On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Halo assembly bias and its effects on galaxy clustering

The clustering of dark halos depends not only on their mass but also on their assembly history, a dependence we term `assembly bias'. Using a galaxy formation model grafted onto the Millennium Simulation of the LCDM cosmogony, we study how assembly bias affects galaxy clustering. We compare the original simulation to `shuffled' versions where the galaxy populations are randomly swapped among halos of similar mass, thus isolating the effects of correlations between assembly history and environment at fixed mass. Such correlations are ignored in the halo occupation distribution models often used populate dark matter simulations with galaxies, but they are significant in our more realistic simulation. Assembly bias enhances 2-point correlations by 10% for galaxies with M_bJ-5logh brighter than -17, but suppresses them by a similar amount for galaxies brighter than -20. When such samples are split by colour, assembly bias is 5% stronger for red galaxies and 5% weaker for blue ones. Halo central galaxies are differently affected by assembly bias than are galaxies of all types. It almost doubles the correlation amplitude for faint red central galaxies. Shuffling galaxies among halos of fixed formation redshift or concentration in addition to fixed mass produces biases which are not much smaller than when mass alone is fixed. Assembly bias must reflect a correlation of environment with aspects of halo assembly which are not encoded in either of these parameters. It induces effects which could compromise precision measurements of cosmological parameters from large galaxy surveys.Comment: 8 pages, 4 figures, accepted for publication in MNRA

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

Multiscale Discriminant Saliency for Visual Attention

The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between center and surround classes. Discriminant power of features for the classification is measured as mutual information between features and two classes distribution. The estimated discrepancy of two feature classes very much depends on considered scale levels; then, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden markov tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic sub-squares. Then, saliency value for each dyadic square at each scale level is computed with discriminant power principle and the MAP. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multiscale discriminant saliency method (MDIS) against the well-know information-based saliency method AIM on its Bruce Database wity eye-tracking data. Simulation results are presented and analyzed to verify the validity of MDIS as well as point out its disadvantages for further research direction.Comment: 16 pages, ICCSA 2013 - BIOCA sessio

Rapamycin induces transactivation of the EGFR and increases cell survival.

The mammalian target of rapamycin (mTOR) signaling network regulates cell growth, proliferation and cell survival. Deregulated activation of this pathway is a common event in diverse human diseases such as cancers, cardiac hypertrophy, vascular restenosis and nephrotic hypertrophy. Although mTOR inhibitor, rapamycin, has been widely used to inhibit the aberrant signaling due to mTOR activation that plays a major role in hyperproliferative diseases, in some cases rapamycin does not attenuate the cell proliferation and survival. Thus, we studied the mechanism(s) by which cells may confer resistance to rapamycin. Our data show that in a variety of cell types the mTOR inhibitor rapamycin activates extracellularly regulated kinases (Erk1/2) signaling. Rapamycin-mediated activation of the Erk1/2 signaling requires (a) the epidermal growth factor receptor (EGFR), (b) its tyrosine kinase activity and (c) intact autophosphorylation sites on the receptor. Rapamycin treatment increases tyrosine phosphorylation of EGFR without the addition of growth factor and this transactivation of receptor involves activation of c-Src. We also show that rapamycin treatment triggers activation of cell survival signaling pathway by activating the prosurvival kinases Erk1/2 and p90RSK. These studies provide a novel paradigm by which cells escape the apoptotic actions of rapamycin and its derivatives that inhibit the mTOR pathway

Preparation and properties of all high Tc SNS-type edge DC SQUIDs

High-Tc SNS-type Josephson junctions and DC SQUIDs were successfully fabricated using hetero-epitaxially grown multilayers of YBa2Cu3Ox and PrBa2 Cu3O. These layers are c-axis oriented, and hence edges of the multilayers give rise to a current flow in the ab-plane between the electrodes of a Josephson junction. The necessary structuring was done by Ar ion beam etching. The individual junctions exhibit a supercurrent up to 80 K. The IcRn product of these junctions usually has a lower limit of 8 mV at 4.2 K. Voltage modulation of the first DC SQUIDs can be observed up to 66 K. The voltage modulation for various bias currents investigated at 4.2 K noise measurements were performed. Details on the fabrication and measurements are presente

Heavy Supersymmetric Particle Effects in Higgs Boson Production Associated with a Bottom Quark Pair at LHC and Tevatron

If all the supersymmetry particles (sparticles) except a light Higgs boson are too heavy to be directly produced at the Large Hadron Collider (LHC) and Tevatron, a possible way to reveal evidence for supersymmetry is through their virtual effects in other processes. We examine such supersymmetric QCD effects in bottom pair production associated with a light Higgs boson at the LHC and Tevatron. We find that if the relevant sparticles (gluinos and squarks) are well above the TeV scale, too heavy to be directly produced, they can still have sizable virtual effects in this process. For large $\tan\beta$, such residual effects can alter the production rate by as much as 40 percent, which should be observable in future measurements of this process.Comment: results for Tevatron added, version in PR

A general maximum entropy principle for self-gravitating perfect fluid

We consider a self-gravitating system consisting of perfect fluid with spherical symmetry. Using the general expression of entropy density, we extremize the total entropy $S$ under the constraint that the total number of particles is fixed. We show that extrema of $S$ coincides precisely with the relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic equilibrium. Furthermore, we apply the maximum entropy principle to a charged perfect fluid and derive the generalized TOV equation. Our work provides a strong evidence for the fundamental relationship between general relativity and ordinary thermodynamics.Comment: 13 pages, no figure. The arguments have been improved so that the assumption p=p(\rho) is no longer neede