On certain information-theoretic concepts in the theory of graphs
Information-theoretic concepts in theory of random graphs - entropy functions for probability distributions and Markov chains
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Information-theoretic concepts in theory of random graphs - entropy functions for probability distributions and Markov chains
This study introduces a novel Graph Neural Network (GNN) architecture that leverages infrared and collinear (IRC) safety and equivariance to enhance the analysis of collider data for Beyond the Standard Model (BSM) discoveries. By integrating equivariance in the rapidity-azimuth plane with IRC-safe principles, our model significantly reduces computational overhead while ensuring theoretical consistency in identifying BSM scenarios amidst Quantum Chromodynamics backgrounds. The proposed GNN architecture demonstrates superior performance in tagging semi-visible jets, highlighting its potential as a robust tool for advancing BSM search strategies at high-energy colliders.
Statistical communication theory for learning and adaptive system programs, and signal design
First order perturbation analysis of atom lifetime undergoing dipole transition due to presence of resonating atom
Robust detection of binary signal in additive noise, using extreme value theory /EVT/ to estimate probability density function and system error and threshold
This paper considers the extent to which Martian craters can be explained by considering asteroidal impact. Sections I, II, and III of this paper derive the diameter distribution of hypothetical asteroidal craters on Mars from recent Palomar-Leiden asteroid statistics and show that the observed Martian craters correspond to a bombardment by roughly 100 times the present number of Mars-crossing asteroids. Section IV discusses the early bombardment history of Mars, based on the capture theory of Opik and probable orbital parameters of early planetesimals. These results show that the visible craters and surface of Mars should not be identified with the initial, accreted surface. A backward extrapolation of the impact rates based on surviving Mars-crossing asteroids can account for the majority of Mars craters over an interval of several aeons, indicating that we see back in time no further than part-way into a period of intense bombardment. An early period of erosion and deposition is thus suggested. Section V presents a comparison with results and terminology of other authors.
Multivariate statistical analysis including divergence, probability of misclassification, information theory, and matrix analysis
An investigation into the kinetics of molecular clustering processes which occur in the highly supersaturated vapor of a CO2 free jet is described. Terminal cluster concentrations in expansions from room temperature and reservoir pressures in the range from 400 to 900 torr were determined for trimeric CO2 for nozzle diameters of .0076 cm, .015 cm, and .023 cm and in the case of CO2 tetramer and pentamer for .015 cm nozzle diameter. The measurements were made mass spectrometrically in a supersonic molecular beam apparatus. A kinetic analysis was developed from an extension of the critical nucleus concept of nucleation theory and rate equations based on intermolecular collisions. The observed cluster populations could be accounted for by the theory by adopting sticking probabilities of approximately .03 for monomer impinging on dimer, trimer, and tetramer.
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
A generalized method for obtaining individual level population ratios is used to obtain relative intensities of extreme ultraviolet Fe XV emission lines in the range 284-500 A, which are density dependent for electron densities in the tokamak regime or higher. Four lines in particular are found to attain quite high intensities in the high-density limit. The same calculation provides inelastic contributions to linewidths. The method connects level populations and level widths through total probabilities t(ij), related to 'taboo' probabilities of Markov chain theory. The t(ij) are here evaluated for a real atomic system, being therefore of potential interest to random-walk theorists who have been limited to idealized systems characterized by simplified transition schemes.
A theory of initial conditions is necessary for a complete explanation of the presently observed large scale structural features of the universe, and a quantum theory of cosmology is probably needed for its formulation. The kinematics of quantum cosmology are reviewed, and some candidates for a law of initial conditions are discussed. The proposal that the quantum state of a closed universe is the natural analog of the ground state for closed cosmologies and is specified by a Euclidean sum over histories is sketched. When implemented in simple models, this proposal is consistent with the most important large-scale observations.
This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.
The present report deals with the processes accompanying the planing of a planing boat or a seaplane on water . The study is largely based upon theoretical investigations; mathematical problems and proofs are not discussed. To analyze theoreticaly actual planing processes, giving due consideration to all aspects of the problem, is probably not possible. The theories therefore treat various simple limiting cases, which in their entirety give a picture of the planing processes and enable the interpretation of the experimental results. The discussion is concerned with the stationary planing attitude: the boat planes at a constant speed V on an originally smooth surface.
Fixed point probability row vector of regular or ergodic transition matrices simplified using generalized matrix inversion theory
Relationship between test particle correlation functions and conditional probability functions as established in studies of kinetic theory of plasmas
A theoretical study of vibrational excitations and dissociations of nitrogen undergoing a nonequilibrium relaxation process upon heating and cooling is reported. The rate coefficients for collisional induced vibrational transitions and transitions from a bound vibrational state into a dissociative state have been calculated using an extension of the theory originally proposed by Schwarz (SSH) et al. (1952). High-lying vibrational states and dissociative states were explicitly included but rotational energy transfer was neglected. The transition probabilities calculated from the SSH theory were fed into the master equation, which was integrated numerically to determine the population distribution of the vibrational states as well as bulk thermodynamic properties. The results show that: (1) the transition rates have a minimum near the middle of the bound vibrational levels, causing a bottleneck in the vibrational relaxation and dissociation rates; (2) high vibrational states are always in equilibrium with the dissociative state; (3) for the heating case, only the low vibrational states relax according to the Landau-Teller theory; (4) for the cooling case, vibrational relaxation cannot be described by a rate equation; (5) Park's (1985, 1988) two-temperature model is approximately valid; and (6) the average vibrational energy removed in dissociation is about 30 percent of the dissociation energy.
This paper outlines a procedure for performing induction under uncertainty. This procedure uses a probabilistic representation and uses Bayes' theorem to decide between alternative hypotheses (theories). This procedure is illustrated by a robot with no prior world experience performing induction on data it has gathered about the world. The particular inductive problem is the formation of class descriptions both for the tutored and untutored cases. The resulting class definitions are inherently probabilistic and so do not have any sharply defined membership criterion. This robot example raises some fundamental problems about induction; particularly, it is shown that inductively formed theories are not the best way to make predictions. Another difficulty is the need to provide prior probabilities for the set of possible theories. The main criterion for such priors is a pragmatic one aimed at keeping the theory structure as simple as possible, while still reflecting any structure discovered in the data.
The very large electromagnetic dissociation (EMD) cross section recently observed by Hill, Wohn, Schwellenbach, and Smith do not agree with Weizsacker-Williams (WW) theory or any simple modification thereof. Calculations are presented for the reaction probabilities for this experiment and the entire single and double nucleon removal EMD data set. It is found that for those few reactions where theory and experiment disagree, the probabilities are exceptionally large. This indicates that WW theory is not valid for these reactions and that one must consider higher order corrections and perhaps even a non-perturbative approach to quantum electrodynamics (QED).