SEARCH · Engineering Papers
Results for “SET THEORY”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The selection of construction sub-contractors using the fuzzy sets theory
The paper presents the algorithm for the selection of sub-contractors. Main area of author’s interest is scheduling flow models. The ranking task aims at execution time as short as possible Brigades downtime should also be as small as possible. These targets are exposed to significant obsolescence. The criteria for selection of subcontractors will not be therefore time and cost, it is assumed that all those criteria be meet by sub-contractors. The decision should be made in regard to factors difficult to measure, to assess which is the perfect application of fuzzy sets theory. The paper will present a set of evaluation criteria, the part of the knowledge base and a description of the output variable.
Dark-matter halo assembly bias: Environmental dependence in the non-Markovian excursion-set theory
In the standard excursion-set model for the growth of structure, the statistical properties of halos are governed by the halo mass and are independent of the larger-scale environment in which the halos reside. Numerical simulations, however, have found the spatial distributions of halos to depend not only on their mass but also on the details of their assembly history and environment. Here we present a theoretical framework for incorporating this 'assembly bias' into the excursion-set model. Our derivations are based on modifications of the path-integral approach of Maggiore and Riotto that models halo formation as a non-Markovian random-walk process. The perturbed density field is assumed to evolve stochastically with the smoothing scale and exhibits correlated walks in the presence of a density barrier. We write down conditional probabilities for multiple barrier crossings and derive from them analytic expressions for descendant and progenitor halo mass functions and halo merger rates as a function of both halo mass and the linear overdensity δ {sub e} of the larger-scale environment of the halo. Our results predict a higher halo merger rate and higher progenitor halo mass function in regions of higher overdensity, consistent with the behavior seen in N-body simulations.
A method for classification of red, blue, and green galaxies using fuzzy set theory
ABSTRACT Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant contamination in these samples. Fuzzy sets are vague boundary sets that can efficiently capture the classification uncertainty in the absence of any precise boundary. We propose a method for classification of galaxies according to their colours using fuzzy set theory. We use data from the Sloan Digital Sky Survey (SDSS) to construct a fuzzy set for red galaxies with its members having different degrees of ‘redness’. We show that the fuzzy sets for the blue and green galaxies can be obtained from it using different fuzzy operations. We also explore the possibility of using fuzzy relation to study the relationship between different galaxy properties and discuss its strengths and limitations.
Checking Questionable Entry of Personally Identifiable Information Encrypted by One-Way Hash Transformation
Background: As one of the several effective solutions for personal privacy protection, a global unique identifier (GUID) is linked with hash codes that are generated from combinations of personally identifiable information (PII) by a one-way hash algorithm. On the GUID server, no PII is permitted to be stored, and only GUID and hash codes are allowed. The quality of PII entry is critical to the GUID system. Objective: The goal of our study was to explore a method of checking questionable entry of PII in this context without using or sending any portion of PII while registering a subject. Methods: According to the principle of GUID system, all possible combination patterns of PII fields were analyzed and used to generate hash codes, which were stored on the GUID server. Based on the matching rules of the GUID system, an error-checking algorithm was developed using set theory to check PII entry errors. We selected 200,000 simulated individuals with randomly-planted errors to evaluate the proposed algorithm. These errors were placed in the required PII fields or optional PII fields. The performance of the proposed algorithm was also tested in the registering system of study subjects. Results: There are 127,700 error-planted subjects, of which 114,464 (89.64%) can still be identified as the previous one and remaining 13,236 (10.36%, 13,236/127,700) are discriminated as new subjects. As expected, 100% of nonidentified subjects had errors within the required PII fields. The possibility that a subject is identified is related to the count and the type of incorrect PII field. For all identified subjects, their errors can be found by the proposed algorithm. The scope of questionable PII fields is also associated with the count and the type of the incorrect PII field. The best situation is to precisely find the exact incorrect PII fields, and the worst situation is to shrink the questionable scope only to a set of 13 PII fields. In the application, the proposed algorithm can give a hint of questionable PII entry and perform as an effective tool. Conclusions: The GUID system has high error tolerance and may correctly identify and associate a subject even with few PII field errors. Correct data entry, especially required PII fields, is critical to avoiding false splits. In the context of one-way hash transformation, the questionable input of PII may be identified by applying set theory operators based on the hash codes. The count and the type of incorrect PII fields play an important role in identifying a subject and locating questionable PII fields.
On the abundance of extreme voids II: a survey of void mass functions
The abundance of cosmic voids can be described by an analogue of halo mass functions for galaxy clusters. In this work, we explore a number of void mass functions: from those based on excursion-set theory to new mass functions obtained by modifying halo mass functions. We show how different void mass functions vary in their predictions for the largest void expected in an observational volume, and compare those predictions to observational data. Our extreme-value formalism is shown to be a new practical tool for testing void theories against simulation and observation.
Path integral suppression of badly behaved causal sets
Abstract Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be dynamically excluded if something like our Universe is to emerge from the theory. Here we show that the most common of these ‘bad’ causal sets, the Kleitman–Rothschild orders, are strongly suppressed in the gravitational path integral, and we provide evidence that a large class of other ‘bad’ causal sets are similarly suppressed. It thus becomes plausible that continuum behavior could emerge naturally from causal set quantum theory.
A proof of the conjecture on the twin primes
In this short note, we have proved the conjecture on twin primes using some thoughts of the set theory. Firstly, using the original sieve method and a new notation(concept)introduced by myself, the conjecture on twin primes is summed up as an elementary successive limit, afterwards we form a subsequence of positive integers,and using it,we prove that the successive limits are commutative and complete the proof of the conjecture on twin primes We also give a more straightforward proof of the conjecture.
Computation of the halo mass function using physical collapse parameters: application to non-standard cosmologies
In this article we compare the halo mass function predicted by the excursion set theory with a drifting diffusive barrier against the results of N-body simulations for several cosmological models. This includes the standard ΛCDM case for a large range of halo masses, models with different types of primordial non-Gaussianity, and the Ratra-Peebles quintessence model of Dark Energy. We show that in all those cosmological scenarios, the abundance of dark matter halos can be described by a drifting diffusive barrier, where the two parameters describing the barrier have physical content. In the case of the Gaussian ΛCDM, the statistics are precise enough to actually predict those parameters at different redshifts from the initial conditions. Furthermore, we found that the stochasticity in the barrier is non-negligible making the simple deterministic spherical collapse model a bad approximation even at very high halo masses. We also show that using the standard excursion set approach with a barrier inspired by peak patches leads to inconsistent predictions of the halo mass function.
Large scale anisotropic bias from primordial non-Gaussianity
In this work we study the large scale structure bias in models of anisotropic inflation. We use the Peak Background Splitting method in Excursion Set Theory to find the scale-dependent bias. We show that the amplitude of the bias is modified by a direction-dependent factor. In the specific anisotropic inflation model which we study, the scale-dependent bias vanishes at leading order when the long wavelength mode in squeezed limit is aligned with the anisotropic direction in the sky. We also extend the scale-dependent bias formulation to the general situations with primordial anisotropy. We find some selection rules indicating that some specific parts of a generic anisotropic bispectrum is picked up by the bias parameter. We argue that the anisotropic bias is mainly sourced by the angle between the anisotropic direction and the long wavelength mode in the squeezed limit.
Branch-and-Bound algorithm applied to uncertainty quantification of a Boiling Water Reactor Station Blackout
Evaluation of the impacts of uncertainty and sensitivity in modeling presents a significant set of challenges in particular to high fidelity modeling. Computational costs and validation of models creates a need for cost effective decision making with regards to experiment design. Experiments designed to validate computation models can be used to reduce uncertainty in the physical model. In some cases, large uncertainty in a particular aspect of the model may or may not have a large impact on the final results. For example, modeling of a relief valve may result in large uncertainty, however, the actual effects on final peak clad temperature in a reactor transient may be small and the large uncertainty with respect to valve modeling may be considered acceptable. Additionally, the ability to determine the adequacy of a model and the validation supporting it should be considered within a risk informed framework. Low fidelity modeling with large uncertainty may be considered adequate if the uncertainty is considered acceptable with respect to risk. In other words, models that are used to evaluate the probability of failure should be evaluated more rigorously with the intent of increasing safety margin. Probabilistic risk assessment (PRA) techniques have traditionally been used to identify accident conditions and transients. Traditional classical event tree methods utilize analysts’ knowledge and experience to identify the important timing of events in coordination with thermal-hydraulic modeling. These methods lack the capability to evaluate complex dynamic systems. In these systems, time and energy scales associated with transient events may vary as a function of transition times and energies to arrive at a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. Unfortunately DPRA methods introduce issues associated with combinatorial explosion of states. This study presents a methodology to address combinatorial explosion using a Branch-and-Bound algorithm applied to Dynamic Event Trees (DET), which utilize LENDIT (L – Length, E – Energy, N – Number, D – Distribution, I – Information, and T – Time) as well as a set theory to describe system, state, resource, and response (S2R2) sets to create bounding functions for the DET. The optimization of the DET in identifying high probability failure branches is extended to create a Phenomenological Identification and Ranking Table (PIRT) methodology to evaluate modeling parameters important to safety of those failure branches that have a high probability of failure. The PIRT can then be used as a tool to identify and evaluate the need for experimental validation of models that have the potential to reduce risk. Finally, in order to demonstrate this methodology, a Boiling Water Reactor (BWR) Station Blackout (SBO) case study is presented.
The PDF4LHC21 combination of global PDF fits for the LHC Run III
A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton–hadron and hadron–hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark studies are carried out in order to disentangle the origin of the differences between the three global PDF sets. In particular, dedicated fits based on almost identical theory settings and input datasets are performed by the three groups, highlighting the role played by the respective fitting methodologies. We compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15, demonstrating their good overall consistency and a modest reduction of PDF uncertainties for key LHC processes such as electroweak gauge boson production and Higgs boson production in gluon fusion. We study the phenomenological implications of PDF4LHC21 for a representative selection of inclusive, fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination is made available via the LHAPDF library and provides a robust, user-friendly, and efficient method to estimate the PDF uncertainties associated to theoretical calculations for the upcoming Run III of the LHC and beyond.
Causal sets and an emerging continuum
Abstract Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent results showing that almost all non-manifoldlike causal sets are, in fact, very strongly suppressed in the gravitational path integral. This does not quite demonstrate the emergence of a continuum—we do not yet understand the remaining unsuppressed causal sets well enough—but it is a significant step in that direction.
Scattering Amplitudes and QFT Insight (Final Scientific Report)
The calculation of scattering amplitudes provides an invariant window into the physical dynamic content of relativistic quantum field theory. Yet with traditional methods, for empirically relevant theories, these calculations scale with a factorial complexity in external particles and precision. If we aspire to collapse the theoretical uncertainty obscuring new physics hidden at all scales from the microscopic probed at high energy colliders to the largest effective field theory in the universe governing the evolution of large scale structure, this complexity challenge necessitates new ideas and methods in calculation. Novel approaches like the color-kinematics duality and the associated double-copy construction have drastically simplified the situation, relating both gauge and gravity theory predictions to a much smaller kernel of invariant kinematic data. This project supporting research by the PI's Amplitudes and Insights group at Northwestern University looked to push insight deep into both the IR and the UV by establishing how novel structures must constrain the predictions of counterterms in both gauge and gravity theories, setting the groundwork to exploring the high energy behavior of particular gravity theories via constituent gauge-theory calculations, and confronting fundamental challenges at the interface between QFT amplitudes analysis and next generation gravitational wave science as well as well as inflationary and large scale structure cosmology.
MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems
Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.
Resonant non-Gaussianity with equilateral properties
We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of resonant N-point functions give a constraint of f{sub NL}∼<O(5) for equilateral non-Gaussianity with resonant origin, but this constraint can be avoided when additional U(1)s are involved in the breaking of the shift symmetry. We comment on the questions arising from possible embeddings of this idea in a string theory setting.
Classical and quantum stability in putative landscapes
Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.
Improved Modelling for the Assembly Discontinuity Factors in the APEC Method
Modern reactor analysis of light water reactor depends largely on a two-step procedure based on the simplified equivalence theory (SET). Consequently, the resulting homogenized two-group cross-section (XS) and associated discontinuity factor (DF) are subject to noticeable, intrinsic uncertainties. In our previous study, we introduced the albedo-corrected parameterized equivalence constants (APEC) method, which is a new leakage correction method applicable to the fuel assembly homogenized two-group XS of the standard two-step procedure. In the APEC method, fuel assembly two-group XS is expressed as a simple polynomial function of assembly-wise current-to-flux ratio (CFR), and it was demonstrated that two-group XSs can be well corrected during a nodal calculation and the nodal accuracy is improved a lot. However, since the conventional assembly discontinuity factor (ADF) is still used in the current APEC method, a small but non-negligible error is unavoidable. Therefore, it is necessary to include improved DF model in the APEC method for a higher accuracy. The functionalized discontinuity factor (FDF) using the definition of CFR was investigated by authors before the development of the APEC method, where it was motivated by the boundary perturbation theory by F. Rahnema. However, in our previous study on FDF, lattice calculations were performed only with one-dimensional two-group diffusion equation and could not be applied to actual core analysis. In this paper, feasibility study of DF functionalization is performed based on a 2-D method of characteristics (MOC) lattice code, DeCART2D.