Combining Models of Approximation with Partial Learning

In Gold's framework of inductive inference, the model of partial learning requires the learner to output exactly one correct index for the target object and only the target object infinitely often. Since infinitely many of the learner's hypotheses may be incorrect, it is not obvious whether a partial learner can be modifed to "approximate" the target object. Fulk and Jain (Approximate inference and scientific method. Information and Computation 114(2):179--191, 1994) introduced a model of approximate learning of recursive functions. The present work extends their research and solves an open problem of Fulk and Jain by showing that there is a learner which approximates and partially identifies every recursive function by outputting a sequence of hypotheses which, in addition, are also almost all finite variants of the target function. The subsequent study is dedicated to the question how these findings generalise to the learning of r.e. languages from positive data. Here three variants of approximate learning will be introduced and investigated with respect to the question whether they can be combined with partial learning. Following the line of Fulk and Jain's research, further investigations provide conditions under which partial language learners can eventually output only finite variants of the target language. The combinabilities of other partial learning criteria will also be briefly studied.Comment: 28 page

Fibroid explants reveal a higher sensitivity against MDM2-inhibitor nutlin-3 than matching myometrium

<p>Abstract</p> <p>Background</p> <p>Spontaneous cessation of growth is a frequent finding in uterine fibroids. Increasing evidence suggests an important role of cellular senescence in this growth control. Deciphering the underlying mechanisms of growth control that can be expected not only to shed light on the biology of the tumors but also to identify novel therapeutic targets.</p> <p>Methods</p> <p>We have analyzed uterine leiomyomas and matching normal tissue for the expression of p14^Arfand used explants to see if reducing the MDM2 activity using the small-molecule inhibitor nutlin-3 can induce p53 and activate genes involved in senescence and/or apoptosis. For these studies quantitative real-time RT-PCR, Western blots, and immunohistochemistry were used. Statistical analyses were performed using the student's <it>t </it>test.</p> <p>Results</p> <p>An in depth analysis of 52 fibroids along with matching myometrium from 31 patients revealed in almost all cases a higher expression of p14^Arfin the tumors than in the matching normal tissue. In tissue explants, treatment with the MDM2 inhibitor nutlin-3 induced apoptosis as well as senescence as revealed by a dose-dependent increase of the expression of <it>BAX </it>as well as of <it>p21</it>, respectively. Simultaneously, the expression of the proliferation marker Ki-67 drastically decreased. Western-blot analysis identified an increase of the p53 level as the most likely reason for the increased activity of its downstream markers <it>BAX </it>and <it>p21</it>. Because as a rule fibroids express much higher levels of p14^Arf, a major negative regulator of MDM2, than matching myometrium it was then analyzed if fibroids are more sensitive against nutlin-3 treatment than matching myometrium. We were able to show that in most fibroids analyzed a higher sensibility than that of matching myometrium was noted with a corresponding increase of the p53 immunopositivity of the fibroid samples compared to those from myometrium.</p> <p>Conclusions</p> <p>The results show that uterine fibroids represent a cell population of advanced cellular age compared to matching myometrium. Moreover, the data point to members of the p53-network as to potential novel therapeutic targets for the treatment of uterine fibroids.</p

Optical one-way quantum computing with a simulated valence-bond solid

One-way quantum computation proceeds by sequentially measuring individual spins (qubits) in an entangled many-spin resource state. It remains a challenge, however, to efficiently produce such resource states. Is it possible to reduce the task of generating these states to simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource for one-way quantum computing, do not naturally occur as ground states of physical systems. This led to a significant effort to identify alternative resource states that appear as ground states in spin lattices. An appealing candidate is a valence-bond-solid state described by Affleck, Kennedy, Lieb, and Tasaki (AKLT). It is the unique, gapped ground state for a two-body Hamiltonian on a spin-1 chain, and can be used as a resource for one-way quantum computing. Here, we experimentally generate a photonic AKLT state and use it to implement single-qubit quantum logic gates.Comment: 11 pages, 4 figures, 8 tables - added one referenc

Particle creation rate for dynamical black holes

We present the particle creation probability rate around a general black hole as an outcome of quantum fluctuations. Using the uncertainty principle for these fluctuation, we derive a new ultraviolet frequency cutoff for the radiation spectrum of a dynamical black hole. Using this frequency cutoff, we define the probability creation rate function for such black holes. We consider a dynamical Vaidya model, and calculate the probability creation rate for this case when its horizon is in a slowly evolving phase. Our results show that one can expect the usual Hawking radiation emission process in the case of a dynamical black hole when it has a slowly evolving horizon. Moreover, calculating the probability rate for a dynamical black hole gives a measure of when Hawking radiation can be killed off by an incoming flux of matter or radiation. Our result strictly suggests that we have to revise the Hawking radiation expectation for primordial black holes that have grown substantially since they were created in the early universe. We also infer that this frequency cut off can be a parameter that shows the primordial black hole growth at the emission moment.Comment: 10 pages, 1 figure. The paper was rewritten in more clear presentation and one more appendix is adde

Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these short-comings. Its so-called 'embarrassing parallelizability' allows us to solve many problems and extract physical information which elude the symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.Comment: 36 page

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde