33243327
Certain Predicates Defined by Induction Schemata
It is known that we can introduce in number theory (for example, the system Z of Hilbert-Bernays) by induction schemata certain predicates of natural numbers which cannot be expressed explicitly within the framework of number theory. The question arises how we can define these predicates in some richer system, without employing induction schemata. In this paper a general notion of definability by induction (relative to number theory), which seems to apply to all the known predicates of this kind, is introduced; and it is proved that in a system L 1 which forms an extension of number theory all predicates which are definable by induction (hereafter to be abbreviated d.i.) according to the definition are explicitly expressible. In order to define such predicates and prove theorems answering to their induction schemata, we have to allow certain impredicative classes in L 1 . However, if we want merely to prove that for each constant number the special case of the induction schema for a predicate d.i. is provable, we do not have to assume the existence of impredicative classes. A certain weaker system L 2 , in which only predicative classes of natural numbers are allowed, is sufficient for the purpose. It is noted that a truth definition for number theory can be obtained in L 2 . Consistency proofs for number theory do not seem to be formalizable in L 2 , although they can, it is observed, be formalized in L 1 . In general, given any ordinary formal system (say Zermelo set theory), it is possible to define by induction schemata, in the same manner as in number theory, certain predicates which are not explicitly definable in the system. Here again, by extending the system in an analogous fashion, these predicates become expressible in the resulting system. The crucial predicate instrumental to obtaining a truth definition for a given system is taken as an example.
29040872
A Variant to Turing's Theory of Computing Machines
The principal purpose of this paper is to offer a theory which is closely related to Turing's [1] but is more economical in the basic operations. I t will be proved that a theoretically simple basic machine can be imagined and specified such tha t all partial recursive functions (and hence all solvable computation problems) can be computed by it and tha t only four basic types of instruction are employed for the programs: shift left one space, shift right one space, mark a blank space, conditional transfer. In particular, erasing is dispensable, one symbol for marking is sufficient, and one kind of transfer is enough. The reduction is somewhat similar to the realization of, for instance, the definability of conjunction and implication in terms of negation and disjunction, or of the definability of all these in terms of Sheffer's stroke function. As a result, i t becomes less direct to prove that certain things can be done by the machines, but a little easier to prove that certain things cannot be done. This serf-contained theory will b e presented, as far as possible, in a language which is familiar to those who are engaged in the use and construction of largescale computers. Turing's theory of computable functions antedated but has not much influenced the extensive actual construction of digital computers. These two aspects of theory and practice have been developed almost entirely independently of each other. The main reason is undoubtedly that logicians are interested in questions radically different from those with which the applied mathematicians and electrical engineers are primarily concerned. I t cannot, however, fail to strike one as rather strange that often the same concepts are expressed by very different terms in the two developments. One is even inclined to ask whether a rapprochement might not produce some good effect. This paper wiU, it is believed, be of use to those who wish to compare and connect the two approaches. Extensive use of Turing [1] and Kleene [2] (Chapter XI I I ) will be made, although the exposition is sufficient in itself.
1953614
Alternative Proof of a Theorem of Kleene
42852449
A Formal System of Logic
The main purpose of this paper is to present a formal system P in which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly, P is a system which differs from the inconsistent system of [ 1 ] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements (sets, membership-eligible classes). It will be proved that if the weaker system of [ 2 ] is consistent, then P is also consistent. After the discovery of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions (see [ 3 ], [ 4 ]). Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [ 2 ], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all.
29402189
Non-Standard Models for Formal Logics
showed that there must be a model in which that portion of the model which is supposed to represent the positive integers of the formal logic is not in fact isomorphic to the positive integers; indeed it is not even well ordered by what is supposed to be the relation of <. For the purposes of the present paper, we do not need a precise definition of what is meant by a standard model of a formal logic. The non-standard models which we shall discuss will be flagrantly non-standard, as for instance a model of the sort whose existence is proved by Henkin. It will suffice if we and our readers are in agreement that a model of a formal logic is not a standard model if either: (a) The relation in the model which represents the equality relation in the formal logic is not the equality relation for objects of the model. (b) That portion of the model which is supposed to represent the positive integers of the formal logic is not well ordered by the relation <. (c) That portion of the model which is supposed to represent the ordinal numbers of the formal logic is not well ordered by the relation <. Our first result is that there is no standard model for the system known as "Quine's New Foundations" (see [2] and [3]). This is proved for the logic originally proposed by Quine (see [2]), which is a system of such apparent weakness that so far no one has succeeded in proving the axiom of infinity in the system. Clearly, if there is no standard model for this apparently weak system, there cannot be a standard model for any apparently stronger system which one might form by adding additional axioms, such as the axiom of infinity. A natural reaction to this result would be to suspect that there is no model of any sort for Quine's New Foundations; that is to suspect that it is inconsistent. An alternative (and much less likely) reaction would be to suspect that the property of not having a standard model is perhaps a not uncommon property of strong formal logics, and to suspect that perhaps several of the familiar strong formal logics have no standard model. Unlikely as this might appear at first sight, we will present considerable evidence in favor of the idea. In particular we shall show that it is a property of each of the familiar formal logics that if it is w-consistent then one cannot prove in the logic itself that if the logic is consistent it must have a standard model; in fact, one cannot prove this statement about the logic even in certain stronger logics if these stronger logics are simply consistent.
11313688
Existence of Classes and Value Specification of Variables
In mathematics, when we want to introduce classes which fulfill certain conditions, we usually prove beforehand that classes fulfilling such conditions do exist, and that such classes are uniquely determined by the conditions. The statements which state such unicity and existence of classes are in mathematical logic consequences of the principles of extensionality and class existence. In order to illustrate how these principles enable us to introduce classes into systems of mathematical logic, let us consider the manner in which Godel introduces classes in his book on set theory. For instance, before introducing the definition of the non-ordered pair of two classes Godel puts down as its justification the following two axioms: By A4, for every two classes y and z there exists at least one non-ordered pair w of them; and by A3, w is uniquely determined in A4.
796248
An auctioning reputation system based on anomaly
Existing reputation systems used by online auction houses do not address the concern of a buyer shopping for commodities - finding a good bargain. These systems do not provide information on the practices adopted by sellers to ensure profitable auctions. These practices may be legitimate, like imposing a minimum starting bid on an auction, or fraudulent, like using colluding bidders to inflate the final price in a practice known as shilling.We develop a reputation system to help buyers identify sellers whose auctions seem price-inflated. Our reputation system is based upon models that characterize sellers according to statistical metrics related to price inflation. We combine the statistical models with anomaly detection techniques to identify the set of suspicious sellers. The output of our reputation system is a set of values for each seller representing the confidence with which the system can say that the auctions of the seller are price-inflated.We evaluate our reputation system on 604 high-volume sellers who posted 37,525 auctions on eBay. Our system automatically pinpoints sellers whose auctions contain potential shill bidders. When we manually analyze these sellers' auctions, we find that many winning bids are at about the items' market values, thus undercutting a buyer's ability to find a bargain and demonstrating the effectiveness of our reputation system.
18424476
Proving theorems by pattern recognition I
Certain preliminary results on doing mathematics by machines (“mechanical mathematics”) were reported in an earlier paper [20]. The writer suggested developing inferential analysis as a branch of applied logic and as a sister discipline of numerical analysis. This analogy rests on the basic distinction of pure existence proofs, elegant procedures which in theory always terminate, and efficient procedures which are more complex to describe but can more feasibly be carried out in practice. In contrast with pure logic, the chief emphasis of inferential analysis is on the efficiency of algorithms, which is usually attained by paying a great deal more attention to the detailed structures of the problems and their solutions, to take advantage of possible systematic short cuts. The possibilities of much more elaborate calculations by machines provide an incentive to studying a group of rather minute questions which were formerly regarded as of small theoretical interest. When the range of actual human computation was narrow, there seemed little point in obtaining faster procedures which were still far beyond what was feasible. Furthermore, on account of the versatility of machines, it now appears that as more progress is made, strategies in the search for proofs, or what are often called heuristic methods, will also gradually become part of the subject matter of inferential analysis. An analogous situation in numerical analysis would be, for example, to make the machine choose to apply different tricks such as taking the Fourier transform to obtain a solution of some differential equation.
465231
BLAST++: BLASTing queries in batches
UNLABELLED
BLAST++ is a tool that is integrated with NCBI BLAST, allowing multiple, say K, queries to be searched against a database concurrently. The results obtained by BLAST++ are identical to that obtained by executing BLAST on each of the K queries, but BLAST++ completes the processing in a much shorter time.


AVAILABILITY
http://xena1.ddns.comp.nus.edu.sg/~genesis/blast++


SUPPLEMENTARY INFORMATION
http://xena1.ddns.comp.nus.edu.sg/~genesis/blast++
47209500
LTR_FINDER: an efficient tool for the prediction of full-length LTR retrotransposons
Long terminal repeat retrotransposons (LTR elements) are ubiquitous eukaryotic transposable elements. They play important roles in the evolution of genes and genomes. Ever-growing amount of genomic sequences of many organisms present a great challenge to fast identifying them. That is the first and indispensable step to study their structure, distribution, functions and other biological impacts. However, until today, tools for efficient LTR retrotransposon discovery are very limited. Thus, we developed LTR_FINDER web server. Given DNA sequences, it predicts locations and structure of full-length LTR retrotransposons accurately by considering common structural features. LTR_FINDER is a system capable of scanning large-scale sequences rapidly and the first web server for ab initio LTR retrotransposon finding. We illustrate its usage and performance on the genome of Saccharomyces cerevisiae. The web server is freely accessible at http://tlife.fudan.edu.cn/ltr_finder/.
11622519
Applying Knowledge Sharing for Business Intelligence Collaboration
IT services need an automatic and flexible ability to react to dynamic changes in their environment. Managing change effectively and reducing the negative effects of day-to-day operations has become one of the most important tasks in IT service management, which require hiring highly skilled IT professionals with correspondingly high labor costs. There is a challenge to select, implement and integrate the right resources quickly and effectively. Although there is a growing body of research into IT management, many techniques are either too narrow (focusing on a single component rather than the entire system), or they address only configuration data collection and integration. Instead, one needs to scale or respond to special domain knowledge, collaboration and the right data for helping IT professionals to improve their work. In this paper, we propose a knowledge-sharing based collaborating management system for IT service management. It aims to bridge the gap between domain experts’ knowledge and manageable systems. We developed a proof-of-concept of an impact analysis service based on knowledge-sharing; it establishes an IT service management collaboration paradigm and ecosystem, leveraging the expert’s rich knowledge and experience to improve the management quality and reduce the cost. A case study driven by customers demonstrates that collaboration with knowledge sharing is effective both at constructing useful system analysis services and in using those services to improve system management.