An inequality between the diameter and the inverse dual degree of a tree

Let T be a nontrivial tree with diameter D(T) and radius R(T). Let I(T) be the inverse dual degree of T which is defined to be , where for uV(T). For any longest path P of T, denote by a(P) the number of vertices outside P with degree at least 2, b(P) the number of vertices on P with degree at least 3 and distance at least 2 to each of the end-vertices of P, and c(P) the number of vertices adjacent to one of the end-vertices of P and with degree at least 3. In this note we prove that . As a corollary we then get with equality if and only if T is a path of at least four vertices. The latter inequality strengthens a conjecture made by the program Graffiti.postprin

An empirical study of web interface design on small display devices

This paper reports an empirical study that explores the problem of finding a highly-efficient, user-friendly interface design method on small display devices. We compared three models using our PDA interface simulator: presentation optimization method, semantic conversion method, and zooming method. A controlled experiment has been carried out to identify the pros and cons of each method. The results show that of the three interface methods, the zooming method is slightly better than the semantic conversion method, while they both outperform the optimizing presentation method. © 2004 IEEE

A total variation regularization based super-resolution reconstruction algorithm for digital video

Super-resolution (SR) reconstruction technique is capable of producing a high-resolution image from a sequence of low-resolution images. In this paper, we study an efficient SR algorithm for digital video. To effectively deal with the intractable problems in SR video reconstruction, such as inevitable motion estimation errors, noise, blurring, missing regions, and compression artifacts, the total variation (TV) regularization is employed in the reconstruction model. We use the fixed-point iteration method and preconditioning techniques to efficiently solve the associated nonlinear Euler-Lagrange equations of the corresponding variational problem in SR. The proposed algorithm has been tested in several cases of motion and degradation. It is also compared with the Laplacian regularization-based SR algorithm and other TV-based SR algorithms. Experimental results are presented to illustrate the effectiveness of the proposed algorithm.£.published_or_final_versio

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies {Jε}, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each Jε is nonsmooth and is expressed as the sum of an l1 regularization term and a smooth nonconvex function. Furthermore, the local minimization of each Jε is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.published_or_final_versio

Oxidation of AlInAs for current blocking in a photonic crystal laser

To make an electrically pumped photonic crystal membrane laser is a challenging task. One of the problems is how to avoid short circuiting between the p- and n-doped parts of the laser diode, when the membrane thickness is limited to 200-300nm. We propose to use the oxide of AlInAs to realize a current blocking function. In this way, based on submicron selective area re-growth, we aim for electrically injected photonic crystal lasers with high output power, small threshold currents and low power consumption. Here results are presented on the oxidation of AlInAs. The results show that it is feasible to use the oxide of AlInAs for current blocking in an InP-based membrane photonic crystal laser

Effective temperature for black holes

The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their quasinormal modes are natural candidates for an interpretation in terms of quantum levels. The spectrum of black hole's quasinormal modes can be re-analysed by introducing a black hole's effective temperature which takes into account the fact that, as shown by Parikh and Wilczek, the radiation spectrum cannot be strictly thermal. This issue changes in a fundamental way the physical understanding of such a spectrum and enables a re-examination of various results in the literature which realizes important modifies on quantum physics of black holes. In particular, the formula of the horizon's area quantization and the number of quanta of area result modified becoming functions of the quantum "overtone" number n. Consequently, the famous formula of Bekenstein-Hawking entropy, its sub-leading corrections and the number of microstates are also modified. Black hole's entropy results a function of the quantum overtone number too. We emphasize that this is the first time that black hole's entropy is directly connected with a quantum number. Previous results in the literature are re-obtained in the limit n \to \infty.Comment: 10 pages,accepted for publication in Journal of High Energy Physics. Comments are welcom

Behaviour of engineered cementitious composite-encased stub concrete columns under axial compression

Although high-strength concrete (HSC) has higher compressive strength than normal-strength concrete (NSC), its application in column construction is often limited by its brittleness and limited post-peak ductility. In this preliminary study, hybrid fibre engineered cementitious composite (ECC) is proposed as a potential encasement material to confine the HSC core and to increase the column's ductility. The behaviours of the proposed ECC-encased concrete stub column under axial compression are studied experimentally. Thirty stub columns, including six NSC/HSC, six ECC and 18 ECC-encased NSC/HSC (ECC-NSC/HSC) are tested under axial compression. The effects of ECC strength, ECC encasement thickness, concrete strength and cross-section shapes (circular, square and rectangular) are then investigated and reported in terms of failure modes, strength ratios, post-peak ductility and energy dissipation capacity of the stub columns. It is found that, when comparing with NSC/HSC stub columns, although no significant improvement in the ultimate strength was observed, the ECC encasement improved the performance of ECC-NSC/HSC stub columns by reducing brittleness and improving the post-peak behaviour during failure

Adipose tissue-derived stem cells in oral mucosa tissue engineering: Enhanced migration and proliferation in co-culture with oral keratinocytes in vitro

Tissue-engineered oral mucosa holds a great prospect in urethroplasty and adipose tissue-derived stem cells (ADSCs) may play an important role in this field. In this research, canine oral keratinocytes (OKs) and ADSCs were harvested and cultured in vitro. The affinity between the two cell lines was evaluated by analyzing their migration and proliferation patterns in a co-culture environment. The results demonstrate that both canine ADSCs and OKs showed improved migration in the presence of the other cell line as a co-culture when compared to monoculture. Further, conditioned medium using the supernatant of one cell line accelerated the other cell line’s proliferation rate. Hence, it was concluded that the affinity between OKs and ADSCs was fitting; the presence of ADSCs accelerated the migration and proliferation of OKs in vitro. These results indicate that it is practical to use ADSCs and OKs to construct a tissue-engineered oral mucosa, since the presence of the former could activate the latter in vitro, maybe even in vivo. This may help to build tissue-engineered oral mucosa, which may be a new method for urethroplasty.Key words: Urethroplasty, adipose tissue-derived stem cells, oral keratinocytes, tissue engineering

Residence time control in micromixers with vortex shedding

Residence time control is an important indicator of micromixer design. When using vortex shedding to enhance mixing efficiency in a micromixer, the relationship between residence time and vortex shedding becomes important; if residence time is shorter than shedding time, the fluid elements flow through the channel too quickly with no contribution of vortex shedding to mixing. Both residence time and vortex shedding depend on geometrical and flow parameters and hence in order to optimize micromixer design the effect of these parameters on mixing need to be well understood. Furthermore, the onset of vortex shedding in confined flows such as those encountered in micromixers need be elucidated. In this work, the flow field past a single cylindrical pin in a microchannel is studied experimentally using a high-speed PIV system. The effects of confinement on vortex formation are examined. Vortex shedding was observed for a channel height of two pin diameters and the shedding frequency increased with increasing lateral confinement (i.e. upon decrease in channel width at the same pin diameter). Therefore, controlling residence time via wake oscillations in pin microchannels is highly dependent on confinement