Chapter 1: School Days
Rockwick, Highoak.
Jasmine Berry adjusted her glasses in her reflection until she was satisfied followed by double checking her green eyeglasses straps which complimented her green t-shirt. She leaned back and checked her outfit for the day. A green t-shirt and blue jeans and tennis shoes.
The hazel eyed girl with shoulder-length brown hair kept in two pigtailed braids twirled in front of the mirror and checked herself out. She beamed. Finding her outfit more than acceptable for the current day. Spring Break had been perfect for recharging her batteries and hanging out with her friends but now it was back to school and there would be no rest until Summer Vacation in a couple of months and then she could really party with them.
But that was for the future. Right now, School had to get ready for her. She grabbed her bag and bounded out of her room and down the stairs.
After enjoying breakfast, Jasmine hurried out of the house to the bus stop. Their little town of Rockwick was an amazing jumble of different styles: rickety wooden shops, marble and brick houses, huge stone churches. Everything had been beaten down and baked by the sun - and sunlight was everywhere: in the dust, in the vivid colors, in the smells of spices and overripe fruit. The town was a maze of narrow winding streets, as complex as the heart. A wild and winding whose floor pattern must have been designed by a crazy person and yet the inhabitants of Rockwick had learned to navigate it. The chaos had a method to it and once you learned to navigate it, it was plenty of fun. Plus they enjoyed the occasional laugh around newcomers to the town who kept getting turned around and confused by the layout of the town.
After navigating the twisting turns of the town, she finally arrived at the bus stop where her friends were relaxing. Misty Pendleton, Brian Palmer and Ada Caldwell. "Hey guuuuuys!" Jasmine called out to them while waving wildly. They looked up and cheered and waved back.
"About time you got here! Were trying to sleep in?" Misty teased. Misty is young woman of average height with long light-blonde hair she kept tied in a long ponytail, healthy tanned skin and she has blue eyes like the sea. She's wearing a white Nirvana T-shirt and Cream Colored Boho Cropped Skinny Jeans with gray thigh high socks, and red Mary-Jane Shoes.
They high-fived up high and down low and then walked back over to the bus stop.
"Not even close! I just had to navigate a maze that's all. I don't live quite as close to the stop as you do."
"Hmph. Excuses are like derrières, darling." Misty scolded her.
"True but some... derrières are nice and slappable." Jasmine fired back with a smirk.
"That is also true but please do mind your manners. We are proper ladies after all."
"Still staying in character for the play I see."
She placed a hand on her chest and then she extended her other hand while gesticulating dramatically. "I am a proper actress after all. I have no choice but to immerse myself in my roles if I am to ever walk the fabled Red Carpet!"
"You are aware that Hollywood is full of a-holes right?" Brian asked her. You can't help but compare this gentleman to a glorious phoenix. His wide eyes are turquoise and gleam mysteriously. He has shoulder length, straight, bright red hair that is styled in a way reminiscent of a Robin blowing in the wind. His body is notably sleek. He's wearing an orange t-shirt, black jeans and dark shoes.
"Quiet you. Do not design to tread upon my dreams!"
"Can and will." He joked with her.
"Never change, you guys." Ada laughed. This buxom young lady in the Splendid Roller Rugby Tee and a Skort puts you in mind of a dignified swan. She has coffee-colored eyes. Her luxurious, straight, dark hair is long and is worn in a utilitarian, businesslike style. She is tall and has a leggy build. Her skin is pale and she has knobby ears.
"I wouldn't dream of it." Misty smiled.
The crew joked around until the bus rolled up and they filed in. While it was driving them to school though, Jasmine kept her eyes peeled outside the whole ride. "Where are you?"
"Still looking for her huh?"
"I haven't seem Clementine all week! Didn't you notice that? Even discounting the fact that our town is designed like a maze, she just disappeared during Spring Break and she never takes the bus. We only see her at school, she's closed off and I want to know why. I want to get to the bottom of her mystery."
"Clementine Kane is an introvert. What's wrong with that?" Brian reasoned.
"Nothing." Jasmine replied. "But I want to know. I'm fresh off of Spring Break, my batteries are recharged and I want to solve a mystery."
"Okay and?"
"And I'm dragging you guys into it with me."
"I mean, is it even necessary?" Ada asked her. "So she's slightly enigmatic and her socks never match, what's the big deal? Just because she's quiet is no reason to stalk her or anything. If you have to ask her something, why not just straight up talk to her?"
"I know what you're saying, but she's always walking around with those earbuds in or working in the library and she disappears during lunch. Seriously. People have seen it. She grabs her food, bounces and then she comes back around the corner after lunch is over. Just like how she disappeared during break. Where does she go? What's her story? I want to get to know her so I can stop going crazy over this."
"Clementine...Clementine...wait, isn't she the shy girl with the earplugs and the socks? Wears a skirt? Freckles?" Brian asked.
"That's her. You know her?"
"Not too well. I've heard she's taking all of the AP Classes though so she's probably a Brainiac. I bet those earbuds are like books on tape or something."
"Maaan if she's taking all of those her family must be loaded." Ada drummed her fingers on the seat. "The courses are free but the tests aren't. They can charge you up to $92.00 for those. Depending on her hours, they could be racking up $644.00 or more. Not to mention figuring out how many tests each class would give you over the course of a year and if she's taking them every year that could get out of control fast. According to salary data for farmers, ranchers and other agricultural managers from May 2016, the average salary is $75,790 a year. In contrast, they make a median salary of $66,360, with half getting lower salaries and half being paid more. They must have some crazy good products if they're able to afford it year after year."
"Mayhap they are selling that dreadful Tomacco plant like those awful Brannons?" Misty questioned in a joking manner.
"Thankfully. Nobody's seen those creeps after they were ran out of town and their crops were destroyed. She must come from money."
"I dunno. I figure if somebody in Rockfort was rich, we'd know about it."
"We won't know until we ask and I think that's the best way to do it. If we see her in the hallways we can ask her to hang out with us if she gets some free time. Quick, clean and simple."
"Huh. Okay yeah that's way easier. Lets just do that."
They got comfortable in their seats while the bus navigated their quiet little, crazily designed mazelike labyrinthine mountain town until they reached their school and the driver parked so they could file out.
The school's design was suitably bizarre fitting with the design of the rest of the town. It looked like bigger than normal school building mixed with the Selfridges Building's design, with a steel framework and sprayed concrete façade, all in a shape resembling a spider. It was a little strange to an outsider and indeed most citizens of Rockwick were surprised whenever they first laid their eyes upon it but it grew on you as you got used to it. Despite it's bizarre exterior the interior was nice clean and modern. The design was intended to put you at ease as you wondered the halls of Rockwick High in comfort with navy blue diamond carpeting, nice clean hallways and classrooms, comfortable chairs, spacious lockers, good lighting and more! Rockwick High was a very nice place to attend school if you could get over how weird it looked outside and how weird it could be to navigate before you get used to it.
As the students filed in from the various school buses and their parents dropping them off or the bikers riding up to it, Jasmine kept an eye out for Clementine. It took awhile to pick her out of the crowd but she eventually spotted her rounding a corner. She was wearing her usual outfit. A black jacket over a white blouse with buttons, black fingerless gloves and a dark pleated skirt, mismatched socks and black and white shoes. She has short, layered, hair and freckles across the bridge of her nose. Her hair is more rosewood than black walnut, more like fresh chestnuts with their glossy skins in autumn light. She has a tall and skinny almost lanky figure of average height and yet she's carrying her big heavy backpack like it weighs nothing. She had her white and gold earbuds in as she casually navigated through the waves of people like they weren't even there!
Jasmine smiled. Time to make a new friend.
It took a bit of effort for Jasmine to catch up to her due to Clementine simultaneously power walking and expertly navigating the crowded hallway. Even with all of the students coming and going from all sides she casually navigated around them so fluidly it was like she was a ghost. Thankfully once the crowd cleared up a bit Jasmine was finally able to catch up with her and she started power walking next to her. She was still having trouble keeping up but she was close enough to be able to get her attention. "Hi there!" Jasmine greeted. She didn't hear her over her music though so she tried again and waved to her. "Hello!" She waved. "Hi, I'm Jasmine! I don't think we've met or anything, we don't have any classes together, but I thought I'd take the chance to get to know you today right? So, ah, I'm Jasmine and you're...you're Clementine right?" She asked her.
Clementine finally noticed Jasmine and looked around before pointing at herself. Jasmine nodded and offered her hand. "I'm Jasmine Berry."
Clementine slowly took out one of the earbuds and Jasmine noticed it was almost like was bracing herself before she answered. "Hello?"
"Hiya. I'm Jasmine Berry!"
"Oh. Okay. I'm Clementine Kane."
"Nice to meet you, Clementine." She offered her hand until Clementine reached out and gently shook it.
Jasmine noticed how light her handshake was. It was gentle. Like you were shaking hands with a baby. She also looked a little nervous when reaching out but she still went through the handshake regardless. "Hello."
"Hi. I've noticed you around school before but I don't think we've officially met. You're in different classes then me and all so we obviously haven't had the chance so here I am introducing myself to you now." She explained. "So, uh, anyway, hi again. What are you listening to?"
"Oh right. This is...Luna Lazarus's lectures."
"Luna Lazarus? The Super Super Genius from Rosewater?"
"Yes."
"Man oh man you can actually keep up with her lectures? I tried to but it was way too advanced for me." Jasmine confessed.
"Yes. It's very advanced but I can understand it. Her work on biology, medicine, computer science, physics, electronic engineering, neurology, psychology, and genotype interactions are impressive. To say the least and I enjoy listening to her lectures. They're soothing and thought provoking."
"Seriously? So is she like an expert in everything?" Jasmine asked incredulously.
"As I understand it, she's an expert in all fields of science and can speak and write all languages flawlessly without exception." Clementine replied casually. "She's certainly very impressive. But she doesn't go here and we do. So can I help you with today?"
"Well, to be honest, I thought you looked lonely and I haven't seen you around in awhile or hanging out with anyone so I thought I'd extend an olive branch."
"Oh thank you. You're very kind." She glanced at a clock. "However, we should probably hurry to our classes, Jasmine."
"Right, yeah, of course. I hope I get a chance to introduce you to my friends later. See you later, Clementine."
"I would like that. Thank you." She replied. "I'll see you later, Jasmine." She put the bud back in her ear and disappeared into the crowd.
"That went well. That went really well." Jasmine told her friends as they caught up with her.
"Well? Analysis?"
"She's cool. It turns out she's just shy. We just have to ease her out of her shell." Jasmine assured them as she walked to class with her friends. "It turns out she's a Lazarus fan."
"Really?"
"Yeah. You were actually right about the books on tapes thing. She's been listening to her lectures and even better? She can actually keep up with them."
"Woah seriously?" Brian asked. "I think she's cool too but I got lost in those lectures...and her eyes."
Misty ruffled his hair in response. "She is so, so far out of your league, she's in another galaxy playboy."
"Don't give up on your dreams, Brian!" Ada cheered him on.
"Don't encourage him."
"I'm the wing-girl. I encourage my homies. Speaking personally however, I have my eyes on someone waaay more exotic."
"Oh? And who would that be?"
Ada pointed to a poster someone had placed on a wall.
"Ohhhhhh him huh?" Brian asked. "You really think he's real? Or...she? Or whoever this guy is?"
"Could be? How else do you explain what happened to those people?"
"An excellent question for another time. We have got to get to class." Jasmine reminded her friends. "Going to be one hell of a Lunch Topic either way."
"We'll hold you to that. In the meantime, I want everyone to form theories and whomever comes up with the craziest one wins a prize." Brian offered his friends.
"As for said prize, we'll come up with that when we get there." Ada joked and the friends parted to their respective classes.
"So...like, I don't know whether The Raincoat is a robot or something else entirely, but I do know that he or she was able to carve the Greek Letters χῖ and ϰ carved into a metal truck trailer. Falling rubble wouldn't just do that no matter how many rocks fell down on the truck. They might wreck the trailer sure but there's no way that falling rocks would coincidentally do that kind of damage to a truck. Something else happened there."
"Like what? Like there's some kind of superhuman out there?" Brian asked her in disbelief.
"I don't know. Maybe? It's the only explanation I can come up with. Seriously what else would do that to a truck?"
"Okay, but, supposing that, if there really is a superhuman out there, why not use their powers to make money and get rich like a sane person?"
"Maybe he or she isn't interested in that. Besides, if The Raincoat did go public, you just know the government would go after him to cut him up and dissect him to find out how his powers work."
"Seriously, Jazz? You of all people are drinking the conspiracy-aid?" He chuckled.
"I mean...when you look at the dimwits in charge...I'm just saying!"
"That's fair. Anyway, I'll catch you later!"
"We can bring this back up at lunch!" She promised and walked away.
Jasmine arrived in her math class and took her notebook and math homework out as she prepared for the lecture.
"Psst, hey Jazz, you hear about The Raincoat?" A student asked from behind her.
"Yeah, he's all everyone's talking about lately, Benny. It's crazy right?"
"Crazy is right. I heard he's an alien robot and he's preparing the planet for invasion." Benton 'Benny' Hobbs was a lean and tall student wearing a green t-shirt and grey pants with messy light brown hair and hazel eyes. He was well known as one of the most easygoing and laid back students at the school.
"Heh, who knows? You might just be right about that. It would explain his super powers." She reasoned. "Hey, you think his spaceship talks to him too?'
"Oh yeah. It tells him to take the world and seduce the beautiful women."
"An alien sex mission? Really?"
"Hey, if Kirk can go out into space to seduce green women, there's no reason that aliens can't come here to do the same."
"Gross. But fair."
"Heads up guys!" Another student called to them as the door opened up and their teacher walked into the room. Well, not so much walked in as...moonwalked into the room in her usual fashion. Because one thing the class had learned about Miss Sofia Snyder is that she never did anything normally besides her outfits. She wore an all white skirt-suit with blue leggings and shoes with her chocolate brown hair tied in a short ponytail. Her eyes were framed by black framed glasses.
Miss Snyder moonwalked into the room and danced over to her desk before stopping and taking out her headphones and turned off her phone. "Hello again class! Welcome back to Advanced Geometric Algorithms! I'm super happy to see you all back here again and I hope you're all rested up, bright eyed and bushy tailed from break because I'm going to put you through your paces kids! But first, if you would all pass your Spring Break Homework up to the front desk of each row so I can collect them and assign any bonus points you earned!" She called to them all in a singsong voice.
Everyone who completed the Extra Credit Spring Break Homework Assignment passed the papers up to the front desk in front of them until the pile reached the front desks of each row where she gathered them and placed them in her desk for later grading.
"Thank you much kids! I'm so happy to see you're taking your education seriously! Now, if you will take your textbooks out and turn them to Chapter 3, we can begin today's lecture!" Miss Snyder informed them cheerfully.
The students did so and she did a spinning pirouette before striking a disco pose and she began writing on the board while beginning her lecture.
"The proteomic research deals with the systematic analysis of complete profiles of the proteins expressed in a given cell, tissue or biological system at a given time. In this field, 2D–gel electrophoresis
(2–DE) is a well–established and widely used technique to separate proteins in a sample. A 2–DE gel
is the product of two sequentially performed separations in acrylamide gel media: isoelectric focusing as first dimension and a separation by molecular weight as second dimension. The result of that
process is a 2D pattern of spots each representing a protein. There is a variety of staining methods to
display protein spots: Coomassie blue and silver-staining and / or fluorescent and radioactive labeling. Mass spectrometry and the visual (usually computer aided) comparison (matching) with already
analyzed gel images of such a sample are used to identify proteins. The visual analysis of such 2–
DE image series intends to identify those proteins that change their expression (size, intensity) and
reflect/cause certain biochemical and biomedical conditions of an organism, see [26]. However, this
Computer Science Department, University of Arizona, email:alon@CS.Arizona.EDU
y
Institut f¨ur Informatik, Freie Universit¨at Berlin, Takustr. 9, D-14195 Berlin, email:name@inf.fu-berlin.de
z
Deutsches Herzzentrum Berlin, Augustenburger Platz 1, D-13353 Berlin
x
Supported by Deutsche Forschungsgemeinschaft, grant FL 165/4–2.
{
Supported by Deutsche Forschungsgemeinschaft, grant AL 253/4–3.
1
requires high throughput analysis tools and the major challenge is to obtain both robust and reliable
algorithmic solutions that work automatically, or at least need only little user interaction. As we
will see, this goal in conjunction with efficiency requirements makes it necessary to start with simple
(sometimes oversimplified) modelling assumptions.
A second strand of research was initiated in [22]. Here the challenge consists of creating analysis
software that is able to perform interlaboratory gel image comparisons and to deal with images from
various databases via the Internet.
The intensive research on these questions emphasizes the strong demand from the practitioners
for better algorithmic solutions.
The aim of this paper is to demonstrate how ideas from computational geometry help to meet
these challenges in the context of the two most basic problems in gel analysis: Spot detection: Given a scanned 2–DE gel image identify spot regions. Gel matching: Given two images by their spot lists, perform a matching procedure to identify
those spot pairs that correspond to each other, so that the matching reflects both geometric and
spot intensity resemblance of the images.
In this paper we survey algorithmic studies and implementation work that was done while developing
the 2–DE analysis software system CAROL ([9]). It contains both new results (Section 2, Subsection
3.4) and partly published ones (Section 3, [17]). Interestingly, this application problem has also lead
to new theoretical questions in geometry.
In Section 2 we address the spot detection question in the following context. Originally the
CAROL project was designed to answer only matching queries for gel images. It turned out that
available spot detection algorithms did not adequately support the underlying philosophy that is based
on the similarity of geometric point patterns. Thus the spot detection approach presented here aims
at determining the point pattern of a gel as precise as possible rather than computing exact shapes
and volume data of spots. We assume that each spot has approximately the shape of an axis-parallel
ellipse. This is a widely accepted, but surely simplified, modeling assumption, see for example [5] or
[14]. However, spots that are very close to each other may partially overlap and “merge”. This can
lead to rather complicated local pixel regions, as depicted in Figure 1, compare [20].
In [23] a spot detection algorithm is described that relies on a watershed transformation applied
to the gradient image. The most difficult part is the interpretation of twin spots, streaks (left side
in Fig.1), and so–called complex regions (right side in Fig.1) as unions of ellipses. This especially
applies to the case of oversaturated regions in silver stained gels.
Figure 1: Twin spots, streaks, and a complex region
In fact, in [23] the latter case of interpreting complex regions was left open and in the implementation
the user had to edit these complex regions by hand. Here we present an algorithmic solution to this
2
question based on a Linear Programming (LP) formulation. To the best of our knowledge it is the first
algorithmic attempt to deal with spot detection of complex oversaturated regions in a single image.
An alternative approach has been studied in [6], where the information of multiple already aligned
images is used for a subsequent spot detection.
There is an inherent uncertainty in the images due to the electrophoresis process itself which is
highly susceptible to faults and geometric distortions. The reader may argue just by looking at the
images, that there is no hope to come up with a perfect spot detection algorithm. This is certainly true.
Yet we can cope with this ambiguity, at least to some extent by computing a ranked list of proposals
how a complex region could be covered instead of computing only the “best” covering, which could
be erroneous. Then, in the matching algorithm, we have the possibility to accept the matching of two
ambiguous regions if there is a pair of proposed coverings that match.
The matching algorithm itself is described in Section 3. Assume that a source and a target image
are given by their spot lists. We first transform the lists into geometric point patterns, where a spot is
represented by the ellipse center coordinates and additionally we code the real size/intensity of the spot
into a single integer value. The lists can be of significantly different size and, additionally, we allow
the images to show only partially overlapping sections of the gels. Thus the task is to find a maximal–
cardinality one–to–one matching of the spot lists, so that this mapping respects both the geometry of
the images and the relative spot intensities i.e., relatively intensive source spots should be mapped to
relatively intensive target spots. The geometric matching criterion is based on similarity of imaginary
edges which link spots. Two edges are similar if their length ratio and the difference of their angles
formed with the x–axis are within preset tolerance bounds. Our algorithmic solution, which we call
global–via–local matching, works in two stages. Firstly, we compute matchings for several small local
patterns, which are chosen in a grid–like fashion. For this local matching we use a modified alignment
method known from point pattern matching ([2]) combined with geometric hashing. A significant
speed–up is gained by reducing the set of all source / target edges to those belonging to the history
of the incremental Delaunay triangulation of the spot lists in the order of their decreasing intensities.
Having sets of matching candidates for each of the local patterns, we select a subset that is consistent
with the overall grid topology. The matching spot pairs computed this way later serve as “landmarks”
in the second stage. Landmarks were also used in previous algorithmic solutions, but they had to
be set manually. The novelty of our solution is to generate them automatically. The subsequent
extension from landmarks to a maximal global matching is rather standard by local neighborhood
comparisons. Since this step uses mainly geometric information, it is capable to match spots with
different intensities, that correspond to significantly regulated proteins. Moreover in the extension
step it is possible to exploit the proposal lists for ambigious spot regions, as computed in the spot
detection. This way, we present a first step towards the simulation of how an expert would compare
images by visual inspection, namely, by intertwining the spot detection with the matching process.
Figure 2 shows two 2–DE gel images originated from a transfection experiment of cultured EaHy
cells with 800 (left) and 1000 protein spots. Their original size is about 23cm by 29cm. For the
purpose of illustration in Figure 3 and 4 more details are shown of the small rectangular window
regions marked in Figure 2. (For simplicity ellipses were replaced by circles.)
In both Sections 2 and 3 we also refer to related theoretical issues and open problems in computational geometry that could further improve our solution. In Section 4 we outline implementation
issues and describe experimental results.
2 Spot Detection in Complex Regions as an Ellipse Covering Problem
Spot detection is to a wide extent an image processing problem. In fact, if the spots are well separated, classical methods like filtering and watershed transformation on the gradient image provide a
satisfying algorithmic solution, see [23]. As mentioned above, the core combinatorial problem is the
interpretation of complex pixel regions as unions of axis parallel ellipses.
The following formalization is a compromise stemming from discussions with practitioners who
solve these covering instances by peer review. First, we remark that complex regions are typically
saturated (black), and therefore gray level information does not help for the detection. We assume that
a connected pixel pattern R is given, which is fat in the sense that there are neither short horizontal
nor vertical cuts consisting of only two pixels. In the application R is usually a simply connected
subpattern of a 100 100–pixel square.
Spot sets detected with black spots indicating the local matching
To make use of the powerful machinery of geometric approximation algorithms we identify pixels
with their center points. Then the region R can be represented by two sets of points C and F , where
C is a sample of points to be covered (inside R) and F is a set of forbidden points (outside R). One
can obtain these sets walking along the boundary of R and choosing points inside and outside within
a small distance. This approach somehow mimics the general practice of experts who are looking
for ellipses approximating long parts of the boundary of R. The advantage that both sets are of small
cardinality has to be paid for by the fact that the computed cover could have some hole in the interior of
the region. To avoid this one also can choose C as the set of all grid points in R (from an appropriately
dense grid). Then, of course, the cardinality m of C can be quadratic in n, the size of F .
Now we can formulate the approximate covering problem from the application point of view. For
numbers 0 ; 1 the problem is to find a smallest-cardinality set E of axis–parallel ellipses
fulfilling the following conditions.
1. (Fitting) Each ellipse E 2 E respects F , i.e., it does not intersect F .
2. (Intersection) The boundaries of every pair of ellipses E;E0
in E intersects in at most 2 points,
and area(E \ E0) minfarea(E); area(E0)g.
3. (Covering) S
E2E E covers at least a (1 )–portion of pixels in C.
The aim to find minimal–cardinality coverings is in accordance with Occam’s razor principle, since
the smallest cardinality set is, in absence of a master gel, the simplest hypothesis to explain how
a complex region could have been evolved. At first sight one would require to cover all points in
R, however in order to cope with noise the covering condition allows to leave a small portion of
points uncovered. The fitting condition ensures that the selected ellipses do not cover much more
than the region R. From the way the gel production process spreads a protein in the two dimensions,
practitioners usually conclude that two spots do not form a cross. We incorporated this notion in the
intersection condition.
Following the standard methodology of set cover approximation, our ellipse covering problem
splits into two parts:
1. Find a basic set E of ellipses such that each ellipse E 2 E fulfills the fitting property, and
R S
E2E E.
Select a minimum cardinality subset E E which respects the intersection and covering properties.
Remark that (the boundary of) an axis–parallel ellipse can be represented by the solutions of the
equation
(x c)
2
a2 +
(y d)
2
b2 1=0 (1)
with parameters a; b; c; d 2 IR, where (c; d) is the ellipse center, and a and b are the lengths of
the halfaxes. Thus a straightforward approach is to discretize the parameter space of all possible
ellipses, and define E to be the set of all inclusion maximal ellipses fulfilling the fitting property.
One way to avoid misinterpretation of streaks is to exclude ellipses of an ”extreme” shape, i.e., to
require a=b 2 [1=; ] for a suitable constant 1. This also reduces the complexity of E. The
selection of E E can then be easily done in a greedy fashion. We implemented this approach,
however both runtime and the quality of the solution did not meet our expectations, see e.g. Figure 5.
In Subsection 2.3 we study from a theoretical point of view how to improve on both, making use of
advanced geometric data structures and techniques. In Subsection 2.2 we present an alternative LPbased approach, which avoids the explicit construction of a large basic set E, and instead combines
construction and selection of ellipses. Experimental results show that both quality and runtime of the
LP-approach are superior to the simple brute force solution."
www2.cs.arizona.edu/~alon/papers/jcb.pdf
Jasmine continued taking the notes as she followed along with the lesson with the others but while doing so she couldn't help but jot down the theories she'd heard so far about The Raincoat in order of her favorites.
Android?
Alien?
Alien Android?
Robot?
Mutant?
Government Agent?
Viral Marketing Campaign?
Hoax?
She ended up circling Alien Android as her favorite theory and went back to her notes.
After the lecture ended they worked on a computational geometry assignment.
In a process similar to what was presented in class. The main steps (and the algebra needs to be completed) are:
Complications The convex in is d=4.O(n^2 )
as per Clarkson-Shore Theorem:
point She Object / object.
5 points form a butterfly (configuration) from 2 abcd tetrahedrons, abce glued to each other in an abc triangle. The butterfly / configuration in conflict with w objects, these are the points seen by at least one of the tetrahedra. These points and the fifth point of the configuration are located on different sides of the super-plane containing the tetrahedron.
so:
N_(≤w)=O(w^d E(N_0 (n/w) ) )=O(w^3 n^2 ).
The probability that a weight configuration will be created isw: Therefore the expectation of the number of butterflies formed:p_w=O(1/w^5 )
∑▒〖〖p_w N〗_w=⋯=O(n^2)〗
A. You can calculate enoughAgThe level of normalcy N In linear time by a trip on, for example KDFS (to be specified). Complexity of the convex in 3 dimensions eTheA. The Euler formula holds that there are at most ribs and at most wigs, when it is the number of vertices.O(n)3n-62n-4n Per wig of K corresponds to a vertex of N (the direction of the external normal to the wig), for each arc of K corresponds to a large circle arc of N (the normal directions of the planes supporting the side), and to each vertex of K corresponds to a wig of N.
B. It can be shown that in unspecified cases, the planes can be rotated until one of the specified cases is obtained. It is important to show that there is a direction in which such a rotation only reduces the distance, by using the Pythagorean theorem.
D. We will construct the normal diagram and the reverse diagram. We will useDD'sweep lineAcross the unit ball To find incisions between ribs and ribs. Each such incision gives two ribs nominated for the case DD'(ii). To find candidates for case (i) you can process D into a data structure that supports point location, go through wig wig and look in the data structure for the opposite normal. (In fact there is no need for early processing, since the normal directions of the wigs are known in advance, and during the sweep Find each one in the reverse diagram when you get to it (as we saw in class).
3) a) In the dual representation we have nCircles are equal in radius and we want to find a point that is in the maximum number of these circles. We will performsweep On the dual circles (with each circle split into its upper and lower parts), and consider the points of intersection between them, and as a result the wigs of the array they form (enough to maintain the wigs that straighten the sweepCutter). For each wig we will hold a counter of how many circles it contains, and every time we encounter a new wig (to the right of a cutting point or to the right of the leftmost point of a circle) it is easy to calculate the value of its counter using those of adjacent wigs (to be specified). We return a point on the wig with a maximum counter value.
B) Note that the critical radii in which the answer to a) varies are radii in which three circles meet at one point, or two circles touch each other. Consider the collection of these radii and then run a binary search on them to find the desired minimum radius. At each step of the search we will run the algorithm in a); If he found a point at leastkCircles will continue to smaller radii, and if not, to larger radii. (The algorithms obtained in this question are not very efficient ...)
4) Separate into two calculations, one for the vertical sides of P and one to the horizontal ribs. Since the cases are symmetrical, it is enough to explain that in the case of vertical ribs, we will refer to this case. Of and the points of P. We will scan from left to right, we will go over all the points in x-str:Q
- If we encounter a left endpoint of section m Q we put it in y-str.
- If we encounter a right endpoint of a section from Q We'll take it out what y-str.
- If we encounter a rib from P (we will only refer to verticality here) will be searched in y-str using a cooRDiets ey its the first segment that is below the top endpoint and the first segment that is above the bottom endpoint. We will check how many segments are between them by rank queries. These are the segments of Q that intersect with the side of P. We will update the numerator. There are points in x-str and y-str. Actions.O(n)O(logn)O(n logn)
Any students that had trouble or questions about the assignments could simply ask Miss Snyder for clarification. After completing their assignments they handed them in and Miss Snyder cheerfully collected them and then danced back to her desk. The bell rang soon after and she clapped her hands. "Very good today class! Very good very good very good! Remember your homework assignments tonight: Problem 5.6a on page 116! Problem 6.14 on page 144! Problem 7.11 on page 161 and Problems 8.2 and 8.5 on page 179! That's 40 points all together kids! Do your best! I believe in you!"
"YES MA'AM!" The kids replied and quickly filed out of the classroom.
"Urrrrrgh. My head is spinning." Lucille Levy sighed as they walked the hallway. Lucille is a tall girl with aqua-blue eyes and long, scarlet hair that she kept tied in a long braided ponytail. She's wearing a stylish top and skirt. "Miss Snyder is a great teacher but her class comes way too early in the morning."
"Could be worse. We could still have that offbeat tone deaf tempo douche."
Thatcher." Jasmine shuddered. "If I ever see that sadist again it'll still be too soon."
Mad Dog Creakle Thatcher, just one of the many derogatory nicknames the students had come up with for the former music teacher, was a violent thug who somehow bumbled his way into becoming a music teacher. How exactly he accomplished this had been a mystery for the ages given that his teaching method resolved around screaming obscenities, demeaning his students and hurling objects around in a violent tantrum if anybody didn't meet his batshit standards topped off by threatening the students into keeping silent. This lasted until recording devices an anonymous student had planted in the room not only caught his behavior but then proceeded to put it all online. This had emboldened the students to come forward with their own stories. While his lawyer was able to protect him from the filming, the students statements had done far more damage and coupling this with their parents demanding his head and the faculty turning on him en masse, Thatcher was left disgraced and lost his teaching license. He narrowly avoided jail but he was left on two years house arrest. In a town where everybody hated his guts.
That's the thing about Rockwickians: They look after their own.
Suffice to say after his two years of house arrest were up, Thatcher moved far, far, far away from their town and had never returned.
On the day he was set to leave town, Miss Snyder had marched up to his house and whispered something in his ear. Nobody knew what she said that day but reportedly he had come stumbling out of his house scared out of his wits and ran to his car like the hounds of hell were on his tail.
The Mystery Filmer had not been located but the students believed he was still out there somewhere. Watching over the school like a guardian angel.
Thatcher was used as both a cautionary tale and an urban legend around the school with everyone trying to make him more monstrous with each retelling. The current 'lore' pictured him as a blatant rip-off of Jigsaw and The Trunchbull, who straps his students to intricate and overtly cruel torture devices which activate if they score a less than optimal grade in their assignments.
"Nooooot myyyyyy teeeeemmmpoooo! Oooook!" Benny drawled in a long drawn out simpleton voice while beating his chest.
The girls had a good laugh over that.
"Hey listen though, forgot that nobody. He's probably in prison somewhere or whatever while we're living it up in Rockwick. It's best to just laugh at his stupidity and move on with a big laugh and a smile!"
"My man!" He and Jazz high fived. "Anyway! Yeah. Forgetting about that loser now. I've got a Neuroscience lecture next anyway so I kinda need my mind clear."
"Ah man. I don't know how you get through that class."
"I know right? It can get a bit graphic at times but I'm certainly learning a lot. I can recite information about Biopsies, Craniotomies, Extended bifrontal craniotomies, Supra-orbital craniotomies, Retro-sigmoid craniotomies, Orbitozygomatic craniotomies, Translabyrinthine craniotomies, MRI-guided laser ablations,
Endonasal endoscopic surgeries and Neuroendoscopies from heart now...also we've done fake surgeries on fake brains soooo that's a thing."
"Huh. You know, I've never really thought about it, but do you think other High Schools teach this kind of stuff?" Benny questioned.
"I don't see why not." Lucille shrugged. "We're just a little town. If our school can teach them why wouldn't other schools? Anyway! I'll see you guys after Combinatorics.* " She waved to her friends and hurried down the hallway.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc. To fully understand the scope of combinatorics requires a great deal of further amplification, the details of which are not universally agreed upon. According to H.J. Ryser, a definition of the subject is difficult because it crosses so many mathematical subdivisions. Insofar as an area can be described by the types of problems it addresses, combinatorics is involved with
"Looks like I drew the big straw. I've got Philosophy and the Science of Human Nature, baby! Victory for Benny!"
"Yeah, yeah, don't rub it in Benny boy. Just kick some butt in your class alright?"
"Will do. Gonna be straight A's all the way!"
She waved goodbye again and they parted.
Arriving in her Fundamentals Of Neuroscience And Brain Surgeries Course, she took her seat and relaxed until class got started.
Professor Hideki Youta Kichirō Ottavio Cattaneo and his wife Professor Léa Eléonore Faucher Cattaneo waited until the bell rang to happily welcome the kids back.
The Italian-Japanese-American Hideki was an adult man with a rather tall stature, and muscular yet slender build. He is mentioned to be very handsome by the people around him, boys and girls alike. He has straight black hair with a dark blue tint which reaches down to his nape. His bangs are shorter than his hair and parts towards the right side in the form of an "M-style", which partly covers his left eye.
Professor Lea was a French-African-American woman with a beautiful figure and silky black hair tied into a ponytail. Her hazel eyes were covered by fancy glasses. Like her husband she was wearing a fancy suit and labcoat.
"Hello again kids. Glad to see you remembered your way through the halls." Hideki joked to a couple of chuckles from the class. "But really we're delighted to have you back for another amazing class full of fun amazing Neuroscience!"
"I'm sure you kids kept up with your reading but just to make sure we've prepared a quick little quiz to help refresh your memories!" Lea informed them sweetly and grabbed the stack of papers from the table. She passed out the piles to the front desk of each row to pass back to the students behind them. Jeff laughed nervously as she looked over her quiz. "Hooo boy. It is good to be back."
1. A drug that decreases the activity of dopamine within the dorsolateral prefrontal cortex would be expected to
A. Induce both positive and negative symptoms of schizophrenia
B. Induce only the positive symptoms of schizophrenia
C. Be an effective treatment for schizophrenia
D. Decrease the levels of dopamine in the nucleus accumbens
E. Be an effective treatment for thought and language disorder
2.PCP acts as a(n) ________ at ___________receptors
A. Agonist; NMDA
B. Antagonist; dopamine
C. Agonist; acetylcholine
D. Antagonist; NMDA
E. Antagonist; GABA
3. Which of the following would be a negative symptom of schizophrenia?
A. Hearing voices that repeat senseless words and phrases
B. Experiencing a feeling of euphoria at the start of an episode
C. Believing that doctors are part of the plot to poison you
D. Thinking you are the most powerful being on earth
E. Exhibiting flattened emotional expression
4. In which of the following would you expect to observe an enlarged hippocampal formation
A. A London cabby who has 30 years of experience
B. A pigeon that wanders from roost to roost
C. A bird that only eats from your backyard feeder
D. A person who has just started training as a London cabby
E. A chickadee tested in the early summer
5. The hippocampus receives inputs from
A. The entorhinal cortex
B. The amygdala
C. Various regions of the limbic cortex
D. All association areas of the neocortex
E. All of the above
6. Patient RB who sustained brain damage while in cardiac arrest, exhibited profound anterograde amnesia. What region of the brain was injured?
A. Field CA1 of the hippocampal formation
B. The perirhinal cortex
C. The parahippocamal cortex
D. The amygdala
E. The central nucleus of the amygdala
7. The verbal abilities of HM are intact except
A. He cannot talk of events that occurred prior to 1953
B. His ability to spell simple words such as "and" and "but"
C. He cannot talk about mathematical operations
D. He is not proficient in post 1953 American vocabulary
E. Both a and c
8. The common aspect of all natural reinforcers relates to
A. The release of dopamine within the nucleus accumbens
B. The release of norepinephrine within the locus coeruleus
C. The release of dopamine within the lateral hypothalamus
D. Inactivation of frontal cortex
E. Activation of the medulla
9. Imagine that you have ingested a drug that prevents alcohol from binding to the GABA/A receptor just before you join friends at a bar. Which of the following would you expect to happen to you?
A. You show no signs of sedation, even after nine beers
B. One beer puts you to sleep
C. The pill makes the alcohol taste bitter, causing you to vomit
D. You find alcohol more intoxicating
E. You have impaired cerebellar function
10. PET studies show that schizophrenic patients treated with amphetamine show ______ from the striatum and a corresponding ________
A. Reduced release of dopamine, increase in positive symptoms
B. Reduced release of GABA, decrease in positive symptoms
C. Greater release of dopamine, decrease in negative symptoms
D. Greater release of dopamine, increase in positive symptoms
E. Reduced release of serotonin, increase in negative symptoms
11. John has been diagnosed with schizophrenia and has shown improvement in positive symptoms while taking chlorpromazine. Which of the following actions below, if taken by John, would be expected to greater worsen his positive schizophrenia symptoms?
A. John stops taking CPZ and takes cocaine
B. John takes double the CPZ dose per day
C. John takes reserpine in addition to CPZ
D. John mixes alcohol with CPZ
E. John ingests alpha-methyl-para-tyrosine in addition to CPZ
12. Alternating episodes of elation and sadness are referred to as
A. Bipolar disorder
B. Severe depression
C. Severe mania
D. Unipolar depression
E. Schizoaffective disorder
13. The function of monoamine oxidase is to
A. Provide the precursor for the catecholamines
B. Convert dopamine into norepinephrine
C. Convert norepinephrine into epinephrine
D. Convert catecholamines and serotonin into inactive forms
E. Speed up the digestion of cheese in the gut
14. The monoamine hypothesis states that depression is caused by
A. Loss of cells in the prefrontal cortex
B. Insufficient activity of monoaminergic neurons
C. Excessive activity of dopamine systems
D. Overactivity of monoaminergic neurons
E. Excessive activity of serotonin synapses
15. All of the following support the monoamine hypothesis of depression EXCEPT
A. Reserpine causes depression
B. CSF levels of 5-HIAA are low in suicidal patients
C. Monoamine agonists produce depression
D. Families of subjects with low 5-HIAAA were more likely to include people with depression
E. Monoamine antagonists produce depression
www.proprofs.com/quiz-school/story.php?title=principles-neuroscienceShe breathed in and slowly exhaled as she looked over the quiz, wrote her name down, looked it over again and got to work on her answers.
Question 1: A. Induce both positive and negative symptoms of schizophrenia
Question 2: D. Antagonist; NMDA
Question 3: E. Exhibiting flattened emotional expression
Question 4: A. A London cabby who has 30 years of experience
Question 5: E. All of the above
Question 6: A. Field CA1 of the hippocampal formation
Question 7: D. He is not proficient in post 1953 American vocabulary
Question 8: A. The release of dopamine within the nucleus accumbens
Question 9: A. You show no signs of sedation, even after nine beers
Question 10: D. Greater release of dopamine, increase in positive symptoms
Question 11: A. John stops taking CPZ and takes cocaine
Question 12: A. Bipolar disorder
Question 13: D. Convert catecholamines and serotonin into inactive forms
Question 14: B. Insufficient activity of monoaminergic neurons
Question 15: C. Monoamine agonists produce depression
She looked it over again to ensure she was happy with her answers, nodded and set her pencil down and took a breather.
After the quiz was over and the papers were collected the class was treated to a pair of videos to help ease them back into the class after spring break though they were informed to take notes.
All of which was completely normal, Jess was sure.
After the class was given their assignments and class let out, they waved goodbye to their teachers and headed out.
"First day back and we're already being assigned quizzes eh? They sure don't hold back do they?" One of the students asked her.
"I know right? This is why you have to keep up with your studies man. You never know when they might decide to drop a test on you."
Leia leaned her head out the door. "That's coming up by the way! Study hard children!"
"Yes ma'am! Thanks a lot Jass."
Jess smirked and stuck her tongue out.
After another couple of classes, including Entertainment Engineering & Design and Turfgrass Science, it was finally time for lunch and she was practically skipping. Not only did Jasmine get to see her friends again but they could finally start getting to know Clementine!
True to their word; Misty Pendleton, Brian Palmer and Ada Caldwell were all waiting for her in the cafeteria. It was a nice and fancy place. With clean tiles and stainless steel furniture, nice looking pillars with speakers on them playing comforting soothing music and nice paintings hanging on the walls. The kids could smell the aromas of Rockfort High School's Delicious Delicacies even from their spot in line!
"We've had a few fun classes but we're good. Allow me to introduce my friends: Misty Pendleton, Brian Palmer and Ada Caldwell."
"Sup? I'm Brian."
"How do you do Miss Kaine? My name is Misty Pendleton and we are ever so glad to make your acquittance."
"It's nice to finally meet you properly Clementine." Ada greeted her.
"Hello. Hello to all of you." She greeted and offered her hand. They happily shook hers up and down while she was as gentle as a lamb with them.
"Hey come on now you don't need to be that gentle. Feel free to show your muscles." Brian told her and gave her hand a squeeze as a joke. Nothing happened. He looked up at Clementine and chuckled quietly before squeezing again. Nothing. She smiled and let go.
"I work on a farm."
"Riiight. Cool. So what do you there anyway?"
"Farm stuff." She replied with a shrug.
"Cool. If you ever need any help you can give us a call." Brian offered. "I think it would be fun actually."
Misty considered countering this but decided to table it for later.
"Heck with it. I could probably do a day of work in between my world domination plans." Ada joked.
*Clementine will remember that.
"Well, if you ever need help, feel free to just let us know." Misty agreed. "Anyway, what classes did you have?"
"AP Military Strategy and Tactics, Astrobiology and the Search for Extraterrestrial Life, Cryptozoology 101 and Programming."
"Wow. You are out there Clementine. Any signs of Extraterrestrials yet?"
"Only circumstantial evidence so far I'm afraid."
"You might be in luck." He replied. "Have you heard about The Raincoat?"
"Do you mean The Movie Posters people have been putting up around the school?"
"They're more along the lines of normal photoshopped posters than movie posters. The Raincoat is that vigilante that everybody said has been running around saving people around the world." Ada explained. "She or He, we don't know for sure, completely totaled a truck. I saw it on the news."
"Ohhhh that raincoat. The Superman guy. Gal. Him. Her. Whichever. Do you think he's real?"
"Either that or it is one hell of a viral marketing campaign." Misty joked.
"And that is today's Lunch Topic. Interested in joining us?"
"Sure. That sounds like fun."
"Hey by the way? What are you listening to?" Misty asked her. Pointing to the one ear bud she had in her ear.
"A Luna Lazarus Lecture On Nanotechnology."
"Cool!"
"So what's she talking about? What does Miss Lazarus have planned with her nanotech?"
"Using it to treat diseases and other issues with the human body. Therapeutic nanotechnology could be used to deliver drugs, reconstructs brain cells and restores cognitive function. Nanotech contact lenses could be to provide medication, sun protection and vital statistics in treating eye disorders. Nanotechnology can medicate and repair ears reversing hearing loss and vertigo. Nanopolymers can regenerate skin and tissue. To treat diseases like ovarian and breast cancer, nanosensors 1,000 times better than mammograms could find breast cancer and nano-instruments destroy and prevent cancer growth. Nanoparticles on bones repair breaks and strengthen bones in mere days or weeks. In addition, robotic processes transmit information to the brain so patients feel and use them like native limbs. Nanotherapies could be designed to self-adjust to fight bacterial and viral infections, saving millions of lives each year. Robotic limbs, suits and muscular augmentations could increase muscle strength to 100 times human capacity for long missions. Implanted biosensors could manage glucose and vital signs for diseases such as diabetes, releasing meds and detecting emergencies." Clementine summarized.
"But of course that's just the icing. The real fun stuff is what she discusses after: Precise injections of nanobots that attach to different parts of the body, begin replicating, and re-engineering parts of the body, creating smart materials that will replace and improve every part of the human body to upgrade it into a transhuman that's never tired, always at peak performance, has flawless skin, unbreakable bones, super muscles and senses, genetically reprogrammed cells that can self-repair at an accelerated rate, widened neurons in the brain to increase reaction time and intelligence, creating a web of osteoderms in the skin to create flexible but durable shell that is invisible to the naked eye to help the human body resist excessive and harsh damage among other things."
"Well dang that certainly sounds cool." Brian agreed. "How does the super strength work though? Muscle density?"
"That's half right. She suggests that nanotechnology could be used to reduce the production of functional myostatin, allowing muscles to grow more dense and tougher while simultaneously enhancing their body tissue, skin, muscles, bones, etc to become extremely dense and solid, allowing them to withstand harmful forces on the body such as crushing weights, impacts, pressures and changes in temperatures, making them stronger and more durable. The specifics of it are very technical but that's the summary and gist of it."
"Well if anybody could do it, it's Luna Lazarus." Ada agreed. "That woman is a super genius to be sure."
"My head is swimming. That all sounds like something out of Sci-Fi Movies. It would be cool though." Brian added. "Hey wait a second! Wait wait wait! I've got it! The Raincoat! She or he's a Nano-Super!" He invented the term on the spot. "A Nanomachine Powered Superhuman! Like, a Superpowered Prototype that Luna Lazarus created!"
Clementine giggled.
"Well, I wouldn't say it's an impossibility. It's just as possible as every other theory. So we're going with the robot theory?"
"It sounds good to me."
"We can discuss it further when we get to the table. Come on guys! Chow time!"
The students grabbed their fine foods and then a table.
Clementine bought herself Tarragon Chicken Salad Sandwiches, Misty got her Pizza Cauliflower Bites, same as Jasmine, Brian got Baked fiery buffalo wings and Ada settled on Turkey Chili. Dining at Rockwick High was just so absolutely divine.
"Alright boys and girls! Lets begin today's Lunch Topic: The Identity Of The Raincoat! I want to hear ideas people!"
"Hot Take: She or he's a Space Alien." Clementine joked.
"Alright, space alien, first one on the table. Lets hear your reasoning."
"Super fast, super strong, can be in several places at once, and has camouflaging powers to blend in with the night. Nobody normal can do that and certainly not someone from planet Earth. Heretofore, Space Alien. That's how it always works in the comics after all. We can therefore surmise that he or she gets his or her powers from the Earth's Yellow Sun via The Photonucleic Effect on top of coming from an alien planet with higher gravity than Earth. Lets say...around ten times. It would explain the invulnerability, super strength and super speed." She explained to them.
"Okay then. That is a very good argument. Who would like to go next?"
"Lazarus Android." Ada chimed in. "I've never seen any proof of alien life, no offense Clementine, but androids are a real thing. They've been making more advanced robots every day and they've even started making giant mechas now! If anybody could make a superpowered android, it would be Luna Lazarus. Those crime fighting moments were set up by the government to test out the androids abilities. How else would you explain The Raincoat's superpowers and finding all of those crime scenes? It was all set up."
"That does sound more realistic." Clementine admitted.
"So we have Alien and Android. Who wants to go next?"
"Guys, seriously, she's a Nano-Machine powered Superhuman!" Brian smiled. "We just discussed how uber nanomachines could make someone, right? So, here's what happened. The Government used some super prototype nanomachines to make a superhuman and now they're testing him out in combat scenarios!"
"Wait how is that different than my theory?" Ada asked.
"Your ideas an android, a machine construct that combine artificial intelligence and a mechanical body with a human-like appearance, while mine was a nanomachine person which would make him or her closer to a cyborg."
"Ohhhh. Right, right. Okay carry on. Who's next?"
"That would be...moi!" Misty smiled. "And the answer is simple: The Raincoat is really a nanomachine infused alien android powered by sunlight!"
"Oh come on Misty. You can't just copy other people's answers like that!"
"Says who, Brian?"
"It's against the rules."
"Since when do our Lunch Topics have rules?"
"Since now."
"Overruled." Jess smirked.
"I second that notion." Misty agreed.
"I shall remain neutral." Clementine stated for the record.
"Ada! Come on, back me up here?"
Ada took a quarter out of her pocket and flipped in the air, caught it and slapped it on her palm before looking at it. "Annnnd I'm siding with Brian this time."
"That leaves us tied. Clementine, since you're new to the group, we'll need you to break the tie for us. So are you Team Brian or Team Jess?"
They smiled at her expectantly until Clementine carefully placed the ear buds back in her ears and resumed her lunch. "The food here is really good."
"Hey, is it okay if I sit here?" A student asked them. They looked up to see a teen in punk goth attire standing there with his plate. He was wearing a black t-shirt and shorts with black fingerless gloves on his hands and a black wristband on his right wrist, topped off with black horn rimmed glasses on his face.
"Sure man we got plenty of space. Have a seat, bro!" Brian greeted him.
"Thanks man. I'm new. Jack Mccormick." He introduced himself.
"Nice to meet you newbie! I'm Jasmine, and this is Misty, Brian, Ada and Clementine."
They introduced themselves one by one until Clementine did a double take and suddenly sprung out of her chair with her phone in her pocket and grabbed a football that had been flying at the back of Jack's head!
"What the heck?!" Jack exclaimed as he jumped.
Clementine looked across the cafeteria to see a tall student in a football jersey staring at her in disbelief while his two buddies on either side of him laughed and applauded her quick save. Clementine stood up and smiled. "I'll be right back."
"Woah woah woah! Hey, Clementine, you don't want to get involved with those guys!" Brian insisted to her. "Just drop the football and sit back down."
"Clem, those were some awesome reflexes, but those guys are nuts!" Ada told her.
She nodded. "It will be fine. Enjoy your lunch guys." She told them and walked across the cafeteria while the trio approached her. Instead of meeting them in the middle however, Clementine pivoted and instead walked closer to the door where a trash can was sitting and with the trio close behind her she casually dropped the football in the trash, dusted off her hands and walked away with her hands behind her back.
"Ohhhhh shiiii-"
"Brian!"
"I'm on it. Go find a teacher or something!" He told the girls and hurried over to Clementine while the trio were digging the football out of the trash and wiping it down.
"Clem! Clem come on we have to go." Brian insisted and grabbed her arms.
"I don't think so. Sorry but I am not done eating yet and neither are any of you. Come on, lets sit back down and get back to lunch."
"Clementine seriously! That guy's-"
"Hey what the hell's your problem?!" The leader of the trio snapped at her. "We were just joking around! You didn't need to throw it in the trash like that!"
"I am sorry but if you cannot play with it responsibly then you do not deserve it." Clementine informed him casually while changing the phone to ViewTube to find something to listen to. She'd been listening to lectures all morning after all.
"Seriously, Caleb, it's just a football, she didn't do anything wrong alright?"
"Shut up loser. I didn't give either of you bitches permission to speak to me." Caleb Cassius Chambers snapped at him. He was one of the tallest guys in school with a physique to mix and a mostly shaved head and his features made him look like he was carved out of stone. Unfortunately, his personality was on the downright nasty side.
"Real mature." Clementine retorted in a bored tone while searching through the videos. Caleb tried to grab her phone away from her but she casually side-stepped him seemingly without paying attention. He tried again only for the same thing to happen!
Brian took a few steps back unsure of what he was seeing. Cassius was one of the toughest guys in school but she was treating him like a joke!
"Help her Brian!" Jasmine insisted to him.
"Which one?" Brian asked as she danced around Caleb's attempts to grab her. He soon got tired of this and he tried to punch her in the face only for her to duck under him and then keep doing what she was doing, circling around him and side stepping everything he tried, outright humiliating the bully without throwing a punch!
Clementine smiled as she apparently found a song she liked and hit play. She began to mouth the words even as she dodged around him, did a pirouette and resumed mouthing the lyrics to Adam Lambert's For Your Entertainment.
One of Caleb's buddies tried to tackle Clementine from behind but suddenly tripped over his untied shoelaces and fell on his face to the laughter of the lunchroom.
Jack adjusted his glasses and enjoyed his lunch while he watched the whole thing unfold. "...This is a weird school."
"Dammit! STAND STILL" Caleb shouted at her.
"Nope. I don't wanna." Clementine pouted.
He reared back to prepare for a big windup punch at her face and then he threw the punch but he completely whiffed it! Caleb tried a right cross at her jaw but she dodged it. He tried a straight punch at her face but she slipped it. He tried an uppercut at her jaw but she leaned back and dodged it. He swung at her face again but she ducked under his arm and circled back around. He tried a swinging backhand but she ducked under him again. He tried again and again to the same result. It was like he was trying to ice-skate uphill! No matter how hard he tried he didn't get anywhere! Caleb would know. He'd tried it in the past when he was a kid. He might as well have been trying to punch the air for all of the success he was having against Clementine!
"What in the hell? No, seriously, how is she doing that?" Ada asked. "I'm not complaining of course but how?!"
Misty meanwhile had ran off to find a teacher. Or at least a security guard!
Caleb finally stopped his attempted beatdown on Clementine to catch his breath while one of his friends circled around behind her. "You...y-you...you're finished....after I catch my breath...ohhh man....you're fast. You're vest fast. Hooooo boy."
"Are you done now? Can I go back to my lunch now?" Clementine asked him a bored tone.
"Oh you want to eat something?" He asked as he straightened up. "How would you like to eat my fist?" Caleb sneered as his buddy charged her from behind aiming to Football Tackle her to the floor so Caleb could land a devastating punch on her face and knock her head off only for Clementine to dodge him at the last minute and pirouette away. Meanwhile, Caleb's buddy lost his footing and he ended up colliding with Caleb and knocking him over before he could stop himself! Caleb had the wind knocked out of him as they both crashed to the floor.
"Uggghh...oh, OH! Caleb! S-sorry about that man! I tripped!"
"Get off me." Caleb pushed his friend off of him and tried to catch his breath as the rest of the lunchroom laughed at them. "What the hell did you even-HUH?! Oh you've gotta be kidding me!"
His buddy turned around and stared in disbelief. "No way. You have to be joking." A banana peel. He'd slipped on a freaking banana peel! "Well ain't that a kick in the head?"
"That...DOES IT!" He screamed and ran at her in a blind rage while Clementine was pulling her chair back out. She calmly looked back at Caleb and then hopped over the chair to the other side of it and walked away. Caleb ran on top of the chair and leaped above her and tried to punch Clementine only for her to side step him once again. He was so focused on trying to hit Clementine that he completely forgot about his landing and he slipped and fell on his face.
"Better learn balance. Balance is key. Balance good, karate good. Everything good." Clementine advised him. "Balance bad, better pack up, go home. Understand?"
"SHUT UP AND FIGHT ME LIKE A MAN!" Caleb shouted at her while he scrambled to his feet.
"I'm a girl." She reminded him.
"Then stand still and I'll smack you like one!" Caleb shouted back and attacked her again. It was all the same though. No matter what he tried she just bobbed and weaved and danced around him. No matter how much he mixed it up she saw right through it and outmaneuvered him with ease. He might as well have been trying to catch a ghost. Eventually one of Caleb's buddies attacked her from behind by trying to swing a tray at her head only for her to dive out of the way at the last second causing him to smack Caleb with the tray while Caleb's punch hit his own friend in the face!
"OW Dude! What the hell?"
"Owwww~ Ah man! Ow! I was aiming for her! What are you doing?"
"I was trying to smack that little brat! What are you doing?!"
Clementine meanwhile had returned to her seat and was now sitting with her legs crossed and a her drink in her hand and her other hand underneath it as she leisurely sipped it.
Caleb took a break to catch his breath and re-evaluate this entire situation. "Jus...just give me a second." He told her. "I-I'll be right with you...oh man. What is going on here?" She hadn't thrown a single punch and spent the whole fight running away but somehow they were the ones getting their asses kicked! "What the hell are you?"
"My name is Clementine Kane and I'm a Farmgirl. You on the other hand could use some anger management classes. Now we can continue this little dance of ours or I can get back to my lunch. And I am feeling rather hungry. So please leave me and my friends be. I'm sure everyone else would like to get back to their own lunches too. Have a good day." She turned around and went back to her lunch.
Caleb and his buddies were left staring slack jawed at this display. Not only the utter humiliation they'd just suffered and the subsequent disrespect after this girl just ran circles around them. And now they were standing here tired and gasping for breath and sweating and she didn't even have a single hair out of place. The trio stammered for words until one of them just yelled out "Oh to HELL with this!" One of them shoved the other two and picked up a chair.
"Woah woah! Adam wait just a-"
"SHUT IT CALEB!" He shouted and ran at Clementine and threw the entire chair at her! Clementine responded by standing up and holding up her backpack to shield herself and block the chair and pushed the chair down. She placed her backpack on her own chair, lifted up the first one, righted it and slid it over to him while the moron was still coming at her causing Adam to trip over it and fall on his face like his friends had been doing all day. Clementine walked over to him and knelt down next to Adam. "I gave you a chance. Several chances. I kept trying to walk away and resolve this peacefully but you have continued to harass me and antagonize me over this." She held five fingers up in front of her face as the thug tried to pull himself up. He froze up and his eyes widened in fear as her fingers curled up into a fist. "This is what you want isn't it?" She brought her hand back and Adam began to whimper. "To drive your fist through your victim's face, to savor the fear in their eyes while you mercilessly beat them into bloody pulps no matter how much they beg and cry for mercy?" She reached out with her hand and gently opened it to gently, gingerly, honk his nose between two fingers. So gentle it was as if she was playing a newborn baby. "Luckily for you I'm not like that. Honk honk." She stood up, brushed herself off and offered him a hand and waited patiently while Adam hesitantly reached for it and took her hand and accepted her hand up.
"Oh come on man, stop shaking, I was just messing with you." She took the chair back to the table. "You guys have a lot to learn about comedy by the way."
Misty returned to the lunchroom with the principal and a security guard in tow to the sound of uproarious applause and cheers for Clementine! Caleb and his cronies were sitting at an empty table tired sore and exhausted while Clementine was sitting back at the table with the group eating her lunch now joined by a few other students.
"Ummmm...Miss Pendleton? I thought you said there was a disturbance here? What exactly did we miss?"
Misty took a look around the lunchroom and then she pulled out her phone. "Wait for it."
It didn't take long before the 'fight' was uploaded to the internet. "Here you are sir. I would like to reiterate once again however that those three boys over there were the ones that started it. All Clementine did was try to defend herself and others."
The Principal and The Security Guard watched the whole affair on the phone.
"Can this really even be considered a fight?" The Security Guard asked. "She's not even doing anything."
The Principal waited until the end of the video where Clementine once again tripped up one of the boys and then threatened him before helping him up.
"Alright so. I'm going to have to talk her about that but I think we can chalk her up as the innocent party here." He handed her back the phone and walked into the middle of the room and clapped his hands. "Alright, alright everybody, break it up, sit down and go back to your lunches! Caleb, Drew, Adam and Clementine? I'm going to need to speak with you in my office."
Clementine looked up from her lunch. "Can I get a box?"
Clementine sat in the Principal's office with her lunch in a rectangular container situated on her lap while she waited for The Principal to finish questioning Caleb and his two friends. The principal was keeping hold of the plasticware until further notice though. Despite the empty seat between them, and the fact that Clementine clearly wasn't paying attention to them, Adam and Dru were visibly nervous about her just being there.
"Alright, look, I admit things got a bit out of hand but she's the one who started it alright? My buddies and I were tossing the football around with each other, just goofing off, and then it gets thrown a little too hard and flies across the lunchroom. That was stupid, I admit it, but she caught it so there wasn't any problem. We asked for it back but then she just walks right past us and throws it away! She flat out throws it in the trash! So naturally after we took it out and cleaned it off I asked what her problem was and told her to apologize but she just went and picked a fight with me. I understand that things got heated but it wasn't all our fault. She started it and just kept antagonizing us. She kept tripping us and even tricked me and my friend into hitting each other! It wasn't all our fault!"
Principal Featherstonehaugh just red his cheek on his hand while he listened to Caleb lie to him and waited until he was finished. Featherstonehaugh was a classy gentleman, with a fine blue suit and tie worn over a pressed white shirt with fine black loafers and a golden watch. He has a well maintained beard on his face and well combed hair. His features were like stone as he listened to the stream of lies coming out of Caleb's mouth.
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He waited until he was done and then showed him the video. "Mr. Chambers I would advise you not to lie to me. I heard your screaming and swearing on the way to the lunchroom. It certainly sounded like you and your friends were the aggressors there. Furthermore, everyone politely recorded the fight. Is this you and your friend trying to hit Miss Kane with a tray and a punch?"
"W-well, yes but I-"
"And is this your friend throwing a chair at Miss Kane?"
"Okay I tried to stop that-"
"Yes or no Mister Chambers?"
"Yes sir."
"Uh huh. Sounds like this is all the evidence I need. Now why don't you tell me the truth and why you did it?"
"The truth...well, you see, the truth is...it feels good to establish a hierarchy. I'm at the top and the losers and nerds are at the bottom. It feels good to put them in their place. It feels good to smack them around and watch them cry. I threw the football and that nerd because I find it funny. I take pleasure from things like that. Fuck you!" Caleb Chambers snapped at him in confession. "Happy now, Featherweight? I'm the Alpha here and I can do whatever I want to these losers."
"Yeah that's a Suspension Confession if I've ever heard one. You're wrong on a few points however. Any man who must say 'I am King' is no true King at all and any man who must declare himself an Alpha is no Alpha. Even if it was true, and it very clearly isn't." He played the video again. "That doesn't give you the right to hurt anyone. If you were as great as you claim to be you would be leading by example and building other people up instead of violently lashing out at them and throwing a childish tantrum."
Caleb had no real answer to that. "I...uhm...look sir, I-I'm sorry. I've just had a bad time of it lately. My Uncle's truck got destroyed by what is probably an alien and now he's in the hospital and my dad has been working to pay his bills and he just got a major DUI and-"
"See now isn't this better? A healthy communication can be a lot of help for you. I would recommend talking to our counselors and a therapist about your problems. Unfortunately you're still looking at a suspension period for your actions here today to be handed down after I finish questioning the others followed by one week detention after you return from your suspension. I didn't tolerate Ferris acting out, I'm certainly not going to tolerate your behavior. You are dismissed."
Caleb sighed and stepped out of the office and slumped into the chair.
Adam was called next followed by Drew followed finally by Clementine. Still holding her boxed lunch she sat down in his office and looked around. "Wow. This is the first time I've been in your office, sir. This is a nice room. Very classy."
"Thank you Miss Kane. Now, would you mind explaining what happened in the cafeteria today in your own words?"
"Sure. I was sitting with my new friends and we were enjoying lunch and theorizing about The Raincoat and joking around when Jack came around to join us. That was when Caleb threw the football at the back of his head. I saw it coming just in time though and I caught it. Now I had the football and my mother always said that if I was going to misuse a toy then she was going to take it away. Seeing as how Caleb had thrown his football away so recklessly, I decided to drop it into a trash can to teach a lesson. However this caused the situation to escalate and he approached me angrily. I attempted to de-escalate and avoid him but he continued trying to grab me and shout at me. However I dodged his attempts and did not hit back. Any injuries resulting from our confrontation were the result of his own recklessness and those of his friends."
She paused.
"Well, I assume they are friends. They were hitting each other a lot." She shrugged. "Anyway, I continued avoiding conflict until one of them threw a chair at me when I was trying to walk away and end the situation. I stopped this and kicked a chair his way and he tripped over it. As none of my other attempts to end this situation had worked, I decided to pretend to be a bad guy to scare him and then I ended it with a joke. I realize that threatening him might not have been the best way to handle the situation but they had just tried to pulverize me."
"I see...alright I appreciate your honesty. You're right in that you are the victim here, not the aggressor. You are also right that threatening him in the way you did and kicking a chair at him were not proper responses. Considering their actions in comparison however, I'm going to let you off lightly: I would like to write a seven page essay in MLA Format on conflict resolution. Cite your sources properly, etc. I want this essay laminated and on my desk by Friday for review. In addition I would like you to speak to a school counselor about what happened today. Finally, just like the other three, I am going to be calling your parents about what happened today. Odds are they'll probably see the video anyway so they might as well hear about it from me beforehand."
"That's fair sir."
"Alright then. I appreciate your politeness and honesty today. I'll write you a hallpass after the phone calls are taken care of."
"Thank you again sir."
"Okay! That's that then. Oh, but, one more question: Where did you learn to dodge like that?"
"I watch a lot of Jackie Chan Movies. Plus I live on a farm. You learn to be quick on your feet there."
He chuckled. "I can imagine. Alright, feel free to wait outside."
"Thank you again sir."
"Thank you."
She started to walk to the door but then she turned back around and walked back over to him. "Sir? May I have my utensils and headphones back?"
"Your utensils yes but the headphones will stay with me until you're ready to leave the office."
"Understood sir."
She accepted the plastic utensils and stepped out.
The three bullies just glared at her while Clementine resumed eating her lunch.
Principal Featherstonehaugh dialed the number for the Kane Farm and drummed his fingers on the desk while he waited.
After a couple rings the phone picked up and the beautiful sing song voice of Marie Kane answered on the other end. "Hello. Kane Residence. How many I help you?"
"Hello Miss Kane it's nice to speak with you again. This is Principal Featherstonehaugh. How are you doing today?"
"Oh hello Mister Feathers! What's up?"
"It's about your daughter. Clementine was in a fight at school today." Marie went quiet on the other end of the line. "Miss Kane? Miss Kane are you still there?"
"Ohmygod.Ohmygodohmygodohmygodohmygodohmygod....is she okay? Are those kids okay? Is everyone okay? What happened?"
"Alright, Miss Kane, Miss Kane. Please calm down and allow me to explain what happened."
"I...see. Okay. So nobody was hurt?"
"Some bruises but their pride was wounded worse than their bodies. However, her threats to the student isn't something we can overlook. Incidentially, where did she learn to fight like this?"
"She watches a lot of action movies and she practices the moves in her room when she thinks we won't notice."
"Okay then. That's about what she said. Okay we'll need you and your husband to come in and have a sit down with the other parents."
"Oh of course sir. Sure. We'll be happy to do so."
"Excellent. We'll continue our discussion when you arrive. I'll see you then." He hung up and called the Chambers family.
Marie Kane sat down on the stairs next to her husband Justin Kane.
Marie is a tall woman, standing at 6'1, a bit taller in her work boots, with short, reddish brown hair she has tied up in a bun in the back and green eyes that match her green dress which is covered by a white apron.
Justin is even taller than his wife. Broad shouldered, rugged and muscular, with big feet and hands. He has darker brown hair with a light goatee on his face.
He is dressed in the usual wear of a farmer.
"It's okay, Marie. It's alright. She didn't hurt anybody. Feathers said it himself. Those boys were hurting themselves more than her. Not like they could hurt her even if she stood there anyway. Hell, it's probably for the best that she dodged around them like that. If they broke their hands on her we'd really have a mess on our hands."
"I know. I know. I'm not worried about her not fighting. I'm worried about what would happen if she did. She handled it the right way today. Even if I wish she would've just walked away, she handled it alright. But I'm worried about what would happen if she did. The town wouldn't stand a chance."
"Marie, Marie, Marie, Marie. Look at me honey. She's a good kid. We're raising her right all things considered. She spent her Spring Break away from home looking for people to save for Chrissake."
"Yeah. She did. She's a good kid. Our daughter's a good kid. She's a sweetheart. She's our Angel. The sky gave her to us. But we'll still need to have a talk with her. Can't have her threatening the other kids even as a joke after all."
"That's the spirit honey. Just remember. She's our little angel and nothing's going to change that. She's a good sweet kid. We just need to sit Clementine down for a talk and she'll understand alright?"
"You're right. I'm worried about nothing." Marie stood up and brushed off her apron. "Alright, come on, lets go get changed into something fancy. It'll make the conversation with Feathers go easier."