arXiv subjects

Kevin H. Knuth

Publications and source records attributed to Kevin H. Knuth.

At least 37 records · Page 2Linked to original sources

arXiv2015

Characterization of Kepler-91b and the Investigation of a Potential Trojan Companion Using EXONEST

Presented here is an independent re-analysis of the Kepler light curve of Kepler-91 (KIC 8219268). Using the EXONEST software package, which provides both Bayesian parameter estimation and Bayesian model testing, we were able to re-confirm the planetary nature of Kepler-91b. In addition to the primary and secondary eclipses of Kepler-91b, a third dimming event appears to occur approximately $60^o$ away (in phase) from the secondary eclipse, leading to the hypothesis that a Trojan planet may be located at the L4 or L5 Lagrange points. Here, we present a comprehensive investigation of four possibilities to explain the observed dimming event using all available photometric data from the Kepler Space Telescope, recently obtained radial velocity measurements, and N-body simulations. We find that the photometric model describing Kepler-91b and a Trojan planet is highly favored over the model involving Kepler-91b alone. However, it predicts an unphysically high temperature for the Trojan companion, leading to the conclusion that the extra dimming event is likely a false-postive.

astro-ph.EP↗

arXiv2015

Combining Photometry From Kepler and TESS to Improve Short-Period Exoplanet Characterization

Planets emit thermal radiation and reflect incident light that they recieve from their host stars. As a planet orbits it's host star the photometric variations associated with these two effects produce very similar phase curves. If observed through only a single bandpass this leads to a degeneracy between certain planetary parameters that hinder the precise characterization of such planets. However, observing the same planet through two different bandpasses gives one much more information about the planet. Here, we develop a Bayesian methodology for combining photometry from both \emph{Kepler} and the Transiting Exoplanet Survey Satellite (TESS). In addition, we demonstrate via simulations that one can disentangle the reflected and thermally emitted light from the atmosphere of a hot-Jupiter as well as more precisely constrain both the geometric albedo and dayside temperature of the planet. This methodology can further be employed using various combinations of photometry from the James Webb Space Telescope (JWST), the Characterizing ExOplanet Satellite (CHEOPS), or the PLATO mission.

astro-ph.IM↗

arXiv2015

The Deeper Roles of Mathematics in Physical Laws

Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as exemplified by the laws of physics. In this essay, I claim that much of the utility of mathematics arises from our choice of description of the physical world coupled with our desire to quantify it. This will be demonstrated in a practical sense by considering one of the most fundamental concepts of mathematics: additivity. This example will be used to show how many physical laws can be derived as constraint equations enforcing relevant symmetries in a sense that is far more fundamental than commonly appreciated.

math.HO↗

arXiv2015

Difficulties applying recent blind source separation techniques to EEG and MEG

High temporal resolution measurements of human brain activity can be performed by recording the electric potentials on the scalp surface (electroencephalography, EEG), or by recording the magnetic fields near the surface of the head (magnetoencephalography, MEG). The analysis of the data is problematic due to the fact that multiple neural generators may be simultaneously active and the potentials and magnetic fields from these sources are superimposed on the detectors. It is highly desirable to un-mix the data into signals representing the behaviors of the original individual generators. This general problem is called blind source separation and several recent techniques utilizing maximum entropy, minimum mutual information, and maximum likelihood estimation have been applied. These techniques have had much success in separating signals such as natural sounds or speech, but appear to be ineffective when applied to EEG or MEG signals. Many of these techniques implicitly assume that the source distributions have a large kurtosis, whereas an analysis of EEG/MEG signals reveals that the distributions are multimodal. This suggests that more effective separation techniques could be designed for EEG and MEG signals.

physics.data-an↗

arXiv2015

Convergent Bayesian formulations of blind source separation and electromagnetic source estimation

We consider two areas of research that have been developing in parallel over the last decade: blind source separation (BSS) and electromagnetic source estimation (ESE). BSS deals with the recovery of source signals when only mixtures of signals can be obtained from an array of detectors and the only prior knowledge consists of some information about the nature of the source signals. On the other hand, ESE utilizes knowledge of the electromagnetic forward problem to assign source signals to their respective generators, while information about the signals themselves is typically ignored. We demonstrate that these two techniques can be derived from the same starting point using the Bayesian formalism. This suggests a means by which new algorithms can be developed that utilize as much relevant information as possible. We also briefly mention some preliminary work that supports the value of integrating information used by these two techniques and review the kinds of information that may be useful in addressing the ESE problem.

physics.data-an↗

arXiv2014

Information-Theoretic Methods for Identifying Relationships among Climate Variables

Information-theoretic quantities, such as entropy, are used to quantify the amount of information a given variable provides. Entropies can be used together to compute the mutual information, which quantifies the amount of information two variables share. However, accurately estimating these quantities from data is extremely challenging. We have developed a set of computational techniques that allow one to accurately compute marginal and joint entropies. These algorithms are probabilistic in nature and thus provide information on the uncertainty in our estimates, which enable us to establish statistical significance of our findings. We demonstrate these methods by identifying relations between cloud data from the International Satellite Cloud Climatology Project (ISCCP) and data from other sources, such as equatorial pacific sea surface temperatures (SST).

physics.data-an↗

arXiv2014

A Potential Foundation for Emergent Space-Time

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.

math-ph↗

arXiv2014

The Problem of Motion: The Statistical Mechanics of Zitterbewegung

Around 1930, both Gregory Breit and Erwin Schroedinger showed that the eigenvalues of the velocity of a particle described by wavepacket solutions to the Dirac equation are simply $\pm$c, the speed of light. This led Schroedinger to coin the term Zitterbewegung, which is German for "trembling motion", where all particles of matter (fermions) zig-zag back-and-forth at only the speed of light. The result is that any finite speed less than $c$, including the state of rest, only makes sense as a long-term average that can be thought of as a drift velocity. In this paper, we seriously consider this idea that the observed velocities of particles are time-averages of motion at the speed of light and demonstrate how the relativistic velocity addition rule in one spatial dimension is readily derived by considering the probabilities that a particle is observed to move either to the left or to the right at the speed of light.

quant-ph↗

arXiv2014

Information-Based Physics, Influence, and Forces

In recent works, Knuth and Bahreyni have demonstrated that the concepts of space and time are emergent in a coarse-grained model of direct particle-particle influence. In addition, Knuth demonstrated that observer-made inferences regarding the free particle, which is defined as a particle that influences others, but is not itself influenced, result in a situation identical to the Feynman checkerboard model of the Dirac equation. This suggests that the same theoretical framework that gives rise to an emergent spacetime is consistent with quantum mechanics. In this paper, we begin to explore the effect of influence on the emergent properties of a particle. This initial study suggests that when a particle is influenced, it is interpreted as accelerating in a manner consistent with special relativity implying that, at least in this situation, influence can be conceived of as a force.

quant-ph↗

arXiv2014

A Bayesian Analysis of HAT-P-7b Using the EXONEST Algorithm

The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, HAT-P-7b. EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Model Selection, which is implemented with the MultiNest algorithm. These models take into account planetary effects, such as reflected light and thermal emissions, as well as the effect of the planetary motion on the host star, such as Doppler beaming, or boosting, of light from the reflex motion of the host star, and photometric variations due to the planet-induced ellipsoidal shape of the host star. By calculating model evidences, one can determine which model best describes the observed data, thus identifying which effects dominate the planetary system. Presented are parameter estimates and model evidences for HAT-P-7b.

astro-ph.EP↗

arXiv2014

EXONEST: Bayesian Model Selection Applied to the Detection and Characterization of Exoplanets Via Photometric Variations

EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian Inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian Model Selection, a unique aspect of EXONEST is the capability to distinguish between reflective and thermal contributions to the light curve. A case-study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the non-transiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically-relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.

astro-ph.EP↗

arXiv2014

Bayesian Source Separation Applied to Identifying Complex Organic Molecules in Space

Emission from a class of benzene-based molecules known as Polycyclic Aromatic Hydrocarbons (PAHs) dominates the infrared spectrum of star-forming regions. The observed emission appears to arise from the combined emission of numerous PAH species, each with its unique spectrum. Linear superposition of the PAH spectra identifies this problem as a source separation problem. It is, however, of a formidable class of source separation problems given that different PAH sources potentially number in the hundreds, even thousands, and there is only one measured spectral signal for a given astrophysical site. Fortunately, the source spectra of the PAHs are known, but the signal is also contaminated by other spectral sources. We describe our ongoing work in developing Bayesian source separation techniques relying on nested sampling in conjunction with an ON/OFF mechanism enabling simultaneous estimation of the probability that a particular PAH species is present and its contribution to the spectrum.

astro-ph.IM↗

arXiv2013

Revealing Relationships among Relevant Climate Variables with Information Theory

A primary objective of the NASA Earth-Sun Exploration Technology Office is to understand the observed Earth climate variability, thus enabling the determination and prediction of the climate's response to both natural and human-induced forcing. We are currently developing a suite of computational tools that will allow researchers to calculate, from data, a variety of information-theoretic quantities such as mutual information, which can be used to identify relationships among climate variables, and transfer entropy, which indicates the possibility of causal interactions. Our tools estimate these quantities along with their associated error bars, the latter of which is critical for describing the degree of uncertainty in the estimates. This work is based upon optimal binning techniques that we have developed for piecewise-constant, histogram-style models of the underlying density functions. Two useful side benefits have already been discovered. The first allows a researcher to determine whether there exist sufficient data to estimate the underlying probability density. The second permits one to determine an acceptable degree of round-off when compressing data for efficient transfer and storage. We also demonstrate how mutual information and transfer entropy can be applied so as to allow researchers not only to identify relations among climate variables, but also to characterize and quantify their possible causal interactions.

physics.data-an↗

arXiv2013

Informed Source Separation: A Bayesian Tutorial

Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the source separation problem. This approach has a specific advantage in that it requires the designer to explicitly describe the signal model in addition to any other information or assumptions that go into the problem description. This leads naturally to the idea of informed source separation, where the algorithm design incorporates relevant information about the specific problem. This approach promises to enable researchers to design their own high-quality algorithms that are specifically tailored to the problem at hand.

stat.ML↗

arXiv2013

Information-Based Physics: An Observer-Centric Foundation

It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can result in laws apparently worthy of a universal nature-centric physics. Over the last decade, we have found that the consistent apt quantification of algebraic and order-theoretic structures results in calculi that possess constraint equations taking the form of what are often considered to be physical laws. I review recent derivations of the formal relations among relevant variables central to special relativity, probability theory and quantum mechanics in this context by considering a problem where two observers form consistent descriptions of and make optimal inferences about a free particle that simply influences them. I show that this approach to describing such a particle based only on available information leads to the mathematics of relativistic quantum mechanics as well as a description of a free particle that reproduces many of the basic properties of a fermion. The result is an approach to foundational physics where laws derive from both consistent descriptions and optimal information-based inferences made by embedded observers.

quant-ph↗

arXiv2013

Optimal Data-Based Binning for Histograms

Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a straightforward data-based method of determining the optimal number of bins in a uniform bin-width histogram. By assigning a multinomial likelihood and a non-informative prior, we derive the posterior probability for the number of bins in a piecewise-constant density model given the data. In addition, we estimate the mean and standard deviations of the resulting bin heights, examine the effects of small sample sizes and digitized data, and demonstrate the application to multi-dimensional histograms.

physics.data-an↗

arXiv2013

Information-Based Physics and the Influence Network

This essay considers a simple model of observers that are influenced by the world around them. Consistent quantification of information about such influences results in a great deal of familiar physics. The end result is a new perspective on relativistic quantum mechanics, which includes both a way of conceiving of spacetime as well as particle "properties" that may be amenable to a unification of quantum mechanics and gravity. Rather than thinking about the universe as a computer, perhaps it is more accurate to think about it as a network of influences where the laws of physics derive from both consistent descriptions and optimal information-based inferences made by embedded observers.

quant-ph↗

arXiv2013

Bayesian Odds-Ratio Filters: A Template-Based Method for Online Detection of P300 Evoked Responses

Template-based signal detection most often relies on computing a correlation, or a dot product, between an incoming data stream and a signal template. While such a correlation results in an ongoing estimate of the magnitude of the signal in the data stream, it does not directly indicate the presence or absence of a signal. Instead, the problem of signal detection is one of model-selection. Here we explore the use of the Bayesian odds-ratio (OR), which is the ratio of posterior probabilities of a signal-plus-noise model over a noise-only model. We demonstrate this method by applying it to simulated electroencephalographic (EEG) signals based on the P300 response, which is widely used in both Brain Computer Interface (BCI) and Brain Machine Interface (BMI) systems. The efficacy of this algorithm is demonstrated by comparing the receiver operating characteristic (ROC) curves of the OR-based (logOR) filter to the usual correlation method where we find a significant improvement in P300 detection. The logOR filter promises to improve the accuracy and speed of the detection of evoked brain responses in BCI/BMI applications as well the detection of template signals in general.

q-bio.NC↗