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1413 results in Ebooks in network science

Page 52 of 71

  • EPILOGUE - ON DETERMINISM AND FREE WILL

  • Erwin Schrodinger
  • Foreword by Roger Penrose
  • Book:
    What is Life?
    Published online:
    05 September 2014
    Print publication:
    26 March 2012, pp 86-90

  • Summary

    As a reward for the serious trouble I have taken to expound the purely scientific aspects of our problem sine ira et studio, I beg leave to add my own, necessarily subjective, view of the philosophical implications.

    According to the evidence put forward in the preceding pages the space-time events in the body of a living being which correspond to the activity of its mind, to its self-conscious or any other actions, are (considering also their complex structure and the accepted statistical explanation of physico-chemistry) if not strictly deterministic at any rate statistico-deterministic. To the physicist I wish to emphasize that in my opinion, and contrary to the opinion upheld in some quarters, quantum indeterminacy plays no biologically relevant role in them, except perhaps by enhancing their purely accidental character in such events as meiosis, natural and X-ray-induced mutation and so on – and this is in any case obvious and well recognized.

    For the sake of argument, let me regard this as a fact, as I believe every unbiased biologist would, if there were not the well-known, unpleasant feeling about ‘declaring oneself to be a pure mechanism’. For it is deemed to contradict Free Will as warranted by direct introspection.

  • Autobiographical Sketches

  • Erwin Schrodinger
  • Foreword by Roger Penrose
  • Book:
    What is Life?
    Published online:
    05 September 2014
    Print publication:
    26 March 2012, pp 165-184

  • Summary

    I lived far apart from my best friend, actually the only close friend I ever had, for the greater part of my life. (Maybe that is why I have often been accused of flirtatiousness instead of true friendship.) He studied biology (botany to be exact); I physics. And many a night we would stroll back and forth between Gluckgasse and Schlüsselgasse engrossed in philosophical conversation. Little did we know then that what seemed original to us had occupied great minds for centuries already. Don't teachers always do their best to avoid these topics for fear that they might conflict with religious doctrines and cause uncomfortable questions? This is the main reason for my turning against religion, which has never done me any harm.

    I am not sure whether it was right after the First World War or during the time I spent in Zurich (1921–7) or even later in Berlin (1927–33) that Fränzel and I spent a long evening together again. The small hours of the morning found us still talking in a cafe on the outskirts of Vienna. He seemed to have changed a lot with the years. After all, our letters had been few and far between and of very little substance.

    I might have added earlier that we also spent our time together reading Richard Semon. Never before or after did I read a serious book with anyone else.

  • 4 - THE QUANTUM-MECHANICAL EVIDENCE

  • Erwin Schrodinger
  • Foreword by Roger Penrose
  • Book:
    What is Life?
    Published online:
    05 September 2014
    Print publication:
    26 March 2012, pp 46-55

  • Summary

    Und deines Geistes höchster Feuerflug

    Hat schon am Gleichnis, hat am Bild genug.

    goethe

    PERMANENCE UNEXPLAINABLE BY CLASSICAL PHYSICS

    Thus, aided by the marvellously subtle instrument of X-rays (which, as the physicist remembers, revealed thirty years ago the detailed atomic lattice structures of crystals), the united efforts of biologists and physicists have of late succeeded in reducing the upper limit for the size of the microscopic structure, being responsible for a definite large-scale feature of the individual – the ‘size of a gene’ – and reducing it far below the estimates obtained on pp. 29–30. We are now seriously faced with the question: How can we, from the point of view of statistical physics, reconcile the facts that the gene structure seems to involve only a comparatively small number of atoms (of the order of 1,000 and possibly much less), and that nevertheless it displays a most regular and lawful activity – with a durability or permanence that borders upon the miraculous?

    Let me throw the truly amazing situation into relief once again. Several members of the Habsburg dynasty have a peculiar disfigurement of the lower lip (‘Habsburger Lippe’). Its inheritance has been studied carefully and published, complete with historical portraits, by the Imperial Academy of Vienna, under the auspices of the family.

  • 7 - IS LIFE BASED ON THE LAWS OF PHYSICS?

  • Erwin Schrodinger
  • Foreword by Roger Penrose
  • Book:
    What is Life?
    Published online:
    05 September 2014
    Print publication:
    26 March 2012, pp 76-85

  • Summary

    Si un hombre nunca se contradice, será porque nunca dice nada.

    miguel de unamuno (quoted from conversation)

    NEW LAWS TO BE EXPECTED IN THE ORGANISM

    What I wish to make clear in this last chapter is, in short, that from all we have learnt about the structure of living matter, we must be prepared to find it working in a manner that cannot be reduced to the ordinary laws of physics. And that not on the ground that there is any ‘new force’ or what not, directing the behaviour of the single atoms within a living organism, but because the construction is different from anything we have yet tested in the physical laboratory. To put it crudely, an engineer, familiar with heat engines only, will, after inspecting the construction of an electric motor, be prepared to find it working along principles which he does not yet understand. He finds the copper familiar to him in kettles used here in the form of long, long wires wound in coils; the iron familiar to him in levers and bars and steam cylinders is here filling the interior of those coils of copper wire. He will be convinced that it is the same copper and the same iron, subject to the same laws of Nature, and he is right in that.

  • 6 - THE MYSTERY OF THE SENSUAL QUALITIES

  • Erwin Schrodinger
  • Foreword by Roger Penrose
  • Book:
    What is Life?
    Published online:
    05 September 2014
    Print publication:
    26 March 2012, pp 153-164

  • Summary

    In this last chapter I wish to demonstrate in a little more detail the very strange state of affairs already noticed in a famous fragment of Democritus of Abdera – the strange fact that on the one hand all our knowledge about the world around us, both that gained in everyday life and that revealed by the most carefully planned and painstaking laboratory experiments, rests entirely on immediate sense perception, while on the other hand this knowledge fails to reveal the relations of the sense perceptions to the outside world, so that in the picture or model we form of the outside world, guided by our scientific discoveries, all sensual qualities are absent. While the first part of this statement is, so I believe, easily granted by everybody, the second half is perhaps not so frequently realized, simply because the non-scientist has, as a rule, a great reverence for science and credits us scientists with being able, by our ‘fabulously refined methods’, to make out what, by its very nature, no human can possibly make out and never will be able to make out.

    If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electro-magnetic waves of wave-length in the neighbourhood of 590 millimicrons.

  • 17 - Interactive Channel Coding

  • from Part III - Multihop Networks
  • Abbas El Gamal, Young-Han Kim, University of California, San Diego
  • Book:
    Network Information Theory
    Published online:
    05 June 2012
    Print publication:
    08 December 2011, pp 427-458

  • Summary

    The network models we studied so far involve only one-way (feedforward) communication. Many communication systems are inherently interactive, allowing for cooperation through feedback and information exchange over multiway channels. In this chapter, we study the role of feedback in communication and present results on the two-way channel introduced by Shannon as the first multiuser channel. The role of multiway interaction in compression and secure communication will be studied in Chapters 20 and 22, respectively.

    As we showed in Section 3.1.1, the capacity of a memoryless point-to-point channel does not increase when noiseless causal feedback is present. Feedback can still benefit point-to-point communication, however, by simplifying coding and improving reliability. The idea is to first send the message uncoded and then to use feedback to iteratively reduce the receiver's error about the message, the error about the error, and so on. We demonstrate this iterative refinement paradigm via the Schalkwijk–Kailath coding scheme for the Gaussian channel and the Horstein and block feedback coding schemes for the binary symmetric channel. We show that the probability of error for the Schalkwijk–Kailath scheme decays double-exponentially in the block length, which is significantly faster than the single-exponential decay of the probability of error without feedback.

    We then show that feedback can enlarge the capacity region in multiuser channels. For the multiple access channel, feedback enlarges the capacity region by enabling statistical cooperation between the transmitters. We show that the capacity of the Gaussian MAC with feedback coincides with the outer bound obtained by allowing arbitrary (instead of product) joint input distributions. For the broadcast channel, feedback can enlarge the capacity region by enabling the sender to simultaneously refine both receivers’ knowledge about the messages. For the relay channel, we show that the cutset bound is achievable when noiseless causal feedback from the receiver to the relay is allowed. This is in contrast to the case without feedback in which the cutset bound is not achievable in general.

    Finally, we discuss the two-way channel, where two nodes wish to exchange their messages interactively over a shared noisy channel. The capacity region of this channel is not known in general. We first establish simple inner and outer bounds on the capacity region.

  • 13 - Multiple Description Coding

  • from Part II - Single-Hop Networks
  • Abbas El Gamal, Young-Han Kim, University of California, San Diego
  • Book:
    Network Information Theory
    Published online:
    05 June 2012
    Print publication:
    08 December 2011, pp 320-335

  • Summary

    We consider the problem of generating two descriptions of a source such that each description by itself can be used to reconstruct the source with some desired distortion and the two descriptions together can be used to reconstruct the source with a lower distortion. This problem is motivated by the need to efficiently communicate multimedia content over networks such as the Internet. Consider the following two scenarios:

  • • Path diversity: Suppose we wish to send a movie to a viewer over a network that suffers from data loss and delays. We can send multiple copies of the same description of the movie to the viewer via different paths in the network. Such replication, however, is inefficient and the viewer does not benefit from receiving more than one copy of the description. Multiple description coding provides a more efficient means to achieve such “path diversity.” We generate multiple descriptions of the movie, so that if the viewer receives only one of them, the movie can be reconstructed with some acceptable quality, and if the viewer receives two of them, the movie can be reconstructed with a higher quality and so on.

  • • Successive refinement: Suppose we wish to send a movie with different levels of quality to different viewers. We can send a separate description of the movie to each viewer. These descriptions, however, are likely to have significant overlaps. Successive refinement, which is a special case of multiple description coding, provides a more efficient way to distribute the movie. The idea is to send the lowest quality description and successive refinements of it (instead of additional full descriptions). Each viewer then uses the lowest quality description and some of the successive refinements to reconstruct the movie at her desired level of quality.

    • The optimal scheme for generating multiple descriptions is not known in general. We present the El Gamal–Cover coding scheme for generating two descriptions that are individually good but still carry additional information about the source when combined together. The proof of achievability uses the multivariate covering lemma in Section 8.4. We show that this scheme is optimal for the quadratic Gaussian case. The key to the converse is the identification of a common-information random variable. We then present an improvement on the El Gamal–Cover scheme by Zhang and Berger that involves sending an additional common description.

  • 8 - General Broadcast Channels

  • from Part II - Single-Hop Networks
  • Abbas El Gamal, Young-Han Kim, University of California, San Diego
  • Book:
    Network Information Theory
    Published online:
    05 June 2012
    Print publication:
    08 December 2011, pp 197-226

  • Summary

    We resume the discussion of broadcast channels started in Chapter 5. Again consider the 2-receiver DM-BCp(y1, y2|x) with private and common messages depicted in Figure 8.1. The definitions of a code, achievability, and capacity regions are the same as in Chapter 5. As mentioned before, the capacity region of the DM-BC is not known in general. In Chapter 5, we presented the superposition coding scheme and showed that it is optimal for several classes of channels in which one receiver is stronger than the other. In this chapter, we study coding schemes that can outperform superposition coding and present the tightest known inner and outer bounds on the capacity region of the general broadcast channel.

    We first show that superposition coding is optimal for the 2-receiver DM-BC with degraded message sets, that is, when either R1 = 0 or R2 = 0. We then show that superposition coding is not optimal for BCs with more than two receivers. In particular, we establish the capacity region of the 3-receiver multilevel BC. The achievability proof involves the new idea of indirect decoding, whereby a receiver who wishes to recover only the common message still uses satellite codewords in decoding for the cloud center.

    We then present Marton's inner bound on the private-message capacity region of the 2-receiver DM-BC and show that it is optimal for the class of semideterministic BCs. The coding scheme involves the multicoding technique introduced in Chapter 7 and the new idea of joint typicality codebook generation to construct dependent codewords for independent messages without the use of a superposition structure. The proof of the inner bound uses the mutual covering lemma, which is a generalization of the covering lemma in Section 3.7. Marton's coding scheme is then combined with superposition coding to establish an inner bound on the capacity region of the DM-BC that is tight for all classes of DM-BCs with known capacity regions. Next, we establish the Nair–El Gamal outer bound on the capacity region of the DM-BC. We show through an example that there is a gap between these inner and outer bounds. Finally, we discuss extensions of the aforementioned coding techniques to broadcast channels with more than two receivers and with arbitrary messaging requirements.

  • 22 - Information Theoretic Secrecy

  • from Part IV - Extensions
  • Abbas El Gamal, Young-Han Kim, University of California, San Diego
  • Book:
    Network Information Theory
    Published online:
    05 June 2012
    Print publication:
    08 December 2011, pp 549-582

  • Summary

    Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network?

    In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding.

    If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself!

    We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.

Page 52 of 71