Theorems related to symmetric nonlinear decomposition

Decomposition methods can provide the rescue from the “curse of dimensionality”, which often prevents the successful numerical solution of large scale nonlinear mathematical programming problems. A symmetric nonlinear decomposition theory has been elaborated by T.O.M. Kronsjö (4) as an extension of a theory by the same author (3). The stringent proof of the convergence of this decomposition algorithm requires some results on necessary optimality conditions for certain mathematical programming problems. In this paper we state and prove some theorems providing these results.     

Theorems on the decomposition of a large nonlinear convex separable economic system in the dual direction

Large mathematical programming problems often arise as the result of the economic planning process. When such a problem is not only large, but nonlinear as well, there is a need to make it more manageable by breaking it down into several smaller and more easily handled subproblems. The subproblems are solved separately with the coordination activity carried out by a “master problem”. A decomposition method can be seen as a “dialogue” between the master problem and the subproblems, where the flow of information back and forth between the former and the latters results in a series of approximations converging to the solution of the overall problem. Such a decomposition method was elaborated by Benders [1] for linear programmes and generalized to nonlinear convex separable programmes by Kronsjö [4] and by Geoffrion [3]. After considering our basic nonlinear programming problem from a two-stage minimization point of view, we review the Kronsjö nonlinear decomposition algorithm. Then we establish some properties of a function related to this algorithm.     

A new algorithm for use in computer identification

On 9 May 1987, a Soviet-made IL-62M Polish airliner, LOT Flight 5055, crashed, exploded, and burned, killing the crew and 183 passengers. A forensic science team from the Armed Forces Institute of Pathology, comprised of 6 dental officers, 3 forensic pathologists, and 3 medical photographers, worked in concert with the Polish forensic science team. The small number of antemortem records and the extreme fragmentation of the remains presented a new scenario for computer use. Typically, the Computer-Assisted Postmortem Identification (CAPMI) software is used to compare remains against an antemortem database. Results are listed by the number of tooth-to-tooth matches based on restorative or other characteristics or both. The Polish disaster confounded this approach to some degree, however, and suggested a reconsideration of the theory on which the sort is made, that is, that the cases with maximum number of matches to preexisting dental records would be the most likely identification (ID) match. A hypothesis was constructed that, if searches were accomplished for fragments with a minimum number of mismatches, the correct matches would appear higher in the rank order. Six antemortem records (that had all dental information) were sorted against one hundred and twelve postmortem fragmented records. The resulting report was reordered so that records were listed by minimum number of mismatches. There was significant improvement in rank placement for all of the records. Thus it was accepted that in the situation of highly fragmented remains a different sorting based on the number of mismatches is indicated. Programming changes to make this option available have been implemented in the new version of CAPMI.     

The decomposition and graphical analysis of crime and sanctions data: A cross-national application

This article attempts to illustrate the utility of isoquant map analysis from the field of production theory in microeconomics for the analysis of criminal justice data. Cross-national comparisons of aggregate crime and justice data are used to demonstrate the ability of this technique to reveal important patterns that are often obscured by simple rate comparisons and multivariate treatments such as pooled time-series analysis. For each jurisdiction, aggregate trends in criminal justice processing rates are systematically analyzed as a sequence of two-input production processes: gross imprisonment rates (prison population divided by resident population) can be partitioned in terms of the crime rate and punitiveness (prison population divided by the number of offenses); punitiveness can, in turn, be partitioned in terms of severity and certainty of punishment; certainty of punishment can then be partitioned, seriatim, in terms of the incarceration rate, the conviction rate, and the arrest or clearance rate and the rate at which citizens report crimes. Cross-national data collected by Farrington, Langan, and Wikström are used to illustrate the utility of the method for displaying comparisons of the decomposition of aggregate criminal justice data for the United States, England, and Sweden.     

A robust detection algorithm for copy-move forgery in digital images

With the availability of the powerful editing software and sophisticated digital cameras, region duplication is becoming more and more popular in image manipulation where part of an image is pasted to another location to conceal undesirable objects. Most existing techniques to detect such tampering are mainly at the cost of higher computational complexity. In this paper, we present an efficient and robust approach to detect such specific artifact. Firstly, the original image is divided into fixed-size blocks, and discrete cosine transform (DCT) is applied to each block, thus, the DCT coefficients represent each block. Secondly, each cosine transformed block is represented by a circle block and four features are extracted to reduce the dimension of each block. Finally, the feature vectors are lexicographically sorted, and duplicated image blocks will be matched by a preset threshold value. In order to make the algorithm more robust, some parameters are proposed to remove the wrong similar blocks. Experiment results show that our proposed scheme is not only robust to multiple copy-move forgery, but also to blurring or nosing adding and with low computational complexity.     

A clustering algorithm using DNA marker information for sub-pedigree reconstruction

In a mass disaster scenario in which many people are dead, it may be that small family groups are among the dead, and investigators may need to identify such groups, e.g., to return bodies to living relatives for burial. We consider the problem of identifying small groups of closely related people within a large group of people through the use of DNA marker information. We propose a likelihood-ratio-based distance measure of the relatedness between pairs of individuals and use an estimate of this measure as a means of clustering related people into groups. We show the effectiveness of our approach on real examples and through simulations, which suggest that the method is quite reliable for identifying very close relationships. We discuss the use of our clustering algorithm in a two-stage pedigree reconstruction procedure and suggest directions in which the analysis could be extended. Applications include the identification of family groups among bodies found in mass graves and identification of family groups in animal populations.     

Factors affecting decomposition and Diptera colonization.

Understanding the process of corpse decomposition is basic to establishing the postmortem interval (PMI) in any death investigation even using insect evidence. The sequence of postmortem changes in soft tissues usually gives an idea of how long an individual has been dead. However, modification of the decomposition process can considerably alter the estimate of the time of death. A body after death is sometimes subject to depredation by various types of animals among which insects can have a predominant role in the breakdown of the corpse thus, accelerating the decomposition rate. The interference of the insect community in the decomposition process has been investigated by several experimental studies using animal models and very few contributions directly on cadavers. Several of the most frequent factors affecting PMI estimates such as temperature, burial depth and access of the body to insects are fully reviewed. On account of their activity and world wide distribution, Diptera are the insects of greatest forensic interest. The knowledge of factors inhibiting or favouring colonization and Diptera development is a necessary pre-requisite for estimating the PMI using entomological data.     

Insect succession and carrion decomposition in selected forests of Central Europe. Part 1: Pattern and rate of decomposition

Pig carrion decomposition and insect succession were monitored in different seasons and forests of Central Europe. Pattern of decomposition as well as onset, duration and rate of decompositional processes were measured. Pattern of decomposition was the same in almost all cases with putrefaction, active and advanced decay. In the majority of carcasses active decay was driven by larvae of Calliphoridae with a clear seasonal shift in dominant taxa. However, in some spring, alder forest cases active decay was driven by larvae of Necrodes littoralis (Coleoptera: Silphidae). As a rule the mosaic decomposition was observed. In spring a significant delay in onset of all decompositional processes was found. Season significantly affected rate of active decay due to a much higher rate in summer. Decomposition in alder forest proceeded faster than in pine-oak forest and hornbeam-oak forest. Differences between the latter two forests were practically negligible. Implications for forensic entomology are discussed.     

Differential decomposition patterns in charred versus un-charred remains

Although researchers have examined many aspects of fire modification, the rate and pattern of decomposition in charred remains have not been studied previously. This study utilized 48 domestic pigs, divided into 24 charred (head, neck, and limbs burned to Crow-Glassman level 1 and torso to level 2) and 24 un-charred pig carcasses. Decomposition of control carcasses was scored at 50 accumulated degree days (ADD) intervals, and charred carcasses were also observed and photographed at this time. A Charred Body Scale was subsequently created, and charred carcasses were scored retrospectively for the same ADD intervals. Analysis using a mixed-effect repeated measures model indicated that, while decomposition rate was not statistically different between the two groups (p = 0.2692), the charred remains initially displayed an ostensibly more advanced pattern. Body regions displaying significant charring decomposed at a faster rate (p < 0.001), while areas with very light levels of charring decomposed at a significantly slower rate (p < 0.001).     

A BASIC algorithm for calculating the postmortem interval from arthropod successional data.

A computer algorithm, implemented in the BASIC language, is presented for calculating the postmortem interval (PMI) from arthropod successional data. Entomology-assisted determination of the PMI promises to be a reliable technique in cases of homicide, suicide, accidental death, and unattended death due to natural causes. The program requires, as input, the identity of arthropod taxa recovered from human remains in a death scene investigation and machine-readable data on carrion-associated arthropod taxa and their known successional patterns of activity for the same geographical area. The program performs rapid comparisons of these lists and, on output, calculates an upper and lower estimate of the PMI, identifies the definitive taxa for these limits, and determines if the remaining corpse taxa have known successional patterns that are consistent for this estimate. An alternate output is provided if one or more corpse taxa do not overlap all the others at any single time in the succession. In that event, the user is prompted to recheck the identity of the non-overlapping taxon or taxa or reevaluate the environmental circumstances surrounding the case in question. Results of the analysis are saved to an ASCII file for output to a printer for making paper copies useful for the entomologist's Case Study Final Report. This program may make possible wider use of this technique in law enforcement and medical investigator offices that utilize both forensic entomologist expertise and IBM PCs (or compatible computers).     

A report of decomposition rates of a special burial type in Edmonton, Alberta from an experimental field study

Regional studies that examine decomposition rates of certain faunal remains can help to determine time since death. Forensic anthropologists have long used qualitative decomposition data, but linking these to more quantitative data could improve time since death estimations. Experiments were developed in which domestic pigs (Sus scrofa) were buried with varying characteristics then excavated and observed over a period of 15 months in Edmonton, Alberta. Data recorded after two weeks, five weeks, three months, one year, and 15 months were correlated with stages of decomposition as well as time since death, climate data, grave type, clothing, burial depth, and other factors. Results from these experiments provide useful regional information about stages of decomposition in a burial context. Pigs buried in June were skeletonized by approximately three to five weeks, while those buried in May were skeletonized between five weeks and three months. Climate data, insects, and grave type contributed the most to advanced decomposition, mainly in the form of mummification, and skeletonization.     

Longitudinal neighborhood profiles in delinquency: The decomposition of change

The methods that traditionally have been used to examine changing spatial distributions of crime and delinquency rates are not able to analyze parsimoniously the full range of within-community variation in these rates over time. In this paper, we present a variant of Bryk and Raudenbush's(Psychol. Bull. 101: 147–158, 1987) hierarchical linear model that can simultaneously examine the full range of within- and between-group variation contained in longitudinal data sets. The method is illustrated through an analysis of the delinquency rates characterizing Chicago's neighborhoods between 1930 and 1970.     

The decomposition of rabbit carcasses and associated necrophagous Diptera in Kuwait

Rabbit carcasses were used to compare rates of decomposition and associated assemblages of Diptera at four discernable habitat types in Kuwait; a country of a region with a paucity of such reference data. Carcasses in an urban habitat showed faster decomposition (as measured by percentage weight loss) than in agricultural, coastal or desert habitats, even with accumulated degree days (ADD) as the explanatory variable (t=2.73, df=34, p=0.010) to compensate for temperature differences. Taxa of Diptera at the four habitats became more similar as decomposition progressed, suggesting such differences between habitats were not marked. The occurrence of Chrysomyia megacephala and Lucilia sericata had not previously been recorded in Kuwait.     

Mapping the lateral extent of human cadaver decomposition with soil chemistry

Soil below decomposing cadavers may have a different lateral spatial extent depending upon whether scavengers have access to the human cadaver or not. We examined the lateral spatial extent of decomposition products to a depth of 7cm of soils beneath two decomposing corpses, one in which the subject was autopsied, unclothed and placed under a wire cage to restrict scavenger access and one in which the subject was not autopsied, unclothed and exposed to scavengers. The two bodies had accumulated degree days (ADD) of 5799 and 5469 and post mortem interval (PMI) of 288 and 248d, respectively. The spatial extent for dissolved organic carbon (DOC) and organic nitrogen (DON) for both bodies was large but similar suggesting some movement off site for both compounds. Mean DOC was 1087±727 and 1484±1236μgg(-1) dry soil under the two corpses relative to 150±68μgg(-1) in upslope control soils. Sulfate tended to have 'hot spots' of lower values relative to the control soils indicative of anaerobic respiration. pH was lower and electrical conductivity was higher in the soil under both decomposing cadavers relative to control soils. Some of the nutrients examined downslope of the human remains were significantly higher than control soils upslope suggesting movement of decomposition products off-site which could be an important factor when using human remains detector dogs.     

Identification of decomposition volatile organic compounds from surface-deposited and submerged porcine remains

Cadaver dogs are routinely used internationally by police and civilian search organisations to locate human remains on land and in water, yet little is currently known about the volatile organic compounds (VOCs) that are released by a cadaver underwater; how this compares to those given off by a cadaver deposited on land; and ultimately, how this affects the detection of drowned victims by dogs. The aim of this study was to identify the VOCs released by whole porcine (Sus scrofa domesticus) cadavers deposited on the surface and submerged in water using solid phase microextraction gas chromatography mass spectrometry (SPME GC–MS) to ascertain if there are notable differences in decomposition odour depending on the deposition location.For the first time in the UK, the volatile organic compounds (VOCs) from the headspace of decomposing porcine cadavers deposited in both terrestrial and water environments have been detected and identified using SPME-GCMS, including thirteen new VOCs not previously detected from porcine cadavers. Distinct differences were found between the VOCs emitted by porcine cadavers in terrestrial and water environments. In total, seventy-four VOCs were identified from a variety of different chemical classes; carboxylic acids, alcohols, aromatics, aldehydes, ketones, hydrocarbons, esters, ethers, nitrogen compounds and sulphur compounds. Only forty-one VOCs were detected in the headspace of the submerged pigs with seventy detected in the headspace of the surface-deposited pigs. These deposition-dependent differences have important implications for the training of cadaver dogs in the UK. If dog training does not account for these depositional differences, there is potential for human remains to be missed.Whilst the specific odours that elicit a trained response from cadaver dogs remain unknown, this research means that recommendations can be made for the training of cadaver dogs to incorporate different depositions, to account for odour differences and mitigate the possibility of missed human remains operationally.