Three types of monotonicity of averaging functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions, which are one of the basic tools in knowledge-based systems. The functions known as means (or averages) are idempotent and typically are monotone, however there are many important classes of means that are non-monotone. Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging functions. In this paper we discuss the concepts of directional and cone monotonicity, and monotonicity with respect to majority of inputs and coalitions of inputs. We establish the relations between various kinds of monotonicity, and illustrate it on various examples. We also provide a construction method for cone monotone functions.

Weakly monotonic averaging functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important nonmonotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions, and proves that several families of important nonmonotonic means are actually weakly monotonic averaging functions. Specifically, we provide sufficient conditions for weak monotonicity of the Lehmer mean and generalized mixture operators. We establish weak monotonicity of several robust estimators of location and conditions for weak monotonicity of a large class of penalty-based aggregation functions. These results permit a proof of the weak monotonicity of the class of spatial-tonal filters that include important members such as the bilateral filter and anisotropic diffusion. Our concept of weak monotonicity provides a sound theoretical and practical basis by which (monotonic) aggregation functions and nonmonotonic averaging functions can be related within the same framework, allowing us to bridge the gap between these previously disparate areas of research.

On weak monotonicity of some mixture functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. Here we study means that are not necessarily monotone. Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging functions. We provide results for the weak monotonicity of some importantclasses of mixture functions. With these results we are able to extend and improve the understanding of this very important class of functions.

Characterizing compactness of geometrical clusters using fuzzy measures

Certain tasks in image processing require the preservation of fine image details, while applying a broad operation to the image, such as image reduction, filtering, or smoothing. In such cases, the objects of interest are typically represented by small, spatially cohesive clusters of pixels which are to be preserved or removed, depending on the requirements. When images are corrupted by the noise or contain intensity variations generated by imaging sensors, identification of these clusters within the intensity space is problematic as they are corrupted by outliers. This paper presents a novel approach to accounting for spatial organization of the pixels and to measuring the compactness of pixel clusters based on the construction of fuzzy measures with specific properties: monotonicity with respect to the cluster size; invariance with respect to translation, reflection, and rotation; and discrimination between pixel sets of fixed cardinality with different spatial arrangements. We present construction methods based on Sugeno-type fuzzy measures, minimum spanning trees, and fuzzy measure decomposition. We demonstrate their application to generating fuzzy measures on real and artificial images.

Biased experts and similarity based weights in preferences aggregation

In a group decision making setting, we consider the potential impact an expert can have on the overall ranking by providing a biased assessment of the alternatives that differs substantially from the majority opinion. In the framework of similarity based averaging functions, we show that some alternative approaches to weighting the experts' inputs during the aggregation process can minimize the influence the biased expert is able to exert.

Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Improving tenants' trust in SaaS applications using dynamic security monitors

It is almost impossible to prove that a given software system achieves an absolute security level. This becomes more complicated when addressing multi-tenant cloud-based SaaS applications. Developing practical security properties and metrics to monitor, verify, and assess the behavior of such software systems is a feasible alternative to such problem. However, existing efforts focus either on verifying security properties or security metrics but not both. Moreover, they are either hard to adopt, in terms of usability, or require design-time preparation to support monitoring of such security metrics and properties which is not feasible for SaaS applications. In this paper, we introduce, to the best of our knowledge, the first unified monitoring platform that enables SaaS application tenants to specify, at run-time, security metrics and properties without design-time preparation and hence increases tenants’ trust of their cloud-assets security. The platform automatically converts security metrics and properties specifications into security probes and integrates them with the target SaaS application at run-time. Probes-generated measurements are fed into an analysis component that verifies the specified properties and calculates security metrics’ values using aggregation functions. This is then reported to SaaS tenants and cloud platform security engineers. We evaluated our platform expressiveness and usability, soundness, and performance overhead.

Aggregation and consensus for preference relations based on fuzzy partial orders

We propose a framework for eliciting and aggregating pairwise preference relations based on the assumption of an underlying fuzzy partial order. We also propose some linear programming optimization methods for ensuring consistency either as part of the aggregation phase or as a pre- or post-processing task. We contend that this framework of pairwise-preference relations, based on the Kemeny distance, can be less sensitive to extreme or biased opinions and is also less complex to elicit from experts. We provide some examples and outline their relevant properties and associated concepts.

The modulated grating hologram

A phase and amplitude, off-axis hologram has been synthesized from three computer-generated transmission masks, using a multiple-exposure holographic recording method. Each of the masks controls one fixed-phase component of the complex hologram transmittance. The basic grating is generated optically, relieving the computer of the burden of drawing details the size of each fringe. The maximum information capacity of the computer plotting device can then be applied to the generation of the grating modulation function. By this method large digital holograms (25 mm by 25 mm) have been synthesized in dichromated gelatin. The recording method is applicable to virtually any holographic medium.

The modulated grating hologram was designed primarily for the application of spatial filtering, in which the requirement is a hologram with large dynamic range and large free spectral range. Choice of a low-noise, high-efficiency medium such as dichromated gelatin will allow exceptionally large dynamic range. Independence of the optically-generated carrier grating from the computer-generated modulation functions allows arbitrarily large free spectral range.

The performance of a holographic spatial filter will be limited ultimately by noise originating from imperfections in the holographic medium. The characteristics of this noise are analyzed, and in the case of a high diffraction efficiency hologram are shown to differ significantly from previous analyses. The dominant noise source in holograms of high diffraction efficiency will be scattering of the first order or imaging wave by deformations in the hologram surface or other effects of low spatial frequency. Experimental measurements in various low-noise holographic media verify these predictions.

Influence of composition on the structure, electric and magnetic properties of Pd-Mn-P and Pd-Co-P amorphous alloys

The influence of composition on the structure and on the electric and magnetic properties of amorphous Pd-Mn-P and Pd-Co-P prepared by rapid quenching techniques were investigated in terms of (1) the 3d band filling of the first transition metal group, (2) the phosphorus concentration effect which acts as an electron donor and (3) the transition metal concentration.

The structure is essentially characterized by a set of polyhedra subunits essentially inverse to the packing of hard spheres in real space. Examination of computer generated distribution functions using Monte Carlo random statistical distribution of these polyhedra entities demonstrated tile reproducibility of the experimentally calculated atomic distribution function. As a result, several possible "structural parameters" are proposed such as: the number of nearest neighbors, the metal-to-metal distance, the degree of short-range order and the affinity between metal-metal and metal-metalloid. It is shown that the degree of disorder increases from Ni to Mn. Similar behavior is observed with increase in the phosphorus concentration.

The magnetic properties of Pd-Co-P alloys show that they are ferromagnetic with a Curie temperature between 272 and 399°K as the cobalt concentration increases from 15 to 50 at.%. Below 20 at.% Co the short-range exchange interactions which produce the ferromagnetism are unable to establish a long-range magnetic order and a peak in the magnetization shows up at the lowest temperature range . The electric resistivity measurements were performed from liquid helium temperatures up to the vicinity of the melting point (900°K). The thermomagnetic analysis was carried out under an applied field of 6.0 kOe. The electrical resistivity of Pd-Co-P shows the coexistence of a Kondo-like minimum with ferromagnetism. The minimum becomes less important as the transition metal concentration increases and the coefficients of ℓn T and T^2 become smaller and strongly temperature dependent. The negative magnetoresistivity is a strong indication of the existence of localized moment.

The temperature coefficient of resistivity which is positive for Pd- Fe-P, Pd-Ni-P, and Pd-Co-P becomes negative for Pd-Mn-P. It is possible to account for the negative temperature dependence by the localized spin fluctuation model and the high density of states at the Fermi energy which becomes maximum between Mn and Cr. The magnetization curves for Pd-Mn-P are typical of those resulting from the interplay of different exchange forces. The established relationship between susceptibility and resistivity confirms the localized spin fluctuation model. The magnetoresistivity of Pd-Mn-P could be interpreted in tenns of a short-range magnetic ordering that could arise from the Rudennan-Kittel type interactions.

Efficient RkNN Retrieval with Arbitrary Non-Metric Similarity Measures

A RkNN query returns all objects whose nearest k neighbors
contain the query object. In this paper, we consider RkNN
query processing in the case where the distances between
attribute values are not necessarily metric. Dissimilarities
between objects could then be a monotonic aggregate of dissimilarities
between their values, such aggregation functions
being specified at query time. We outline real world cases
that motivate RkNN processing in such scenarios. We consider
the AL-Tree index and its applicability in RkNN query
processing. We develop an approach that exploits the group
level reasoning enabled by the AL-Tree in RkNN processing.
We evaluate our approach against a Naive approach
that performs sequential scans on contiguous data and an
improved block-based approach that we provide. We use
real-world datasets and synthetic data with varying characteristics
for our experiments. This extensive empirical
evaluation shows that our approach is better than existing
methods in terms of computational and disk access costs,
leading to significantly better response times.

Induction of neutralizing antibodies in mice immunized with an amino-terminal polypeptide of Streptococcus mutans P1 protein produced by a recombinant Bacillus subtilis strain

The oral pathogen Streptococcus mutans expresses a surface protein, P1, which interacts with the salivary pellicle on the tooth surface or with fluid-phase saliva, resulting in bacterial adhesion or aggregation, respectively. P1 is a target of protective immunity. Its N-terminal region has been associated with adhesion and aggregation functions and contains epitopes recognized by efficacious antibodies. In this study, we used Bacillus subtilis, a gram-positive expression host, to produce a recombinant N-terminal polypeptide of P1 (P1(39-512)) derived from the S. mutans strain UA159. Purified P1(39-512) reacted with an anti-full-length P1 antiserum as well as one raised against intact S. mutans cells, indicating preserved antigenicity. Immunization of mice with soluble and heat-denatured P1(39-512) induced antibodies that reacted specifically with native P1 on the surface of S. mutans cells. The anti-P1(39-512) antiserum was as effective at blocking saliva-mediated aggregation of S. mutans cells and better at blocking bacterial adhesion to saliva-coated plastic surfaces compared with the anti-full-length P1 antiserum. In addition, adsorption of the anti-P1 antiserum with P1(39-512) eliminated its ability to block the adhesion of S. mutans cells to abiotic surfaces. The present results indicate that P1(39-512), expressed and purified from a recombinant B. subtilis strain, maintains important immunological features of the native protein and represents an additional tool for the development of anticaries vaccines.

Construction of k-Lipschitz triangular norms and conorms from empirical data

This paper examines the practical construction of k-Lipschitz triangular norms and conorms from empirical data. We apply a characterization of such functions based on k-convex additive generators and translate k-convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients. This is the basis of a simple linear spline-fitting algorithm, which guarantees k-Lipschitz property of the resulting triangular norms and conorms.

Citation based journal rankings : an application of fuzzy measures

Here we investigate the use of fuzzy measures and averaging aggregation functions for understanding the behavior and tendencies of decision-makers in an ordinal classification problem. Using the Aotools package to approximate the data, we classify each journal based on aggregation of the ISI Web of knowledge indices and discuss the results.

Some results on Lipschitz quasi-arithmetic means

We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k.