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Islam Versus Ahl Al Kitab Past And Present
Book title: Islam Versus Ahl Al Kitab Past And Present
Maryam Jameelah
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IslamBasics-Islam the Only Alternative
By Dr. Maryam JAMEELAH
How can we be certain that
Islam is the only infallible Truth?
Islam means submission to the will of God through unquestioning obedience to His Law in the Holy Quran and the Sunnah of the Holy Prophet Muhammad (peace and blessings of Allah be upon him). Judaism is named after the tribe of Judah and Christianity after Jesus Christ (peace be upon him). Thus even the names of these faiths illustrate their restrictive character. The name of Islam proves its universality. What a contrast to the views expressed during a recently held interfaith conference in Washington D.C. where Dr.Isaac Franck, Executive Vice-President of the Jewish Community Council of Washington said that Judaism considers itself as valid only for Jews and does not attempt to impose its views upon non-Jews. He declared: "The validity of non-Jewish the theological beliefs is not subject to our evaluation or judgment." To me this is conclusive proof that Judaism must be false because an omnipotent God would never restrict His truth to a single people. Truth by its very nature must be universal!
Islam is unique among all other religions in that it alone possesses an authentic scriptures. The Holy Quran informs us that the Jews and Christians have corrupted their scriptures by mixing the original revelation with human interpolations and interpretations until the former could not be distinguished from the latter. Under the devastating impact of "Higher Criticism" very few, if any, Jewish or Christian scholars today accept their Holy Books as infallible Divine revelation. Jews and Christians themselves admit that they do not possess their original Texts but only translations that have been undergoing numerous alterations for many centuries and are still being changed. The Holy Quran exists exactly as it was revealed to the Holy Prophet. It has been preserved in its original text forever. The languages of the former revelations to the Jews and Christians have long been dead. Today nobody can speak those languages and only a few scholars claim to be able to decipher them. Even if these scriptures had been preserved to this day in their original and unadulterated form, nobody could correctly understand them and interpret their injunctions, much less translate them into actual practice. In contrast, the language of the Holy Quran is a living language, spoken and understood by millions throughout the world. Even those who have no time to study Arabic, can easily find others who know it sufficiently to explain the meaning of the Quran. Each of the existing sacred books has been addressed to a particular people and contains commandments which seem to have been intended only for a restricted time and place, while the Holy Quran is explicitly addressed to the whole human race with an eternal code embracing life in its totality. The teachings of Judaism are restricted by their nationalist, racist emphasis while the acceptance of secularism on principle virtually negates Christianity's claim to universality.
Concerning the earlier Prophets and religious teachers, very little of their life histories have come down to us. Thus we know less about Moses (peace be upon him) than Socrates and nothing at all concerning Jesus Christ (peace be upon him) before he began his brief three-year career of preaching.
A cursory Glance through any Hadith collection will give an idea how accurately and carefully the minutest details of the Prophet's life teachings have been recorded. There one finds astonishing details of his features, limbs of body, his gait, the manner of his conversation and speech, his smile, dress, food, sleep, his manner of eating, drinking and relaxing, his love for perfumes, his elegance, catholicity, of his taste, his fondness for riding, his zest for worship, his mode of salutation, his facial expression, his behaviour in joy and sorrow, his wars, his way of offering condolence, his mode of offering prayers and observing fasts, his pilgrimages, his intense devotion to God, his noble feelings and sentiments, his perseverance, his dealings with his fellow beings, his honesty, his hospitality, his deep rooted sympathy for his own kith and kin, his dealings with strangers, with enemies, his hatred for back-biting and vanity, his simplicity, his bravery, his determination, his truthfulness, his adherence to his promises, his forgiveness, his behaviour towards his equals, towards his elders and youngers, his treatment of women, his kindness to mankind and animals, his means of livelihood, his experiences as a traveller, as a warrior, as a law-giver, as a father, as a brother, as a ruler, as a saint, as a pious hermit, as an arbitrator; in fact, all phases and aspects of his life have been carefully recorded. One is amazed at the boldness and courage with which he laid open before the people not only his public but also his private life. who can stand the ordeal of voluntarily offering himself as an object of observation for all the twenty-four hours throughout his life?
Only a person of unusual integrity and honesty, possessing a high degree of self-confidence, self-control and self-determination could do it. It was Muhammad (peace and blessings of Allah be upon him) who alone can stand this test. He not only permitted people to peep into the innermost chambers of his sacred life but also exhorted them to broadcast its details to others because even these facets were as divinely illuminated as his public career.
A Muslim is therefore enjoined to follow the Prophet's example in his private life with the same sincerity and faithfulness as he is commanded in respect of the sphere of his public life. Every word that he uttered and every action that he performed are the public trust to be faithfully handed over to humanity from generation to generation as Divinely inspired
Islam alone constitutes a complete, all-embracing, comprehensive way of life where the individual versus his society and material versus the spiritual are balanced into a perfect harmony. The laws of Islam are called the Shariah that provides an infallible Guidance of all aspects of individual and collective life. The Shariah embraces religious ritual, personal character, morals, intimate habits, family relationships, social and economic affairs, administration, rights and duties of citizens, judicial system, laws of war and peace and international relations. These injunctions enable the faithful to distinguish between what is good and evil, what is beneficial and harmful, what is useful or injurious, what are the virtues we must cultivate and encourage and what we must avoid; the sphere of our personal freedom and its limitations and what methods we must adopt to establish a genuine Islamic community. Islam teaches that unaided intellect and personal experience alone are unreliable and defective guides which can never discover sound ethical values. The purpose of ethical endeavour in Islam is to seek the pleasure of God. In Islam, morality is absolute and unchanging because its laws are instituted by God and not by man. The true Muslim does not change with the changing times but forces the times to conform to his standards.
Islam abhors the doctrine of secularism. The Muslim can thrive only in an Islamic environment which is his duty to establish:
Those who imagine that the morality of Islam makes of it a heavy burden for humanity derive this belief from the tribulations undergone by the individual Muslims living in a society which is not governed by Islam. Under such circumstances the morality of Islam is a heavy burden; it almost crushes the individuals who live with their pure Islam in the polluted society of ignorance… . A specific environment is indispensable for the life of this concept, an environment with its own specific values.... Islam is a realistic system and it therefore supposes that the people who live according to its path will be living in an Islamically governed society. Without this environment, the life of the individual become impossible or at least extremely difficult. Therefore whoevr wishes to be a Muslim should know that he cannot devote himself to his practice of Islam except in a Muslim environment dominated by Islam. He is mistaken if he imagines that he can realize his Islam in the midst of a society ignorant of Divine guidance.
Alone among all the religions of the world, Islam created a state dominated by religious and moral motives, thereby demonstrating that political power can and ought to be subordinated to ethical ends and that religion must not be allowed to serve the ends of any political system devoid of moral ideals.
Islam teaches us that one must attain spiritual progress through active participation in normal every day life and for this reason condemns the practice of monasticism, asceticism or celibacy. The doctrines of Islam are characterized by their simplicity, explicitness and highly realistic attitude towards human problems, indulging neither in excessive `optimism nor pessimism, and enjoining moderation in all things. Islam is free from incomprehensible theology or burdensome rituals. Religious creeds shrouded in philosophical complexities may give intellectual pleasure to the few but can never inspire ordinary men and women to be steadfast in virtue.
The racism and nationalism of Judaism makes a mockery of its ethical teachings while Christianity's propagation of the doctrine of the Trinity and the vicarious atonement of mankind's sins by Jesus Christ (peace be upon him) nullifies all its moral values. In Islam there are no such loopholes.
The correct course of life for man is to live in complete obedience to God. It is not for man to determine his mode of worship and obedience; it is for God to decide this. God, being his master, has raised from time to time prophets for the guidance of humanity and has revealed His books through them. It is the duty of man to take the code of his life from these sources of divine guidance.
Man is answerable to God for all his actions in life. The time for rendering an account will be in the life-hereafter and not in this world. The short span of worldly life is really an opportunity to prepare for that great test. In this life, all efforts of man should be centred on the object of soliciting the blessings of God in the Hereafter. He, with all his faculties and potentialities, is on trial. There will be an impartial assessment of his conduct in life by a Being Who keeps a complete and correct record, not merely of his movements and actions and their influence on all that is in the world, but also a full record of his innermost ideas, feelings and intentions. (Pp. 38-39)
According to Islam, God has appointed the human soul as His vicegerent in the universe ...The body has been created, with the sole object that the soul should make use of it in the exercise of its authority and the fulfillment of its duties and responsibilities. Hence the body is not a prison house for the Soul but its workshop or factory and if there is any possibility for the growth and development of the soul, it is only through the use of the powers, machines and instruments provided by this work shop. Consequently, this world is a field in which God has sent us to work and do our duty towards Him…The spiritual development which is possible in this world should not take the form of man turning his face away from this workshop and retreating to some uninhabited corner. Rather, the only form it should take is that man should live and work in it and give the best account of himself. It is in the nature of an examination center for him. Every aspect and sphere of life, is as it were, like a question paper in this test; the home, the family, the neighborhood, the society, the market place, the office, the factory, the school, the law courts, the police station, the parliament, the peace conference and the battlefield, all represent `question papers' on different subjects which man has been called upon to answer. If he does not take any question paper or leaves most of the answers blank, he is bound to fail in the examination. The only possibility of success would be in
a man's spending his whole time and giving his whole attention to this examination and to attempt as far as possible to answer all the question papers handed over to him. (pp. 106-108)
Islam is the only religion which preaches a pure and unadulterated monotheism that tolerates no compromises with nationalism, racism, trinitarianism, saint-worship, veneration of images or priesthood. Wholehearted acceptance of the doctrine of Tauhid or the Unity of God makes the believer broadminded and sympathetic to all his fellow beings made by the same Creator, produces an unsurpassed dignity and self respect, makes him indifferent to and independent and fearless of all powers other than those of God, at the same time generating in him humility and modesty The believer in Tauhid is a righteous man because he is convinced that unless he acts justly, he cannot succeed. The believer does not despair and lose hope regardless of adversity. His faith that God is the Master of all the universe, whose powers and mercy are infinite, gives him immense consolation in trouble so that he never yields to pessimism and despondency. Suicide is unthinkable. The true believer will persevere in his work with patience and implicit trust in God to the end. Faith in Islam fills the believer with unrivalled courage. Since he is convinced that his life and property belong exclusively to God, he is ready to sacrifice them at any moment for His pleasure Since God alone can bestow life or death, no weapon.
no man or animal has the power to inflict any harm upon him unless it be God's will. The true believer believes that God has set his span of life in advance so that all the forces of the world combined are powerless to take away his life a moment before the appointed decree. Belief in Islam blesses the faithful with complete serenity and contentment. The believer knows that wealth belongs to God and He gives to whom He pleases. Power, honour, reputation and authority are all bestowed according to His will and it is man's duty only to strive according to His law. Success or failure depend entirely upon the will of God; if He wills to succeed, no power in the world can prevent Him from doing so and if He does not will it, no power can force Him while atheists and polytheists think that success and failure depend upon their own unaided efforts or the help or opposition of worldly forces. Consequently, they become enslaved to jealousy and frequently resort to sordid practices to try to gain what they want. Thus it can be seen that Islam is not only the sole effective prescription for righteousness but the most potent medicine for mental health as well.
Alone among the religions of the world, Islam made a practical reality of international brotherhood based upon a commonly shared outlook on life, common practices and ideals of conduct. Islam views life as an organic whole not to be shattered into fragments. Islam follows the Muslim in every act of his life-social, political and economic. A Muslim cannot be a Muslim in the mosque and a nationalist or Socialist in politics. He is a Muslim everywhere. Islam is no mere accessory to life but life itself!
Why does not Islam regard the non-Muslim as equal to the Muslim? If Muslims cannot regard Judaism or Christianity on a plane of equality with Islam, the non-Muslim will wonder what kind of treatment Hindus, Buddhists, pagans, agnostics and atheists can expect to receive under Muslim rule.
Islam is a universal faith open to everyone without distinction of race, nationality, cultural or intellectual attainment, social status, age or sex. Because only God can give His faith to whom He will, the Muslim regards every non-Muslim as a potential Muslim. For this reason, he is commanded to be fair and just even to those non-Muslims who are his confirmed enemies and compassionate to non-Muslims who have never committed any overt, hostile act. Islam commands the Muslim to be kind and just to non-Muslims because if we do not set an example of virtue, how can we expect others to follow us? The conviction that Is lam is the only Truth and that all divergent ways are false and evil, does not make the pious Muslim an arrogant fanatic. The Holy Quran forbids spying, backbiting and heretic-hunting. Nobody is compelled to accept Islam under Muslim rule by force. The Muslim always stands before God in the utmost humility.
Indeed you ought to realize that the pious man is he who is good in God's sight in the mansion of eternity and that is something unknown to man, postponed to the End. . . . (Therefore) you ought not to look at anyone without considering that he is superior to you. Thus, if you see a child you say, `This person has never sinned against God but I have sinned and so he is better than I' and if you see an older person, you say, `This man was a servant of God before me and is certainly better than I' and if be is a scholar you say, `This man has been given what I am ignorant of; then how shall I be like him?' and if he is ignorant, you say, This man has sinned against God in ignorance so God's case against me is stronger and I do not know what end He will give to me and what end to him,' and if he is an infidel, you say, `I do not know; perhaps he will become a Muslim and his life will end in doing good and because of his acceptance of Islam, his sins will be forgiven but as for me - God is our refuge perhaps God will lead me astray so that I become an infidel and my life ends in doing evil and then tomorrow he will be among those brought near to God and I shall be among the condemned' . . . So let fear of the End occupy you and keep you from making yourself, despite the doubt about your death, to be above the servants of God most high. Your certitude and faith at present do not exclude the possibility of your changing in the future for God is the disposer of hearts; He guides whom He will and leads astray whom He will …
The opposition of Islam to divergent faiths, philosophies and ideologies not directed towards any hatred of individuals but rather the system that has produced them. It is not persons which Islam opposes but perverted values and evil ways of life which lead only to ruin and disaster, but because all non-Islamic ways are wrong, the leaders who personify these values and are fighting with all sorts of cruel and treacherous means day and night to obliterate the truth of Islam from the world, become hateful and therefore must be bated and opposed with every resource we possess.
Hatred of evil and falsehood is not a sin but the highest virtue. Hate is the natural reaction of love. We cannot love a thing without hating what is the opposite to it and our hatred is in proportion to our love. The purpose of hate is to clear the path of love, to approach near to the beloved ideal and to love it more ardently. War, when fought in the service of truth, justice and virtue is a positive good. Pacificism is tantamount to non-resistance to evil and leads to apathy, indifference and all kinds of moral corruption.
Islam teaches that a common faith is the Only bond which can unite the human race. A man should be judged only on the criterion of whether he is believer or a non-believer and how effectively he implements his faith in his practical daily life. Such distinctions as race, nationality or social status are mere accidents of birth over which the individual has no control. Any discrimination on these grounds is rank injustice. The individual is responsible for what he believes and what he does. He is always at liberty to determine his faith and control his behaviour.
Conflicting ideologies, where the interest of one group cannot be attained except at the expense of its rivals, can never be united or even peacefully co-exist simply by proclaiming the fact that all are human beings. The utter failure of such world organizations as the League of Nations and the United Nations is proof of this fallacy. Universal peace and brotherhood can only be attained when the majority of mankind embrace common ideals. Suppose a husband and wife had nothing in common. Everything he considered good, she considered evil; whatever he thought was beautiful, she regarded as ugly; everything he thought important, she considered trivial; everything he believed was true, she rejected as false-they would be quarreling continuously and could not live together for a single day! They could not reconcile their differences and save their marriage simply by the assertion that both are human beings! Although it cannot be denied that all human beings possess common qualities, in the ideological battle, the human tie alone is not enough!
On what foundation can a lasting reconciliation between Muslims, Jews and Christians be based? We must realize that under the existing circumstances, no friendship is possible. Jewry and Christendom have joined hands to destroy us and all we cherish. Zionism, freemasonry, Christian missionary activity and Orientalism have combined to annihilate us religiously, culturally and even physically. It would be sheer folly to kiss the hands that are beating us!.
Peaceful relations and mutual respect among us can only be achieved through strength. We must cease indulging in apologetics and present the Islamic message to the world honestly and forthrightly. Before we can hope to succeed with Tabligh on a large scale, we must first convert the nominal Muslims into true believers. We must establish a full-blooded Islamic state where the world will witness our precepts translated into action. Finally, we must crush the conspiracies of Zionism, free-masonry, Orientalism and foreign missions both with the pen and with the sword. We cannot afford peace and reconciliation with the Ahl al Kitab until we can humble them and gain the upper hand.


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Miles Davis at Newport 1955-1975: The Bootleg Series Vol. 4
Columbia/Legacy
Two legendary institutions are highlighted in this latest installment of The Bootleg Series: Miles Davis and the Newport Jazz Festival—in fact, this year marks the 60th anniversary of the trumpeter's first appearance at the festival. Like any other Miles Davis compilation, this 4-disc set with nearly four hours of mostly unreleased music is a microcosm of the artist's unconventional and groundbreaking career, spanning jazz's evolution: from modal jazz to post-bop to jazz rock and fusion. The first disc alone is historic in that Davis's 1955 Newport debut, which features the trumpeter accompanied by musicians such as Gerry Mulligan and Thelonious Monk (that set includes a beloved Davis staple "'Round Midnight). The 1958 performance features the legendary sextet with John Coltrane, Cannonball Adderly, Bill Evans, Jimmy Cobb and Paul Chambers – the lineup that would later appear on the classic Kind of Blue. Eight and nine years later, Davis returned to Newport with perhaps his greatest Quintet personnel: Wayne Shorter, Herbie Hancock, Ron Carter, and Tony Williams, performing some of the numbers that would be associated with that lineup: "Gingerbread Boy," "Seven Steps to Heaven," "Footprints" along with earlier compositions as "So What," "All Blues" and "Stella By Starlight." Perhaps the most exhilarating of the Newport performances (not only just in Rhode Island, but also in New York, Berlin and Switzerland) came later in the late 60s through the mid 70s when Davis and another shifting-lineup went electric, highlighted by the towering and influential Bitches Brew album—whose several cuts like "Miles Run the Voodoo Down," "Sanctuary" and the title song are featured on the last two discs. The sound of that period is marked by not only Davis's darting trumpet but also some jagged-sounding guitar, electric piano, and funky, swinging drumming; one could only imagine what the audiences at Newport must have thought of hearing music– at time explosive, other times moody and atmospheric– that was more suitable at the Fillmore West than at a jazz festival. This exhilarating music from this boxed set clearly shows the symbiotic relationship between Davis and Newport. Davis' music certainly evolved during 20 years, but the only constant was sense of majesty and awe emanating from his and his band's performances.
July 23, 2015 Leave a commentMiles Davis
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Sorry, you missed Krystal Klear & Gerd Janson... at The Academy.
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I would like to personally invite you to become a member of the Birmingham Police Department. We are seeking qualified applicants who are interested in improving the quality of life for area residents through aggressively yet ethical enforcement of the law and community service. Our officers must exemplify the values of duty, honor and selfless service while exhibiting dignity and respect in their daily interactions with the community.
The Birmingham Police Department is a thoroughly modern agency of municipal government, serving an area in excess of 160 square miles. Our services reflect an on-going commitment not only to law enforcement and crime prevention but also to good community relations, all of which are hallmarks of a progressive organization.
Applications may be filled out on line at www.jobsquest.org.
Find Out About The Birmingham Police Department Recruit Training Program now. For Further Information Contact: Birmingham Police Department Hiring Unit, 1710 1st Avenue North, Birmingham, Alabama 35203, 205-254-1712 – Office, 205-297-8426 – Fax.
The Birmingham Police Academy curriculum includes approximately 920 hours of instructions, including 480 hours required by the Alabama Peace Officers Standards and Training Commission. All training aids and materials are furnished. Academy training is based on a five day week, eight hour per day schedule and lasts approximately 20 weeks. Subjects taught include search and seizure, criminal law, patrol procedures, police community relations and first aid, firearms, defensive tactics and physical fitness. A recruit must successfully complete all training requirements of the State of Alabama and the Birmingham Police Department.
After successful completion of the Police Academy training, recruits are sworn in and assigned to a Field Training Officer (FTO) in the Patrol Division under the field Training Program. The Field Training Program is designed to produce a highly trained and positively motivated police officer capable of meeting or exceeding standards of performance required by the department. This program is a bridge between academy training and the actual performance of a police officer in the field.
A minimum of 16 weeks is spent working with a field training officer. Police officers who successfully pass this phase of training, gain experience in the Patrol Division, and possess the necessary skills that can be considered for transfer to one of the department's career specialties after a minimum of three years of service such as: Task Force Officer, School Resource Officer, Range/Academy Instructor, Tactical Officer, Mounted Patrol Officer, Explosive Ordinance Technician, Detective, Crime Scene Technician, Canine Handler, Polygraph Examiner, Freeway Patrol or Motor Scout.
Birmingham Police Department is an Equal Opportunity Employer.


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Today's workout was great, except for the part where my necklace got all tangled up in my earbuds. This annoys me more than anything, as it typically takes about five minutes to undo what can only be described as a hot mess. It's true that five minutes isn't all that long, but when you're working against the clock and trying hard to keep your heart rate up—five minutes is like five years. Plus, I lost my claim on the calf press machine. But these things happen, so I moved on once I convinced my necklace and earbuds to part ways.
So what made my workout so great? I know, right. Get to the juicy stuff already! (Pa-tience...) I upped the ante a little by using the pyramid method. This form of strength training really challenges the muscles with added weight and any time you do this, you're essentially pushing yourself to reach new benchmarks. Or, more simply, you're kicking it up a notch which is always a good thing.
If you've never used the pyramid method, it goes something like this: Three sets of an exercise. 15 repetitions at X weight. 12 repetitions at X+5 weight. 10 repetitions at (X+5) + 5 weight.
Of course, you can do 12/10/8 repetitions as well. You get the basic drift, right? It's all about decreasing reps while increasing the weight. And you could, theoretically, do it in reverse, too. Either way, you'll work on building up those muscles.
Give it a try if you're looking for something new. And if you're not looking for something new, well...give it a try! I'm always interested in your feedback.
Question: Do you incorporate the pyramid method into your training? How and why?
I love the Pyramid Method, I just started doing Jackie Warners workout. I really feel it the next day!!


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Q: Funneling echoes into an output file I'm asynchronously posting to a PHP file that echoes out a few key things. I want to write all of its output to a logfile. What would be the simplest way to do this?

A: I would use a simple wrapper, like http://www.redips.net/php/write-to-log-file/. All you need to do is include the file, instantiate the Logger class, and set a path. You would need to perform the logging operation after/before each echo.

A: <?php
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BRENDAN RODGERS is set to hand summer signings Mario Balotelli and Adam Lallana their Liverpool debuts in Sunday's trip to Tottenham (1.30pm).
Italian ace Balotelli is set to make his first Reds appearance following his £16m move from AC Milan, while £25m signing Lallana has recovered from a knee injury to take his place in the matchday squad.
Alberto Moreno (ankle), Martin Skrtel (knock) and Glen Johnson (thigh) will all be assessed prior to kick-off at White Hart Lane after picking up injuries in Monday's 3-1 loss to Manchester City.
Defensive pair Jon Flanagan and Daniel Agger and Oussama Assaidi (all knee) will miss the trip to north London.
Meanwhile, Tottenham boss Mauricio Pochettino could hand a debut to Federico Fazio after the Argentine defender completed a move from Europa League winners Sevilla on Wednesday.
Striker Roberto Soldado (neck and back) is unlikely to be fit, while right-back Kyle Walker (groin) is definitely out.
Tottenham provisional squad: Lloris, Friedel, McGee, Naughton, Dier, Kaboul, Fazio, Chiriches, Vertonghen, Davies, Rose, Veljkovic, Capoue, Bentaleb, Sandro, Paulinho, Dembele, Eriksen, Lamela, Lennon, Chadli, Townsend, Holtby, Adebayor, Kane, Soldado.
Liverpool provisional squad: Mignolet, Lovren, Skrtel, Enrique, Gerrard, Henderson, Allen, Coutinho, Sterling, Sturridge, Jones, Manquillo, Toure, Sakho, Lucas, Can, Lambert, Markovic, Moreno, Balotelli, Lallana.


Since I write this from Boston, I shouldn't admit or gloat that we missed most of the storm that has kept nearly every single Atlantic person outside our Watergate home—except the Food Channel's own doughty Dan Fromson, who has amazingly forded the snow banks and sluggish public transport pace in what James Fallows calls Siberia-on-the-Potomac, along with a handful of others (the avalanche of emails in my inbox proves that everybody's working! from wherever they're burrowed in).
And I certainly shouldn't use it as an excuse to have delayed welcoming two contributors I've long been hoping would appear on the Food Channel, especially when the debut of one, yesterday, centers on my favorite luncheon meat. Ian Knauer was a leading light of the late Gourmet's test kitchen, whose colleagues told me I needed to have him here. I saw from his excellent taste in recipes, and knew why as soon as we met: everything about his approach to food is informed by his experience on his family's farm in the not accidentally named Knauertown, Pennsylvania. He hunts, he fishes, he tends bees, and he cooks using the knowledge he's earned growing up working on a farm—and working now, as often as he can get down from Brooklyn, where he lives.
His debut post is only peripherally about Lebanon bologna, an oddly sweet beef sausage that once you try you want to have in place of any other sandwich meat. It's a beautifully written remembrance of his grandfather, and will make you want to learn much more about him—and also taste Lebanon bologna, particularly given the emotion he invests it with.
While serving customers Dietrich would slip Yoder and me little tastes of products other than the copious array of salamis and sausages already set out in tiny cubes: liverwurst, for instance, something I hadn't thought of since it meant grade-school sandwiches no one could trade, and so good that I wanted to spread it on German rye bread; and a kind of salami I'd never had that is emblematic of the Pennsylvania Dutch larder—Lebanon bologna, named for the county where it was first commercially produced. What makes it typical is the use of beef rather than pork, a distinct sweetness, and a gentle spicing with hints of ginger, paprika, mustard, and mace. (I got this list from Hot Links and Country Flavors, by the master sausage maker Bruce Aidells with Denis Kelly; Dietrich would reveal few of her "seasonings.") The Lebanon bologna, unlike other things I tasted at the store, was subtly smoked and not particularly salty.
Boy, did I like that visit—and the fastnachts, square Lenten doughnuts made from a yeast dough containing mashed potatoes, butter, and lard. Time for another visit! Meanwhile, though, I'm looking forward to much more from Ian, who will be a great guide to a part of the world I still know far too little about, and who is a great cook too.
And I bet you've been enjoying Tom Mylan's posts as much as I have. Mylan is one of the new breed of cool butchers in cool places—The Meat Hook, in Brooklyn. He's also a very accomplished, and funny, writer. We're really lucky to have him—and I'll have him to thank for a few fewer cut fingertips in the next few weeks.


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Ron Kochman, KCL Co-Founder, Passes Away at 85
Kevin Kochman, KCL co-founder and president, is sad to announce the passing of his father Ronald (Ron) Kochman. "Ron was a visionary who used technology to help make his foodservice design and consulting firm more productive. He and I founded KCL to help others do the same."
Bringing CAD Technology to the Foodservice Design Industry
Kevin and Ron saw the potential for AutoCAD to enhance the foodservice industry. In 1985, the pair founded Kochman Consultants, Ltd. (KCL) to deliver computer aided design (CAD) to the foodservice industry. They built their brand on the promise of helping designers, dealers, consultants, and architects save time and money.
In addition to training industry professionals on computer basics like how to use a mouse, one of their early decisions was to standardize their symbol library on 5.25" floppy disks. The Kochman duo also worked with industry leaders to set CAD-based design standards.
Serving two audiences, manufacturers and designers, was not simple but Ron's solid reputation as a food facilities consultant and passion for customer service attracted people to his unique symbol libraries and other newfangled tech products.
"If you met Ron in person, you know his passion for and knowledge of the foodservice industry," said Kevin. "He was sad to miss the 2019 NAFEM Show, and now the industry will miss him."
Ron is survived by his wife Judy, children Kevin (Eve), Kim (Brad), and many dear grandchildren and nephews.
Donations in Ron's honor may be made to the Greater Chicago Food Depository or the Illinois Holocaust Museum.
An early tech adopter, Ron revolutionized the foodservice design industry
Booth 4216 at #NAFEM2023
2023 KCL Updates and Additions
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\section{Introduction}

Over the past two decades, spectral clustering has established itself as one of the most prominent clustering methods \citep{Shi00,Ng02}.
The effectiveness of spectral clustering in identifying complex structures in data is a direct consequence of its close connection with kernel machines \citep{Dhillon04}.
Because of this connection, however, it is also apparent that spectral clustering inherits the scalability issues of kernel machines.
In spectral clustering, the computational challenge is to determine the spectral properties of the so called Laplacian matrix \citep{vonLuxburg07}.
Denoting by $n$ the number of samples, storing the Laplacian matrix requires $\mathcal{O}(n^2)$ space while calculating the spectrum of the Laplacian requires $\mathcal{O}(n^3)$ computations.

Several approaches have been proposed to reduce the complexity of spectral clustering, such as employing power methods to identify the principal eigenvectors of the Laplacian \citep{Boutsidis15}.
While this approach is exact in the limit of iterations and does not require storing the Laplacian, the complexity is dominated by the iterative multiplication of the Laplacian matrix by vectors, leading to $\mathcal{O}(n^2)$ computations.
In order to further reduce this complexity to $\mathcal{O}(n)$, a number of approximations are proposed in the literature.
A popular technique based on the Nystr\"om approximation relies on a small set of inducing points to approximate the spectrum of the Laplacian matrix \citep{Fowlkes04}.
Other recent approximations which attempt to compress the dataset appear in \citet{Yan09} and \citet{Li16}.
These approximations recover tractability and make it possible to apply spectral clustering to large data sets.
However, approximations can generally affect the quality of the clustering solution, as we illustrate in the experiments.

This paper proposes a novel iterative way to solve spectral clustering in $\mathcal{O}(n)$, while retaining exactness in the calculation of the spectrum of the Laplacian in the limit of the iterations.
Denoting by $L$ the Laplacian matrix, the idea hinges on the possibility to cast the algebraic problem of identifying its principal eigenvectors as the following trace optimization problem
\begin{equation} \label{eq:constrained:optimization}
\argmin_{W \in \mathcal{R}^{n \times k}} \left\{ \mathrm{Tr} \left(-\frac{1}{2} W^{\top} L W \right) \right\} \qquad \mathrm{subject\ to} \qquad W^{\top} W = I
\end{equation}
We propose to solve the constrained optimization problem by means of stochastic gradient optimization.
In view of the orthonormality constraint the elements of $W$ lie on the so called Stiefel manifold, and appealing to theoretical guarantees of convergence of stochastic gradient optimization on manifolds, we can prove that our proposal computes the exact spectrum of $L$ in the limit of the iterations \citep{Bonnabel13}.
In order to simplify the tuning of the optimization procedure, we adapt Adagrad \citep{Duchi11} for stochastic gradient optimization on the Stiefel manifold.
The novelty of our proposal stems from the use of stochastic linear algebra techniques to compute stochastic gradients in $\mathcal{O}(n)$.
This leads to computations of stochastic gradient that require processing of a limited number of columns of the full Laplacian matrix, motivating us to name our proposal Mini-Batch Spectral Clustering.

The results on a variety of clustering problems with $n$ up to $580K$ give credence to the value of our proposal.
We can tackle large scale spectral clustering problems achieving the same level of accuracy of the approach that uses the exact spectrum of $L$ at a fraction of the computing time.
We also compare against approximate spectral clustering methods and show that approximations lead to faster solutions that are suboptimal compared to what we can achieve with the proposed method, especially for large data sets\footnote{Code to reproduce all results in the paper is available upon request.}.

\paragraph{Summary of contributions}
(i) We formulate the solution of spectral clustering as a constrained optimization problem that we solve using adaptive stochastic gradient optimization;
(ii) We present a novel way of computing stochastic gradients linearly in the number of data that does not require storing the Laplacian matrix;
(iii) We analyze the variance of the proposed estimator of the exact gradient to explain the impact of algorithm parameters.
(iv) We demonstrate that our proposal allows us to tackle large-scale spectral clustering problems by reporting results on data sets of size up to $n = 580K$. Crucially, we can achieve clustering solutions of similar accuracy and orders of magnitude faster compared to the approach that computes the exact spectrum of $L$, and higher accuracy compared to approximate methods at a comparable cost.

\section{Spectral clustering}

\subsection{Background}

Define $X = \{\mathbf{x}_1, \ldots, \mathbf{x}_n\}$ to be a set of $n$ samples.
The formulation of spectral clustering introduces an undirected graph $\mathcal{G}$ based on $X$, where the $n$ nodes of $\mathcal{G}$ represent the $n$ input data in $X$, and the edges are weighted according to a similarity measure between the inputs.
The graph $\mathcal{G}$ is expressed by an $n \times n$ adjacency matrix $A$, where each entry $a_{ij}$ determines the weight associated with the edge connecting inputs $i$ and $j$.
Typically, the elements of the adjacency matrix are defined through off-the-shelf kernel functions, e.g., the Radial Basis Function (RBF) kernel \cite{Scholkopf01}.

Spectral clustering attempts to cluster the elements of $X$ by analyzing the spectral properties of the graph $\mathcal{G}$.
In particular, the objective of spectral clustering is to partition the graph so as to minimize some graph cut criterion, e.g., the normalized cut \citep{Shi00}.
The graph cut problem is generally NP-hard, but its relaxation leads to the definition of the clustering problem as the solution of an algebraic problem \citep{Chung97}.
In particular, following the spectral clustering algorithm proposed by \citet{Ng02}, the graph Laplacian is defined as a normalized version of the adjacency matrix
\begin{equation}
L = D^{-\frac{1}{2}} A D^{-\frac{1}{2}}
\end{equation}
where $D$ is the diagonal matrix of the degrees of the $n$ nodes.
Spectral clustering represents each data point using the corresponding component of the top $k$ eigenvectors of the Laplacian $L$, and computes the solution to the clustering problem by applying $k$-means in this representation.
The difficulty in solving the graph cut problem then becomes calculating the spectrum $L$; this requires $\mathcal{O}(n^3)$ computations and $\mathcal{O}(n^2)$ space, making it prohibitive -- if not unfeasible -- for large data sets.
The aim of this paper is to address this scaling issue of spectral clustering without sacrificing the accuracy of the solution, as explained next.

\subsection{Spectral clustering as a constrained optimization problem}

The first step to reduce the complexity in finding the top $k$ eigenvectors of $L$, is to cast this algebraic operation as solving the constrained optimization problem in Eq.~\ref{eq:constrained:optimization}.
This is an optimization problem involving $n \times k$ parameters representing the $n$ components of the top $k$ eigenvectors of $L$.
The objective function rewards maximization of a score that, at convergence, is the sum of the $k$ largest eigenvalues.
The constraint $W^{\top} W = I$ gives rise to the so called Stiefel manifold in $\mathcal{R}^{n \times d}$; this imposes orthonormality on the columns of $W$ which, at convergence, represent the eigenvectors associated with the $k$ largest eigenvalues.

The constrained optimization problem in Eq.~\ref{eq:constrained:optimization} can be solved by formulating standard optimization algorithms to deal with the Riemannian metric on the manifold \citep{Smith14}, which typically rely on search operations along geodesics.
Alternative schemes, such as the Cayley transform, have been proposed to tackle optimization problems on Riemannian manifolds \citep{Wen13}.
All these optimization schemes require calculating the gradient of the objective function
\begin{equation} \label{eq:exact:gradient}
G = \nabla_W \mathrm{Tr} \left( -\frac{1}{2} W^{\top} L W \right) = -L W
\end{equation}
This costs $\mathcal{O}(n^2)$ and does not require storing $L$ anymore, which is an improvement with respect to computing the full spectrum of $L$.
However, while casting spectral clustering as a constrained optimization problem improves scalability, when $n$ is large it may still take a prohibitive amount of time to be practical.
In the next section we present our proposal to reduce the complexity to solve the constrained optimization problem to $\mathcal{O}(n)$ with the guarantee of obtaining the exact solution of the in the limit of the iterations.

\section{Mini-Batch Spectral Clustering (MBSC)}

The intuition behind our proposal is that it is possible to solve the constrained optimization problem in Eq.~\ref{eq:constrained:optimization} relying exclusively on stochastic gradients \cite{Bonnabel13}.
By inspecting the expression of the exact gradient in Eq.~\ref{eq:exact:gradient}, we show how stochastic linear algebra techniques can be employed to unbiasedly estimate exact gradients ($\mathcal{O}(n^2)$ cost) with stochastic gradients at $\mathcal{O}(n)$ cost.

\subsection{Stochastic optimization on Stiefel manifolds}

\begin{figure}[t]
 \centering
 \includegraphics[trim={2.2cm 2.7cm 0 0}, clip, width=0.28\textwidth]{figs/manifold1.pdf} \hspace{2cm}
 \includegraphics[trim={2.2cm 2.7cm 0 0}, clip, width=0.28\textwidth]{figs/manifold2.pdf}
 \caption{Left: Exact gradient $G$ with a few $\tilde{G}$ and their projection onto the tangent space $T_WM$ of a manifold $M$ at a given $W$ giving $H$ and $\tilde{H}$. Right: Retraction scheme that approximates the exponential map at $W$.}
\label{fig:manifold}
\end{figure}

Stochastic gradient optimization on manifolds is based on the notion of Riemannian gradients, which are elements of the tangent space at a given $W$ that determine the direction of steepest increase of the objective function on the manifold.
For the Stiefel manifold, the Riemannian gradient is \citep{Bonnabel13}
\begin{equation}
H = (I - W W^{\top}) G
\end{equation}
In the case where an unbiased version $\tilde{G}$ of the gradient $G$ is available, namely $\mathrm{E}[\tilde{G}] = G$, an intuitively sensible strategy is to perform stochastic gradient optimization on the manifold.
Formally, this would amount in moving along geodesics for a given length based on the noisy version of the gradient.
Defining $\gamma_t$ as the equivalent of the usual step-sizes in stochastic gradient optimization, and $\exp_{W}()$ as the exponential map at $W$, the update equation would then be $W^{\prime} = \exp_{W}\left(-\gamma_t \tilde{H} \right)$,
where $\tilde{H} = (I - W W^{\top}) \tilde{G}$ is the unbiased Riemannian gradient of the objective function.
This approach can be shown to converge to the exact solution of the constrained optimization problem in Eq.~\ref{eq:constrained:optimization} \cite{Bonnabel13}.
However, computing the exponential map to simulate the trajectory of the solver on the manifold requires solving potentially expensive differential equations.

An alternative that avoids computing the exponential map altogether is to replace this calculation with an approximation $W^{\prime} = R_{W}\left(-\gamma_t \tilde{H} \right)$ that is much easier to calculate.
If the so called retraction $R_{W}$ satisfies the property that $d(R_W(\delta v), \exp_W(\delta v)) = \mathcal{O}(\delta^2)$, where $v$ is an alement of the tangent space, then it is still possible to prove convergence to the exact solution \cite{Bonnabel13}.
A simple and computationally convenient retraction function that satisfies this property is
\begin{equation}
W^{\prime} = \mathrm{QR}_Q\left(W - \gamma_t (I - W W^{\top}) \tilde{G} \right)
\end{equation}
where $\mathrm{QR}_Q$ extracts the orthonormal factor $Q$ of a $\mathrm{QR}$ decomposition.
This simple retraction moves the optimization in the direction of the stochastic Riemannian gradient $\tilde{H} = (I - W W^{\top}) \tilde{G}$ and applies an orhtonormalization step to ensure that the update is projected back onto the manifold.
Under this choice of retraction, we can appeal to the theoretical results in \citet{Bonnabel13} that ensure convergence to the exact solution in the limit of the iterations similarly to standard stochastic gradient optimization.
An illustration of the retraction scheme is provided in Fig.\ref{fig:manifold}.

\begin{algorithm}[t]
\caption{Stochastic Riemannian gradient on Stiefel Manifold using Mini-Batches}
\label{alg:Htilde}
\DontPrintSemicolon
\SetKwFunction{Htilde}{Htilde}
\Htilde{$L$, $p$, $N_{\mathbf{r}}$, $W$} { \\
Initialize $\tilde{G} \in R^{n\times{k}}$ with elements equal to zero \\
 \For{$i=1$ \KwTo $N_{\mathbf{r}}$}{
   Draw the components of $\mathbf{r}_i$ \\
   $\tilde{G}$ += $\frac{1}{N_r}$ $L \mathbf{r}_i \mathbf{r}_i^{\top} W$
 }
 Return $\tilde{H}$ = $(I-W W^{\top})\tilde{G}$

}
\end{algorithm}

\begin{algorithm}[t]
\caption{Mini-Batch Spectral Clustering}\label{alg:MBSC}
\DontPrintSemicolon
\KwIn{Normalized Laplacian Matrix $L \in R^{n\times{n}}$, number of clusters $k$, regularization factor $\varepsilon$}
\SetKwInOut{Parameter}{Parameters}
\Parameter{Master step length $\lambda$, maximum iteration steps $T$}
\KwOut{Cluster labels of each data points}
Initialize $W^{(0)} \in R^{n\times{k}}$ as a random orthonormal matrix \\
Initialize $M^{(0)} \in R^{n\times{k}}$ with elements equal to zero \\
\For{$t=1$ \KwTo $T$}{
      $\tilde{H}^{(t)}$ = \texttt{Htilde}($L$, $p$, $N_{\mathbf{r}}$, $W^{(t-1)}$) \\
      $M_{ij}^{(t)}$ = $M_{ij}^{(t-1)}$ + $|\tilde{H}_{ij}^{(t)}|^{2}$ \\
      $\displaystyle \hat{H}_{ij}^{(t)} = \frac{\tilde{H}_{ij}^{(t)}}{\varepsilon + \sqrt{M_{ij}^{(t)}}}$ \\
      $W^{(t)} = W^{(t-1)} - \lambda \hat{H}^{(t)}$ \\
      $W^{(t)} = \mathrm{QR}_Q(W^{(t)})$ \\
    }
Apply $k$-means on $W^{(T)}$ to get the cluster labels\\
\end{algorithm}

\subsection{Calculation of stochastic gradients in $\mathcal{O}(n)$}

The introduction of stochasticity in the calculation of $\tilde{G}$ follows on from ideas that have been proposed to calculate unbiased stochastic approximations to algebraic quantities, such as traces and log-determinants \citep{Chen11,FilipponeICML15}.
In particular, we define a vector $\mathbf{r}$ such that $\mathrm{E}[\mathbf{r} \mathbf{r}^{\top}] = I$ and we rewrite the expensive matrix product as
\begin{equation}
G = L W = L I W = L \mathrm{E}[\mathbf{r} \mathbf{r}^{\top}] W = \mathrm{E}[ L \mathbf{r} \mathbf{r}^{\top} W ]
\end{equation}
which suggests that we can replace the exact calculation of $L W$ with the estimator
\begin{equation} \label{eq:stochastic:gradient}
\tilde{G} = \frac{1}{N_r} \sum_{i=1}^{N_r} L \mathbf{r}_i \mathbf{r}_i^{\top} W
\end{equation}

The key to making computations linear in $n$ is to define the components of the random vectors $\mathbf{r}_i$ as drawn from the set $\{-p^{-\frac{1}{2}}, 0, +p^{-\frac{1}{2}}\}$ with probabilities $(p/2, 1 - p, p/2)$ respectively.
It is straightforward to verify that $\mathrm{E}[\mathbf{r}_i \mathbf{r}_i^{\top}] = I$, and $p$ can be chosen to enforce any proportion of zeros in the $\mathbf{r}_i$ vectors.
With this mechanism to inject stochasticity in the calculation of the gradients, we are effectively ignoring some columns of the matrix $L$ whenever there is a zero in the corresponding positions of the $\mathbf{r}_i$ vectors.
This makes it possible to update the parameters $W$ during the solution of the constrained optimization problem in Eq.~\ref{eq:constrained:optimization}, by only selecting a few columns of the full Laplacian.
If the average number of non-zero elements is chosen to be independent of $n$, the calculation of the stochastic gradient is $\mathcal{O}(n)$, making the proposed iterative solver linear in the number of samples.
The memory footprint of the algorithm is a distinctive feature of our proposal; if the degree matrix $D$ is precomputed, calculating the columns of $L$ requires to compute stochastic gradients requires evaluating and normalizing only $\mathcal{O}(n)$ elements of the adjacency matrix $A$.

Given that only a subset of the columns in $L$ are used at each iteration to calculate stochastic gradients, we term our proposal Mini-Batch Spectral Clustering (MBSC).
Instead of defining a probability $p$ to select columns and to repeat this $N_{\mathbf{r}}$ times, we can fix the number and indices of columns that are selected at each iteration (size of the mini-batch) to be $m = l N_{\mathbf{r}}$ and interpret $p = l/n$.
While this is intuitively sensible, fixing the indices of the mini-batches would violate the property that $\mathrm{E}[\mathbf{r}_i \mathbf{r}_i^{\top}] = I$.
One easy way around this issue is to constantly change the way data are split into mini-batches, e.g., by shuffling the data, and this would recover the property $\mathrm{E}[\mathbf{r}_i \mathbf{r}_i^{\top}] = I$.
Even though it is not the focus of the current paper, we envisage the possibility to develop a distributed version of the proposed MBSC algorithm based on our formulation.
The proposed MBSC algorithm is sketched in Algorithms~\ref{alg:Htilde} and~\ref{alg:MBSC}, where,
for the sake of clarity, $L$ is assumed to be stored.
For memory constrained systems where storing the whole Laplacian matrix is unfeasible, our proposal can easily be adapted to avoid storing it, and we report on the performance of this variant in the experiments.

\subsection{Variance of stochastic gradients}

Here we are interested in quantifying the impact of the choice of $p$ and $N_{\mathbf{r}}$ in the calculation of stochastic gradients; to this end, we analyze the variance of the proposed estimator of the exact gradients.
Without loss of generality, we focus on the variance of a given column of the stochastic gradient $\tilde{G}$, namely the one associated with a given eigenvector, say $\mathbf{w} := W_{\cdot s}$.
Recall that the exact gradient with respect to $\mathbf{w}$ would be $G_{\cdot s} = L \mathbf{w}$ and assume that we use a single vector $\mathbf{r}$ to unbiasedly estimate this as $\tilde{G}_{\cdot s} = L \mathbf{r} \mathbf{r}^{\top} \mathbf{w}$.
The covariance of $\tilde{G}_{\cdot s}$ is
$$
\mathrm{cov}\left(L \mathbf{r} \mathbf{r}^{\top} \mathbf{w} \right) =
\mathrm{E}[ (L \mathbf{r} \mathbf{r}^{\top} \mathbf{w}) (L \mathbf{r} \mathbf{r}^{\top} \mathbf{w})^{\top} ]
- \left(\mathrm{E}[ L \mathbf{r} \mathbf{r}^{\top} \mathbf{w} ] \right) \left(\mathrm{E}[ L \mathbf{r} \mathbf{r}^{\top} \mathbf{w} ] \right)^{\top}
$$
After some manipulations, that we leave to the supplementary material, we obtain
$$
\mathrm{diag}\left[\mathrm{cov}\left(L \mathbf{r} \mathbf{r}^{\top} \mathbf{w} \right)\right] =
\mathrm{diag}\left[G_{\cdot s} G_{\cdot s}^{\top} \right] + \left(\frac{1}{p} - 3\right) \mathrm{diag}\left[ L \mathrm{diag}(\mathrm{diag}(\mathbf{w} \mathbf{w}^{\top})) L^{\top} \right] + \mathrm{diag}\left[ L L^{\top} \right]
$$
Given that $\mathrm{diag}(\mathrm{diag}(\mathbf{w} \mathbf{w}^{\top})) < I$, then $\mathrm{diag}\left[ L \mathrm{diag}(\mathrm{diag}(\mathbf{w} \mathbf{w}^{\top})) L^{\top} \right] \leq \mathrm{diag}\left[ L L^{\top} \right]$ when $L$ has positive elements.
Also, since $L L^{\top}$ has positive diagonal entries, we can further bound
\begin{equation}
\mathrm{diag}\left[\mathrm{cov}\left(L \mathbf{r} \mathbf{r}^{\top} \mathbf{w} \right)\right] \leq
\mathrm{diag}\left[G_{\cdot s} G_{\cdot s}^{\top} \right] + \frac{1}{p} \mathrm{diag}\left[ L L^{\top} \right]
\end{equation}
The first term contains the square of the components of the exact gradient that will vanish at convergence.
The second term depends on the choice of $p$.
We can rewrite the bound in terms of the mini-batch size $m = l N_{\mathbf{r}}$, for which $p=l/n$, and when $N_{\mathbf{r}}$ vectors $\mathbf{r}_i$ are used to calculate stochastic gradients as in Eq.~\ref{eq:stochastic:gradient}.
\begin{equation}
\mathrm{diag}\left[\mathrm{cov}\left(L \mathbf{r} \mathbf{r}^{\top} \mathbf{w} \right)\right] \leq
\frac{1}{N_{\mathbf{r}}}\mathrm{diag}\left[G_{\cdot s} G_{\cdot s}^{\top} \right] + \frac{n}{l N_{\mathbf{r}}} \mathrm{diag}\left[ L L^{\top} \right]
\end{equation}
This reveals that we have two ways of reducing the variance of stochastic gradients; one is to increase $N_{\mathbf{r}}$ and another is to increase $l$.
Imagine that we fix the mini-batch size $m = l N_{\mathbf{r}}$; is it better to increase $l$ and reduce $N_{\mathbf{r}}$, or the other way around?
For the second term it does not matter.
For the first instead, given that it depends only on $N_{\mathbf{r}}$, it is clear that we should favor increasing $N_{\mathbf{r}}$ and reducing $l$.
This entails that we should consider averaging stochastic gradients over several subsets of a mini-batch instead of a few large ones.
This result is interesting because in other popular mini-batch approaches increasing the mini-batch size or the number of repetitions is equivalent.
In our proposed MBSC, because of the nonlinearity of the estimator with respect to the vectors $\mathbf{r}_i$, the bound on the variance shows an unintuitive asymmetry between $N_{\mathbf{r}}$ and $l$.
A further consideration we can make is that this suggestion is most useful during the first phase of the optimization; towards convergence, the first term will be small and dominated by the second term that is inversely proportional to the mini-batch size $m$.

\section{Experiments}

Throughout the experiments, we make use of the Radial Basis Function (RBF) adjacency function:
$$
a_{ij} = \exp\left( -\frac{\| \mathbf{x}_i - \mathbf{x}_j \|}{\sigma^2} \right) \qquad i \neq j
$$
where we set $a_{ij} = 0$ when $i = j$.
The RBF adjacency function assigns a large weight to the edge connection inputs that are close in the input space, whereas it assigns a small weight to edges connecting inputs that are far apart.
The parameter $\sigma$ determines the rate of decay of the adjacency function, which can be tuned, e.g., using local statistics on the distances between pairs of points \cite{Zelnik04selftuning}.

We assess clustering performance using the normalized mutual information (NMI) score between the cluster labels and the ground truth class labels.
To reliably measure computational cost of all methods involved in the comparison, we count the amount of floating-point addition and multiplication operations they require, given the affinity matrix, and we also report running time statistics.
We implemented all the algorithms in Python using the $\texttt{numpy}$ and $\texttt{scikit-learn}$ packages.
All our experiments are conducted under Ubuntu Linux $14.04$ with $10$-core CPU and $20\mathrm{GB}$ memory.

Table~\ref{tab:database} summaries the statistics of the data sets, taken from LibSVM \citep{libSVM}, that we consider in the experiments.
To construct the \texttt{Covtype-I} set, we randomly sample $14129$ samples from the first two classes of the original \texttt{Covtype} data set and merge the data samples of classes $4$, $5$ and $6$ into one single class.
The purpose is to avoid severe imbalances between classes.
We make use of all data samples of the original \texttt{Covtype} data set to build the \texttt{Covtype-II} set.

We organize the experimental study in two parts.
In both parts, we aim to show the performance of the proposed MBSC algorithm against other state-of-the-art algorithms for solving spectral clustering.
In particular, we compare our proposal with the solution of the power iteration-based algorithm in \citet{Boutsidis15} and the Nystr\"om approximation-based spectral clustering in \citet{Fowlkes04}.
In the first part, this comparison is carried out on moderately large data sets comprising $10K$, $58K$ and $60K$ samples.
For these, we can also report the performance of the spectral clustering approach in \citet{Shi00} where the spectrum of the normalized Laplacian is computed exactly (denoted as ``Exact'' in the plots).
In the second part, we repeat the same comparison on two larger sized data sets, comprising $100K$ and $580K$ samples, where we cannot compute the exact spectrum of $L$.

\begin{table}[t]
\centering
\caption{Summary of the characteristics of the data sets considered in the experiments.}
\label{tab:database}
\begin{tabular}{|c|c|c|c|c|}
\hline
Data set & $\#$ of samples & $\#$ of features & $\#$ of classes & $\sigma$ \\ \hline
 \texttt{Pendigits} & 10992 & 16 & 10 & 223.61\\ \hline
 \texttt{Shuttle} & 58000 & 9 & 7 & 0.45\\ \hline
 \texttt{MNIST} & 60000 & 780 & 10 & 4.08 \\ \hline
 \texttt{Covtype-I} & 100000 & 54 & 5 & 1.15\\ \hline
 \texttt{Covtype-II} & 581012 & 54 & 7 & 1.15\\ \hline
\end{tabular}
\end{table}

\subsection{Comparative evaluation}
We conduct a comparative evaluation of the proposed MBSC with state-of-the-art spectral clustering algorithms on the \texttt{Pendigits}, \texttt{Shuttle} and \texttt{MNIST} data sets \citep{libSVM}.
In the proposed MBSC approach, we experiment with different choices of the mini-batch size to assess its impact on performance.
To comprehensively analyze the performance of the proposed method, the iterative stochastic gradient descent on the manifold runs until we make one full pass through the whole data set.
In practice, the stochastic gradient descent process can be stopped either if the difference between the spectral embedding $W$ derived at two successive iteration steps is less than a threshold, or if a fixed number of iteration is achieved.
For the Nystr\"om approximation, we report a few choices on the number of samples selected to construct the approximate eigenvectors, namely $10$, $50$, $100$, $500$ and $1000$.

\begin{figure}[t]
  \centering
    \includegraphics[width=0.32\textwidth,height=0.32\textwidth]{figs/pendigits_comparison_rplots.pdf}
    \includegraphics[width=0.32\textwidth,height=0.32\textwidth]{figs/shuttle_comparison_rplots.pdf}
    \includegraphics[width=0.32\textwidth,height=0.32\textwidth]{figs/mnist_comparison_rplots.pdf}
  \caption{
NMI versus counts of floating-point operations on the \texttt{Pendigits}, \texttt{Shuttle} and \texttt{MNIST} data sets.
NMI for the exact spectral clustering is shown as a constant dashed line.
MBSC with the largest mini-batches runs for $3.8s$, $107s$ and $112s$ to achieve an average NMI score of $0.67$, $0.48$ and $0.47$ on the three data sets, whereas the power method takes $20s$, $935s$ and $987s$ to get a stable clustering output.
The Nystr\"om approximation needs $1000$ samples to obtain the optimal clustering accuracy, which takes $15.2s$, $198s$ and $211s$ on the three data sets.
}\label{fig:comparison}
\end{figure}

Figure~\ref{fig:comparison} illustrates the NMI scores of the proposed MBSC algorithm, the power method, and the Nystr\"om approximation versus the amount of floating-point operations.
In the figure, for the proposed MSBC and the Nystr\"om approximation we report the average plus and minus one standard deviation of the NMI score over $10$ repetitions.

Recalling that $m$ is the mini-batch size, $k$ is the number of top eigenvectors and the number of clusters, each iteration of MBSC
requires $2nkm + 6nk^2 - k^2$ floating point operations.
The power method starts by generating an $n$-by-$k$ Gaussian random matrix $S$, which costs $\mathcal{O}(nk)$ operations.
It then computes a matrix product between the $n$-by-$n$ affinity matrix and $S$, and iteratively applies the same multiplication for a total cost of
$4{n^2}k - 2nk$ floating point operations.
The final step of the power method performs Singular Value Decomposition (SVD) on an $n$-by-$k$ matrix.
Since $n{\gg}k$, we adopt the estimate of SVD complexity in \citep{Golub96}, which costs $2nk^2 + 2k^3$ operations.
Finally, in order to calculate the number of floating point operations for the Nystr\"om approximation we follow the pseudo code in \citep{Fowlkes04},
for which the total count of floating point operations is $6nk+8k^3-3k^2+4n{k^2}-3k+2nkm+nm+2n{m^2}+m^2+m^3-n$.

In Figure~\ref{fig:comparison}, we can observe how the variance of the clustering performance of MSBC diminishes throughout iterations.
Larger mini-batches lead to faster variance reduction of the stochastic gradient, thus producing faster convergence to the solution.
Compared with the power method, the proposed MBSC needs distinctively less computations, while achieving higher or similar clustering accuracy.
Another interesting observation is that the proposed MBSC achieves stable clustering accuracy before it makes a full pass through the whole data set.
The Nystr\"om approximation is computationally fast on all three data sets.
Nevertheless, its time and space complexity increase drastically if the number of inducing points increases.
On the \texttt{Pendigits} and \texttt{Shuttle} data sets, with less running time, the proposed MBSC method requires smaller mini batches to conduct clustering and achieves better clustering performance than the Nystr\"om approximation.
On the \texttt{MNIST} data set, instead, the Nystr\"om approximation produces strikingly good clustering results when the number of selected samples is larger than $500$.
However, the proposed MBSC method converges to the clustering accuracy of the exact spectral clustering even when the size of the mini-batch size is small, e.g., less than $100$.

\subsection{Use case: spectral clustering on larger data sets}

\begin{table}[t]
\centering
\caption{Running time comparison on \text{Covtype-I} and \text{Covtype-II} data. $T$ is the number of iterations.}
\label{tab:covtype}
\begin{tabular}{|c|c|c|c||c|c|c|c|}
\hline
\multicolumn{4}{|c||}{\texttt{Covtype-I}} & \multicolumn{4}{|c|}{\texttt{Covtype-II}} \\
\hline
Algorithm & $T$ & NMI & time (s) & Algorithm & $T$ & NMI & time (s) \\ \hline
 MBSC-E-400 & 200 & 0.40 & 998  & MBSC-E-1000 & 200 & 0.14 & 7500  \\ \hline
 MBSC-E-800 & 200 & 0.40 & 2100 & MBSC-E-2000 & 200 & 0.14 & 12610 \\ \hline
 Nystrom-400 & - & 0.38 & 78   & Nystrom-1000 & - & 0.09 & 2520   \\ \hline
 Nystrom-800 & - & 0.38 & 965  & Nystrom-2000 & - & 0.11 & 11420   \\ \hline
 Power method & 3 & 0.40 & 9300 & Power Method & \multicolumn{3}{|c|}{Too expensive}  \\ \hline
\end{tabular}
\end{table}

To demostrate that the proposed approach can tackle large-scale spectral clustering problems, we implemented the proposed MBSC algorithm without storing the Laplacian matrix, and applied it on two data sets comprising $100K$ and $580K$ samples.
This variant of the code, that we denote as MBSC-E, computes the necessary columns of $L$ to construct stochastic gradients on-the-fly.

Table~\ref{tab:covtype} reports the overall running time and NMI of MBSC-E on the two data sets, where MBSC-E produces stable clustering results after $200$ iterations.
In addition, we compare against the Nystr\"om approximation and the power method.
In the comparison, the Nystr\"om approximation selects a subset of the same size of the mini-batch in MBSC-E.
On the \texttt{Covtype-II} data set, the power method fails to obtain clustering results within an acceptable time, and we omit it from Table~\ref{tab:covtype}.

While running time is heavily dependent on implementation and system architecture, we argue that this is probably in favor of the Nystr\"om approximation, for which we are using well optimized scientific computing packages.
In any case, the purpose of this experiment is to demonstrate that the proposed MBSC algorithm, being exact in the limit of iterations, can achieve higher performance than approximate methods on large scale spectral clustering problems.
Crucially, we demonstrate that this is possible at a comparable computational cost with approximate methods.

On both \texttt{Covtype-I} and \texttt{Covtype-II} data sets, MBSC achieves consistently better clustering accuracy than the Nystr\"om approximation.
Because the computational cost of the Nystr\"om approximation rapidly increases with the size of the approximating set, it requires longer than MBSC-E to achieve a comparable clustering accuracy.
Furthermore, compared with the power method, MBSC-E shows superior computational efficiency for large-scale spectral clustering problems.
Remarkably, MBSC-E requires less than $1\mathrm{GB}$ and $3.6\mathrm{GB}$ memory to run on the two data sets, respectively.

\section{Conclusions}
With the aim of improving scalability of spectral clustering, in this work we formulated normalized cut spectral clustering as an optimization problem with an orthonormality constraint that we could solve using stochastic gradient optimization.
We proposed a novel adaptive stochastic gradient optimization framework on Stiefel manifolds to compute the spectrum of Laplacian matrices, with computation of stochastic gradients linear in the number of samples.
We provided theoretical justifications and empirical analyses to demonstrate how our proposal can tackle large-scale spectral clustering problems in a practical way.

The proposed stochastic optimization is characterized by attractive robustness to parameter selection and scalability properties, leading to the same clustering accuracy of spectral clustering approaches that use the exact spectrum of the Laplacian at a fraction of the cost.
The results also support the motivation behind our proposal that approximate methods can potentially affect clustering performance.
In cases where approximate methods perform well, as we reported in one of the experiments, we can see our proposal as a practical way to obtain the gold-standard of the ``exact'' approach at a reasonable cost.
Furthermore, the proposed method does not need to load the whole Laplacian matrix into memory, making it especially suitable for handling large-scale spectral clustering with a limited memory footprint.

There are a number of extensions that we are currently investigating, such as the possibility to combine our framework with other approximate methods, for example to be able to afford more inducing points when performing spectral clustering using the Nystr\"om approximation.
Another extension is to leverage approximations to reduce the variance of the stochastic gradients without introducing any bias to accelerate stochastic gradient optimization.
A Spark/TensorFlow implementation of the proposed algorithm is under development.

\subsubsection*{Acknowledgments}

The Authors would like to thank Yun Shen from Symantec Research Labs for his support in setting up the experiments and optimizing the implementation of the algorithms.

\small

redpajama_set_name: RedPajamaArXiv


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The Europe Spectrum Analyzer Market Size would grow at a growth rate of 7.1% CAGR during the forecast period (2017 - 2023).
Spectrum analyzers are used in manufacturing and designing of field services, repairing electrical devices and check their performance, identify errors, and also troubleshoot accordingly. When electrical signals pass through a system, spectrum analyzers are used to analyze signal frequency and amplitude in logarithmic scale. The Europe spectrum analyzer market would grow at a steady pace during the forecast period. Spectrum analyzers are widely accepted in various industry verticals.
Some of the top verticals with wide application of spectrum analyzer are Aerospace, Government & Defense and Telecom & IT. In High energy Physics application areas, there would be a great demand for real-time spectrum analyzers. Companies are also introducing advanced options in spectrum analyzers which would ultimately attracts more and more industry verticals for the usage of spectrum analyzer during the forecast period.
The growing demand for wireless devices and vibrant semiconductor & electronic industry would drive the market for spectrum analyzers. Based on Products, the Spectrum Analyzer market is segmented into Benchtop, Portable, and Handheld. Based on Network Technologies, the market is segmented into Wireless and Wired.
The verticals covered under the report include Semiconductor & Electronics, Telecom & IT, Industry & Energy Sector, Healthcare, Healthcare & Life Sciences, and Others. Based on Country, Spectrum Analyzer market is segmented into Germany, UK, France, Russia, Spain, Italy and Rest of Europe. Germany remained the dominant Country in the Europe Spectrum Analyzer market in 2016. France and Russia would witness promising CAGR during the forecast period (2017-2023).
The report covers the analysis of key stake holders of the Spectrum Analyzer market. Key companies profiled in the report include Keysight Technologies, Fortive Corporation, Cobham Plc., Giga-Tronics Incorporated, National Instruments Corporation, Teledyne Technologies Inc., Yokogawa Electric Corporation, and LP Technologies Inc.


text:
Ana Maria Uribe 1951-2004
Rhizome | Fri Apr 2nd, 2004 8 a.m.
In the late 1960s Argentine artist Ana Maria Uribe began creating typoemas -- static black-on-white visual compositions rendered using a standard office typewriter. Anticipating the keyboard's pancultural ubiquity and its potential for artmaking, these early works provided a foundation for the anipoemas that emerged in the 1980s. The creative possibilities afforded by new computer technology led Uribe to incorporate animation, sound and eventually colour into later projects while retaining the frame size and single-font restrictions intrinsic to her creative process. The ease of dissemination provided by the internet allowed the her to cultivate an international audience, and yet her work transcended language through exploration of the plasticity of letters and symbols and their potential for the generation of meaning as visual objects. Her works are infused with a sense of rhythm and dance


You may think that working out how many people work in your organisation is a simple head-counting process, but in large companies, and particularly multi-nationals, the reality can be different.
Discrepancies can arise when different departments use separate models to make the count. Firstly, who is making the calculation – HR, business units or the finance department? Secondly, are they counting full-time workers, temporary staff replacing full-timers on leave and part-timers? Are contractors involved in the list? Although any of those criteria may be valid, if multiple counts are carried out confusion can reign, and reports to CEOs can be misleading, so how does an HR executive ensure that a CEO takes note of their workforce data?
The main issue is to own the information and not get into a tussle with other departments and managers over presentation rights, ensuring that if there is a conflict of information to the CEO, yours is the number which can be established as correct.
This may involve establishing a close working relationship with the head of finance. In the final analysis this will save you both time and energy. It is important to recognise that HR changes and systems may move at a slower pace than other departments.
The HR managers have myriad administrative issues to deal with such as updating roles, job descriptions, compensation formulas, stock options and bonus reviews. Add external legislative matters such as workplace discrimination and possible discussions with unions or local authorities, and the HR change process can need time to catch up and re-align with strategic business plans.
Once you have established that your headcount is the one to take note of, it is important to explain to your CEO exactly what this number impacts upon. Explain how adequate staffing, or the lack thereof, will impact on revenue, investment and attracting new talent. This will help to place HR on a similar level to other departments such as finance.
Showing how the headcount is linked to other business dynamics will ensure your CEO takes note of HR reports on these issues. This will mean you provide a link between talent and performance in the same way that the finance department offers an insight into investment selection and profit. Much is made of investing in staff, so show the value of the staff in your report, highlighting which departments need improvement.
By pointing out where staff levels need to be revised, you will introduce the concept of targets, giving your CEO a glimpse of the future and making your report much more relevant.
Companies need to plan ahead, and your analysis of workplace numbers can highlight which departments may need investment.
This brings us to costs and valuing the staff within the organisation and how they influence the bottom line. By providing the CEO with a model which enables them to contrast labour costs and productivity, you will be enhancing the role of the HR department in the company's management structure.
Your CEO will soon realise the importance of knowing exactly how many people are contributing to the company's activities and understand that this involves more than a simple headcount and is crucial to the company's future success.


Taken from one of the glass negatives in our photo collection this is one of those amazing photos which tells its own story! The photo is from the photography of Walter Peavey who lived at 74 Central Street; later the home of Leon and Gerri Hammond.
The dirt road you see across the picture is Central Street near the beginning of Lowell Road. Of the two homes we see, the one on our left is currently 1 Lowell Road. The one on our right is 65 Central Street. Both Central Street and Lowell Road are dirt roadways. The steam railroad crossed the Merrimack River just below the Taylor Falls Bridge where the abutments can still be seem. On the Hudson side the tracks went north easterly and behind these homes and emerged at about the location of the former Hetzer's Bike Shop. The train ran on the overpass you see in this photo and on to Hudson Center.
The trolley line crossed from Nashua on the Taylor Falls Bridge and ran on or along side Central Street and then down Lowell Road. The lower level of this overpass was used by the trolley line and vehicle/horse drawn traffic. Look closely and you can see the trolley tracks along Central Street.
Although both the train and trolley tracks had been removed by the 1940's, the overpass and stone abutments remained into the 1950's when they were also removed in order to improve what had become a dangerous intersection.
By Ruth M Parker in Lowell Road, Steam Railroad, Uncategorized on June 3, 2016 .


Currently, even with 150,000 hunters in the woods, these methods produce less than 7% of Maine's annual bear harvest.
Bear hunting season runs from the beginning of September to the end of November, a full three months. By September, important bear foods such as raspberries, blackberries, and blueberries are already gone by for the year. Other naturally- occurring foods that may be available during the bear hunting season can include mast such as beechnuts and acorns; wild and cultivated apples; and cultivated crops such as corn, oats, barley, and broccoli. Many of these natural food sources are not widely available to either bears, or to hunters. Beechnut, acorn, and wild apple crops vary widely by year, and by location. Even when available, they are usually quickly depleted by bears, coyotes, foxes, raccoons, porcupines, deer, turkeys, partridge, squirrels, and small mammals. When the food is gone these sites are abandoned. Likewise, agricultural crops are not widely distributed, and they are not likely to be available throughout the 3-month bear season. In fact, most small grain crops are harvested by early September.
Some bears are currently harvested over naturally-occurring foods. But these sites are far too limited to accommodate the additional bear hunters needed to manage bear populations. Hunting over naturally-occurring foods in Maine cannot replace the bear harvest lost if the use of bait, dogs, and traps are banned.
Still-hunting is a specialized hunting strategy that involves moving slowly and quietly through the hunting area, in hopes of spotting a game animal before it detects you. Few hunters are really good at still-hunting. Pursuing bears by still-hunting can be particularly challenging. Not many hunters have ever seen a bear in the woods, often after spending several decades of hunting in Maine. Main is 90% forested, the most wooded of all the states, and our forests tend to be dense, with visibility often less than 50 yards. Hunters cannot shoot what they cannot see! Bears clearly have the advantage against still-hunters. Bears have extremely acute senses of smell, sight, and hearing. If you encounter one at all, chances are it saw or smelled you first, and silently padded away without your knowing it. Even if 10,000 or more additional hunters took to the woods to still-hunt bears, success rates would be far too low to compensate for the bear harvest lost if the use of bait, dogs, and traps are banned.
Occasionally, Maine hunters blunder into a bear while in pursuit of other game. Some of that 7% of our bear harvest is currently taken opportunistically.
Berries like these blueberries are one of the most important natural food crops for Maine bears. Unfortunately, these crops have gone by when bear hunting season opens.
Can this method yield more bears? No. Some 30,000 moose hunters hunt in Maine's bear range each year. They certainly carry the right hunting equipment to kill bears.
However, encounters with bears are likely brief and fleeting, and moose hunters are focused on killing moose, not bears. In addition, any hunter desiring to kill a bear prior to November must be in possession of a bear permit. Most moose hunters do not currently even bother to purchase a bear permit, undoubtedly because of the very few bears seen while moose hunting. They are not likely to begin doing so.
Many more thousands of Maine hunters travel to bear territory to hunt partridge (ruffed grouse) during October and November. They also very rarely see bears. And partridge hunters are not equipped with the right ammo to kill a bear. Birdshot is neither adequate nor legal for bear hunting.
That leaves deer hunters. There are still tens of thousands of hunters pursuing deer during Maine's November firearms season. However, deer hunting participation has declined since the deer population crashed in 2008 and 2009 in the northern half of Maine. Particularly absent are the non-residents, who happen to be rather keen on bagging a bear. It's likely that a large share of that 7% of current bear harvests is taken by deer hunters during some years, but not during others.
Another factor: When natural foods are scarce, Maine's bears enter hibernation earlier than normal, sometimes even in late September. During some years, most of DIFW's research bears are hibernating well before the November deer season, and hence are unavailable for harvest. The harvest of bears taken while deer hunting will not increase much, if at all, above current rates.
The inescapable conclusion is that hunting over naturally- occurring bait, still-hunting, and incidental harvest of bears cannot begin to replace the bear harvest we currently achieve using bait, dogs, and traps. If Question 1 passes, overall bear harvests will drop precipitously, and will remain low. This chronic harvest deficit will inevitably lead to the aggressive growth of Maine's bear population, with attendant serious problems.
Typical dense Maine forest, and great bear habitat. Visibility is about 20 yards at most. Try sneaking quietly up on a bear in this cover. Bob Noonan photo.


The Neighbourhood Development Programme (NDP) Unit was established in 2006 and is responsible for managing the Neighbourhood Development Partnership Grant (NDPG).
The NDPG is driven by the notion that public investment and funding can be used creatively to attract private and community investment to unlock the social and economic potential in targeted underserved neighbourhoods, generally townships.
This in turn will not only improve the quality of life of residents but also contribute to South Africa's economic performance.
The purpose of the grant is to therefore fund, support and facilitate the planning and development of neighbourhood development programmes and projects that provide catalytic infrastructure to leverage third party public and private sector investment for future and more sustainable development.
The management of the NDPG, and includes a planning grant, for Technical Assistance (TA) and a Capital Grant (CG).
The NDP Unit recently joined the Inter-Governmental Relations (IGR) division at National Treasury to work in conjunction with the City Support Programme.
The strategic role of urban centres in enabling the necessary conditions for achieving key government outcomes is well documented locally and internationally. During 2011/12 the NDP evaluated the performance of the NDP grant and as a result embarked on a process of strategic planning to deepen value for money and long term impact. The result was the formulation of a new strategy, known as the Urban Networks Strategy (UNS) which is a pro-poor/pro-growth investment approach.
The strategy which is aimed at facilitating the eradication of spatial inequality to enable the creation of liveable, sustainable, resilient, efficient and integrated human settlements. The focus of this strategy is to shift infrastructure investments towards the creation of efficient and effective urban centres through an approach of spatial targeting of public investment, primarily infrastructure. The Urban Network is a city-wide interconnected hierarchy of strategic nodes and public transport links between and within nodes. It consists of primary and secondary networks that interconnect at strategic nodes known as urban hubs, which are located within marginalised areas, typically townships.
The new strategy is reflected in the amendment of the 2014/2015 DORA NDPG Framework which states that future NDPG allocations will be focused on municipalities and projects that align with the NDPG's prioritisation criteria. These for example include population densities, levels and diversity of economic activity, concentration of poverty and the presence of connectivity networks i.e. public transport. The application of these criteria across the NDPG portfolio of municipalities has resulted in the identification of 18 urban municipalities and include South Africa's larger urban centres as well as key regional service centres.
The focus of this Urban Networks Strategy, as the name implies, is to shift infrastructure investments towards the creation of efficient and effective urban centres that will increase economic growth, create employment and increase access to urban amenities, especially for the poor located in marginalised settlement areas, such as townships. The NDP will work in partnership with other strategic spatial, transit orientated grants including the Public Transport Infrastructure and Systems (PTIS) Grant and Urban Settlement Development Grant (USDG) to support the implementation of projects across the urban network.
The balance of the municipalities in the NDPG portfolio has been classified as rural NDP municipalities.


text:
Bank of England Relaxes Capital Requirements, But Have Traditional Banks Fallen Short of Boosting SME Growth in the Past?
July 6, 2016 @ 9:27 am By JD Alois
Yesterday the Financial Policy Committee (FCP) of the Bank of England relaxed bank capital requirements in a proactive move designed to stave off a looming, Brexit driven slowdown.
Bank of England Governor Mark Carney stated;
"The UK has entered a period of uncertainty and significant economic adjustment. The efforts of the Bank of England will not be able fully and immediately to offset the market and economic volatility that can be expected while this adjustment proceeds. More fundamentally, the future potential of this economy and its implications for jobs, real wages and wealth are not the gifts of the Bank of England, but will be driven by major decisions made by others in the public and private sectors."
Carney outlined a four-point plan the B of E would deliver to mitigate the EU Referendum shock;
Identify clearly the risks to financial stability and be straight with the British people about them;
build on series of measures taken over recent years that have increased the resilience of the financial system;
Supplement this core strength with contingency measures implemented in the past few months to address immediate risks to financial stability; and
Take action to support jobs and growth during a period of heightened
uncertainty.
Louise Beaumont, Head of Public Affairs at GLI Finance called the FCP decision as indicative of concern that UK SME's will not be able to access the capital needed to drive growth;
"Yesterday's decision by the FPC clearly recognises that the ability for SMEs to access capital is likely to be significantly compromised as Brexit uncertainty hits financial markets and consumer confidence.
Beaumont also stated that past efforts designed to stimulate traditional banks into providing more effective credit have fallen short of intended goals;
"It is, however, important to remember that previous measures to stimulate lending by traditional banks have often failed to deliver the desired outcomes, and that it is imperative that the alternative finance industry also continues to support SMEs as it has done since the aftermath of the 2008 financial crisis.
Beaumont believes that platforms that can offer specialist products that are "best suited to SMEs' particular needs have a crucial role to play not just in helping SMEs survive, but also supporting the inevitable growth opportunities that will emerge as they adjust to a new post-Brexit normal."
Kevin Caley, founder and Chairman of P2P lender ThinCats, called Carney's move the right decision;
"Mr Carney's decision to reduce capital buffers for banks and free up £150billion is undoubtedly the right decision for the British economy. But it remains to be seen whether this will actually benefit SMEs. The onus is truly on banks to respond in the correct way, by reassuring businesses that they can access the funding they desperately need.
Caley also said that alternative finance providers will play a vital role in supporting the UK economy.
"The economy requires stimulus from the ground up and until high-street lenders recognise and act upon this, the alternative finance sector will continue to play a vital role in bridging the funding gap."
It will take some time for the Brexit aftershocks to settle, in the meantime it is all hands on deck.
Here is the Speech by the Governor of the Bank of England, Mark Carney, on the Brexit
Bank of England Cuts Rates: Alternative Finance Leaders Respond
Funding for Lending Extended. GLI Finance Says Program Does Not Solve the Problem
Bank of England States Lending to SMEs Increases in February, GLI Says Not So Fast as Longer Term Problems are Concealed
ThinCats Chairman Lauds BoE "Safe Pair of Hands", Predicted Lower Rates Bad for Savers
GLI Finance Says More Needs to be Done to Support UK SMEs
Hunt for New Governor of Bank of England Commences
Bank of England Governor Mark Carney: "Profound Changes Demand a New Finance. And a New Finance Demands a New Bank"
Louise Beaumont: UK Elections Reflect Support of Economic Policy
A Future of Fintech: Bank of England Publishes Future of Finance Report Identifying Trends Shaping Financial Services
Governor of Bank of England Mark Carney: Cryptocurrencies are Failing as Money
Investoo CEO David Merry: Bank of England Chief Mark Carney's Comments on Cryptocurrency & AML are "Confusing"
Louise Beaumont: UK Economy Suffers Due Two Failings of Credit Eco-System
The Innovative Finance ISA is Available Today, Meanwhile Some Large P2P Platforms Wait for FCA Approval
View from the UK: Why the Alternative Finance Industry Needs Greater Regulation
This entry was posted in Global, Opinion and tagged bank of england, brexit, gli finance, louise beaumont, mark carney, uk, united kingdom. Bookmark the permalink.


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Some patents are better than others. The best ones – irrespective of their degree of novelty – seem to possess a simplicity and elegance that makes them not only a powerful example of the Inventive Principles of TRIZ, but a spark in their own right to a host of inventive solutions to other problems.
Many casing or pipework structures employ bolted flanges to join adjacent sections that at some point are required to be dis-assembled. Casings on gas-turbine engines are a particularly good example. Flanged joints between casings in such applications are required to seal against extremely high temperature and high pressure conditions across a wide range of operating conditions and loads. A typical gas-turbine flanged joint may require over a hundred bolts to ensure adequate functionality.
Of course, the presence of such large numbers of bolts presents a considerable penalty to operators in terms of both the amount of maintenance time required to dis-assemble an engine and also a not inconsiderable weight penalty.
From a design perspective, we may see flanges as a classic compromise situation; one in which the designer is trying to strike a delicate balance between a requirement for a large number of bolts to ensure adequate sealing and a desire for a small number of bolts in order to improve maintainability and reduce weight.
In the fullness of time, some of these suggestions may operate (possibly in combination) to achieve an Ideal Final Result flange joint design (*). In the meantime, however, Inventive Principle 'Another Dimension' was used to profound effect in offering the potential for possibly halving the number of bolts around a flange whilst maintaining the sealing performance.
(*) For example it is already possible to seal a relatively low duty flanged joint with one bolt – using a V-band clamp type arrangement.
One of the great beauties of this elegant idea is that it manages to solve the design contradiction without the need for any additional parts or complexity. In essence, all that has changed from a manufacturing standpoint is that the faces of the flange are formed at a slight angle to one another rather than being parallel.
Tests on an prototype flange (reported at ISABE 1989 in Athens) demonstrated the ability of the design to not only seal a flange with around half the number of bolts of the traditional parallel surface flange, but to do it more effectively across the entire range of operating conditions a gas-turbine may be expected to face.
Like some of the best examples in the Effects part of the TechOptimizer software, this patent provides an excellent demonstration of the Inventive Principles in action. It can also be used as a powerful spark to help solve a wide range of other types of problem; self-locking nuts and a novel valve seal to name but two upcoming examples.