Three theorems regarding testing graph properties

Property testing is a relaxation of decision problems in which it is required to distinguish YES ‐instances (i.e., objects having a predetermined property) from instances that are far from any YES ‐instance. We presents three theorems regarding testing graph properties in the adjacency matrix representation. More specifically, these theorems relate to the project of characterizing graph properties according to the complexity of testing them (in the adjacency matrix representation). The first theorem is that there exist monotone graph properties in ???? for which testing is very hard (i.e., requires to examine a constant fraction of the entries in the matrix). The second theorem is that every graph property that can be tested making a number of queries that is independent of the size of the graph can be so tested by uniformly selecting a set of vertices and accepting iff the induced subgraph has some fixed graph property (which is not necessarily the same as the one being tested). The third theorem refers to the framework of graph partition problems, and is a characterization of the subclass of properties that can be tested using a one‐sided error tester making a number of queries that is independent of the size of the graph. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 23–57, 2003     

A Fiedler-like theory for the perturbed Laplacian

The perturbed Laplacian matrix of a graph G is defined as DL = D?A, where D is any diagonal matrix and A is a weighted adjacency matrix of G. We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use the notion of Perron component for the perturbed Laplacian matrix of a graph and show how its second smallest eigenvalue can be characterized using this definition.     

A new set of basis functions for the discrete geometric approach

By exploiting the geometric structure behind Maxwell’s equations, the so called discrete geometric approach allows to translate the physical laws of electromagnetism into discrete relations, involving circulations and fluxes associated with the geometric elements of a pair of interlocked grids: the primal grid and the dual grid.     

Robust classification of low-grade cervical cytology following analysis with ATR-FTIR spectroscopy and subsequent application of self-learning classifier eClass

Although the UK cervical screening programme has reduced mortality associated with invasive disease, advancement from a high-throughput predictive methodology that is cost-effective and robust could greatly support the current system. We combined analysis by attenuated total reflection Fourier-transform infrared spectroscopy of cervical cytology with self-learning classifier eClass. This predictive algorithm can cope with vast amounts of multidimensional data with variable characteristics. Using a characterised dataset [set A: consisting of UK cervical specimens designated as normal (n = 60), low-grade (n = 60) or high-grade (n = 60)] and one further dataset (set B) consisting of n = 30 low-grade samples, we set out to determine whether this approach could be robustly predictive. Variously extending the training set consisting of set A with set B data produced good classification rates with three two-class cascade classifiers. However, a single three-class classifier was equally efficient, producing a user-friendly, applicable methodology with improved interpretability (i.e., better classification with only one set of fuzzy rules). As data from set B were added incrementally to the training set, the model learned and evolved. Additionally, monitoring of results of the set B low-grade specimens (known to be low-grade cervical cytology specimens) provided the opportunity to explore the possibility of distinguishing patients likely to progress towards invasive disease. eClass exhibited a remarkably robust predictive power in a user-friendly fashion (i.e., high throughput, ease of use) compared to other classifiers (k-nearest neighbours, support vector machines, artificial neural networks). Development of eClass to classify such datasets for applications such as screening exhibits robustness in identifying a dichotomous marker of invasive disease progression.     

Unusual high exposure to ultraviolet-C radiation

UV radiation is known to cause acute and chronic eye and skin damage. The present case report describes a 90 min accidental exposure to UV-C radiation of 26 medical school students. Germicidal lamps were lit due to a malfunctioning of the timer system. Several hours after irradiation exposure, all subjects reported the onset of ocular symptoms, subsequently diagnosed as photokeratitis, and skin damage to the face, scalp and neck. While the ocular symptoms lasted 2-4 days, the sunburn-like condition produced significant erythema followed by deep skin exfoliation. The irradiation was calculated to be approximately 700 mJ cm(-2) absorbed energy, whereas the actual radiation emitted by the lamps was 0.14 mW cm(-2) (the radiometric measurements confirmed these calculi, because the effective irradiance measured from the height of the autopsy table to about 1 m under the UV-C lamp varied from 0.05 to 0.25 mW cm(-2)) but, more likely, the effective irradiance, according to skin phototype and symptoms, was between 50 and 100 mJ cm(-2). The ocular and skin effects produced by such a high irradiation (largely higher than that accepted by the American Conference of Governmental Industrial Hygienists [ACGIH] threshold limit values [TLVs]) appeared reversible in a relatively short time.     

Functions of bounded variation on the classical Wiener space and an extended Ocone–Karatzas formula

We prove an extension of the Ocone–Karatzas integral representation, valid for all BV$BV$ functions on the classical Wiener space. We also establish an elementary chain rule formula and combine the two results to compute explicit integral representations for some classes of BV$BV$ composite random variables.     

Recent developments in the theory of orographic cyclogenesis: Impact of orographic modifications on statistical properties

Summary Recent developments in the normal mode theory of lee cyclogenesis are presented. The topographic modifications of the most unstable eigenmode are computed in the most general case of primitive equations and isolated topography. The basic state about which linearization is performed is a midlatitude jet with maximum speed at tropopause level. The orographic modification consists in a pressure dipole scaling on the Rossby deformation radius already found in previous theoretical and numerical studies. The modifications of the statistical properties introduced by topography on the nonlinear feedback between zonal wind and transient waves are determined using a simple quasi-geostrophic two-layer model. Systematic differences are found to be consistent with the predictions of linear theories. A brief discussion on the limits of the linear theory is also included Paper presented at the IV Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 22–24, 1987, Rome.     

Urban crematoria emissions as they stand with current practice

In order to assess the pollutant load attributable to crematoria, a study was undertaken on the emissions from cremators sited in urban areas. This paper reports some preliminary results from the testing program on an urban cremator emission as it stands with current cremation practices in Italy. Results concern the concentration of the following parameters at the stack: total particulate matter, metals (As, Cd, Co, Cr, Cu, Hg, Mn, Ni, Pb, Sb, Sn, Tl, V, Zn), organic micropollutants such as dioxins (PCDD_s), dibenzofurans (PCDF_s), polycyclic aromatic hydrocarbons (PAH_s) and polychlorinated biphenyls (PCB_s).     

InclusiveK *'s and∑ *'s production in 360 GeV/cpp interactions using the European hybrid spectrometer

We have studied the inclusive production of strange meson and baryon resonances in 360 GeV/cpp interactions. Cross sections forK ^*+(892) andK ^*?(892) are estimated to be 4.42±0.62 mb and 2.54±0.47 mb respectively and those for∑ ⁺(1385) and∑ ^?(1385) are 0.67±0.11 mb and 0.26±0.07 mb respectively. Longitudinal and transverse momentum distributions forK ^*(892) and Σ(1385) are presented, as well as for their decay productsK ⁰ and Λ. An estimation is given on theK ^*(1430) and∑ ^*(1915) productions.     

Evidence for two back-to-back high-p T jets inK + p interactions at 70 GeV/c

Nucleon structure functions obtained from neutrino and anti-neutrino scattering on iron nuclei at high energies (E _v =30 to 250 GeV) are presented. These results are compared with the results of other lepton-nucleon scattering experiments. The structure functions are used to test the validity of the Gross-Llewellyn-smith sum rule, which measures the number of valence quarks in the nucleons, and to obtain leading and second order QCD fits.