Finding an Euclidean anti--centrum location of a set of points

An obnoxious facility is to be located inside a polygonal region of the plane, maximizing the sum of the k smallest weighted Euclidean distances to n given points, each protected by some polygonal forbidden region. For the unweighted case and k fixed an O(n²logn) time algorithm is presented. For the weighted case a thorough study of the relevant structure of the multiplicatively weighted order-k-Voronoi diagram leads to the design of an O(kn³+n³logn) time algorithm for finding an optimal solution to the anti-t-centrum problem for every t=1,…,k, simultaneously.     

Embedding HMMs-based models in a Euclidean space: the topological hidden Markov models

Current extensions of hidden Markov models such as structural, hierarchical, coupled, and others have the power to classify complex and highly organized patterns. However, one of their major limitations is the inability to cope with topology: When applied to a visible observation (VO) sequence, the traditional HMM-based techniques have difficulty predicting the n-dimensional shape formed by the symbols of the VO sequence. To fulfill this need, we propose a novel paradigm named “topological hidden Markov models” (THMMs) that classifies VO sequences by embedding the nodes of an HMM state transition graph in a Euclidean space. This is achieved by modeling the noise embedded in the shape generated by the VO sequence. We cover the first and second level topological HMMs. We describe five basic problems that are assigned to a second level topological hidden Markov model: (1) sequence probability evaluation, (2) statistical decoding, (3) structural decoding, (4) topological decoding, and (5) learning. To show the significance of this research, we have applied the concept of THMMs to: (i) predict the ASCII class assigned to a handwritten numeral, and (ii) map protein primary structures to their 3D folds. The results show that the second level THMMs outperform the SHMMs and the multi-class SVM classifiers significantly.     

A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s K_α operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K_α operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.     

Parameterized complexity of control problems in Maximin election

Elections are a central model in a variety of areas. This paper studies parameterized computational complexity of five control problems in the Maximin election. We obtain the following results: constructive control by adding candidates is W[2]-hard with respect to the parameter “number of added candidates”; both constructive and destructive control by adding/deleting voters are W[1]-hard with respect to the parameter “number of added/deleted voters”.     

Robust model selection with flexible trimming

The forward search provides data-driven flexible trimming of a C_p statistic for the choice of regression models that reveals the effect of outliers on model selection. An informed robust model choice follows. Even in small samples, the statistic has a null distribution indistinguishable from an F distribution. Limits on acceptable values of the C_p statistic follow. Two examples of widely differing size are discussed. A powerful graphical tool is the generalized candlestick plot, which summarizes the information on all forward searches and on the choice of models. A comparison is made with the use of M-estimation in robust model choice.     

A goodness-of-fit test for Archimedean copula models in the presence of right censoring

A goodness-of-fit testing procedure for Archimedean copula (AC) models is developed based on right-censored data. The proposed approach extends an existing method, which is suitable for the Clayton model, to general AC models. Asymptotic properties of the proposed test statistics under the true model assumption are derived. Simulation analysis shows that the proposed test has reasonable performance. Finally, two real data examples are analyzed for illustrative purposes.     

Where philosophy meets clinical science

Nowadays, there is a renewed interest in bone changes in experimental and clinical nephrology. However, the need for understanding the peculiarity of bone can be traced back to the 5th century BC, when Empedocles of Acragas put forward a theory of a world made of air, water, fire, and earth governed by love and hate. By observing the various body tissues, he strove to demonstrate that they consisted of 4 elements assembled with different mathematical ratios (logos). Blood is considered the most perfect tissue, because the ratio between elements is one. Bone is a very unusual tissue because it is made of 2 parts of earth, 2 parts of water, and 4 parts of fire. This kind of reasoning could be considered the first cry in the birth of quantitative chemistry.     

Synthesis and photovoltaic properties of an alternating phenylenevinylene copolymer with substituted-triphenylamine units along the backbone for bulk heterojunction and dye-sensitized solar cells

We have fabricated bulk heterojunction (BHJ) photovoltaic devices based on the as cast and thermally annealed P:[6,6]-phenyl-C-61-butyric acid methyl ester (PCBM) blends and found that these devices gave power conversion efficiency (PCE) of about 1.15 and 1.60% respectively. P is a novel alternating phenylenevinylene copolymer which contains 2-cyano-3-(4-(diphenylamino)phenyl)acrylic acid units along the backbone and was synthesized by Heck coupling. This copolymer was soluble in common organic solvents and showed long-wavelength absorption maximum at 390-420 nm with optical band gap of 1.94 eV. The improvement of PCE after thermal annealing of the device based on the P:PCBM blend was attributed to the increase in hole mobility due to the enhanced crystallinity of P induced by thermal treatment. In addition, we have fabricated BHJ photovoltaic devices based on the as cast and thermally annealed PB:P:PCBM ternary blend. PB is a low band gap alternating phenylenevinylene copolymer with BF₂-azopyrrole complex units, which has been previously synthesized in our laboratory. We found that the device based on this ternary blend exhibited higher PCE (2.56%) as compared to either P:PCBM (1.15%) or PB:PCBM (1.57%) blend. This feature was associated with the well energy level alignment of P, PB and PCBM, the higher donor-acceptor interfaces for the exciton dissociation and the improved light harvesting property of the ternary blend. The further increase in the PCE with thermally annealed ternary blend (3.48%) has been correlated with the increase in the crystallinity of both P and PB. Finally, we used copolymer P as sensitizer for quasi solid state dye-sensitized solar cell and we achieved PCE of approximately 3.78%.     

H optimal approximation for causal spline interpolation

In this paper, we give a causal solution to the problem of spline interpolation using H^∞ optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to reconstruct the inter-sample values. This leads to non-causality of the filter, and this becomes a critical issue for real-time applications.Our objective here is to derive a causal system which approximates spline interpolation by H^∞ optimization for the filter. The advantage of H^∞ optimization is that it can address uncertainty in the input signals to be interpolated in design, and hence the optimized system has robustness property against signal uncertainty.We give a closed-form solution to the H^∞ optimization in the case of the cubic splines. For higher-order splines, the optimal filter can be effectively solved by a numerical computation. We also show that the optimal FIR (finite impulse response) filter can be designed by an LMI (linear matrix inequality), which can also be effectively solved numerically. A design example is presented to illustrate the result.