The imbalance of an edge e = {u, v} in a graph is defined as i(e) = |d(u)−d(v)|, where d(·) is the vertex degree. The irregularity I(G) of G is then defined as the sum of imbalances over all edges of G. This concept was introduced by Albertson who proved that I(G)\leqslant 4n^{3}/27 (where n = |V(G)|) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves the Laplacian spectral radius λ., Felix Goldberg., and Obsahuje seznam literatury
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inhomogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally gives the Lagrangian multiplier. We concentrate on aspects involved in the first and third step mainly, and advertise a multi-level method that allows for a stable computation of the intermediate and final quantities in optimal computational complexity.
Over the past 40 years, much has been published on the ultrastructure and cellular development of embryonic structures in a wide range of cestodes. However, the literature contains many discrepancies in both terminology and interpretations because of the facts that these organisms are phylogenetically diverse within their respective orders and families, the habitats that affect embryonic envelope structure are diverse, and the work has been done in various laboratories around the world. This review and synthesis was initiated by a working group of biologists from around the world convened at the Fifth International Workshop on Cestode Systematics and Phylogeny in České Budĕjovice, at the Institute of Parasitology of the Biology Centre, Academy of Sciences of the Czech Republic. It brings together the data from published work and establishes a uniform terminology and interpretation based on the data as they are presented. A consensus was reached for standardised definitions of the oncosphere, hexacanth, coracidium, embryonic envelopes, outer envelope, inner envelope, embryophore, vitelline capsule, shell, and outer coat. All of these are defined as components of the embryo or its vitellocyte-derived or uterine-derived coatings.
Different methods for Blind Source Separation (BSS) have been recently proposed. Most of these methods are suitable for separating either a mixture of sub-Gaussian source or a mixture of super-Gaussian sources. In this paper, a unified statistical approach for separating the mixture of sub-Gaussian and super-Gaussian source is proposed. Source separation techniques use an objective function to be optimized. The optimization process requires probability density function to be expressed in the terms of the random variable. Two different density models have been used for representing sub-Gaussian and super-Gaussian sources. Optimization of the objective function yields different nonlinear functions. Kurtosis has been ušed as measure of Gaussianity of a source. Depending upon the sign of kurtosis one of the nonlinearities is ušed in the proposed algorithm. Simulations with artificiaily generated as well as audio signals demonstrate effectiveness of the proposed approach.
A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.
In this paper, we consider a distributed stochastic computation of AXB=C with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of AXB=C, we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm. Moreover, a numerical example is also given to illustrate the effectiveness of the proposed algorithm.
Maintaining liquid asset portfolios involves a high carry cost and is mandatory by law for most financial institutions. Taking this into account a financial institution's aim is to manage a liquid asset portfolio in an "optimal" way, such that it keeps the minimum required liquid assets to comply with regulations. In this paper we propose a multi-stage dynamic stochastic programming model for liquid asset portfolio management. The model allows for portfolio rebalancing decisions over a multi-period horizon, as well as for flexible risk management decisions, such as reinvesting coupons, at intermediate time steps. We show how our problem closely relates to insurance products with guarantees and utilize this in the formulation. We will discuss our formulation and implementation of a multi-stage stochastic programming model that minimizes the down-side risk of these portfolios. The model is back-tested on real market data over a period of two years
In a Discounted Markov Decision Process (DMDP) with finite action sets the Value Iteration Algorithm, under suitable conditions, leads to an optimal policy in a finite number of steps. Determining an upper bound on the necessary number of steps till gaining convergence is an issue of great theoretical and practical interest as it would provide a computationally feasible stopping rule for value iteration as an algorithm for finding an optimal policy. In this paper we find such a bound depending only on structural properties of the Markov Decision Process, under mild standard conditions and an additional "individuality" condition, which is of interest in its own. It should be mentioned that other authors find such kind of constants using non-structural information, i.e., information not immediately apparent from the Decision Process itself. The DMDP is required to fulfill an ergodicity condition and the corresponding ergodicity index plays a critical role in the upper bound.
In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite $(2+\delta )$th moment and the covariance coefficient $u(n)$ exponentially decreases to $0$. The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
BACKGROUND: Radio frequency (RF) and chemical peels have been used for nonablative skin rejuvenation. Both of these cause collagen remodeling in the dermis and neo-collagen formation resulting in facial rejuvenation. There is limited literature on the evaluation of collagen remodeling by objective methods. OBJECTIVE: To compare the benefits of monopolar radiofrequency and glycolic acid peels in facial rejuvenation with regards to histopathology and Ultrabiomicroscopic sonography (UBM). METHODOLOGY: In this study, forty patients with mild to moderate photoaging received four treatments with 3 weeks interval of monopolar radiofrequency on one side of face and glycolic acid peels in increasing concentrations (NeostrataR) on the other side. Pre and post treatment, 2 mm biopsies were taken from both preauricular areas and Ultrasonography using a 35 MHz probe was done from outer canthus of eye and nasolabial folds from both sides of face. A blinded assessment was done to measure the increase in the grenz zone and dermal thickness. RESULTS: In 35/40 patients there was a significant increase in the grenz zone on histopathology and decrease in subepidermal low-echogenic band (SLEB) on UBM of the nasolabial folds on both sides of the face (p < 0.05). CONCLUSION: Radiofrequency and chemical peels showed equal efficacy in the treatment of facial rejuvenation. and D. V. Wakade, C. S. Nayak, K. D. Bhatt