Deterministic Side Research Articles

Imaging Cancer in Pregnancy.

Pregnancy-associated cancer (PAC) is defined as cancer that is detected during pregnancy and up to 1 year postpartum. Although rare (~1:1000 pregnancies), PAC is increasing owing to postponed childbearing and advanced maternal age at conception. Cancer-related symptoms masked by physiologic gestational changes may delay diagnosis. Imaging, clinical management, and treatment require a carefully choreographed multidisciplinary team approach. The risk-benefit of every imaging modality, the strategies to balance the safety of mother and fetus, and the support of the patient and family at every step are crucial. US and MRI are preferred imaging modalities that lack ionizing radiation. Radiation dose concerns should be addressed, noting that most imaging examinations (including mammography, radiography, CT, and technetium 99m-labeled sulfur colloid sentinel lymph node staging) are performed at radiation levels below thresholds at which deterministic side effects are seen. Dose estimates should be provided after each examination. The use of iodinated intravenous contrast material is safe during pregnancy, but gadolinium-based contrast material should be avoided. Accurate diagnosis and staging combined with gestational age affect decisions about surgery and chemotherapy. Whole-body MRI with diffusion-weighted sequences is ideal to screen for primary and metastatic sites, determine disease stage, identify biopsy targets, and guide further cancer site-specific imaging. The authors provide an update of the imaging triage, safety considerations, cancer-specific imaging, and treatment options for cancer in pregnancy. An invited commentary by Silverstein and Van Loon is available online. Online supplemental material is available for this article. ©RSNA, 2022.

Theoretical and Experimental Analyses of Nutrient Control in Electrical Conductivity-Based Nutrient Recycling Soilless Culture System.

An electrical conductivity (EC)-based closed-loop soilless culture system is practical for in-field deployment. Literature on the closed-loop soilless culture nutrient management premise the limitations in managing recycled nutrients under dynamic changes in individual nutrient uptake concentrations. However, recent systems analysis studies predicting solutions for nutrient fluctuation stabilization in EC-based closed-loop soilless culture systems suggest that the system may have a deterministic side in nutrient variation. This study aims to derive a nutrient control principle in an EC-based nutrient recycling soilless culture system by theoretical and experimental analyses. An integrated model of solutes such as K+, Ca2+, and Mg2+ and water transport in growing media, automated nutrient solution preparation, and nutrient uptake was designed. In the simulation, the intrinsic characteristics of nutrient changes among open-, semi- closed-, and closed-loop soilless cultures were compared, and stochastic simulations for nutrient control were performed in the closed-loop system. Four automated irrigation modules for comparing nutrient changes among the soilless culture systems were constructed in the greenhouse. Sweet pepper plants were used in the experiment. In the experimental analysis, nutrient concentration conversion to the proportion between nutrients revealed distinctive trends of nutrient changes according to the treatment level of drainage recycling. Theoretical and experimental analyses exhibited that nutrient variations in open-, semi- closed-, and closed-loop soilless culture systems can be integrated as a function of nutrient supply to the system’s boundary areas. Furthermore, stochastic simulation analysis indicated that the nutrient ratio in the soilless culture system reveals the nutrient uptake parameter-based deterministic patterns. Thus, the nutrient ratio in the closed-loop soilless culture could be controlled by the long-term feedback of this ratio. We expect that these findings provide theoretical frameworks for systemizing nutrient management techniques in EC-based closed-loop soilless culture systems.

Using Different Methods to Predict Oil in Place in Mishrif Formation / Amara Oil Field

The reserve estimation process is continuous during the life of the field due to risk and inaccuracy that are considered an endemic problem thereby must be studied. Furthermore, the truth and properly defined hydrocarbon content can be identified just only at the field depletion. As a result, reserve estimation challenge is a function of time and available data. Reserve estimation can be divided into five types: analogy, volumetric, decline curve analysis, material balance and reservoir simulation, each of them differs from another to the kind of data required. The choice of the suitable and appropriate method relies on reservoir maturity, heterogeneity in the reservoir and data acquisition required. In this research, three types of reserve estimation used for the Mishrif formation / Amara oil field volumetric approach in mathematic formula (deterministic side) and Monte Carlo Simulation technique (probabilistic side), material balance equation identified by MBAL software and reservoir simulation adopted by Petrel software geological model. The results from these three methods were applied by the volumetric method in the deterministic side equal to (2.25 MMMSTB) and probabilistic side equal to (1.24, 2.22, 3.55) MMMSTB P90, P50, P10 respectively. OOIP was determined by MBAL software equal to (2.82 MMMSTB). Finally, the volume calculation of OOIP by using the petrel static model was (1.92 MMMSTB). The percentage error between material balance and the volumetric equation was equal to 20% while the percentage error between the volumetric method and petrel software was 17%.

Quasilinear SPDEs via Rough Paths

We are interested in (uniformly) parabolic PDEs with a nonlinear dependence of the leading-order coefficients, driven by a rough right hand side. For simplicity, we consider a space-time periodic setting with a single spatial variable:∂2u-P(a(u)∂12u+σ(u)f)=0,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\partial_2u -P( a(u)\\partial_1^2u + \\sigma(u)f ) =0,$$\\end{document}where P is the projection on mean-zero functions, and f is a distribution which is only controlled in the low regularity norm of { C^{alpha-2}} for {alpha > frac{2}{3}} on the parabolic Hölder scale. The example we have in mind is a random forcing f and our assumptions allow, for example, for an f which is white in the time variable x2 and only mildly coloured in the space variable x1; any spatial covariance operator {(1 + |partial_1|)^{-lambda_1 }} with {lambda_1 > frac13} is admissible. On the deterministic side we obtain a {C^alpha}-estimate for u, assuming that we control products of the form {vpartial_1^2v} and vf with v solving the constant-coefficient equation {partial_2 v-a_0partial_1^2v=f}. As a consequence, we obtain existence, uniqueness and stability with respect to {(f, vf, v partial_1^2v)} of small space-time periodic solutions for small data. We then demonstrate how the required products can be bounded in the case of a random forcing f using stochastic arguments. For this we extend the treatment of the singular product {sigma(u)f} via a space-time version of Gubinelli’s notion of controlled rough paths to the product {a(u)partial_1^2u}, which has the same degree of singularity but is more nonlinear since the solution u appears in both factors. In fact, we develop a theory for the linear equation {partial_t u - P(apartial_1^2 u +sigma f)=0} with rough but given coefficient fields a and {sigma} and then apply a fixed point argument. The PDE ingredient mimics the (kernel-free) Safonov approach to ordinary Schauder theory.

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs with uncertain parameters. While in previous works (Formaggia et al. 2013, Porta et al. 2014) we assumed a simplified depositional history with only one material, in this work we consider multi-layered basins, in which each layer is characterized by a different material, and hence by different properties. This setting requires several improvements with respect to our earlier works, both concerning the deterministic solver and the stochastic discretization. On the deterministic side, we replace the previous fixed-point iterative solver with a more efficient Newton solver at each step of the time-discretization. On the stochastic side, the multi-layered structure gives rise to discontinuities in the dependence of the state variables on the uncertain parameters, that need an appropriate treatment for surrogate modeling techniques, such as sparse grids, to be effective. We propose an innovative methodology to this end which relies on a change of coordinate system to align the discontinuities of the target function within the random parameter space. The reference coordinate system is built upon exploiting physical features of the problem at hand. We employ the fact that the locations of the material interfaces display a smooth dependence on the random parameters and are therefore amenable to sparse grid polynomial approximations. We showcase the capabilities of our numerical methodologies through two synthetic test cases. In particular, we show that our methodology reproduces with high accuracy multi-modal probability density functions displayed by target state variables (e.g., porosity).

Convergence rates for loop-erased random walk and other Loewner curves

We estimate convergence rates for curves generated by Loewner's differential equation under the basic assumption that a convergence rate for the driving terms is known. An important tool is what we call the tip structure modulus, a geometric measure of regularity for Loewner curves parameterized by capacity. It is analogous to Warschawski's boundary structure modulus and closely related to annuli crossings. The main application we have in mind is that of a random discrete-model curve approaching a Schramm-Loewner evolution (SLE) curve in the lattice size scaling limit. We carry out the approach in the case of loop-erased random walk (LERW) in a simply connected domain. Under mild assumptions of boundary regularity, we obtain an explicit power-law rate for the convergence of the LERW path toward the radial SLE$_2$ path in the supremum norm, the curves being parameterized by capacity. On the deterministic side, we show that the tip structure modulus gives a sufficient geometric condition for a Loewner curve to be H\"{o}lder continuous in the capacity parameterization, assuming its driving term is H\"{o}lder continuous. We also briefly discuss the case when the curves are a priori known to be H\"{o}lder continuous in the capacity parameterization and we obtain a power-law convergence rate depending only on the regularity of the curves.

Characterization of a cable‐free system based on p‐type MOSFET detectors for “in vivo” entrance skin dose measurements in interventional radiology

During radiological interventional procedures (RIP) the skin of a patient under examination may undergo a prolonged x-ray exposure, receiving a dose as high as 5 Gy in a single session. This paper describes the use of the OneDose(TM) cable-free system based on p-type MOSFET detectors to determine the entrance skin dose (ESD) at selected points during RIP. At first, some dosimetric characteristics of the detector, such as reproducibility, linearity, and fading, have been investigated using a C-arc as a source of radiation. The reference setting (RS) was: 80 kV energy, 40 cm × 40 cm field of view (FOV), current-time product of 50 mAs and source to skin distance (SSD) of 50 cm. A calibrated PMX III solid state detector was used as the reference detector and Gafchromic(®) films have been used as an independent dosimetric system to test the entire procedure. A calibration factor for the RS and correction factors as functions of tube voltage and FOV size have been determined. Reproducibility ranged from 4% at low doses (around 10 cGy as measured by the reference detector) to about 1% for high doses (around 2 Gy). The system response was found to be linear with respect to both dose measured with the PMX III and tube voltage. The fading test has shown that the maximum deviation from the optimal reading conditions (3 min after a single irradiation) was 9.1% corresponding to four irradiations in one hour read 3 min after the last exposure. The calibration factor in the RS has shown that the system response at the kV energy range is about four times larger than in the MV energy range. A fifth order and fourth order polynomial functions were found to provide correction factors for tube voltage and FOV size, respectively, in measurement settings different than the RS. ESDs measured with the system after applying the proper correction factors agreed within one standard deviation (SD) with the corresponding ESDs measured with the reference detector. The ESDs measured with Gafchromic(®) films were in agreement within one SD compared to the ESDs measured using the OneDose(TM) system, as well. The global uncertainty associated to the OneDose(TM) system established in our experiments, ranged from 7% to 10%, depending on the duration of the RIP due to fading. These values are much lower than the uncertainty commonly accepted for general diagnostic practices (20%) and of about the same size of the uncertainty recommended for practices with high risk of deterministic side effects (7%). The OneDose(TM) system has shown a high sensitivity in the kV energy range and has been found capable of measuring the entrance skin dose in RIP.

Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates

Viewing the classical Bernstein polynomials as sampling operators, we study a generalization by allowing the sampling operation to take place at scattered sites. We utilize both stochastic and deterministic approaches. On the stochastic side, we consider the sampling sites as random variables that obey some naturally derived probabilistic distributions, and obtain Chebyshev type estimates. On the deterministic side, we incorporate the theory of uniform distribution of point sets (within the framework of Weyl's criterion) and the discrepancy method. We establish convergence results and error estimates under practical assumptions on the distribution of the sampling sites.

Concepts Of Decision Making Under Uncertain, Risky Deterministic Situations

Making decisions is certainly the most important task of a manager and it is often a very difficult one. This paper offers a decision making procedure for solving complex problems step by step. It presents the decision-analysis process for both public and private decision-making, using different decision criteria, different types of information, and information of varying quality. It describes the elements in the analysis of decision alternatives and choices, as well as the goals and objectives that guide decision-making. The key issues related to a decision-maker's preferences regarding alternatives, criteria for choice, and choice modes, together with the risk assessment tools are also presented. The domain of decision analysis models falls between two extreme cases. This depends upon the degree of knowledge we have about the outcome of our actions. One "pole" on this scale is deterministic. The opposite "pole" is pure uncertainty. Between these two extremes are problems under risk. The main idea here is that for any given problem, the degree of certainty varies among managers depending upon how much knowledge each one has about the same problem. This reflects the recommendation of a different solution by each person. Probability is an instrument used to measure the likelihood of occurrence for an event. When you use probability to express your uncertainty, the deterministic side has a probability of 1 (or zero), while the other end has a flat (all equally probable) probability. The following sections of this paper are arranged as below. After introduction in section one, Decision Making under Pure Uncertainty are disscussed in section two. Section 3 and 4, are allocated to decision making under risk and bayesian approach respectively. Fifth section talks about decision tree and influence diagram and finally the paper will end with a brief conclusion.

Self field electromagnetism and quantum phenomena

Abstract Quantum Electrodynamics (QED) has been extremely successful inits predictive capability for atomic phenomena. Thus the greatest hope for any alternative view is solely to mimic the predictive capability of quantum mechanics (QM), and perhaps its usefulness will lie in gaining a better understanding of microscopic phenomena. Many “paradoxes” and problematic situations emerge in QED. To combat the QED problems, the field of Stochastics Electrodynamics (SE) emerged, wherein a random “zero point radiation” is assumed to fill all of space in an attmept to explain quantum phenomena, without some of the paradoxical concerns. SE, however, has greater failings. One is that the electromagnetic field energy must be infinit eto work. We have examined a deterministic side branch of SE, “self field” electrodynamics, which may overcome the probelms of SE. Self field electrodynamics (SFE) utilizes the chaotic nature of electromagnetic emissions, as charges lose energy near atomic dimensions, to try to understand and mimic quantum phenomena. These fields and charges can “interact with themselves” in a non-linear fashion, and may thereby explain many quantum phenomena from a semi-classical viewpoint. Referred to as self fields, they have gone by other names in the literature: “evanesccent radiation”, “virtual photons”, and “vacuum fluctuations”. Using self fields, we discuss the uncertainty principles, the Casimir effects, and the black-body radiation spectrum, diffraction and interference effects, Schrodinger's equation, Planck's constant, and the nature of the electron and how they might be understood in the present framework. No new theory could ever replace QED. The self field view (if correct) would, at best, only serve to provide some understanding of the processes by which strange quantum phenomena occur at the atomic level. We discuss possible areas where experiments might be employed to test SFE, and areas where future work may lie.

?The Deterministic Side of Geostatistics? by A. G. Journel

?The Deterministic Side of Geostatistics? by A. G. Journel

A critique of A. Journel's ?The Deterministic Side of Geostatistics?

A critique of A. Journel's ?The Deterministic Side of Geostatistics?

Answers to Margaret Armstrong and Robert F. Shurtz's comments on ?The deterministic side of geostatistics?

Answers to Margaret Armstrong and Robert F. Shurtz's comments on ?The deterministic side of geostatistics?

Statistics and thermodynamics of fracture

A probabilistic model of the fracture processes unifying the phenomenological study of long term strength of materials, fracture mechanics and statistical approaches to fracture is briefly outlined. The general framework of irreversible thermodynamics is employed to model the deterministic side of the failure phenomenon. The stochastic calculus is used to account for the failure mechanisms controlled by chance; particularly, the random roughness of fracture surfaces.

Pseudo-Random Monte-Carlo Methods

In this paper we investigate the Monte-Carlo method for estimation of the unknown probability of a random event on the ground of relative frequencies and under the condition that random sampling is replaced by a deterministic side input producing binary sequences of high algorithmic complexity. It is proved that if this complexity exceeds a treshold value, the sequences may be used in the Monte-Carlo methods instead of random samples as the obtained estimates converge to the estimated probability when the length of these binary sequences increases.

The design of a location experiment

The search for the relationship between residential location and urban transportation systems has been conducted from the deterministic side, using the tools of microeconomic theory, and from the probabilistic side, using information theory. Until now, the purely probabilistic models were unable to effectively utilize the available data on the economic behavior of residential decision makers. The deterministic models, on the other hand, have met with difficulty in the aggregation of individual behavior. This paper combines what we consider to be the better points of both approaches. The synthesis makes available to the transportation planner a framework which enables him to use the potentially available data to predict the effects on residential location of a change in the transportation system.