内射拓扑分子格

本文证明了任给T_O拓扑分子格(L,η),以下三条等价:(1)(L,η)为正则内射拓扑分子格;(2)L为完备集环且其完备余素元集ht(L)形成一连续格,余拓扑η为该连续格ht(L)上的Scott闭集格;(3)存在T_O内射拓扑空间(X,Τ),(L,η)同胚于(P(X),Τ~c)在拓扑分子格范畴中的Sober化。此外,还给出了正则内射拓扑分子格、(一般)内射拓扑分子格以及正则内射分子格的一般结构。作为应用,重新证明了有指数元的拓扑分子格的结构。     

Missing data in image and signal processing: The case of binary objects

I investigated which portions of the Fourier transform of binary signals, images and three-dimensional objects are necessary to correctly identify an object in the presence of noise. This is practically possible for very small binary data sets since the total number of possible objects is then very limited. There are for example 512 different binary images with 9 pixels. It is easy to see that this number soon becomes impractically large for bigger images or if one allows more than two possible pixel values. It turns out that even in the presence of large amounts of noise a relatively small portion of the Fourier transform is essential for deciding which of all possible binary objects the Fourier transform belongs to. These ‘decision experiments’ can be used as a standard for how well algorithms for retrieval of missing Fourier components perform. In another set of computer experiments I investigate the possibility of retrieving various missing Fourier components algorithmically. The main finding of this second set of computer experiments is that the simple retrieval algorithm (a limited form of ‘projection onto convex sets’) used falls very much short of what one might expect from the ‘decision experiments’.I conclude with a discussion what this discrepancy might be due to and some suggestions how to improve the performance of retrieval algorithms for binary objects.     

Binary compact object inspiral: Detection expectations

We review the current estimates of binary compact object inspiral rates in particular in view of the recently discovered highly relativistic binary pulsar J0737-3039. One of the robust results is that, because of this discovery, the rate estimates for binary neutron stars have increased by a factor of 6–7 independent of any uncertainties related to the pulsar population properties. This rate increase has dramatic implications for gravitational wave detectors. For initial LIGO, the most probable detection rates for double neutron star (DNS) inspirals is 1 event/(5-250) yr; at 95% confidence we obtain rates up to 1/1.5 yr. For advanced LIGO, the most probable rates are 20–1000 events/yr. These predictions, for the first time, bring the expectations for DNS detections by initial LIGO to the astrophysically relevant regime. We also use our models to predict that the largescale Parkes multibeam pulsar survey with acceleration searches could detect an average of three to four binary pulsars similar to those known at present. In comparison, rate estimates for binaries with black holes are derived based on binary evolution calculation, and based on the optimistic ends of the ranges, remain an important candidate for inspiral detection in the next few years. We also consider another aspect of the detectability of binary inspiral: the effect of precession on the detection efficiency of astrophysically relevant binaries. Based on our current astrophysical expectations, large tilt angles are not favored. As a result the decrease in detection rate varies rather slowly with black hole spin magnitude and is within 20–30% of the maximum possible values.     

A powerful approach to real-time mobile objects tracking in crowded environments utilizing 3D video analysis of fixed camera,particle filter and neural network

A powerful approach in the area of real-time mobile objects tracking in crowded environments, utilizing 3D video frames analysis is now taken into real consideration, as a candidate to be improved. The method presented here is able to track a number of real-time mobile objects in the real complex situations in the presence of occlusion, overlapping and various shifts. This is a development of probabilistic estimation theory via particle filter. In one such case, the whole of chosen new features of mobile objects, which are unconsidered in the present probabilistic estimation, should first be analyzed through a novel neural network. Subsequently, the probabilistic estimation in each one of frames may be made in a better outcome, as long as all the mentioned components are integrated. Evaluation of the proposed approach through PETS-09 database has been finally carried out, once the results with respect to a number of standard benchmark procedures indicate that 12% accuracy improvement is acquired.     

基于Linear Sampling方法的二维可穿透区域反演

提出用时间调和声散射远场信息来反演二维可穿透目标的一种Linear Sampling方法,通过提取包含可穿透目标的一个样本区域的支集的点列来实现反演的,因为其在区域内与区域外有显著的不同取值,由此而获得区域的逼近.这个算法特别吸引人之处是不需关于障碍物的任何先验信息.并且只需散射场在某个有限孔径中的部分远场信息,即可获得穿透区域的一个逼近.一些数值算例保证了这个反演算法是有效的和实用的.     

Hybrid organic–inorganic block copolymer nano‐objects from RAFT polymerization‐induced self‐assembly

A simple route to organic–inorganic (O/I) nano‐objects with different morphologies through polymerization‐induced block copolymer self‐assembly is described. The synthetic strategy relies on the chain‐extension of polyhedral oligomeric silsesquioxanes (POSS)‐containing macro‐CTA (PMAiBuPOSS₁₃ and PMAiBuPOSS₁₉) with styrene at 120 °C in octane, a selective solvent of the POSS‐containing block. The polymerization system was proven to afford a plethora of O/I nano‐objects, such as spherical micelles, cylindrical micelles, and vesicles depending on the respective molar masses of the PMAiBuPOSS and polystyrene (PS) blocks. The cooling procedure was also proven to be a crucial step to generate particles with a unique morphology. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4558–4564     

Subtractive Categories and Extended Subtractions

We introduce a notion of an extended operation which should serve as a new tool for the study of categories like Mal’tsev, unital, strongly unital and subtractive categories. However, in the present paper we are only concerned with subtractive categories, and accordingly, most of the time we will deal with extended subtractions, which are particular instances of extended operations. We show that these extended subtractions provide new conceptual characterizations of subtractive categories and moreover, they give an enlarged “algebraic tool” for working in a subtractive category—we demonstrate this by using them to describe the construction of associated abelian objects in regular subtractive categories with finite colimits. Also, the definition and some basic properties of abelian objects in a general subtractive category is given for the first time in the present paper. The second author acknowledges the support of Claude Leon Foundation, INTAS (06-1000017-8609) and Georgian National Science Foundation (GNSF/ST06/3-004).     

Identification of protein binders in works of art by high-performance liquid chromatography–diode array detector analysis of their tryptic digests

Proteins in works of art are generally determined by the relative amounts of amino acids. This method, however, implies a loss of information on the protein structure and its modifications. Consequently, we propose a method based on the analysis of trypsin digests using high-performance liquid chromatography (HPLC) UV diode array detection (DAD) for painting binder studies. All reaction steps are done in the same vial; no extraction methods or sample transfer is needed, reducing the risk of sample losses. A collection of pure binders (collagen, ovalbumin, yolk and casein) as well as homemade and historical paint samples have been investigated with this method. Chromatograms of unknowns at 214 nm and 280 nm are compared with those of the reference samples as a fingerprint. There is a good agreement between many peptides, but others seem to have been lost or their retention time shifted due to small compositional changes because of ageing and degradation of the paint. The results are comparable with the results of other techniques used for binder identification on the same samples, with the additional advantage of differentiation between egg yolk and glair.     

The mathematics of medical imaging in the classroom

The article presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty together with related classroom activities. Clinical medical practice and theoretical and empirical literature in mathematics education and radiology were reviewed to develop and pilot model integrative classroom topics and activities. The techniques of computer-axial tomography (CT) and positron emission tomography (PET) are discussed, followed by a presentation of accessible mathematical applications in numeration and linear algebra for use in a high school classroom. This discussion of the mathematics of a medical speciality, and the related activities, might not only offer teachers and students specific examples of the connections between their everyday study and a professional discipline, but also might foster further investigation into the importance and relevance of mathematics in other technology-based careers.