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# Statistics as The Logic of Science

by | Sep 24, 2020 | Blog

The question of science itself has never been its particular object of inquiry but the existential nature, in its possibility and thereby the nature of its actuality. Science is power, and thus abstracts itself as the desired meta-good, although it is always itself about particularities as an ever-finer branching process. Although a philosophic question, the ‘question of science’ is inherently a political one, as it is the highest good desired by the society, its population, and its government. To make sense of science mathematically-numerically, as statistics claims, it is the scientific process itself that must be understood through probability theory as The Logic of Science (Jaynes).

## Linguistic Analysis of the Invariants of Science: The Laws of Nature

The theory of science, as the proof of its validity in universality, must consider the practice of science, as the negating particularity. The symbolic language of science, within which its practice and results are embedded, necessarily negates its own particularity as well, as thus to represent a structure universally. Science, in the strict sense of having achieved already the goal of universality, is de-linguistified. While mathematics, in its extra-linguistic nature, often has the illusion of universal de-linguistification, such is only a semblance and often an illusion. The numbers of mathematics always can refer to things, and in the particular basis of their conceptual context always do. The non-numeric symbols of mathematics too represented words before short-hand gave them a distilled symbolic life. The de-linguistified nature of the extra-linguistic property of mathematics is that to count as mathematics, the symbols must themselves represent universal things. Thus, all true mathematical statements may represent scientific phenomena, but the context and work of this referencing is not trivial and sometimes the entirety of the scientific labor. The tense of science, as the time-space of the activity of its being, is the tensor, which is the extra-linguistic meta-grammar of null-time, and thus any and all times.

## The Event Horizon of Discovery: The Dynamics between an Observer & a Black Hole

The consciousness who writes or reads science, and thereby reports or performs the described tensor as an action of experimentation or validation, is the transcendental consciousness. Although science is real, it is only a horizon. The question is thus of its nature and existence at this horizon. What is knowable of science is thereby known as ‘the event horizon’, as that which has appeared already, beyond which is mere a ‘black hole’ as what has not yet revealed itself – always there is a not-yet to temporality and so such a black hole can always be at least found as all that of science that has not and cannot be revealed since within the very notion of science is a negation of withdrawal (non-appearance) as the condition of its own universality (negating its particularity). Beginning here with the null-space of black-holes, the physical universe – at least the negative gravitational entities – have a natural extra-language – at least for the negative linguistic operation of signification whereby what is not known is the ‘object’ of reference. In this cosmological interpretation of subjectivity within the objectivity of physical space-time, we thus come to the result of General Relativity that the existence of a black-hole is not independent of the observer, and in fact is only an element in the Null-Set, or negation, of the observer. To ‘observer’ a black-hole is to point to and outline something of which one does not know. If one ‘knew’ what it was positively then it would be not ‘black’ in the sense of not-emitting light within the reference frame (space-time curvature) of the observer. That one cannot see something, as receive photons reflecting space-time measurements, is not a property of the object but rather of the observer in his or her subjective activity of observation since to be at all must mean there is some perspective from which it can be seen. As the Negation of the objectivity of an observer, subjectivity is the negative gravitational anti-substance of blackholes. Subjectivity, as what is not known by consciousness, observes the boundaries of an aspect (a negative element) of itself in the physical measurement of an ‘event horizon.’

These invariants of nature, as the conditions of its space-time, are the laws of dynamics in natural science. At the limit of observation we find the basis of the conditionality of the observation and thus its existence as an observer. From the perspective of absolute science, within the horizon of universality (i.e. the itself as not-itself of the black-hole or Pure Subjectivity), the space-time of the activity of observation (i.e. the labor of science) is a time-space as the hyperbolic negative geometry of conditioning (the itself of an unconditionality). What is a positive element of the bio-physical contextual condition of life, from which science takes place, for the observer is a negative aspect from the perspective of transcendental consciousness (i.e. science) as the limitation of the observation. Within Husserlian Phenomenology and Hilbertian Geometry of the early 20th century in Germany, from which Einstein’s theory arose, a Black-Hole is therefore a Transcendental Ego as the absolute measurement point. Our Solar System is conditioned in its space-time geometry by the MilkyWay galaxy it is within, which is conditioned by the blackhole Sagittarius A* (SgrA). Therefore, the unconditionality of our solar space-time (hence the bio-kinetic features) is an unknown of space-time possibilities, enveloped in the event horizon of SgrA. What is the inverse to our place (i.e. space-time) of observation will naturally only exist as a negativity, what cannot be seen.

## Classical Origins of The Random Variable as The Unknown: Levels of Analysis

Strictly speaking, within Chinese Cosmological Algebra of 4-variables ($$\mu$$, X,Y,Z), this first variable of primary Unknowing, is represented by $$X$$, or Tiān (天), for ‘sky’ as that which conditions the arc of the sky, i.e. “the heavens” or the space of our temporal dwelling ‘in the earth.’ We can say thus that $$X=SgrA$$ is the largest and most relevant primary unknown for solarized galactic life. While of course X may represent anything, in the total cosmological nature of science, i.e. all that Humanity doesn’t know yet is conditioned by, it appears most relevantly and wholistically as SgrA. It can be said thus that all unknowns ($$x$$) in our space-time of observation are within “the great unknown ($$X$$) of SgrA, as thus $$x \in X$$ or $$x \mathcal{A} X$$ for the negative aspectual ($$\mathcal{A}$$) relationship “x is an aspect of X”. These are the relevant, and most general (i.e. universal) invariants to our existence of observation. They are the relative absolutes of, from, and for science. Within more practical scientific judgements from a cosmological perspective, the relevant aspects of variable unknowns are the planets within our solar system as conditioning the solar life of Earth. The Earthly unknowns are the second variable Y, or Di (地) for “earth.” They are the unknowns that condition the Earth, or life, as determining the changes in climate through their cyclical dynamics. Finally, the last unknown of conditionals, Z, refers to people, Ren (人) for ‘men,’ as what conditions their actions. X is the macro unknown (conditionality) of the gravity of ‘the heavens,’ Y the meso unknown of biological life in and on Earth, and Z the micro unknown of psychology as quantum phenomena. These unknowns are the subjective conditions of observation. Finally, the 4th variable is the “object”, or Wu (物), $$\mu$$ of measurement. This last quality is the only $real$ value in the sense of an objective measurement of reality, while the others are imaginary in the sense that their real values aren’t known, and can’t be within the reference of observation since they are its own conditions of measurement within “the heavens, the earth, and the person.” (Bréard, p.82)

In the quaternion tradition of Hamilton, ($$\mu$$, X,Y,Z) are the quaternions, ($$\mu$$, i,j,k). Since the real-values of X,Y,Z in the scientific sense can’t be known truly and thus must always be themselves unknowns, they are treated as imaginary numbers ($$i=\sqrt{-1}$$) with their ‘values’ merely coefficients to the quaternions $$i,j,k$$. These quaternions are derived as quotients of vectors, as thus the unit orientations of measurement’s subjectivity, themselves representing the space-time. We often approximate this with the Cartesian X,Y,Z of 3 independent directions as vectors, yet such is to assume Euclidean Geometry as independence.

## References

[1] E.T. Jaynes. “Complexity, Entropy and the Physics of Information”. In: ed. by W. H. Zurek. Wesley Publishing Co., 1990. Chap. Probability In Quantum Theory.

[2] Andrea Bréard. Nine Chapters on Mathematical Modernity: Essays on the Global Historical Entanglements of the Science of Numbers in China. Springer, 2019.


text: - On the use of the energy norm in trust-region and adaptive cubic regularization subproblems E. Bergou(el-houcine.bergoujouy.inra.fr) Y. Diouane(youssef.diouaneisae.fr) S. Gratton(serge.grattonenseeiht.fr) Abstract: We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called subproblem'' in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called the model". The latter is supposed to be adequate in a neighborhood of the current iterate. In this paper, we address an important practical question related with the choice of the norm for defining the neighborhood. More precisely, assuming here that the Hessian $B$ of the model is symmetric positive definite, we propose the use of the so-called energy norm'' -- defined by $\|x\|_B= \sqrt{x^TBx}$ for all $x \in \real^n$ -- in both TR and ARC techniques. We show that the use of this norm induces remarkable relations between the trial step of both methods that can be used to obtain efficient practical algorithms. We furthermore consider the use of truncated Krylov subspace methods to obtain an approximate trial step for large scale optimization. Within the energy norm, we obtain line search algorithms along the Newton direction, with a special backtracking strategy and an acceptability condition in the spirit of TR/ARC methods. The new line search algorithm, derived by ARC, enjoys a worst-case iteration complexity of $\mathcal{O}(\epsilon^{-3/2})$. We show the good potential of the energy norm on a set of numerical experiments. Keywords: Nonlinear optimization, unconstrained optimization, trust-region algorithm, adaptive regularized framework using cubics, line search algorithm, energy norm, Krylov subspace methods, conjugate gradient. Category 1: Nonlinear Optimization (Unconstrained Optimization ) Citation: ISAE-SUPAERO, Toulouse, France. Download: [PDF]Entry Submitted: 04/26/2017Entry Accepted: 04/26/2017Entry Last Modified: 04/26/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.

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How do I determine the inverse function?

I have this exercise;

For each of the following functions, determine the inverse function.

Here, $\mathbb{R}_{\geq 0}$ denotes the set of all non-negative reals:

$$f : \mathbb{R}_{\geq 0}\to\mathbb{R}, x\mapsto \sqrt{x}$$

But I really don't know where or how to start, could anyone provide some guidance on how to get an inverse function? maybe show some steps? Thank you so much

In general, if you have a function $y = f(x)$ and you want to find the inverse, then you want to rearrange $y = f(x)$ so that $x$ is a function of $y$.

For your example, observe that $y = \sqrt{x}$ so that $y^{2} = x$. Thus your inverse function is $f^{-1}(x) = x^{2}$.

It remains to determine the domain and range. We first note that $f : \mathbb{R}_{\geq 0} \to \mathbb{R}$ has the domain $\mathbb{R}_{\geq 0}$ and the range $\mathbb{R}$. However, the image of $f$ is the set of all elements in the range that are mapped to by $f$ from something in the domain. In this case, the image of $f$ is $\mathbb{R}_{\geq 0}$ (can you see why?). Thus, the domain of $f^{-1}$ will be this set, the image of $f$, and the range of $f^{-1}$ will be the domain of $f$ so that $f^{-1} : \mathbb{R}_{\geq 0} \to \mathbb{R}_{\geq 0}$. Hence the inverse function is $$f^{-1} : \mathbb{R}_{\geq 0} \to \mathbb{R}_{\geq 0},\quad f^{-1}(x) = x^{2}.$$

It is important that the domain of $f^{-1}$ is the image of $f$ otherwise, as drhab points out, one may have something like $$-1\stackrel{f^{-1}}{\to}1\stackrel{f}{\to}1\neq-1,$$ which is not what we want since we should have $f\circ f^{-1} = f^{-1}\circ f = \text{Identity map}$.

• Then $-1\stackrel{f^{-1}}{\to}1\stackrel{f}{\to}1\neq-1$ so no identity (as it should). – drhab Aug 22 '18 at 12:13
• @drhab Ah yes, let me fix that! – Bill Wallis Aug 22 '18 at 12:15

We have $f(R)=R$ and $f$ is injective.

$y= \sqrt{x} \iff y^2=x$, hence $f^{-1}:R \to R$ is given by $f^{-1}(x)=x^2$.

• What is $R$ here? If it is $\mathbb R$ then it is not correct. We get $-1\stackrel{f^{-1}}{\to}1\stackrel{f}{\to}1\neq1$. – drhab Aug 22 '18 at 12:14
• In the original post, the OP wrote $R$ instead of $\mathbb{R}_{\geq 0}$. – Fred Aug 22 '18 at 13:05

You can solve the question in the follwoing manner swap x and y then you will get a function $x=f(y)$ in terms of $y$ again swap x and y
$$y=\sqrt{x}$$ $$y^2=x$$ $$x=y^2$$ $$f^{-1}(x)=x^2$$

• Sorry for being stupid but does "f−1" denote that it's an inverse function? – ValentineJ Aug 22 '18 at 11:03
• yes $f^{-1}(x)$ is the inverse function of $f(x)$ – Deepesh Meena Aug 22 '18 at 11:03
• awesome, great explanation thank you – ValentineJ Aug 22 '18 at 11:04

The function $f:\mathbb R_{\geq0}\to\mathbb R$ prescribed by $x\mapsto\sqrt x$ has no inverse.

This because it is not surjective.

The function $g:\mathbb R_{\geq0}\to\mathbb R_{\geq0}$ prescribed by $x\mapsto\sqrt x$ is bijective, hence has an inverse.

It is the function $\mathbb R_{\geq0}\to\mathbb R_{\geq0}$ prescribed by $x\mapsto x^2$.

For finding this function see the other answers.

• At least be so kind to motivate your downvote. As long as you do not I will not take you serious (whoever you are). – drhab Aug 23 '18 at 17:12


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Drone with SDR for HF antenna field strength measurements, I need a Raspberry Pi based drone kit that I can just buy

I have very little time until I get to the USA to buy the material to put together a drone which I want to use to measure antenna gain patterns for HF radio. Example, a 20m band half-wavelength dipole antenna is 10 m wide and should be mounted 10 m above ground, probably it will have to be less. Additional parasitic elements of about 10 m wide spans are added around the main driven element to achieve directional gain.

The issue is measuring this gain for which one needs to get two wave lengths away and up all around the antenna assembly, which is easily 100 m all around. And for 40m, 80m, 160m band antennas it would scale accordingly.

The measurement device we would need to lift up is an SDR (software defined radio) device, which can be as small as a USB dongle, along with some small receiving antenna. The drone would fly around the transmitting antenna and would measure the antenna's gain pattern on a set of chosen frequencies and transmit power while we would be intermittently transmitting our call sign in Morse code like a beacon. Given the fact that it's an experimental antenna assembly, the drone should re-take the same flight path several times as we adjust the setup.

Since an SDR dongle needs to be plugged into a USB port of a computer running some Linux, the Raspberry PI comes to mind. And to avoid having to carry that as extra payload, I want to have a drone which has a PI as its main control and communication module.

I have seen several PI drone projects, dating as far back as 2016, but even after all that time I have not seen an affordable kit. It should be around $200, as even in 2016 a ZDnet article talked about a DIY PI drone in that budget. Since I have very little time to get the parts together while on a short visit to the USA before returning to South America where everything is twice as expensive, I would like to find something that I can just buy. Do you know of a kit or a state of the art shopping list that is based on a generic drone kit? [Hey Stack-Exchange police: this is not just a shopping question, it is a state of the art question.] What is the state of the art in Raspberry Pi drones now? Much has happened since 2016. How can I tell from looking at drone kits on Amazon for example, how much payload they are able to carry? This is not reported in the specs that I can see. I would like to avoid the RC gear and just use WiFi to control the drone and receive the telemetry data. • I'd assume that if I needed to clarify with a note why my question isn't too broad or off-topic, it probably is in some way. I'm having a hard time understanding what the crux of the question is, so I think it's probably too broad; try narrowing the scope. – ifconfig Jan 2 at 5:14 • I'd recommend trying to strip superfluous narrative structure and add diagrams if possible, to start. – ifconfig Jan 2 at 5:15 • There's quite a few reasons why a RPi isn't really an ideal platform for the real-time control of a drone so I'm guessing outside the odd DIY project every commercial project has used something more suitable. You're probably best focusing on the payload weight issue and treating taking the measurement as a separate issue, even if you did find a RPi based drone it wouldn't be safe to assume the SDR and navigation would work well at the same time. Jan 2 at 11:07 • I don't and I'm not saying it won't work, just that you'd only know for sure by testing it. Jan 2 at 22:56 • @ifconfig I think the deal is to use the flight controller, like a Pixhawk separately, and use the RPI to pass commands to it, such as passing manual RC inputs though that were received via WiFi. I thought I had seen this in out of the box drones: Drone + Camera + Computer --- Cellphone using WiFi (as hotspot or connecting to drone being the AP), and RC joystick connected via bluetooth or USB plugged to phone. I think that exists. The flight controller like Pixhawk would be separate. Jan 4 at 0:34 2 Answers This is very similar to a project I had in mind, also using an SDR for radio spectrum mapping. Unfortunately there is no ready-made solution to your exact problem, and specifically there are no entirely Pi-based drones that I know of. But we can get pretty close by releasing the constraints a bit. The simplest build would be an autopilot-equipped copter with an offboard SBC (e.g. the Pi) and an SDR dongle. The SBC would be linked to the flight controller via MAVLink or similar over UART, which would allow it to receive real-time position data and optionally send commands to the FC. The autopilot will then perform a waypoint mission uploaded either through the autopilot's ground station software or directly from the onboard Pi, sweeping around the antenna in a tight pattern, and the Pi will record and location-stamp the data. When the drone returns you could use some script of your own design to interpolate that log into a continuous spatial intensity map. This kind of solution is great in that you could use any waypoint-capable drone, as it only serves as a carrier for the mapping package, and the only integration you need is receiving GPS. You could even use a second GPS receiver in order to fully decouple the drone from the SDR package. Or you could go the other way and fully control the drone's behavior from the Pi via the link, the FC only providing the basics of flight and leaving the flightpath up to the Pi. For the hardware, use any copter capable of carrying a Pi, dongle and antenna. Fully equipped ardupilot-ready kits capable of carrying a camera can be had for around$200, for which you only need to supply your own battery (and, if you wish, a 2.4G RC control link, which I'd recommend, but you can make do with just the 433MHz groundstation link if you're so inclined).

If you want the Pi to be integrated more closely into the drone, there are several Pi-specific solutions that I know of, but they all involve an external microcontroller-based flight controller board. For instance, there's the Navio by Emlid, which is an Ardupilot-equipped flight controller made in the form factor of a Pi HAT. Then there used to be the Outcast Droneworks MicroHawk, a micro-drone that uses a Pi Zero as part of its body. The page for it is now unavailable, however, so I don't know the current status of the project. In any case, this is in essence the same as sticking a regular FC board and a Pi on the same frame and connecting them together, the only difference is the form factor.

For the autopilot package, Ardupilot, PX4 and INAV are the most popular. All three support MAVLink, and Ardupilot supports onboard Lua scripting in addition to that. There are others as well which you might want to research, but I'd suggest sticking with one of these.

Some parting notes:

I think it would be very beneficial to browse the forums of all of those autopilot packages for threads on mapping missions. Most of the information will likely be about photographic mapping in particular, and thus discuss way sparser patterns and bigger altitudes than what you need, but the principles are exactly the same.

Considering the required spatial resolution of your measurements, especially at shorter wavelengths, you should probably look into DGPS and RTK and maybe set up a local reference station of your own, which would allow you to improve the positioning accuracy dramatically (from ±5m to single centimeters or less).

Also you should mind the polarization of your receiving antenna, otherwise your resulting radiation map may be altered significantly by cross-polarization attenuation. Maybe you could use a circular-polarized antenna, set up several linear antennae on the same drone, or make several passes with the receiving antenna in different orientations relative to the transmitting antenna under test to account for that.

You might check out this video on using a Pixhawk and a rPi with Python. The video just walks you through the serial connection and some Python code for basic control. The Pixhawk is doing all the real time control (Linux isn't good for that part) and the rPi is talking to it over a serial port.

You might also look at the MicroHawk reference in: Do drones with inflight API access for control inputs exist? (although the link seems to be broken at the moment).

• Perhaps you could summarise the main points from the video in your answer. Link-only answers tend to be frowned upon on SE sites. Feb 9 at 19:58
• yeah, I had already mentioned this in my comment to the discussion. but I guess I upvoted the answer even if late ... hey, why not upvote my question also? I guess voting someone up costs very little. Feb 10 at 15:40


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Hi

I'm trying to distinguish between agents that have type mock and thos that don't. In the \BuildAgent\conf\buildAgent.properties file i have added the veariable typemock=True

In the Agent Requirements section of the Build configuration i specify syste.agent.typemock equals True. But it's not working.

Is this the right way to use the buildAgent.properties? obviously not.

Cheers

Alan


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https://dx.doi.org/10.1007/s11207-018-1385-3">

## Coronal Mass Ejection Research Group

#### Title

The Magnetic Field Geometry of Small Solar Wind Flux Ropes Inferred from Their Twist Distribution

#### Abstract

This work extends recent efforts on the force-free modeling of large flux rope-type structures (magnetic clouds, MCs) to much smaller spatial scales. We first select small flux ropes (SFRs) by eye whose duration is unambiguous and which were observed by the Solar Terrestrial Relations Observatory (STEREO) or Wind spacecraft during solar maximum years. We inquire into which analytical technique is physically most appropriate, augmenting the numerical modeling with considerations of magnetic twist. The observational fact that these SFRs typically do not expand significantly into the solar wind makes static models appropriate for this study. SFRs can be modeled with force-free methods during the maximum phase of solar activity. We consider three models: (i) a linear force-free field ($$\nabla\times \mathbf{B} = \alpha \mathbf{B}$$) with a specific, prescribed constant $$\alpha$$ (Lundquist solution), and (ii) with $$\alpha$$ as a free constant parameter (“Lundquist-alpha” solution), and (iii) a uniform twist field (Gold–Hoyle solution). We retain only those cases where the impact parameter is less than one-half the flux rope (FR) radius, $$R$$, so the results should be robust (29 cases). The SFR radii lie in the range $$[{\approx}\,0.003, 0.059]~\mbox{AU}$$. Comparing results, we find that the Lundquist-alpha and uniform twist solutions yielded comparable and small normalized $$\chi^{2}$$ values in most cases. This means that analytical modeling alone cannot distinguish which of these two is better in reproducing their magnetic field geometry. We then use Grad–Shafranov (GS) reconstruction to analyze these events further in a model-independent way. The orientations derived from GS are close to those obtained from the uniform twist field model. We then considered the twist per unit length, $$\tau$$, both its profile through the FR and its absolute value, applying a graphic approach to obtain $$\tau$$ from the GS solution. The results are in better agreement with the uniform twist model. We find $$\tau$$ to lie in the range $$[5.6, 34]~\mbox{turns}/\mbox{AU}$$, i.e. much higher than typical values for MCs. The GH model-derived $$\tau$$ values are comparable to those obtained from GS reconstruction. We find that the twist per unit length, $$L$$, is inversely proportional to $$R$$, as $$\tau\approx0.17/R$$. We combine MC and SFR results on $$\tau(R)$$ and give a relation that is approximately valid for both sets. Using this, we find that the axial and azimuthal fluxes, $$F_{z}$$ and $$F_{\phi}$$, vary as $${\approx}\,2.1 B_{0} R^{2}$$ ($${\times}10^{21}~\mbox{Mx}$$) and $$F_{\phi}/L \approx0.36 B_{0} R$$ ($${\times}10^{21}~\mbox{Mx}/\mbox{AU}$$). The relative helicity per unit length is $$H/L \approx0.75 B_{0}^{2} R^{3}$$ ($${\times}10^{42}~\mbox{Mx}^{2}/\mbox{AU}$$).

12-18-2018

Solar Physics

Springer

#### Digital Object Identifier (DOI)

https://dx.doi.org/10.1007/s11207-018-1385-3

Article

COinS


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ISSN : 2288-3509(Print)
ISSN : 2384-1168(Online)
Journal of Radiological Science and Technology Vol.38 No.3 pp.199-203
DOI : https://doi.org/10.17946/JRST.2015.38.3.02

# Reduction of Entrance Surface Dose Depending on Shielding Methods for Panoramagraphy

Jung-Hyun Choi, Sung-Chul Kim1), Dong-Kyoon Han
1)Department of Radiological, Science Gachon, University

교신저자: 한동균 (13135) 경기도 성남시 수정구 산성대로 553 을지대학교 방사선학과. Tel: 031-740-7245 / E-mail: handk@eulji.ac.kr 김성철 (21936) 인천광역시 연수구 함박뫼로 191 가천대학교 방사선학과. Tel:032-820-4364 / ksc@gachon.ac.kr
July 15, 2015 August 7, 2015 August 31, 2015

## Abstract

Panoramagraphy was the second most used intraoral radiography utilized in Korea, resulting in 17.8% in university dental hospitals, 24.8% in dental hospitals, and 31.4% in dental clinics. Depending on increased demand like orthodontics and implant, panoromagraphy tends to consistently increase.

This study were used lead glasses and lead shielding to reduce unnecessary radiation to the eyeballs and thyroid. ESD was 41.4% when radiation was shielded with the lead glasses while reducing 47.3% of ESD by shielding the X-ray tube area with shielding lead. There was no statistically significant difference. The lead glasses is appropriated to reduce unnecessary radiation exposure to the eyeballs.

# 파노라마 X선 검사시 차폐방법에 따른 Entrance Surface Dose 저감

최 정현, 김 성철1), 한 동균
을지대학교 대학원 방사선학과
1)가천대학교 방사선학과

## 초록

한국에서의 파노라마장치의 사용비율은 치과대학병원에서 17.8%, 치과병원에서 24.8%, 치과의원에서 31.4%로 구내촬영장치 다음으로 많이 사용하고 있는 검사 방법으로, 치아교정 및 인플란트 등의 수요증가에 따라 파노라마 검사는 지속적으로 늘어나고 있는 추세이다.

본 연구에서는 파노라마 검사에 불필요한 안구와 갑상선부위의 선량을 감소시키기 위해 납안경 및 납차폐체를 이용해 보았으며, 납안경으로 차폐를 한 경우 안구의 ESD가 41.4% 감소되었으며, X선관 부위 쪽을 차폐납으로 차 폐할 경우에는 ESD의 47.3%를 감소시킬 수 있음을 알게 되었다. eyeball의 불필요한 선량저감을 위하여 임상에서 는 lead glass를 사용하는 방법이 있으며, 제조사에서는 eyeball부위 피폭을 줄일 수 있는 제어장치를 적극 활용할 필요성이 있는 것으로 나타났다.

## I.Introduction

Pantomography was first developed in 1949 by Dr. Y. V. Paatero in Finland, and Panorex, the first panoramic radiograph, was introduced to the market in the U.S. The Orthopsntomograph, the first panoramic device, has furnished at Seoul National University in Korea since 19691).

For dental radiography, the important organs of the body such as the brain, eye lenses, and thyroid gland can be easily exposed to even small amounts of radiation. Therefore, radio technologists are required to have the ability to acquire accurate radiography technology, correctly understand the characteristics of radiation, and cope with safety management2).

According to the Ministry of Food and Drug Safety (MFDS), the diagnostic reference level3) of patient dose for panoramic radiograph is set as 110.9mGy·cm2 ; however, this reference dose value is based on the Dose Area Product (DAP) meter, so that there is no reference on the areas that are actually exposed to radiation. In addition, according to Choi and his colleagues4), radiation exposure to the eye lenses and thyroid gland, which are sensitive to radiation, was found to be very high, although these were not necessary when having an actual panoramagraphy. For a general panoramagraphy, the areas of visual interpretation include ramus of mandible and these areas cover from the upper infraorbitomeatal line to the lower hyoid bone5). However, with effort, it is possible for radio technologist to prevent unnecessary radiation exposure to the eyeball and thyroid gland. Also, there is no equipment that can control the exposure range of X-ray in panoramagraphy; thus, radiation exposure to the eyeball and thyroid gland can be more dangerous in children with a small head.

According to the Diagnostic X-Ray Equipment Regulation on Safety Management, use of a thyroid shield and lead apron is required when operating a dental panoramic imaging apparatus 6); however there is no regulation on a protective equipment that can shield against radiation exposure to the areas like eye lenses. Also, the previous researcher found that, there is no hospital equipped with the devices that can protected the eye lenses in Korea4).

Thus, this study measured the Entrance Surface Dose (ESD) at the thyroid gland, oral region, and eyeballs in a case of wearing lead glasses and thyroid gland protective gear, and a case of implementing a lead shield-used radiation exposure protective apparatus to assess the reduction of radiation dose.

## II.Equipment and method

The Optically Stimulated Luminescence Dosimeters (OSLDs) were used for measurement of radiation dose. The basic principle of OSLDs is similar to that of the Thermo Luminescence Dosimeter. Once ionized radiation is irradiated to optically stimulated luminescence, electron-hole pairs on the irradiated radiation dose are created and excited electrons that were created through such process are reunited with the hole and some are captured in the energy trap. When light with certain wavelength range is exposed to the captured electron, this captured electron can escape from the energy trap. The possibility of such escape is shown in the formula (1)7).

$p = Φ ξ$
(1)

In this formula, Φ is the intensity of photic stimulation and ξ is the photoionization cross-section.

Meanwhile, ξ(hv) is photoionization cross-section given by8).

$ξ hv = a E i hv − E i 3 / 2 hv hv − γ E i 2$
(2)

where a is a scaling constant, Ei is the optical threshold energy for ionization from trap i, and γ is related to the charge carrier effective mass.

The electron that escaped from the energy trap is recaptured in the trap or united and if the electron generates fluorescence at reunion, the amount of fluorescence is measured to determine the radiation dose. Al2O3:C (aluminum ox ide) i s used as t he o ptically stimulated luminous substance. Its effective atomic number is 11.289), thus it is very sensitive in dosimeter and since the energy difference between conduction band and valance band is large, with 9.5 eV, the energy trap is stably maintained at room temperature7).

Due to such characteristics, the Optically Stimulated Luminescence Dosimeters (OSLDs) that enable measurement from low to high dose, nanoDots and Microstar reader ( Landauer Co. Ltd., USA) were used in this study. Before conducting the experiment, the background value was measured in advance after annealing for 30 minutes using the annealer system (HA-OA001, Hanil Nuclear Co.) and the values that subtracted the background value from the measured values were used for the dose value.

For the lead glasses, 0.7 mmPb lead equivalent (HF- 400S, TORAY) was used whereas 1.0 mmPb lead equivalent was utilized for the thyroid gland protective gear (Fig. 1(a)). For the experiment, a total of 7 nanoDots were used, including the left & right eye lenses and thyroid gland of the Skull Phantom (76-018, Nuclear Associates) and left & right maxillary first premolar. As for the panoramagraphy, Carestream CS-9000 was used and the experimental condition was limited to panoramagraphy to adult men with 70 kV, 10 mA, 14.3 sec. for three times. Then, the average value of three trials was used.

The position of the lead glasses was from the dental root area of the maxillary dentition to infra-orbital groove that did not affect visual interpretation of the maxillary to shield the intended area, and, regarding the lead plate that was used to limit the irradiation range, the lead plate with 1.0 mmPb lead equivalent was used and placed at the front part of the X-ray target area (Fig. 2(a)). After performing panoramagraphy, including the entire mandible and temporomandibular joint, it was verified by a dentist as there was no issue caused for the visual interpretation on panoramagraphy (Fig. 1(b), 2(b)). After the experiment, the ESD of each area in case of shielding and not shielding was compared and the Mann-Whitney U test was performed using SPSS for Windows version 22 to determine statistical significance between the experiment groups.

## III.Results

In the case of not shielding, the ESD of the left and right eyeballs were measured to be 72.96 μGy, 54.97 μGy, and 63.96 μGy, on average, whereas that of the oral region was an average of 22.56 μGy. ESD of the thyroid was 20.97 μGy on average. In the case of using the lead glasses and thyroid gland protective gear, the average ESD was 37.45 μGy in the eyeballs, 21.86 μGy for the oral region, and 12.94 μGy for the thyroid. Compared to the case of not shielding the areas, the ESD of the eyeball decreased 58.6% and that of the thyroid decreased 61.7%.

Also, when the shielding lead to limit the exposure range of X-ray was used, the average ESD for the eyeball was 33.73 μGy while it was 23.18 μGy for the oral region and 13.83 μGy for the thyroid. Likewise, ESD of the eyeball was measured to be 52.7% less in the case of no shielding (Table 1). Regarding the statistical significance between shielding and not shielding, no significant difference was found (Table 2, 3).

## IV.Discussion and conclusion

According to Shin and his colleagues2), panoramagraphy was the second most used intraoral radiography in Korea, resulting in 17.8% in university dental hospitals, 24.8% in dental hospitals, and 31.4% in dental clinics. Depending on increased demand such as orthodontics and implant, use of panoromagraphy tends to consistently increase. In the case of general X-ray machines, the device that limits the exposure range of X-ray is installed; however in the case of panoramagraphy, there is no additional device that limits unnecessary radiation exposure. Therefore, it is considered necessary to implement a controlling that can at least reduce the dose to the eyeballs.

Kim 10) attempted to reduce the dose amount to the eyeballs using lead bending, but, since it was difficult to decide the exact position to be shielded with such lead bending, an issue was raised on the shielding of necessary areas for X-ray. Therefore, this study intended to examine the efficacy of shielding using lead glasses, but, since panoramagraphy generates radiation by rotating X-ray, its shielding effect was not impressive. However, if radiation generated in the X-ray tube is limited, the shielding effect can be maximized as it showed the temporomandibular joint with the infra-orbital groove and the entire mandible 11).

This study shielded to reduce unnecessary radiation to the eyeballs. Although there was no statistically significant difference, the ESD was decreased 41.4%(37.45 μGy) when radiation was shielded with the lead glasses while it decreased 47.3%(33.73 μGy) when shielding the X-ray tube area with shielding lead. Use of the lead glasses to reduce unnecessary radiation exposure to the eyeballs is appropriate; however, it seems to be more effective for controlling the range of radiation generation at the X-ray tube area because of the characteristic of panoramagraphy that generates radiation by rotating x-ray. In addition, it is necessary for manufacturers to actively utilize devices that can control the extent of radiation exposure around the eyes.

## Figure

Experiment arrangement of the lead glasses & thyroid gland protective gear

X-ray image using the lead glasses & thyroid gland protective gear

Experiment arrangement of the X-ray shielding & thyroid gland protective gear

X-ray image X-ray shielding & thyroid gland protective gear

## Table

ESD of each area depending in shielding method

Mann-Whitney U test for not shielding and lead glass & thyroid protector

Mann-Whitney U test for not shielding and Pb that limits unnecessary radiation exposure & thyroid protector

## Reference

1. Kim EK (2011) Use of radiation in the field of dental history and facts , Radiation health Newsletter. Korea National Institute of Food and Drug Safety Evaluation, Vol.18 (4) ; pp.1-4
2. Shin GS , Kim YH , Lee BR (2010) The Actual State and the Utilization for Dental Radiography in Korea , J. of Radiological science and technology, Vol.33 (2) ; pp.109-120
3. Korea Ministry of Food and Drug Safety (2013) Radiation safety management series No.34 , Pediatric Patient dose in General Imaging inspection recommended guidelines,
4. Choi Junghyun , Kim Sungchul , Han Dongkyoon (2014) Study on Entrance Skin Dose at Panoramic radiography in Incheon, Korea , Journal of radiation protection, Vol.39 (4) ; pp.182-186
5. Kang HI , Kim ST , Kim JM (2013) Radiation for dental Imaging , Daihak Pub, pp.195-196
6. The Ministry of Health decree No.291 (2015) Diagnostic x-ray equipment regulation on safety management,
7. Akselroda MS , BZtter-Jensenb L , McKeever SWS (2007) Optically stimulated luminescence and its use in medical dosimetry , Radiation Measurements, Vol.41 (1) ; pp.78-99
8. Von Whitley H , McKeever SWS (2000) Photoionization of deep centers in Al2O3 , Journal of applied physics, Vol.87; pp.-249
9. Bos AJJ (2001) High sensitivity thermoluminescence dosimetry , Nuclear Instruments and methods in physics reach B, Vol.184; pp.3-28
10. Kim CG (2013) Exposure dose Reduction using Pb Banding of own manufacturing , The Journal of Digital Policy & Management, Vol.11 (6) ; pp.269-273


text:
# Have minipage take up entire page height

I'm trying to use a minipage to create a kind of sidebar for my document. Because the minipage has a background color and because the document is intended for viewing rather than printing, I want the minipage to butt right up against three edges of the page (top, left, and bottom).

Here's what I came up with:

\documentclass[10pt]{article}

%\usepackage{showframe}
\usepackage[landscape]{geometry}

\geometry{top=0cm, bottom=0cm, left=0cm, right=0cm}

\definecolor{sidebar}{RGB}{71,62,136}

\setlength{\parindent}{0pt}

\begin{document}

\noindent\fcolorbox{sidebar}{sidebar}%
{%
\begin{minipage}[t][\textheight][t]{0.2\textwidth}
\color{white} % White text
\LARGE Hello

\end{minipage}%
}

\end{document}

However, the minipage is offset slightly from the top of the page, which consquently makes it bigger than the page. Therefore, it is placed on page 2 instead of 1 and still renders offset from the top of page:

How can I get the minipage to butt right up against all three edges?

## 3 Answers

The problem is caused by the \topskip glue, \fboxsep and \fboxrule parameters. Here is an example that works, with exaggerated \fboxsep and \fboxrule values for illustration purposes:

\documentclass[10pt]{article}
\usepackage{xcolor}
\usepackage{calc}
\usepackage[landscape]{geometry}

\geometry{top=0cm, bottom=0cm, left=0cm, right=0cm}

\definecolor{sidebar}{RGB}{71,62,136}

\setlength{\parindent}{0pt}
\setlength{\fboxsep}{10pt}
\setlength{\fboxrule}{20pt}

\begin{document}
\setlength{\topskip}{0pt}

\fcolorbox{black}{sidebar}%
{%
\begin{minipage}[t][\textheight-2\fboxsep-2\fboxrule][t]{0.2\textwidth}
\color{white} % White text
\LARGE Hello

\end{minipage}%
}

\end{document}

The gray color in this screenshot is from the ”behind-page background” displayed by my PDF viewer; it doesn't belong to the page but shows that the \fcolorbox completely fills the page.

Here is a similar example with normal \fboxsep and \fboxrule values, and two identical pages in order to illustrate how to set and restore \topskip to its default value (see below):

\documentclass[10pt]{article}
\usepackage{xcolor}
\usepackage{calc}
\usepackage[landscape]{geometry}

\geometry{top=0cm, bottom=0cm, left=0cm, right=0cm}

\definecolor{sidebar}{RGB}{71,62,136}

\setlength{\parindent}{0pt}

\begin{document}
%\bgroup
\setlength{\topskip}{0pt}

\fcolorbox{sidebar}{sidebar}%
{%
\begin{minipage}[t][\textheight-2\fboxsep-2\fboxrule][t]{0.2\textwidth}
\color{white} % White text
\LARGE Hello

\end{minipage}%
}
\newpage
%\egroup

\fcolorbox{sidebar}{sidebar}%
{%
\begin{minipage}[t][\textheight-2\fboxsep-2\fboxrule][t]{0.2\textwidth}
\color{white} % White text
\LARGE Hello

\end{minipage}%
}
\end{document}

Uncomment the \bgroup and \egroup calls to restore \topskip to its normal value after the first page has been shipped out; then you'll see

Overfull \vbox (1.6pt too high) has occurred while \output is active [2]

for the second page, as expected. The following screenshot was taken in this situation; the first page has \topskip=0pt, while on the second page, it has its default value of 10pt (which can be seen with \showthe\topskip after the uncommented \egroup command):

Notes:

• \topskip is glue added between the top of the page (according to the margins) and the baseline of first box on a page. The height of the first box is withdrawn from \topskip to compute the glue automatically inserted by TeX; moreover, the inserted glue is set to zero in case the result would be negative—i.e., when the first box is higher than \topskip.

• Your example is missing xcolor.

If you are OK with loading tikz you could do

\documentclass[10pt]{article}
\usepackage{tikz}
%\usepackage{showframe}
\usepackage[landscape]{geometry}

%\geometry{top=0cm, bottom=0cm, left=0cm, right=0cm}

\definecolor{sidebar}{RGB}{71,62,136}

\begin{document}
\begin{tikzpicture}[overlay,remember picture]
\fill[sidebar] (current page.north west) rectangle
([xshift=0.2\paperwidth]current page.south west);
\node[anchor=north west,text=white,font=\LARGE] at (current page.north west)
{Hello};
\end{tikzpicture}
\end{document}

In my opinion the best way to compose such boxes is to use the package textpos. It is tailor made for this purpose, and does not interfere with other material on the page, and you can have normal margin for the rest of the text. If you want the box on every page, you place the textbox in the header by redefining the page style.

So easy:

\documentclass[a4paper, 10pt]{article}

\usepackage{showframe}
\usepackage[landscape]{geometry}
\usepackage{xcolor}
\usepackage[absolute]{textpos}
\setlength{\TPHorizModule}{\paperwidth}
\setlength{\TPVertModule}{\paperheight}
\TPGrid[0mm,0mm]{10}{10}                        % Divide page in 10x10 grid

\geometry{left=6.5cm}                           % with textpos you can have normal margins

\definecolor{sidebar}{RGB}{71,62,136}
\textblockcolour{sidebar}
\begin{document}

\begin{textblock}{2}(0,0)                       % Box is 0.2 paperheight place in upper left corner
\rule{0pt}{\paperheight}                        % Zero width rule to show the box
\end{textblock}

\end{document}

NB! The gray border is the background, not a border around the page


text:
# Integration with Trigonometric Functions

Calculus Level 3

Given $$\displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}$$, where $$a, b$$ and $$c$$ are positive integers and $$b$$ and $$c$$ are coprime, what is the value of $$a + b + c$$?

×


text:
Volume 22, issue 2 (2018)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Long-time behavior of $3$–dimensional Ricci flow, C: $3$–manifold topology and combinatorics of simplicial complexes in $3$–manifolds

Richard H Bamler

Geometry & Topology 22 (2018) 893–948
Abstract

In the third part of this series of papers, we establish several topological results that will become important for studying the long-time behavior of Ricci flows with surgery. In the first part of this paper we recall some elementary observations in the topology of $3$–manifolds. The main part is devoted to the construction of certain simplicial complexes in a given $3$–manifold that exhibit useful intersection properties with embedded, incompressible solid tori.

This paper is purely topological in nature and Ricci flows will not be used.

Keywords
$3$–manifolds, simplicial complexes in $3$–manifolds, geometrization of $3$–manifolds, combinatorial geometry
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53C44, 57M15