispersion. This case, however, implies a possibility of capture by the sun and thus becomes a problem of an Oort-type cloud.
Sekanina, Z.↗
More On The Decoder-Error Probability Of Reed-Solomon Codes
Paper extends theory of decoder-error probability for linear maximum-distance separable (MDS) codes. General class of error-correcting codes includes Reed-Solomon codes, important in communications with distant spacecraft, military communications, and compact-disk recording industry. Advancing beyond previous theoretical developments that placed upper bounds on decoder-error probabilities, author derives an exact formula for probability PE(u) that decoder will make error when u code symbols in error.
Cheung, Kar-Ming↗
An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes
Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.
vegetation remote sensing; stochastic radiative tr↗
Median two person game theory and examples of its flexibility in applications
Probability distribution in two person game theory
Kelleher, G. J.↗
Applications of presently planned interplanetary missions to testing gravitational theories
A summary of the probable interplanetary missions for the 1970's is presented, which may prove useful in testing the general theory of relativity. Mission characteristics are discussed, as well as instrumentation. This last includes a low-level accelerometer and S-/X-band transponders and antennas.
Friedman, L. D.↗
Quantum Probability Cancellation Due to a Single-Photon State
When an N-photon state enters a lossless symmetric beamsplitter from one input port, the photon distribution for the two output ports has the form of Bernouli Binormial, with highest probability at equal partition (N/2 at one outport and N/2 at the other). However, injection of a single photon state at the other input port can dramatically change the photon distribution at the outputs, resulting in zero probability at equal partition. Such a strong deviation from classical particle theory stems from quantum probability amplitude cancellation. The effect persists even if the N-photon state is replaced by an arbitrary state of light. A special case is the coherent state which corresponds to homodyne detection of a single photon state and can lead to the measurement of the wave function of a single photon state.
Ou, Z. Y.↗
Random Tensor Networks with Non-trivial Links
Abstract Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have non-trivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko–Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity.
Physics↗
Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses
Here, this work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.
97 MATHEMATICS AND COMPUTING↗
Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments
There is an increasing aspiration to utilize machine learning (ML) for various tasks of relevance to national security. ML models have thus far been mostly applied to tasks and domains that, while impactful, have sufficient volume of data. For predictive tasks of national security relevance, ML models of great capacity (ability to approximate nonlinear trends in input-output maps) are often needed to capture the complex underlying physics. However, scientific problems of relevance to national security are often accompanied by various sources of sparse and/or incomplete data, including experiments and simulations, across different regimes of operation, of varying degrees of fidelity, and include noise with different characteristics and/or intensity. State-of-the-art ML models, despite exhibiting superior performance on the task and domain they were trained on, may suffer detrimental loss in performance in such sparse data environments. This report summarizes the results of the Laboratory Directed Research and Development project entitled Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments. The objective of the project was to develop a new transfer learning (TL) framework that aims to adaptively blend the data across different sources in tackling one task of interest, resulting in enhanced trustworthiness of ML models for mission- and safety-critical systems. The proposed framework determines when it is worth applying TL and how much knowledge is to be transferred, despite uncontrollable uncertainties. The framework accomplishes this by leveraging concepts and techniques from the fields of Bayesian inverse modeling and uncertainty quantification, relying on strong mathematical foundations of probability and measure theories to devise new uncertainty-aware TL workflows.
97 MATHEMATICS AND COMPUTING↗
Analysis of decoders for convolutional codes by stochastic sequential machine methods
Convolutional code decoder modeled as autonomous stochastic sequential machine, considering finite Markov chain theory for error probability
Morrissey, T. N., Jr.↗
The optical scatter channel
Optical scatter channel transmission characteristics, using mathematical model consistent with radiative transfer theory and probability-computing receiver
Holland, A. E.↗