Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

"Magic" dispersion maps with distributed Raman amplification

We analyze pulse propagation in an optical fiber with a periodic dispersion map and distributed amplification. Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes that are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps with distributed Raman amplification to compensate for the fiber loss, we find special schemes that have optimal (chirp-free) launch point locations that are independent of the fiber dispersion. Despite the variation of dispersion with wavelength due to the fiber dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical predictions are verified by direct numerical simulations. The obtained results are applied to a practical multichannel transmission system.

Optimal dispersion maps for multichannel soliton transmission with distributed Raman amplification

Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes with distributed Raman amplification, which are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps, special schemes are found that have optimal (chirp-free) launch point locations that are independent of the fibre dispersion. Despite the variation of dispersion with wavelength due to the fibre dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical results are verified by direct numerical simulations.

A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data Mining

Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data begging to be analyzed efficiently and effectively. In this paper, we propose a rough idea of a possible taxonomy of big data, along with some of the most commonly used tools for handling each particular category of bigness. The dimensionality p of the input space and the sample size n are usually the main ingredients in the characterization of data bigness. The specific statistical machine learning technique used to handle a particular big data set will depend on which category it falls in within the bigness taxonomy. Large p small n data sets for instance require a different set of tools from the large n small p variety. Among other tools, we discuss Preprocessing, Standardization, Imputation, Projection, Regularization, Penalization, Compression, Reduction, Selection, Kernelization, Hybridization, Parallelization, Aggregation, Randomization, Replication, Sequentialization. Indeed, it is important to emphasize right away that the so-called no free lunch theorem applies here, in the sense that there is no universally superior method that outperforms all other methods on all categories of bigness. It is also important to stress the fact that simplicity in the sense of Ockham’s razor non-plurality principle of parsimony tends to reign supreme when it comes to massive data. We conclude with a comparison of the predictive performance of some of the most commonly used methods on a few data sets.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Speech by Mr Micheál Martin TD at Launch of Pre-Registration Nursing Degree Programme

Good afternoon ladies and gentlemen. I am very pleased that you were all able to accept my invitation to join me here today on this landmark occasion for nursing education. It is fitting that all of the key stakeholders from the health and education sectors should be so well represented at the launch of an historic new development. Rapid and unpredictable change throughout society has been the hallmark of the twenty-first century, and healthcare is no exception. Regardless of what change occurs, no one doubts that nursing is intrinsic to the health of this nation. However, significant changes in nurse education are now needed if the profession is to deliver on its social mandate to promote people´s health by providing excellent and sensitive care. As science, technology and the demands of the public for sophisticated and responsive health care become increasingly complex, it is essential that the foundation of nursing education is redesigned. Pre-registration nursing education has already undergone radical change over the past eight years, during which time it has moved from an apprenticeship model of education and training to a diploma based programme firmly rooted in higher education. The Secretary General of my Department, Michael Kelly, played a leading role in bringing about this transformation, which has greatly enhanced the way students are prepared for entry to the nursing profession. The benefits of the revised model of education are clearly evident from the quality of the nurses graduating from the diploma programme. The Commission on Nursing examined the whole area of nursing education, and set out a very convincing case for educating nursing students to degree level. It argued that nurses of the future would be required to possess increased flexibility and the ability to work autonomously. A degree programme would provide nurses with a theoretical underpinning that would enable them to develop their clinical skills to a greater extent and to respond to future challenges in health care, for the benefit of patients and clients of the health services. The Commission has provided a solid framework for the professional development of nurses and midwives, including a process that is already underway for the creation of clinical nurse specialist and advanced nurse practitioner posts. This process will facilitate the transfer of skills across divisions of nursing. In this scenario, it is clearly desirable that the future benchmark qualification for registration as a nurse should be a degree in nursing studies. A Nursing Education Forum was established in early 1999 to prepare a strategic framework for the implementation of a nursing degree programme. When launching the Forum´s report last January, I indicated that the Government had agreed in principle to the introduction of the proposed degree programme next year. At the time two substantial outstanding issues had yet to be resolved, namely the basis on which nurse teachers would transfer from the health sector to the education sector and the amount of capital and revenue funding required to operate the degree programme. My Department has brokered agreements between the Nursing Alliance and the Higher Education Institutions for the assimilation of nurse teachers as lecturers into their affiliated institutions. The terms of these agreements have been accepted by all four nursing unions following a ballot of their nurse teacher members. I would like to pay particular tribute to all nurse teachers who have contributed to shaping the position, relevance and visibility of nursing through leadership, which embodies scholarship and excellence in the profession of nursing itself. In response to a recommendation of the Nursing Education Forum, I established an Inter-Departmental Steering Committee, chaired by Bernard Carey of my Department, to consider all the funding and policy issues. This Steering Committee includes representatives of the Department of Finance and the Department of Education and Science as well as the Higher Education Authority. The Steering Committee has been engaged in intensive negotiations with representatives of the Conference of Heads of Irish Universities and the Institutes of Technology in relation to their capital and revenue funding requirements. These negotiations were successfully concluded within the past few weeks. The satisfactory resolution of the industrial relations and funding issues cleared the way for me to go to the Government with concrete proposals for the implementation of degree level education for nursing students. I am delighted to announce here today that the Government has approved all of my proposals, and that a four-year undergraduate pre-registration nursing degree programme will be implemented on a nation-wide basis at the start of the next academic year, 2002/2003. The Government has approved the provision of capital funding totalling £176 million pounds for a major building and equipment programme to facilitate the full integration of nursing students into the higher education sector. This programme is due to be completed by September 2004, and will ensure that nursing students are accommodated in purpose built schools of nursing studies with state of the art clinical skills and human science laboratories at thirteen higher education sites throughout the country. The Government has also agreed to make available the substantial additional revenue funding required to support the nursing degree programme. By 2006, the full year cost of operating the programme will rise to some £43 million pounds. The scale of this investment in pre-registration nursing education is enormous by any yardstick. It demonstrates the firm commitment of myself and my Government colleagues to the full implementation of the recommendations of the Commission on Nursing, of which the introduction of pre-registration degree level education is arguably the most important. This historic decision, and it is truly historic, will finally put the education of nurses on a par with the education of other health care professionals. The nursing profession has long been striving for parity, and my own involvement in the achievement of it is a matter of deep personal satisfaction to me. I am also pleased to announce that the Government has approved my plans for increasing the number of nursing training places to coincide with the implementation of the degree programme next year. Ninety-three additional places in mental handicap and psychiatric nursing will be created at Athlone, Letterkenny, Tralee and Waterford Institutes of Technology. This will yield 392 extra places over the four years of the degree programme. A total of 1,640 places annually on the new degree programme will thus be available. This is an all-time record, and maintaining the annual student intake at this level for the foreseeable future is a key element of my overall strategy for ensuring that we produce sufficient “home-grown” nurses for our health services. I am aware that the Nursing Alliance were anxious that some funding would be provided for the further academic career development of nurse teachers who transfer to one of the six Universities that will be involved in the delivery of the degree programme. I am happy to confirm that up to £300,000 in total per year will be available for this purpose over the first four years of the degree programme. In line with a recommendation of the Commission on Nursing, my Department will have responsibility for the administration of the nursing degree budget until the programme has been bedded down in the higher education sector. A primary concern will be to ensure that the substantial capital and revenue funding involved is ring-fenced for nursing studies. It is intended that responsibility for the budget will be transferred to the Department of Education and Science after the first cohort of nursing degree students have graduated in 2006. In the context of today´s launch, it is relevant to refer to a special initiative that I introduced last year to assist registered nurses wishing to undertake part-time nursing degree courses. Under this initiative, nurses are entitled to have their course fees paid by their employers in return for a commitment to continue working in the public health service for a period following completion of the course. This initiative has proved extremely popular with large numbers of nurses availing of it. I want to confirm here today that the free fees initiative will continue in operation until 2005, at a total cost of at least £15 million pounds. I am giving this commitment in order to assure this year´s intake of nursing students to the final diploma programmes that fee support for a part-time nursing degree course will be available to them when they graduate in three years time. The focus of today´s celebration is rightly on the landmark Government decision to implement the nursing degree programme next year. As Minister for Health and Children, and as a former Minister for Education, I also have a particular interest in the educational opportunities available to other health service workers to upgrade their skills. I am pleased to announce that the Government has approved my proposals for the introduction of a sponsorship scheme for suitable, experienced health care assistants who wish to become nurses. This new scheme will commence next year and will be administered by the health boards. Successful applicants will be allowed to retain their existing salaries throughout the four years of the degree programme in return for a commitment to work as nurses for their health service employer for a period of five years following registration. Up to forty sponsorships will be available annually. The new scheme will enable suitable applicants to undertake nursing education and training without suffering financial hardship. The greatest advantage of the scheme will be the retention by the public health service of staff who are supported under it, since they will have had practical experience of working in the service and their own personal commitment to upgrading their skills will be informed by that experience. I am confident that the sponsorship scheme will be warmly welcomed by health service unions representing care assistants as providing an exciting new career development path for their members. Education and health are now the two pillars upon which the profession of nursing rests. We must continue to build bridges, even tunnels where needed to strengthen this partnership. We must all understand partnerships donâ?Tt just happen they are designed and must be worked at. The changes outlined here today are powerful incentives for those in healthcare agencies, academic institutions and regulatory bodies to design revolutionary programmes capable of shaping a critical mass of excellent practitioners. You have an opportunity, greater perhaps than has been granted to any other generation in history to make certain those changes are for the good. Ultimately changes that will make the country a healthier and more equitable place to live. The challenge relates to building a seamless preparatory programme which equally respects both education and practise as an indivisible duo whilst ensuring that high tech does not replace the human touch. This is a special day in the history of the development of the Irish nursing profession, and I would like to thank everybody for their contribution. I want to express my particular appreciation of two people who by this stage are well known to all of you – Bernard Carey of my Department and Siobhán O´Halloran of the National Implementation Committee. Bernard and Siobhán have devoted considerable time and energy to the project on my behalf over the past fourteen months or so. That we are here today celebrating the launch of degree level education is due in no small part to their successful execution of the mandate that I gave them. We live in a rapidly changing world, one in which nursing can no longer rely on systems of the past to guide it through the new millennium. In terms of contemporary healthcare, nursing is no longer just a reciprocal kindness but rather a highly complex set of professional behaviours, which require serious educational investment. Pre-registration nurse education will always need development and redesign to ensure our health care system meets the demands of modern society. Nothing is finite. Today more than ever the health system is dependent on the resourcefulness of nursing. I have no doubt that the new educational landscape painted will ensure that nurses of the future will be increasingly innovative, independent and in demand. The unmistakable message from my Department is that nursing really matters. Thank you.

A quick, free scan for all men aged 65+

The Northern Ireland Abdominal Aortic Aneurysm (AAA) Screening Programme began in June 2012 and offers AAA screening to all men aged 65 and over in Northern Ireland. All men in their 65th year receive an invite in the post. All men aged over 65 who have not been screened can request an appointment. The aim of the AAA screening programme is to reduce AAA-related mortality by providing systematic, population-based screening.� This poster was sent out to all GPs, GP practice managers and pharmacies as part of a professional information pack in the run-up to the launch of the programme. The poster is also distributed to relevant voluntary organisations and charities as a means of raising awareness among the target population.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Modeling of ALFA Programs Using PVS Theorem Prover

In Safety critical software failure can have a high price. Such software should be free of errors before it is put into operation. Application of formal methods in the Software Development Life Cycle helps to ensure that the software for safety critical missions are ultra reliable. PVS theorem prover, a formal method tool, can be used for the formal verification of software in ADA Language for Flight Software Application (ALFA.). This paper describes the modeling of ALFA programs for PVS theorem prover. An ALFA2PVS translator is developed which automatically converts the software in ALFA to PVS specification. By this approach the software can be verified formally with respect to underflow/overflow errors and divide by zero conditions without the actual execution of the code.

Modeling of ALFA Programs Using PVS Theorem Prover

In Safety critical software failure can have a high price. Such software should be free of errors before it is put into operation. Application of formal methods in the Software Development Life Cycle helps to ensure that the software for safety critical missions are ultra reliable. PVS theorem prover, a formal method tool, can be used for the formal verification of software in ADA Language for Flight Software Application (ALFA.). This paper describes the modeling of ALFA programs for PVS theorem prover. An ALFA2PVS translator is developed which automatically converts the software in ALFA to PVS specification. By this approach the software can be verified formally with respect to underflow/overflow errors and divide by zero conditions without the actual execution of the code

Robot free will

We introduce the perspex machine which unifies projective geometry and Turing computation and results in a supra-Turing machine. We show two ways in which the perspex machine unifies symbolic and non-symbolic AI. Firstly, we describe concrete geometrical models that map perspexes onto neural networks, some of which perform only symbolic operations. Secondly, we describe an abstract continuum of perspex logics that includes both symbolic logics and a new class of continuous logics. We argue that an axiom in symbolic logic can be the conclusion of a perspex theorem. That is, the atoms of symbolic logic can be the conclusions of sub-atomic theorems. We argue that perspex space can be mapped onto the spacetime of the universe we inhabit. This allows us to discuss how a robot might be conscious, feel, and have free will in a deterministic, or semi-deterministic, universe. We ground the reality of our universe in existence. On a theistic point, we argue that preordination and free will are compatible. On a theological point, we argue that it is not heretical for us to give robots free will. Finally, we give a pragmatic warning as to the double-edged risks of creating robots that do, or alternatively do not, have free will.

Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.