Rand rode across the wide stone bridge leading north from the Caemlyn Gate without looking back. The sun was a pale golden ball just risen above the horizon in a cloudless sky, but the air was cold enough to mist his breath, and the lake winds made his cloak fly about. He did not feel the chill, though, except as something distant and not really connected to him. He was colder than any winter could be. The guards who had come to take him out of the cell the night before had been surprised to find him wearing a small smile. He wore it still, a slight curve of his mouth. Nynaeve had Healed his bruises using the last of the saidar in her belt, yet the helmeted officer who came into the road at the foot of the bridge, a stocky man with blunt features, gave a start at the sight of him, as though his face was still swollen and purple.
Cadsuane leaned from her saddle to speak a few quiet words and hand the officer a folded paper. He frowned at her and began to read, then jerked his head up to stare in amazement at the men and women waiting patiently on their horses behind her. Starting again at the top of the page, he read moving his lips silently, as if he wanted to be sure of every word, and small wonder. Signed and sealed by all thirteen Counsels, the order said that there was to be no checking of peace-bonds, no search of the packhorses. This party’s names were to be blotted out completely in the record books, and the order itself burned. They had never come to Far Madding. No Aes Sedai, no Atha’an Miere, none of them.
“It’s over, Rand,” Min said gently, moving her sturdy brown mare nearer to his gray gelding, though she already stayed as close to him as Nynaeve did to Lan. Lan’s bruises, and a broken arm, had been Healed before she had attended to Rand. Min’s face reflected the worry flowing through the bond. Letting her cloak go on the wind, she patted his arm. “You don’t have to think about it anymore.”
“I’m grateful to Far Madding, Min.” His voice was emotionless, distant, as it had been when he seized saidin in the early days. He would have warmed it for her, but that seemed beyond him. “I really did find what I needed here.” If a sword had memory, it might be grateful to the forge fire, but never fond of it. When they were waved through, he cantered the gray up the hard-packed dirt road and into the hills, and he did not so much as glance back until trees hid any sight of the city.
The road climbed and wound through forested winter hills, where only pine and leatherleaf showed green and most branches were stark and gray, and suddenly the Source was there again, seemingly just beyond the corner of his eye. It pulsed and beckoned and filled him with hunger like starvation. Without thought he reached out and filled the emptiness in himself with saidin, an avalanche of fire, a storm of ice, all larded with the filthy taint that made the larger wound in his side pulse. He swayed in the saddle as his head spun and his stomach clenched even as he fought to ride the avalanche that tried to sear his mind, to soar on the storm that tried to scour his soul. There was no forgiveness or pity in the male half of the Power. A man fought it, or died. He could feel the three Asha’man behind him filling themselves too, drinking at saidin like men just out of the Waste who had found water. In his head, Lews Therin sighed with relief.
Min reined her mount so close to him that their legs touched. “Are you all right?” she said worriedly. “You look ill.”
“I’m as well as rainwater,” he told her, and the lie was not just about his belly. He was steel, and to his surprise, still not hard enough. He had intended sending her to Caemlyn, with Alivia to protect her. If the golden-haired woman was going to help him die, he had to be able to trust her. He had planned his words, but looking into Min’s dark eyes, he was not hard enough to make his tongue form them. Turning the gray in among the bare-branched trees, he spoke to Cadsuane over his shoulder. “This is the place.”
She followed him, of course. They all did.  He would have left her behind, but on that subject, Cadsuane had given him her first advice. You made a bargain with them, boy, the same as signing a treaty. Or giving your word. Keep it, or tell them it’s broken. Otherwise, you are just a thief. Blunt, to the point, and in tones that left no doubt as to her opinion of thieves. He had never promised to follow her counsel, but she was too reluctant about being his advisor at all for him to risk driving her away this soon, so the Wavemistress and the other two Sea Folk rode with Alivia, ahead of Verin and the other five Aes Sedai who had sworn to him, and the four who were Cadsuane’s companions. She would as soon leave him as them, he was certain, maybe sooner.
To other eyes than his, nothing distinguished the place where he had dug before going into Far Madding. To his eyes, a thin shaft that shone like a lantern rose through the damp mulch on the forest floor. Even another man who could channel could have walked through that shaft without knowing it was there. He did not bother to dismount. Using flows of Air, he ripped aside the thick layer of rotting leaves and twigs and shoveled away damp earth until he uncovered a long, narrow bundle tied with leather cords. Clods of dirt clung to the wrapping-cloth as he floated Callandor to his hand. He had not dared carry that to Far Madding. Without a scabbard, he would have had to leave it at the bridge fortress, a dangerous flag waiting to announce his presence. It was unlikely there was another sword made of crystal to be found in the world, and too many people knew that the Dragon Reborn had one. And leaving it here, he had still ended up in a dark, cramped stone box under the . . . No. That was done and over. Over. Lews Therin panted in the shadows of his mind.
Thrusting Callandor under his saddle-girth, he reined the gray around to face the others. The horses held their tails tight against the wind, but now and then one stamped a hoof or tossed its head, impatient to be moving again after so long in the stable. The leather scrip that hung from Nynaeve’s shoulder looked incongruous with all the begemmed ter’angreal she wore. Now that the time was near, she was stroking the bulging scrip, apparently without realizing what she was doing. She was trying to hide her fear, but her chin trembled. Cadsuane was looking at him impassively. Her cowl had fallen down her back, and sometimes a gust stronger than most swayed the golden fish and birds, stars and moons, dangling from her bun.
“I am going to remove the taint from the male half of the Source,” he announced.
The three Asha’man, now in plain dark coats and cloaks like the other Warders, exchanged excited glances, but a ripple passed through the Aes Sedai. Nesune let out a gasp that seemed too large for the slender, bird-like sister.
Cadsuane’s expression never altered. “With that?” she said, raising a skeptical eyebrow at the bundle beneath his leg.
“With the Choedan Kal,” he replied. That name was another gift from Lews Therin, resting in Rand’s head as if it had always been there. “You know them as immense statues, sa’angreal, one buried in Cairhien, the other on Tremalking.” Harine’s head jerked, making the golden medallions on her nose chain click together, at mention of the Sea Folk island. “They’re too big to be moved with any ease, but I have a pair of ter’angreal called access keys. Using those, the Choedan Kal can be tapped from anywhere in the world.”
Dangerous, Lews Therin moaned. Madness. Rand ignored him. For the moment, only Cadsuane mattered.
Her bay flicked one black ear, and at that he seemed more excitable than his rider. “One of those sa’angreal is made for a woman,” she said coolly. “Who do you propose to use that? Or do these keys allow you to draw on both yourself?”
“Nynaeve will link with me.” He trusted Nynaeve, to link with, but no one else. She was Aes Sedai, but she had been the Wisdom of Emond’s Field; he had to trust her. She smiled at him and nodded firmly, her chin no longer trembling. “Don’t try to stop me, Cadsuane.” She said nothing, only studied him, dark eyes weighing and measuring.
“Forgive me, Cadsuane,” Kumira broke into the silence, heeling her dapple forward. “Young man, have you considered the possibility of failure? Have you considered the consequences of failure?”
“I must ask the same question,” Nesune said sharply. She sat very straight in her saddle, and her dark eyes met Rand’s gaze levelly. “By everything I have read, the attempt to use those sa’angreal may result in disaster. Together, they might be strong enough to crack the world like an egg.”
Like an egg! Lews Therin agreed. They were never tested, never tried. This is insane! he shrieked. You are mad! Mad!
 More will have, by now. There is a risk to doing this, but it’s all maybe and might. If I don’t try, the certainty is that more and more men will go mad, maybe scores, maybe all of us, and sooner or later it will be too many to be killed easily. Will you enjoy waiting for the Last Battle with a hundred rabid Asha’man wandering about, or two hundred, or five? And maybe me one of them? How long will the world survive that?” He spoke to the two Browns, but it was Cadsuane who he watched. Her almost black eyes never left him. He needed to keep her with him, but if she tried to talk him out of it, he would reject her advice no matter the consequences. If she tried to stop him . . . ? Saidin raged inside him.
“Will you do the deed here?” she asked.
“In Shadar Logoth,” he told her, and she nodded.
“A fitting place,” she said, “if we are to risk destroying the world.”
Lews Therin screamed, a dwindling howl that echoed inside Rand’s skull as the voice fled into the dark depths. There was nowhere to hide, though. No safe place.
The gateway he wove did not open into the ruined city of Shadar Logoth itself, but to a thinly wooded, uneven hilltop a few miles to the north, where the horse hooves rang on sparse, stony soil that had stunted the leafless trees, and ragged patches of snow covered the ground. As Rand dismounted, his eye was caught by distant glimpses of the place once called Aridhol showing above the trees, towers that ended abruptly in jagged stone, and white onion-shaped domes that could have sheltered a village had they been whole. He did not look for long. Despite the clear morning sky, those pale domes failed to gleam as they should, as if something cast a shadow over the sprawling ruin. Even at this distance from the city, the second never-healing wound in his side had begun to throb faintly. The slash given by Padan Fain’s dagger, the dagger that had come from Shadar Logoth, did not beat together with the pulsing of the larger wound it cut across, but rather against it, alternating.
Cadsuane took charge, issuing brisk commands, as might have been expected. One way or another, Aes Sedai always did, given half a chance, and Rand did not try to stop her. Lan and Nethan and Bassane rode down into the forest to scout, and the other Warders hurried to fasten the horses to low branches out of the way. Min stood up in her stirrups and pulled Rand’s head to where she could kiss his eyes. Without speaking a word, she went to join the men with the horses. The bond surged with her love for him, with confidence and a trust so complete that he stared after her in amazement.
Eben came to take Rand’s mount, grinning from ear to ear. Together with his nose, those ears still seemed to make up half his face, but he was a slender youth rather than gawky, now. “It will be wonderful, channeling without the taint, my Lord Dragon,” he said excitedly. Rand thought Eben might be as much as seventeen, but he sounded younger. “That always makes me want to empty my belly, if I think on it.” He trotted away with the gray, still grinning.
The Power roared in Rand, and the filth tarnishing the pure life of saidin seeped into him, rank runnels that would bring madness and death.
Cadsuane gathered the Aes Sedai around her, and Alivia and the Sea Folk Windfinder, too. Harine grumbled loudly about being excluded, until a finger pointed by Cadsuane sent her stalking across the hilltop. Moad, in his odd blue quilted coat, sat Harine down on an outcrop, and talked soothingly, though sometimes his eyes went to the surrounding trees, and then he slid a hand along the long ivory hilt of his sword. Jahar appeared from the direction of the horses, stripping the cloth wrappings from Callandor. The crystal sword, with its long clear hilt and slightly curving blade, sparkled in the pale sunlight. At an imperious gesture from Merise, he quickened his step to join her. Damer was in that group, too, and Eben. Cadsuane had not asked to use Callandor. That could pass. For now, it could.
“That woman could try a stone’s patience!” Nynaeve muttered, striding up to Rand.  “To the Pit of Doom with her, that’s what I say! Are you sure Min couldn’t be wrong just this once? Well, I suppose not. But still . . . ! Will you stop smiling like that? You’d make a cat nervous!”
“We might as well begin,” he told her, and she blinked.
“Shouldn’t we wait on Cadsuane?” No one would suspect she had been complaining about the Aes Sedai a moment earlier. If anything, she sounded anxious not to upset her.
“She will do what she will do, Nynaeve. With your help, I will do what I must.”
Still she hesitated, clutching the scrip to her chest and casting worried glances in the direction of the women gathered around Cadsuane. Alivia left that group and hurried toward them across the uneven ground holding her cloak closed with both hands.
“Cadsuane says I must have the ter’angreal, Nynaeve,” she said in that soft Seanchan drawl. “Now don’t argue; there isn’t time. Besides, they are no good to you if you’re going to be linked to him.”
This time the look Nynaeve directed toward the women around Cadsuane was near murderous, but she stripped off rings and bracelets, muttering under her breath, and handed the jeweled belt and necklace to Alivia, as well. After a moment, she sighed and unfastened the peculiar bracelet connected to finger rings by flat chains. “You might as well take this, too. I don’t suppose I need an angreal if I’m going to be using the most powerful sa’angreal ever made. But I want them all back, understand,” she finished fiercely.
“I am not a thief,” the hawk-eyed woman told her primly, slipping the four rings over the fingers other left hand. Strangely, the angreal that fitted Nynaeve so well fit on her longer hand just as easily. The two women both stared at the thing.
It came to him then that neither of them acknowledged any possibility that he might fail here. He wished he could be as certain.
“Are you going to wait all day, Rand?” Nynaeve asked when Alivia set off back to Cadsuane, even more quickly than she had come. Smoothing her cloak under her, Nynaeve sat down on an upthrust gray stone the size of a small bench, pulled the scrip onto her lap, and flipped back the leather flap.
Rand folded himself to the ground cross-legged in front of her as she produced the two access keys, smooth white statues a foot tall, each holding a clear sphere in one upraised hand. The figure of a bearded man in robes, she handed to him. That of a robed woman, she set on the ground at her feet. The faces on those figures were serene and strong and wise with years.
“You must put yourself right on the edge of embracing the Source,” she told him, smoothing skirts that did not need smoothing. “Then I can link with you.”
With a sigh, Rand put down the bearded man and released saidin. Raging fire and cold vanished, and the grease-slick vileness of the taint, and with them, life seemed to dwindle, too, turning the world pale and drab. He placed his hands on the ground beside him against the sickness that would strike when he took hold of the Source again, but a different dizziness suddenly spun his head.  Light, if that ever happened while he was actually grabbing hold of saidin . . .
“Now,” he said, and reached for the Source through the bearded man. Reached, but did not seize it. He hung on the brink, wanting to howl with the agony as flickering flames seemed to broil him even while shrieking winds blasted particles of frozen sand across his skin. Watching Nynaeve take a quick breath, he knew it lasted only an instant, yet it seemed he endured for hours before . . .
Saidin flowed through him, all the molten fury and icy tumbling, all the foulness, and he could not control a hair-thin thread. He could see the flow from him into Nynaeve. To feel it seething through him, feel the treacherous tides and shifting ground that could destroy him in a heartbeat, to feel that without being able to fight or control was an agony in itself. He was aware of her, he realized suddenly, in much the same way he was aware of Min, but all he could think of was saidin, flooding through him uncontrolled.
She drew a shuddering breath. “How can you stand . . . that?” she said hoarsely. “All chaos and rage and death. Light! Now, you must try as hard as you can to control the flows while I—” Desperate to gain his balance in that never-ending war with saidin, he did as she said, and she yelped and jumped. “You were supposed to wait until I . . . ” she began in angry tones, then went on in a merely irritated voice. “Well, at least I’m rid of it. What are you so wide-eyed about? I’m the one had her skin yanked off!”
“Saidar,” he murmured in wonder. It was so . . . different.
Alongside the turmoil of saidin, saidar was a tranquil river flowing smoothly. He dipped into that river, and suddenly he was struggling against currents that tried to pull him further in, swirling whirlpools that tried to yank him under. The harder he struggled, the stronger the shifting fluxes grew. Only an instant since he had tried to control saidar, and already he felt as if he was drowning in it, being swept away into eternity. Nynaeve had warned him what he must do, but it seemed so foreign he had not truly believed until now. With an effort, he forced himself to stop fighting the currents, and as quickly as that the river was tranquil once more.
That was the first difficulty, to fight saidin while surrendering to saidar. The first difficulty, and the first key to what he had to do. The male and female halves of the True Source were alike and unalike, attracting and repelling, fighting against each other even as they worked together to drive the Wheel of Time. The taint on the male half had its opposite twin, too. The wound given him by Ishamael throbbed in time with the taint, while the other, from Fain’s blade, beat counterpoint in time with the evil that had killed Aridhol.
Awkwardly, forcing himself to work gently, to use the unfamiliar saidar’s own immense strength to guide it as he wanted, he wove a conduit that touched the male half of the Source at one end and the distantly seen city at the other. The conduit had to be of untainted saidar. If this worked as he hoped, a tube of saidin might shatter when the taint began to leech out of it. He thought of it as a tube, at least, though it was not. The weave did not form at all as he expected it to. As if saidar had a mind of its own, the weave took on convolutions and spirals that made him think of a flower. There was nothing to see, no grand weaves sweeping down from the sky. The Source lay at the heart of creation. The Source was everywhere, even in Shadar Logoth. The conduit covered distance beyond his imagining, and had no length at all. It had to be a conduit, no matter its appearance. If it was not . . .
Drawing on saidin, fighting it, mastering it in the deadly dance he knew so well, he forced it into the flowery weave of saidar. And it flowed through. Saidin and saidar, like and unlike, could not mix. The flow of saidin squeezed in on itself, away from the surrounding saidar, and the saidar pushed it from all sides, compressing it further, making it flow faster. Pure saidin, pure except for the taint, touched Shadar Logoth.
Rand frowned. Had he been wrong? Nothing was happening. Except . . . The wounds in his side seemed to be throbbing faster. Amid the firestorm and icy fury of saidin, it seemed that the foulness stirred and shifted. Just a slight movement that might have escaped notice had he not been straining to find anything. A slight stirring in the midst of chaos, but all in the same direction.
“Go on,” Nynaeve urged. Her eyes were bright, as though just having saidar flow in her was enough for joy.
He drew more deeply on both halves of the source, strengthening the conduit as he forced more of saidin into it, drew on the Power until nothing he did would bring more. He wanted to shout at how much was flowing into him, so much that it seemed he did not exist any more, only the One Power. He heard Nynaeve groan, but the murderous struggle with saidin consumed him.
Fingering the Great Serpent ring on her left forefinger, Elza stared at the man she had sworn to serve. He sat on the ground, grim-faced, staring straight ahead as if he could not see the wilder Nynaeve sitting right in front of him, glowing like the sun. Perhaps he could not. She could feel saidar sweeping through Nynaeve in torrents undreamed of. All the sisters of the Tower combined could have wielded only a fraction of that ocean. She envied the wilder that, and at the same time she thought she might have gone mad from the sheer joy of it. Despite the cold, there were beads of sweat on Nynaeve’s face. Her lips were parted, and her wide eyes stared rapturously beyond the Dragon Reborn.
“It will begin soon, I fear,” Cadsuane announced. Turning away from the seated pair, the gray-haired sister planted her hands on her hips and swept a piercing gaze across the hilltop. “They’ll be feeling that in Tar Valon, and maybe on the other side of the world. Everyone to your places.”
“Come, Elza,” Merise said, the light of saidar suddenly around her.
Elza allowed herself to be drawn into a link with the stern-faced sister, but she flinched when Merise added her Asha’man Warder to the circle. He was darkly beautiful, but the crystal sword in his hands shone with a faint light, and she could feel the incredible seething tumult that must be saidin. Even though Merise was controlling the flows, the vileness of saidin turned Elza’s stomach. It was a midden heap rotting in a sweltering summer. The other Green was a lovely woman in spite of her sternness, but her mouth thinned as if she, too, were struggling not to vomit.
All around the hilltop the circles were forming, Sarene and Corele linked with the old man, Flinn, and Nesune, Beldeine and Daigian with the boy Hopwil. Verin and Kumira even made a circle with the Sea Folk wilder; she was actually quite strong, and everyone had to be used. As soon as each of those circles formed, it moved off the hilltop, each vanishing among the trees in a different direction. Alivia, the very peculiar wilder who seemed to have no other name, strode off north, cloak flapping behind her, surrounded by the glow of the Power. A very troubling woman with those tiny lines around her eyes, and incredibly strong. Elza would have given a great deal to have her hands on those ter’angreal the woman wore.
Alivia and the three circles would provide an encircling defense, if it were needed, but the greatest need lay right there on the hilltop. The Dragon Reborn must be protected at all costs. That job Cadsuane had taken on herself, of course, but Merise’s circle would remain there, too. Cadsuane must have had an angreal of her own, from the amount of saidar she was drawing, more than Elza and Merise combined, yet even that paled beside the Power that flowed though Callandor.
Elza glanced toward the Dragon Reborn and drew a deep breath. “Merise, I know I shouldn’t ask, but may I meld the flows?”
She expected to have to plead, but the taller woman hesitated only a moment before nodding and passing control to her. Almost immediately Merise’s mouth softened, though it could never be called soft. Fire and ice and filth welled up in Elza, and she shuddered. Whatever the cost, the Dragon Reborn had to reach the Last Battle. Whatever the cost.
Riding his cart down the snowy road to Tremonsien, Barmellin wondered whether old Maglin at The Nine Rings would pay what he wanted for the plum brandy in the cart behind him. He was not sanguine. She was tight with silver, Maglin was, the brandy was not very good, and this late in the winter, she might be willing to wait until spring to get better. Suddenly he realized that the day seemed very bright. Almost like summer noon instead of a winter morning. Strangest of all, the glow seemed to be coming from the huge pit beside the road where workmen from the City had been digging away until the previous year. There was supposed to be a monstrous statue down there, but he had never been interested enough to actually look for himself.
Now, almost against his will, he reined in his stout mare and climbed down into the snow to trudge to the brink of the pit.  Squinting through his fingers, he could make out a glowing ball, like a second sun. Abruptly, it came to him that this must the One Power.
 He was going to stay in his own house and drink that brandy himself. All of it.
Strolling lost in thought, Timna barely saw the fallow fields that covered all the hillsides but one around her. Tremalking was a large island, and this far from the sea, the wind carried no hint of salt, yet it was the Atha’an Miere that troubled her. They refused the Water Way, yet Timna was one of the Guides chosen to protect them from themselves, if possible. That was very difficult now, with them all in an uproar over this Coramoor of theirs. Very few remained on the island. Even the Governors, always fretting at being away from the sea as the Atha’an Miere did, had set sail to search for him in any craft they could find.
Suddenly the one unplowed hill caught her eye. A great stone hand stuck out of the ground clasping a clear sphere as large as a house. And that sphere was shining like a glorious summer sun.
All thoughts of the Atha’an Miere gone, Timna gathered her cloak and sat down on the ground, smiling to think that she might see the fulfillment of prophecy and the end of Illusion.

She could feel it. That much of saidar being drawn to one spot was a beacon that any woman in the world who could channel would feel and locate. So he had found a woman to use the other access key. She would have faced the Great Lord—faced the Creator!—with him. She would have shared the power with him, let him rule the world at her side. And he had spurned her love, spurned her!
The fool babbling at her was an important man as such things were accounted here and now, but she did not have time to make certain of his trustworthiness, and without that, she could not leave him to babble, not when she could feel Moridin’s hand caressing the cour’souvra that held her soul. A razor-thin flow of Air sliced the fellow’s beard in two as it took off his head. Another flow shoved the body backward so the blood fountaining from the stub of his neck did not spot her dress. Before body or head hit the stone floor, she had spun her gateway. A beacon she could point to, beckoning her.
As she stepped into rolling forest where scattered carpets of snow littered the ground beneath stark branches bare save for the thick ropes of drooping brown vines, she wondered where the beacon had drawn her. It did not matter. South of her, that beacon shone, enough saidar to lay waste to a continent in one blow. He would be there, him and whoever the woman was he had betrayed her with. Carefully, she drew on the Power to spin a web for his death.
Lightnings such as Cadsuane had never seen streaked down from the cloudless sky, not jagged bolts but lances of silver-blue that struck at the hilltop where she stood, and struck instead the inverted shield she had woven, erupting with a deafening roar fifty feet above her head. Even within the shield the air crackled, and her hair stirred and lifted. Without the aid of the angreal that looked a little like a shrike dangling from her bun, she would not have been able to hold the shield up.
A second golden bird, a swallow, hung from her hand by its thin chain. “There,” she said, pointing in the direction it seemed to be flying. A pity she could not say how far away the Power had been channeled, or whether by a man or a woman, but the direction would have to do. She hoped there would be no . . . mishaps. Her people were out there, too. If the warning came with an attack, though, there could not be much doubt.
As soon as the single word left her mouth, a fountain of flame erupted in the forest to the north, and then another and another, a staggered line racing northward. Callandor shone like a flame in young Jahar’s hands. Surprisingly, from the intensity on Elza’s face and the way she gripped her skirts in fists, she was the one directing those flows.
Merise took a fistful of the boy’s black hair and gently shook his head. “Steady, my pretty,” she murmured. “Oh, steady, my lovely strong one.” He smiled at her, a ravishing smile.
Cadsuane shook her own head slightly. Understanding any sister’s relationship with her Warder was difficult, especially among Greens, but she could not begin to fathom what passed between Merise and her boys.
Her real attention was on another boy, though. Nynaeve was swaying, groaning with the ecstasy of such an unbelievable mass of saidar flooding through her, but Rand sat like a stone, sweat rolling down his face. His eyes were blank, like polished sapphires. Was he even aware of what was happening around him?
The swallow turned on its chain beneath her hand.
“There,” she said, pointing toward the ruins of Shadar Logoth.
Rand could not see Nynaeve any longer. He could not see anything, feel anything. He swam in surging seas of flame, scrambled across collapsing mountains of ice. The taint flowed like an ocean tide, trying to sweep him away. If he lost control for an instant, it would strip away everything that was him and carry that down the conduit, too. As bad, or maybe worse, despite the tide of filth flooding through that odd flower, the taint on the male half of the Source seemed no less. It was like oil floating on water in a coating so thin you would not notice till you touched the surface, yet covering the vastness of the male half, it was an ocean in itself. He had to hold on. He had to. But for how long? How long could he hold on?
If he could undo what al’Thor had done at the source, Demandred thought as he stepped through his gateway into Shadar Logoth, undo it sharply and suddenly, that might well kill the man, or at least sear the ability to channel out of him. He had reasoned out what al’Thor’s plan had to be as soon as he realized where the access key was. A brilliant scheme, he did not mind admitting, however insanely dangerous. Lews Therin had always been a brilliant planner, too, if not so brilliant as everyone made out. Not nearly as brilliant as Demandred himself.
One look at the rubble-strewn street changed his mind about altering anything, though. Beside him rose half a pale dome, its shattered top two hundred feet or more above the street, and above it, the sky held the light of midmorning. From the broken rim of the ruin down to the street, though, the air was dark with shadows, as if night were already falling. The city . . . quivered. He could feel it through his boots.
Fire erupted in the forest, great explosions spun of saidin that hurled trees into the air on gouts of flame that sped toward him, but he was already weaving a gateway. Leaping through, he let it vanish and ran through the vine-draped trees as hard as he could, plowing through patches of snow, stumbling over rocks hidden in the mulch, but not slowing down, never that. The web had been reversed, for caution’s sake, but so had the first, and he had been a soldier. Still running, he heard the explosions he expected, and knew they were racing toward where his gateway had been as surely as they had raced straight toward him among the ruins. They were far enough from him now to present no danger, though. Without slowing, he turned toward the access key. With the amount of saidin pouring through it, there might as well have been a fiery arrow in the sky pointing to al’Thor.
So. Unless someone in this accursed Age had discovered yet another unknown ability, al’Thor must have acquired a device, a ter’angreal, that could detect a man channeling. From what he knew of what people now called the Breaking, after he himself had been imprisoned at Shayol Ghul, any woman who knew how to make ter’angreal would have been trying to create one that would do that. In war, the other side always came up with something you did not expect, and you had to counter it. He had always been good at war. First, he needed to get closer.
Suddenly he saw people off to the right ahead of him through the trees, and sheltered behind a rough gray trunk. A bald-headed old man with a fringe of white hair was limping along between two women, one of them beautiful in a wild way, the other stunning. What were they doing in these woods? Who were they? Friends of al’Thor, or just people in the wrong place at the wrong time? He hesitated to kill them, whoever they were. Any use of the Power would warn al’Thor. He would have to wait until they passed. The old man’s head was turning as if he were searching for something among the trees, but Demandred doubted a fellow that decrepit could see very far.
 That tottering old man was an Asha’man! And at least one of the women must be what passed for Aes Sedai in this time, and joined with the fellow in a ring.
He tried to launch his own attack and crush them, but the old man flung web after web at him without pause, and it was all he could do to fend them off. Those that struck trees enveloped them in flame or blew the trunks apart in splinters. He was a general, a great general, but generals did not have to fight alongside the men they commanded! Snarling, he began to retreat amid the crackle of burning trees and the thunder of explosions. Away from the key. Sooner or later the old man had to tire, and then he could take care of killing al’Thor. If one of the others did not get there first. He hoped fervently they did not.
Skirts hiked to her knees, cursing, Cyndane ran from her third gateway as soon as she was through. She could hear the explosions marching toward the site, but this time she had realized why they came straight for her. Tripping on vines hidden in the snow, bumping into tree trunks, she ran. She hated forests! At least some of the others were here—she had seen those fountaining fires speed elsewhere than at her; she could feel saidar being spun at more than one place, spun with fury—but she prayed to the Great Lord that she would reach Lews Therin first. She wanted to see him die, she realized, and for that, she would have to get closer.
Crouching behind a fallen log, Osan’gar panted from the exertion of running. Those months masquerading as Corlan Dashiva had not made him any fonder of exercise. The explosions that had almost killed him died away, then started up again somewhere in the distance, and he cautiously raised himself enough to peek over the log.  He had never been a soldier, not really. His talents, his genius, lay elsewhere. The Trollocs were his making, and thus the Myrddraal that had sprung from them, and many other creatures that had rocked the world and made his name famous. The access key blazed with saidin, but he could feel lesser amounts being wielded, too, in various directions.
He had expected others of the Chosen to be here ahead of him, had hoped they might have finished the task before he arrived, but plainly they had not. Plainly al’Thor had brought along some of those Asha’man, and by the amount of saidin that had gone into the eruptions that targeted him, Callandor as well. And maybe some of his tame so-called Aes Sedai.
Crouching again, he bit his lip. This forest was a very dangerous place, more so than he had expected, and nowhere for a genius. But the fact remained that Moridin terrified him. The man had always terrified him, from the very beginning. He had been mad with power before they were sealed into the Bore, and since they had been freed, he seemed to think that he was the Great Lord. Moridin would find out somehow if he fled, and kill him. Worse, if al’Thor succeeded, the Great Lord might decide to kill both of them, and Osan’gar as well. He did not care whether they died, but he did very much about himself.
He was not good at judging time by the sun, but it was obviously still short of noon. Hauling himself from the ground, he dabbed at the dirt on his clothes, then gave up in disgust and began to skulk from tree to tree in what he imagined was a stealthy manner. It was toward the key that he skulked. Perhaps one of the others would finish the man before he got close to it, but if not, perhaps he would find the chance to be a hero. Carefully, of course.
Verin frowned at the apparition making its way through the trees off to her left. She could think of no other term for a woman walking through the forest in gems and a gown that shifted through every color from black to white and sometimes even turned transparent! She was not hurrying, but she was heading toward the hill where Rand was. And unless Verin was very much mistaken, she was one of the Forsaken.
“Are we just going to watch her?” Shalon whispered furiously. She had been upset that she was not the one to meld the flows, as if a wilder’s strength counted with Aes Sedai, and hours tramping through the woods had not improved her temper.
“We must do something,” Kumira said softly, and Verin nodded.
“I was just deciding what.” A shield, she decided. A captive Forsaken might prove very useful.
Using the full strength of her circle, she wove her shield, and watched aghast as it rebounded. The woman was already embracing saidar, though no light shone around her, and she was immensely strong!
Then she had no time for thought of anything as the golden-haired woman spun around and began channeling. Verin could not see the weaves, but she knew when she was fighting off an attack on her life, and she had come too far to die here.
Eben hitched his cloak around himself and wished he were better at ignoring the cold. Simple cold, he could ignore, but not the wind that had sprung up since the sun passed its zenith. The three sisters linked to him simply let the wind take their cloaks as they tried to watch every direction at once. Daigian was leading the circle—because of him, he thought—but she was drawing so lightly that he felt barely a whisper of saidin passing through him. She would not want to face that until she had to. He lifted her cowl back into place on her head, and she smiled at him from its depths. The bond carried her affection to him, and his own back, he supposed. With time, he thought he might come to love this little Aes Sedai.
The torrent of saidin far behind him had a tendency to wash out his awareness of other channeling, but he could feel others wielding the Power. The battle had been joined, elsewhere, and so far all the four of them had done was walk. He did not mind that much, really. He had been at Dumai’s Wells, and fought the Seanchan, and he had learned that battles were more fun in a book than in the flesh. What did irk him was that he had not been given control of the circle. Of course, Jahar had not, but he figured Merise amused herself by making Jahar balance a cookie on his nose. Damer had been given control of that circle, though. Just because the man had a few years on him—well, more than a few; he was older than Eben’s da—was no reason for Cadsuane to look at him as if he were a—
“Can you help me? I seem to have lost my way, and my horse.” The woman who stepped from behind a tree ahead of them did not even have a cloak. Instead, she wore a gown of deep green silk cut so low that half of her lush bosom was exposed. Waves of black hair surrounded a beautiful face, with green eyes that sparkled as she smiled.
“A strange place to be riding,” Beldeine said suspiciously. The pretty Green had not been pleased when Cadsuane put Daigian in charge, and she had taken every opportunity to state her opinion of Daigian’s decisions.
“I hadn’t meant to ride so far,” the woman said coming closer. “I see you’re all Aes Sedai. With a . . . groom? Do you know what all the commotion is about?”
Suddenly, Eben felt the blood drain from his face. What he felt was impossible! The green-eyed woman frowned in surprise, and he did the only thing that he could.
“She’s holding saidin!” he shouted, and threw himself at her as he felt Daigian draw deeply on the Power.
Cyndane slowed at the sight of the woman standing among the trees a hundred paces ahead of her, a tall yellow-haired woman who simply watched her come closer. The feel of battles being fought with the Power in other places made her wary at the same time it gave her hope. The woman was plainly dressed in wool, but incongruously decked with gems as if she were a great lady. With saidar in her, Cyndane could see the faint lines at the corners of the woman’s eyes. Not one of those who called themselves Aes Sedai, then. But who? And why did she stand there as if she would bar Cyndane’s way? It did not really matter. Channeling now would give her away, but she had time. The key still shone as a beacon of the Power. Lews Therin still lived. No matter how fierce the other woman’s eyes, a knife would do for her, if she really thought she could be a bar. And just in case she proved to be what they called a wilder, Cyndane prepared a small present for her, a reversed web she would not even see until it was too late.
Abruptly the light of saidar appeared around the woman, but the ready ball of fire streaked from Cyndane’s hand, small enough to escape detection she hoped, but enough to burn a hole through this woman who—
Just as it reached the woman, almost close enough to singe her garments, the web of Fire unraveled. The woman did not do anything; the net simply came apart! Cyndane had never heard of a ter’angreal that would break a web, but it must be that.
Then the woman struck back at her, and she suffered her second shock. She was stronger than Cyndane had been before the Aelfinn and the Eelfinn held her! That was impossible; no woman could be stronger. She must have an angreal, too. Shock lasted only the time it took her to slice the other woman’s flows. She did not know how to reverse them. Maybe that would be enough advantage. She would see Lews Therin die! The taller woman jerked as her cut flows snapped back into her, but even as she shifted her feet with the blow, she channeled again. Snarling, Cyndane fought back, and the earth heaved beneath their feet. She would see him die! She would!
The high hilltop was not very near to the access key, but even so the key shone so brightly in Moghedien’s head that she hungered for just a sip at that immense flow of saidar. To hold so much, the thousandth part of so much, would be ecstasy. She hungered, but this wooded vantage was as near as she intended going. Only the threat of Moridin’s hands caressing her cour’souvra had driven her to Travel here at all, and she had delayed coming, prayed that it would be over before she was forced to. Always she had worked in secrecy, but she had had to flee an attack as soon as she arrived, and in widely separated places in the forest spread out before her, lightnings and fires woven of saidar and others that must have been saidin flashed and flared beneath the mid-afternoon sun. Black smoke rose in plumes from burning clumps of trees, and thunderous explosions rolled through the air.
Who fought, who lived, who died were all matters of indifference to her. Except that it would be pleasant if Cyndane or Graendal perished. Or both. Moghedien would not, not thrashing about in the middle of a battle. And if that were not bad enough, there was what stood beyond the shining key, an immense flattened dome of black in the forest, as though night had turned to stone. She flinched as a ripple passed across the dark surface and the dome heaved perceptibly higher. Madness to go any closer to that, whatever it was. Moridin would not know what she did here, or did not do.
Retreating to the back of the hilltop, away from the shining key and the strange dome, she sat down to do what she had done so often in the past. Watch from the shadows, and survive.
Inside his head, Rand was screaming. He was sure that he was screaming, that Lews Therin was screaming, but he could not hear either voice in the roar. The foul ocean of the taint was flooding through him, howling with its speed. Tidal waves of vileness crashed over him. Raging gales of filth ripped at him. The only reason he knew that he still held the Power was the taint. Saidin could be shifting, flaring, about to kill him, and he would never know. That putrid flood overwhelmed everything else, and he hung on by his fingernails to keep from being swept away on it. The taint was moving. That was all that counted, now. He had to hold on!
“What can you tell me, Min?” Cadsuane kept her feet despite her weariness. Holding that shield through most of a day was enough to tire anyone.
There had not been an attack on the hilltop for some time, and in fact, it seemed the only active channeling she could sense was what Nynaeve and the boy were doing. Elza was pacing an endless circle around the crest of the hill, still linked to Merise and Jahar, but there was nothing for her to do at the moment except scan the hills around them. Jahar was sitting on a stone with Callandor shining faintly in the crook of his arm. Merise sat on the ground beside him with her head on his knee, and he was stroking her hair.
“Well, Min?” Cadsuane demanded.
The girl looked up angrily from the depression in the stony ground where Tomas and Moad had bundled her and Harine. At least the men had sense enough to accept that they could not fight any part of this fight. Harine wore a sullen scowl, and more than once it had been necessary for one of the men to restrain Min from going to young al’Thor. They had actually had to take her knives away, after she tried to use the blades on them.
“I know he’s alive,” the girl muttered, “and I think he’s hurting. Only, if I can feel enough to think he’s hurting, then he’s in agony. Let me go to him.”
“You would only get in the way now.”
Ignoring the girl’s frustrated groan, Cadsuane walked across the uneven ground to where Rand and Nynaeve sat, but for a moment she did not look at them. Even at a distance of miles, the black dome looked immense, rearing a thousand feet at its height. And it was swelling. The surface looked like black steel, though it did not sparkle in the afternoon sun. If anything, the light seemed to dim around it.
 If he was in agony as Min said, he showed no sign of it. And if he was, Cadsuane did not know what she could do, what she dared to do. Disturbing him now in any way might have dire consequences. Glancing at that rising dead-black dome, Cadsuane grunted. Having let him begin in the first place might have dire consequences, too.
With a moan, Nynaeve slipped from her stone seat to the ground. Her dress was sodden with sweat, and strands of hair clung to her slick face. Her eyelids fluttered weakly, and her breasts heaved as she gulped air desperately. “No more,” she whimpered. “I cannot stand any more.”
Cadsuane hesitated, something she was not accustomed to doing. The girl could not leave the circle until young al’Thor released her, but unless these Choedan Kal were flawed in the same way as Callandor, she would be buffered against taking in enough of the Power to damage her. Except that she was acting as a conduit for far more of saidar than the entire White Tower could have handled using every angreal and sa’angreal the Tower possessed. After having that flow through her for hours, simple physical exhaustion might be killing her.
Kneeling beside the girl, Cadsuane laid the swallow on the ground beside her, took the girl’s head in her hands and lessened the amount of saidar she was putting into the shield. Her abilities with Healing were no more than average, but she could wash away some of the girl’s exhaustion at least without falling over herself. She was very conscious of the weakened shield over them, though, and she wasted no time in forming the weaves.
Scrambling to the top of the hill, Osan’gar dropped to the ground on his belly and smiled as he crabbed sideways to shelter behind a tree. From here, with saidin in him, he could see the next crest clearly, and the people on it. Not as many as he had expected. One woman was making a slow circuit around the crest, peering into the trees, but everyone else was still, Narishma sitting with Callandor glowing in his hands and a woman’s head on his knee. There were two other women that Osan’gar could see, one kneeling over the other, but they were obscured by a man’s back. He did not need to see the man’s face to know al’Thor. The key lying on the ground at his side named him. To Osan’gar’s eyes, it shone brightly. In his head, it overwhelmed the sun, a thousand suns. What he could do with that! A pity it had to be destroyed along with al’Thor. But still, he could take Callandor after al’Thor was dead. No one else among the Chosen possessed so much as an angreal. Even Moridin would quail before him once he had that crystal sword. Nae’blis? Osan’gar would be named Nae’blis after he destroyed al’Thor and undid all that he had done here. Laughing softly, he wove balefire. Who would ever have thought that he would turn out to be the hero of the day?
Walking slowly, studying the forested hills around them, Elza suddenly stopped as a flicker of movement caught the corner of her eye.  The day had been very difficult for her. In her captivity among the Aiel tents at Cairhien it had come to her that it was paramount for the Dragon Reborn to reach the Last Battle. It had suddenly become so blindingly obvious that it astounded her she had not seen it before. Now it was clear to her, as clear as saidar made the face of the man trying to hide on that hill while peeking around a tree trunk. Today, she had been forced to fight the Chosen. Surely the Great Lord would understand if she had actually killed any of them, but Corlan Dashiva was only one of those Asha’man. Dashiva raised his hand toward the hill where she stood, and she drew as hard as she could on Callandor in Jahar’s hands. Saidin seemed well suited to destruction, to her. A huge ball of coruscating fire surrounded the other hilltop, red and gold and blue. When it was gone, that other hill ended in a smooth surface fifty feet lower than the old crest.
Moghedien was not sure why she had remained this long. There could not be more than two hours of daylight left, and the forest was quiet. Except for the key, she could not feel saidar being channeled anywhere. That was not to say that someone was not using small amounts somewhere, but nothing like the fury that had raged earlier. The battle was over, the other Chosen dead or flying in defeat. Plainly defeat, since the key still blazed in her head. Amazing that the Choedan Kal had survived continuous use for this long, at this level.
Lying on her belly atop her high vantage point with her chin in her hands, she was watching the great dome. Black no longer seemed to describe it. There was no term for it, now, but black was a pale color by comparison. It was half a ball, now, rearing like a mountain two miles or more into the sky. A thick layer of shadow lay around it, as though it were sucking the last light out of the air. She could not understand why she was not afraid. That thing might grow until it enveloped the entire world, or perhaps shatter the world, as Aran’gar had said it might. But if that happened, there was no safe place, no shadows for the Spider to hide in.
Suddenly something writhed up from that dark smooth surface, like a flame if flames were blacker than black, then another, another, until the dome boiled with Stygian fire. The roar of ten thousand thunders made her clap her hands over her ears and shriek, soundlessly in that crash, and the dome collapsed in on itself in the space of a heartbeat, to a pinpoint, to nothing. It was wind that howled then, rushing toward the vanished dome, dragging her along the stony ground no matter how desperately she clawed for purchase, tumbling her against trees, lifting her into the air. Strangely, she still felt no fear. She thought if she survived this, she would never feel fear again.
Cadsuane let the thing that had been a ter’angreal drop to the ground. It could no longer be called a statue of a woman. The face was as wisely serene as ever, but the figure was broken in two and lumpy like bubbled wax where one side had melted, including the arm that had held the crystal sphere now lying in shattered fragments around the ruined thing. The male figure was whole, and already tucked away in her saddlebags. Callandor was secured, too. It was best not to leave temptation on the open hilltop. Where Shadar Logoth had been there was a now a huge opening in the forest, perfectly round and so wide that even with the sun low on the horizon she could see the far side sloping down into the earth.
Lan, leading his limping warhorse up the slope, dropped the black stallion’s reins when he saw Nynaeve stretched out on the ground and covered to her chin with her cloak. Young al’Thor lay at her side also blanketed in his cloak, with Min curled up against him, her head on his chest. Her eyes were closed, but by her small smile, she was not asleep. Lan barely spared them a glance as he ran the last distance and fell on his knees to raise Nynaeve’s head gently on his arm. She did not stir any more than the boy.
“They are just unconscious,” Cadsuane told him. “Corele says it is better to let them recover on their own.” And how long that might require, Corele had not been prepared to say. Nor had Damer. The wounds in the boy’s side were unchanged, though Damer had expected they would be. It was all very disturbing.
A little farther up the hill, the bald Asha’man was bent over a groaning Beldeine, his fingers writhing just above her as he wove his strange Healing. He had been busy the last hour. Alivia could not stop staring in wonder and flexing the arm that had been broken as well as seared to the bone. Sarene walked unsteadily, but that was just tiredness. She had almost died out there in the forest, and her eyes were still wide with the experience. Whites were not used to that sort of thing.
Not everyone had been so lucky. Verin and the Sea Folk woman were sitting beside the cloak-covered form of Kumira, their lips moving silently in prayers for her soul, and Nesune was trying awkwardly to comfort a weeping Daigian, who cradled young Eben’s corpse in her arms and rocked him like a baby. Greens were used to that sort of thing, but Cadsuane did not like losing two of her people in return for no more than a few singed Forsaken and one dead renegade.
“It’s clean,” Jahar said softly yet again.  Her blue eyes were as stern as ever, but she stroked his black hair gently. “It’s clean.”
Cadsuane exchanged looks with Merise over the boy’s head. Damer and Jahar both said the same thing, the taint was gone, but how could they be sure some scrap did not remain? Merise had allowed her to link with the boy, and she could not feel anything like what the other Green had described, yet how could they be certain? Saidin was so alien that anything could be hidden in that mad chaos.
“I want to leave as soon as the rest of the Warders return,” she announced. There were too many questions for which she had no answers to suit her, but she had young al’Thor now, and she did not intend to lose him. Night fell. On the hilltop, the wind blew dust across the fragments of what had once been a ter’angreal. Below lay the tomb of Shadar Logoth, open to give the world hope. And on distant Tremalking, the word began to spread that the Time of Illusions was at an end.


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Accessing the internal implemenation:
Let create a matrix:
var myMat = rand0(50, 50)
The Array[Array[Double]] v keeps the Matrix internally and can be accessed as:
var ddArr = myMat.getv
Matrix number of rows and columns and can be retrieved as:
myMat.numRows
myMat.numColumns
myMat.Nrows
myMat.Ncols
Matrix length i.e. the total number of elements:
myMat.length
Matlab-like operations:
a. Row selection
Rows from Matrix M can be selected as M(fromRow, toRow, ::), where fromRow is the starting row, toRow is the ending row, e.g.
var mr2_5 = myMat(2, 5, ::) // select rows 2 to 5, all columns, i.e. Matlab's myMat(2:5,:)
var mr25 = myMat(2::5, ::)
Order of row selection is reversed if fromRow > toRow, e.g.
var mr5_2 = myMat(5, 2, ::) // select rows 5 downto, all columns, i.e. Matlab's myMat(5:-1:2.:)
Step to skip rows can be specified as M(fromRow, incR, toRow, ::), where fromRow is the starting row, incRow is the step with which the selection of rows proceeds and toRow is the ending row, e.g.
var mr2_2_8 = myMat(2, 2, 8, ::) // select starting from row 2, increment row index by 2 and ending at row 8, select all columns, i.e. Matlab's myMat(2:2:8, :)
var mr9_2_3 = myMat(9, -2, 3, ::) // i.e. Matlab's myMat(9:-2:3,:)
Columns from Matrix M can be selected as M(::, fromCol, toCol), where fromCol is the starting column, toCol is the ending column, e.g.
var mc3_6 = myMat(::, 3, 6) // select columns 3 to 6, all rows, i.e. myMat(:, 3:6)
Order of column selection is reversed if fromCol > toCol, e.g.
var mc6_3 = myMat(::, 6, 3) // select columns 6 downto 3, all rows, i.e. myMat(:, 6:-1:3)
Step to skip columns can be specified as M(::, fromCol, incC, toCol), where fromCol is the starting column, incC is the step with which the selection of columns proceeds and toCol is the ending column, e.g.
var mc3_2_8 = myMat(::, 3, 2, 9) // select starting from column 3, increment column index by 2 and ending at column 9, select all rows
Selection of a compact rectangular range of the Matrix can be specified as M(fromRow, toRow, fromCol, toCol), e.g.
var m2_5_4_7 =myMat(2, 5, 4, 7) // i.e. Matlab's myMat(2:5, 4:7)
var m5_2_4_7 =myMat(5, 2, 4, 7) // reversing rows, i.e. myMat(5:-1:2, 4:7)
var m2_5_7_4 = myMat(2,5,7,4) // reversing columns, i.e. myMat(2:5, 7:-1:4)
var m5_2_7_4 = myMat(5,2,7,4) // reversing both rows and columns, i.e. myMat(5:-1:2, 7:-1:4)
Selection of a Matrix subrange specifying inrement at both rows and columns:
var mR = myMat(2, 2, 7, 8, -2, 4) // i.e. Matlab's myMat(2:2:7, 8:-2:4)
Basic Matrix Routines
ones(N: Int) – returns a NXN Matrix filled with ones, ones(N: Int, M: Int) – returns a NXM Matrix filled with ones
zeros(N: Int) – returns a NXN Matrix filled with zeros, zeros(N: Int, M: Int) – returns a NXM Matrix filled with ones
diag(N) – returns an NXN diagonal matrix with ones at the diagonal
fill(N: Int, val: Double) – returns a NXN Matrix filled with val, fill(N: Int, M: Int) – returns a NXM Matrix filled with ones
sin(a: Matrix): Matrix, cos(a: Matrix): Matrix, tan(a: Matrix): Matrix, sinh(a: Matrix): Matrix, cosh(a: Matrix): Matrix, tanh(a: Matrix): Matrix, asin(a: Matrix): Matrix, acos(a: Matrix): Matrix, atan(a: Matrix): Matrix: trigonometrical routines
abs(a: Matrix): Matrix, round(a: Matrix): Matrix, floor(a: Matrix): Matrix, ceil(a: Matrix): Matrix, sqrt(a: Matrix): Matrix, pow(a: Matrix, val: Double): Matrix, log(a: Matrix): Matrix, log2(a: Matrix): Matrix, log10(a: Matrix): Matrix, exp(a: Matrix): Matrix, toDegrees(a: Matrix): Matrix, toRadians(a: Matrix)
dot(a: Matrix, b: Matrix): Matrix: dot product of the two matrices, can be written also as: a . b
Aggregation Routines
Columnwise Sum, sum(a: Matrix): Array[Double]
returns the columnwise sums as an Array[Double], e.g.
var a = ones(4, 8)
var ac = sum(a)
ac: Array[Double] = Array(0.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0)
Columnwise Mean, mean(a: Matrix): Array[Double]
returns the columnwise means as an Array[Double], e.g.
var a = ones(4, 8)
var acm = mean(a)
acm: Array[Double] = Array(0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0)
Columnwise Product, prod(a: Matrix): Array[Double]
returns the columnwise products as an Array[Double]
Columnwise Mins, min(a: Matrix): Array[Double]
returns the columnwise minimums as an Array[Double]
Columnwise Maxs, max(a: Matrix): Array[Double]
returns the columnwise maximums as an Array[Double]
Rowwise Sum, sumR(a: Matrix): Array[Double]
returns the rowwise sums as an Array[Double]
Rowwise Mean, meanR(a: Matrix): Array[Double]
returns the rowwise means as an Array[Double], e.g.
var a = ones(4, 8)
var acm = mean(a)
acm: Array[Double] = Array(0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0)
Rowwise Product, prodR(a: Matrix): Array[Double]
returns the rowwise products as an Array[Double]
Rowwise Mins, minR(a: Matrix): Array[Double]
returns the rowwise minimums as an Array[Double]
Rowwise Maxs, maxR(a: Matrix): Array[Double]
returns the rowwise maximums as an Array[Double]


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It has survived not only five centuries
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It is a long established fact that a reader will be distracted by the readable content
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Sept 21, by Nullam | 99 views | 69 Comments
It is a long established fact that a reader will be distracted by the readable content
Various versions have evolved over the years, sometimes by accident, sometimes on purpose


Deuteronomy 2:10
The Emims dwelt therein in times past, a people great, and many, and tall, as the Anakims;


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Application time for postoperative wound dressing following breast augmentation with implants: study protocol for a randomized controlled trial
Division of Plastic Surgery, Universidade Federal de São Paulo, Rua Napoleão de Barros, 715,-4° andar, São Paulo - SP 04024-002, CEP, Brazil
Division of Plastic Surgery, Department of Surgery, Universidade do Vale do Sapucaí, Avenida Alfredo Custódio de Paula, 320, Pouso Alegre - MG 37550-000, CEP, Brazil
Department of Microbiology, Universidade do Vale do Sapucaí, Avenida Alfredo Custódio de Paula, 320, Pouso Alegre - MG 37550-000, CEP, Brazil
Department of Bioestatistics, Universidade do Vale do Sapucaí, Avenida Alfredo Custódio de Paula, 320, Pouso Alegre - MG 37550-000, CEP, Brazil
Breast augmentation with silicone implants is one of the most frequently performed cosmetic surgeries worldwide. Surgical site infection (SSI) remains an important complication of this procedure. One of the most important risk factors for SSI is the presence of microorganisms on the skin surrounding the wound. Guidelines by the Centers for Disease Control (CDC) recommend that surgical wounds be covered with a sterile dressing for 24 to 48 hours. However, a recent study showed that the application of a dressing for six days after breast reduction reduced wound colonization by coagulase-negative staphylococci.
A randomized clinical trial was designed to assess two protocols of postoperative wound care to determine how the application duration of the postoperative dressing influences wound colonization in patients undergoing breast augmentation with silicone implants. Women aged between 18 and 60 years who are candidates for breast augmentation with silicone implants will be randomly allocated to group I (n = 48), in which the dressing will be removed on the first postoperative day, or group II (n = 48), in which the dressing will be removed on the sixth postoperative day. Cutaneous colonization will be assessed by cultures of samples of skin flora taken from the wound region. The incidence of SSI, using standardized CDC criteria, and the perceptions of patients towards the dressing will be secondary outcomes.
An important component of SSI prevention is to minimize all possible risk factors, and the application of postoperative dressing plays a key role in this endeavor. The results of this clinical trial may help to standardize postoperative wound care after breast augmentation with silicone implants.
This trial was registered on 12 March 2012 with ClinicalTrials.gov (identifier: NCT01553604).
The popularity of breast augmentation with silicone implants has grown exponentially in the last decade. Since 2007, this operation is one of the most frequently performed cosmetic surgeries worldwide. In 2012, over 330,000 new breast augmentations were performed in the United States alone 1 . Despite advances in the surgical technique of breast augmentation and the technology for manufacturing breast implants, surgical site infection (SSI) remains an important complication of this procedure 2 , 3 . SSI increases morbidity, financial and personal costs, and the possibility of operative failure, as the implant may need to be removed to treat the infection 4 .
The risk of postoperative SSI in primary augmentation mammoplasty with silicone implants is estimated to be between 0.1 and 2.5% 2 , 4 - 10 . These low rates of SSI make correlations with risk factors or specific interventions difficult, as very large sample sizes are required to determine statistically significant correlations 11 . However, due to the severity of the consequences of implant-related SSI, any contribution towards understanding these risk factors will aid in the development of strategies for preventing infection and improving surgical outcomes 12 .
One of the most important risk factors for SSI is the presence of microorganisms on the skin surrounding the wound 4 , 11 , 13 , 14 . This risk increases when alloplastic material is used 4 . The ability of endogenous skin bacteria to colonize mammary prostheses has been demonstrated in vitro 15 . Bacteria from the endogenous flora or external sources of contamination may adhere to the implant and form an extracellular polysaccharide-rich matrix or biofilm, which surrounds the implant 16 . Bacteria aggregate and adhere to this extracellular matrix, enabling them to evade the host immune response and resist systemic antibiotics. Biofilm formation facilitates plasmid transfer among the bacteria, leading to highly virulent organisms. The minimum inhibitory concentration of antibiotics is 1,000 times greater for biofilms than for planktonic bacteria 17 . The seeding of a foreign body and the subsequent formation of a biofilm are not only difficult to diagnose, but may be very difficult to treat, especially with routine antibiotics 18 . Studies have suggested that chronic subclinical infection related to biofilms on implants may be associated with symptomatic capsular contracture, which is the leading cause of reoperation in mammary prosthetic surgery 19 - 24 .
SSIs are related to preoperative factors (such as patient selection), intraoperative factors (such as type of surgery), and postoperative factors. Surgical wound management during the postoperative period greatly influences the risk of SSI because the skin incision serves as a gateway for microorganisms 4 , 20 , 25 , 26 . Bacteria can access the operative site via the incision. They may multiply and invade tissues to cause infection, depending on their number and pathogenic interaction with the host immune system 19 . However, few studies have justified the normalization of this period 26 .
Care of surgical incisions has long been practiced. The use of dressings has been documented for over 4,000 years, but Joseph Lister introduced the concept of antisepsis only in the nineteenth century. The ideal dressing should protect the wound from trauma and contamination, absorb secretions, and provide the necessary compression to minimize edema and obliterate any dead space. Furthermore, the dressing covers unsightly operative wounds, thereby improving the psychological wellbeing of the patient 26 , 27 .
The standardization of postoperative wound dressings, including those used after breast surgery, has been based on scarce and empirical evidence 28 , 29 . Different materials and techniques for the application of new dressings have been developed, however, conventional gauze-based dressings are still used very often 30 . A systematic review failed to prove the superiority of any one type of dressing over another type, or no dressing, and suggested a need for well-designed clinical trials to determine the ideal application time for postoperative wound dressings, an issue that remains controversial 31 .
Guidelines by the Centers for Disease Control (CDC) recommend that surgical wounds be covered with a sterile dressing for 24 to 48 hours 25 . Subsequent postoperative care should be individualized; there is no ideal home-care protocol. At present, the care of postoperative wounds is not standardized and is based on the individual experience of each surgeon 25 , 26 . A recent study by Veiga-Filho et al. 32 showed that the application of a dressing for six days after breast reduction reduced wound colonization by coagulase-negative staphylococci. These authors also demonstrated that patients preferred to retain the same dressing for six days and considered this method to be safe 32 .
A randomized clinical trial was designed to assess two protocols of postoperative wound care to determine how the application duration of the postoperative dressing influences wound colonization in patients undergoing breast augmentation with silicone implants. The secondary aims are to determine the SSI rates and the perceptions of the patients regarding the comfort, convenience and safety of the postoperative dressing. The trial will be conducted in a double-blinded manner in a university hospital in Brazil (Hospital das Clínicas Samuel Libânio, Universidade do Vale do Sapucaí). This trial has been registered at Clinicaltrials.gov (identifier: NCT01553604).
The Ethical Committee of the Universidade do Vale do Sapucaí have reviewed and approved the study protocol (reference number: 113.612). Only those patients who agree to sign informed consent forms will be included in the study.
Patients will be recruited from the private practices of the first three authors (DAM, DFV and JVF). Women aged between 18 and 60 years who are candidates for breast augmentation with silicone implants via the inframammary fold approach will be eligible for the study. Patients with a body mass index (BMI) above 30 kg/m 2, those on immunosuppressive therapy, those with diabetes, those who smoke, and those with a history of breast cancer or breast surgery will be excluded. Patients with an indication for an areolar or axillar approach and those who had the dressing wet will also be excluded.
On the basis of the literature, an increase in bacterial growth of 100 colony-forming units (CFUs) per plate will be considered clinically significant 32 . For a statistical power of 95% and an alpha test risk of 5%, the sample size has been estimated to be 48 patients per study arm.
Patients will be randomly allocated to group I (n = 48), in which the dressing will be removed on the first postoperative day, or group II (n = 48), in which the dressing will be removed on the sixth postoperative day. Allocation will be determined by a random, computer-generated sequence (Bioestat 5.0, Instituto Mamirauá, Belém, PA, Brazil). An opaque envelope with the patient number will be opened on the first postoperative day to reveal the allocation of the patient.
Patients will be instructed to bathe before surgery with a 4% chlorhexidine-based detergent (Rioquímica Indústria Farmacêutica Ltda., São José do Rio Preto, Brazil) 33 . In the operating room, antisepsis of the surgical site will be performed with a 0.5% chlorhexidine solution in alcohol (Rioquímica Indústria Farmacêutica Ltda., São José do Rio Preto, Brazil) 34 . The nipple areola complexes will remain uncovered during the operation; sterile tapes will not be used to cover them, since this is not the standardized procedure in our hospital. Patients will undergo breast augmentation under general anesthesia. All patients will receive prophylactic antibiotics (cefazolin - União Química Farmacêutica Nacional S.A., São Paulo, Brazil) 35 .
The surgical approach will be via the inframammary fold. Implants (Silimed Indústria de Implantes Ltda., Rio de Janeiro, Brazil) will be placed in the subglandular, submuscular or subfascial position, depending on which is the best course of action for a given patient. The surgical site will be cleaned with sterile saline after the surgery. A sample of skin flora will be obtained for semiquantitative culture before the application of a dressing over the surgical incision.
The dressing will consist of four layers of cotton gauze, covered with micropore tape. The surgical team will not know to which group the patient belongs. On the first postoperative day, the allocation envelopes will be opened. If the patient is allocated to group I, the dressing will be removed, and a sample will be harvested for culture. The patient will be instructed to return to their normal personal hygiene routine and return on the sixth day for reassessment and collection of samples for culture. If the patient is allocated to group II, she will be instructed to not wet the bandage for six days, when it will be removed and a sample will be harvested for culture. Thus, samples of the skin flora will be obtained in the operating room just before placement of the dressing and after removal of the dressing. Additional samples will be obtained on the sixth postoperative day from patients in group I.
A sterile fenestrated paper field with a standard 5 cm per 10 cm area will be placed over the surgical wound on the right breast. A sterile swab soaked in sterile saline will be passed across the predetermined area in a standardized manner. This swab will be placed in a sterile tube containing 1.0 ml of sterile saline and immediately transferred to the laboratory.
Culture methodsStandard culture methods will be used for the identification of microorganisms 36 . Aliquots of 0.2 ml from each sample will be plated on agar medium hypertonic mannitol (HiMedia Laboratories Pvt. Ltd., Mumbai, India) to culture Staphylococcus sp., on blood agar (HiMedia Laboratories Pvt. Ltd., Mumbai, India) to identify hemolytic colonies, on eosin-methylene blue agar (HiMedia Laboratories Pvt. Ltd., Mumbai, India) to identify Enterobacteriaceae, and on Sabouraud agar supplemented with chloramphenicol (HiMedia Laboratories Pvt. Ltd., Mumbai, India) (0.05 mg/ml) to detect fungi. The plates will be incubated in an aerobic atmosphere at 37°C. After 48 hours, a microbiologist will assess the plates. The lab technicians and microbiologist will not know which group each sample belongs to.
Culture results will be expressed as CFUs per plate. When a result exceeds 300 CFUs, it will be recorded as ‘>300 CFU/plate’. Staphylococci will be identified as coagulase-negative staphylococci or Staphylococcus aureus, on the basis of the results of Gram staining, the presence of hemolysis, and the results of the coagulase test.
Patients will be evaluated weekly for four weeks, and then re-evaluated at six months and one year after the operation. The CDC definition and classification of SSIs will be used. As the surgery involves the implantation of prostheses, an SSI is defined as an infection that occurs within one year after the surgery 37 . The patients will use a five-point scale to classify the dressing in terms of comfort, practicality and safety. This assessment will be done at the postoperative week two visit for each patient.
The primary outcome will be cutaneous colonization, expressed as the number of CFUs. The incidence of SSI and the perceptions of patients towards healing will be secondary outcomes. Participation will be completed at one year after surgery, after evaluation for the presence of infection.
The Mann–Whitney U test will be used to test the homogeneity of the groups in terms of age, BMI and duration of surgery. The Friedman test will be used to compare the number of CFUs in the samples collected before, and one and six days after the application of the dressing in group I. If there is a significant difference between these times, then the Friedman test will be supplemented with the multiple comparisons test to determine at which time points significant differences appeared. In group II, the Wilcoxon test will be used to compare the number of CFUs in samples collected before the dressing and on the sixth postoperative day. The Mann–Whitney U test will be used to compare groups I and II in terms of the number of CFUs before and six days after the application of the dressing. Tests will always be applied independently for each medium used.
The Fisher test will be used to compare groups I and II in terms of the rates of infection. The Kolmogorov-Smirnov test will be used to compare the two groups in terms of the perceptions of the patients regarding the comfort, safety and practicality of the dressings. All statistical analyses will be performed using SPSS software (version 18, SPSS Inc., Chicago, United States of America). A P value ≤0.05 will be considered to be statistically significant.
As breast augmentation with silicone implants has become a common procedure, risks factors for complications associated with this procedure must be investigated in detail to improve procedural safety. As modern protocols and guidelines should be based on the principles of evidence-based medicine, well-designed randomized clinical trials are essential to guide or adjust clinical practice 28 .
Attention to the skin incision in breast augmentation is warranted, as this incision acts as a gateway for microorganisms present on the surrounding skin or in external sources of contamination. Incisions for insertion of breast implants are most commonly placed in the inframammary fold, areola or axilla 38 , 39 . Each of these different incisions traverse through the breast ducts at different levels, providing for different potential amounts of contamination by breast duct bacteria-colonized material 40 . However, there is not a clear relationship between incision location and SSI, and literature on this issue is controversial. Wiener, in a review of 430 patients who underwent augmentation surgery, found a significantly higher incidence of capsular contracture when a periareolar incision was used, and he hypothesized that this could be due to bacterial contamination from contact with the endogenous bacteria within the breast tissue 40 . Jacobson et al., in a retrospective chart review of 197 primary breast augmentation patients, observed that transaxillary incisions produced the highest incidence of contracture (6.4%), followed by periareolar (2.4%) and inframammary (0.5%), with a statistically significant difference 41 . Stutman et al. performed a chart review on 619 patients who underwent primary breast augmentation, and found a trend of increased rate of capsular contracture when the inframammary incision was used, but this was without statistical significance 39 . The inframammary incisions have been the most commonly used for primary augmentation mammaplasty, since it is the simplest and most straightforward approach 38 - 40 . For this reason, this was the incision of choice for the current trial.
The use of biomaterials and the increased pathogenicity of bacteria enable colonization of the implant even when the bacterial load is relatively low. It is exceedingly difficult to control bacterial growth after implant colonization has occurred, and this difficulty tends to increase the infection risk 4 . Subclinical implant infection is related to the development of bacterial biofilms and severe capsular contracture around the implant, which are the leading causes of reoperation in breast augmentation 19 . The need to remove the implant can cause psychological trauma to the patient 2 . For these reasons, implant subclinical infection has become a focus of substantial research 19 , 20 .
Bacteria are responsible for most postoperative infections that occur after breast augmentation when implants are used. Gram-positive cocci are part of the skin flora, especially in the upper portion of the trunk, and they account for many implant-related SSIs 42 . Cultures of mammary tissue collected during breast surgery demonstrate that these bacteria are the most frequent endogenous bacteria in the breasts 18 . Infections by opportunistic agents, such as fungi, Gram-negative bacteria and atypical mycobacteria, have also been described 43 - 45 . Therefore, we have opted to culture these organisms as well.
An important component of SSI prevention is to minimize all possible risk factors. The application of postoperative dressing plays a key role in this endeavor 12 . However, it is difficult to demonstrate gains related to the use of dressings for ensuring clean wounds and lowering the infection rate 46 . For this reason, we chose the rate of skin colonization, which is related to the SSI rate 4 , 11 , 13 , 14 , as the primary focus of this study.
The opinion of the patients regarding the proposed treatment is an important factor in the quality of care. Two different surgical dressing strategies are proposed, and determining patients’ perceptions regarding their comfort, convenience and safety is a secondary goal of this study. The results of this clinical trial may help to standardize postoperative wound care after breast augmentation with silicone implants.
Recruitment began in April, 2012. A total of 69 patients have been enrolled in this study and have undergone breast augmentation with silicone implants. All patients will be monitored for the presence of infection until one year after their operation.
BMI: Body mass index
CDC: Centers for Disease Control and Prevention
CFU: Colony forming units
SSI: Surgical site infection
The authors declare that they have no competing interests.
DAM conceived the study and participated in study design, surgical procedures and manuscript draft. JVF and DFV participated in study design, surgical procedures, patients’ follow-up and interpretation of data. FEMF is involved in patients’ follow-up. LFP and ABATL performed microbiology analysis and participated in interpretation of data. NFN participates in the analysis and interpretation of data. LMF participated in the design and coordinates the study. All authors contributed to development of study protocol and all of them read and approved the final version of the manuscript.
This study received grants from Fundação de Amparo à Pesquisa do Estado de Minas Gerais - FAPEMIG.
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