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The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where each element has an associated subset in another set, but can also be viewed as a scheduling problem with infinitely large communication delay, precedence constraints in the form of a bipartite graph, and duplication.

We know that stress-factors, e.g. X-rays, have an effect on cells that is more lethal in rapid exponential growth than in stationary phase. It is this effect which makes radiotherapy effective in cancer treatment. This stress effect can be explained in two ways: (a) more vulnerability in the growth phase, (b) improved protection capacity and repair mechanisms in the stationary phase. Although the two explanations do not exclude each other, they are very different in the sense that (a) is a general mechanism whereas (b) is strain and stress-factor dependent. In this paper we explore major facets of (a). Firstly, we emphasize that (a) can account for known experimental stress-factor evidence. Secondly, we observe that (a) rightly predicts that slow exponential growth (meaning with a doubling time of several hours) results in a lower death rate than fast exponential growth (doubling time of a fraction of one hour), an effect that cannot be explained in the (b) framework because both organisms are in the same phase. Thirdly, we conjecture that the stress-factor effect can be extended to situations of chronic stress due to non-optimal environmental conditions. If correct, this conjecture would imply that even in normal culture conditions the natural death rate is lower in the stationary phase than in the growth phase. Finally, the paper closes with the description of several open questions and of appropriate test-experiments meant to address them., Comment: 21 pages, 4 figures

Named after Clio, the Greek goddess of history, cliophysics is a daughter (and in a sense an extension) of econophysics. Like econophysics it relies on the methodology of experimental physics. Its purpose is to conduct a scientific analysis of historical events. Such events can be of sociological, political or economic nature. In this last case cliophysics would coincide with econophysics. The main difference between cliophysics and econophysics is that the description of historical events may be qualitative as well as quantitative. For the handling of qualitative accounts cliophysics has developed an approach based on the identification of patterns. To detect a pattern the main challenge is to break the "noise barrier". The very existence of patterns is what makes cliophysics possible and ensures its success. Briefly stated, once a pattern is detected, it allows predictions to be made. As the capacity to make successful predictions is the hallmark of any science, it becomes easy to decide whether or not the claim made in the title of the paper is indeed fulfilled. A number of examples of clusters of similar events will be given which should convince readers that historical events can be simplified almost at will very much as in physics. One should not forget that physical effects are also subject to the environment. For instance, if tried at the equator, the experiment of the Foucault pendulum will fail. In the last part of the paper, we describe cliophysical investigations conducted over the past decades; they make us confident that cliophysics can be a valuable tool for decision makers., Comment: 15 pages, 1 figure, 3 tables

We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two derivatives of a conditional entropy function. The bound does not require explicit estimation of the unknown parameters. We provide a step-by-step process for computing the bound, and provide an example application. A comparison with known classical mutual information bounds is provided., Comment: This work has been submitted to the IEEE for possible publication. arXiv admin note: substantial text overlap with arXiv:2012.00970

Infant deaths and old age deaths are very different. The former are mostly due to severe congenital malformations of one or a small number of specific organs. On the contrary, old age deaths are largely the outcome of a long process of deterioration which starts in the 20s and affects almost all organs. In terms of age-specific death rates, there is also a clear distinction: the infant death rate falls off with age, whereas the adult and old age death rate increases exponentially with age in conformity with Gompertz's law. Clearly, it would be satisfactory to explain the two phenomena as being two variants within the same explanatory framework. In other words, a mechanism providing a combined explanation for the two forms of mortality would be welcome. This is the purpose of the present paper. We show here that the same biological effects can account for the two cases provided there is a difference in their severity: death triggered by isolated lethal anomalies in one case and widespread wear-out anomalies in the second. We show that quite generally this mechanism leads indeed, respectively, to a declining and an upgoing death rate. Moreover, this theoretical framework leads to the conjecture that the severity of the death effects, whether in infancy or old age, are higher for organisms which are comprised of a larger number of organs. Finally, let us observe that the main focus of the paper is the drastic difference of the age-specific death rates (i.e. decreasing versus increasing) because this difference is found in many species, whereas the question of the best fit (e.g. Gompertz versus Weibull) is rather specific to human mortality., Comment: 11 pages, 3 figures

This manuscript proposes a significant step in our long-run investigation of infant mortality across species. Since 2016 (Berrut et al. 2016) a succession of studies (Bois et al. 2019) have traced infant mortality from organisms of high complexity (e.g. mammals) down to unicellular organisms. Infant mortality may be considered as a filtering process through which organisms with potentially lethal congenital defects are eliminated. Such defects may have many causes but here we focus particularly on mishaps resulting from non-optimal conditions in the production of proteins, enzymes and other crucial macromolecules. The statistical signature of infant mortality consists in a falling age-specific death rate. The question we address here is whether infant mortality episodes take place in bacteria in the minutes precededing or following cell division. It will be shown that while experiments carried out in the 20th century tried but failed to detect such an effect (mostly because of limited sample size), more recent observations provided consistent evidence of a sizeable mortality, with a rate of the order of 0.7 per 1,000 per hour, in the exponential growth phase of E. coli. A further crucial test will be to measure the age-specific, post-division death rate. An experiment is outlined for that purpose. It is based on the selection of stained cells through flow cytometry and the derivation of their ages at death from their sizes. If an infant mortality effect can be identified in E. coli it can be conjectured that a similar effect also exists in other unicellular organisms, both prokaryote and eukaryote., Comment: 16 p., 5 figures

The influence of per capita income on life expectancy is well documented, mostly through studies of multinational samples. However, one expects fairly weak correlations at both ends of the life span, that is to say in early infancy and in age groups of elderly from 85 to 100 years. The reason is that at both ends mortality is largely controled by biological factors rather than by socio-economic conditions. In order to test this conjecture, we explore the influence of income on age groups, separately in France, the United States and South Korea. More precisely in each country we compare income and mortality data in as many regional subunits as possible. One noteworthy constatation is that, contrary to a common view, personal income is only weakly correlated with infant mortality (i.e. mortality under the age of one year). More broadly, we propose as a conjecture that the common pattern revealed by the analysis of the three countries is also valid in other developed countries., Comment: 9 pages, 4 figures

Biologically, for any organism life does not start at birth but at fertilization of the embryo. Embryonic development is of great importance because it determines congenital anomalies and influences their severity. Whereas there is detailed qualitative knowledge of the successive steps of embryonic development, little is known about their probabilities of success or failure. Embryonic mortality as a function of post fertilization time provides a simple (albeit crude) way to identify major defects. We find that, in line with the few other species for which data are available, the embryonic mortality of zebrafish has a prominent peak shortly after fertilization. This is called the early embryonic mortality (EEM) effect. Although a number of immediate causes of death (e.g. infection, excess of carbon dioxide or of lactic acid, chromosomal defects) can be cited, the common underlying factor remains unknown. After reviewing embryonic mortality data available for chicken and a few other farm animals, we explain that zebrafish are particularly suited for such a study because embryogenesis can be followed from its very beginning and can be observed easily thanks to transparent egg shells. We report the following findings. (i) The mortality peak occurs in the first 15% of the 75-80 hours of embryogenesis and it is about 50 times higher than the low plateau which follows. (ii) The shape of the age-specific death rate is largely independent of the death level. Presently, little is known about the nature of embryonic defects. However, by reviewing two special cases we show that even small initial defects, e.g. spatial cellular asymmetries or irregularities in the timing of development, carry with them lethal effects in later stages of embryogenesis., Comment: 25 pages, 11 figures

Genetic and environmental factors are traditionally seen as the sole causes of congenital anomalies. In this paper we introduce a third possible cause, namely random "manufacturing" discrepancies with respect to ``design'' values. A clear way to demonstrate the existence of this component is to ``shut'' the two others and to see whether or not there is remaining variability. Perfect clones raised under well controlled laboratory conditions fulfill the conditions for such a test. Carried out for four different species, the test reveals a variability remainder of the order of 10%-20% in terms of coefficient of variation. As an example, the CV of the volume of E.coli bacteria immediately after binary fission is of the order of 10%. In short, ``manufacturing'' discrepancies occur randomly, even when no harmful mutation or environmental factors are involved. Not surprisingly, there is a strong connection between congenital defects and infant mortality. In the wake of birth there is a gradual elimination of defective units and this screening accounts for the post-natal fall of infant mortality. Apart from this trend, post-natal death rates also have humps and peaks associated with various inabilities and defects.\qL In short, infant mortality rates convert the case-by-case and mostly qualitative problem of congenital malformations into a global quantitative effect which, so to say, summarizes and registers what goes wrong in the embryonic phase. Based on the natural assumption that for simple organisms (e.g. rotifers) the manufacturing processes are shorter than for more complex organisms (e.g. mammals), fewer congenital anomalies are expected. Somehow, this feature should be visible on the infant mortality rate. How this conjecture can be tested is outlined in our conclusion., Comment: 43 pages, 9 figures

Infant mortality, by which we understand the postnatal stage during which mortality is declining, is a manifestation and embodiment of congenital abnormalities. Severe defects will translate into death occurring shortly after birth whereas slighter anomalies may contribute to death much later, possibly only in adult age. While for many species birth defects would be nearly impossible to identify, infant mortality provides a convenient global assessment. In the present paper we examine a broad range of species from mammals to fish to gastropods to insects. One of the objectives of our comparative analysis is to test a conjecture suggested by reliability engineering according to which the frequency of defects tends to increase together with the complexity of organisms. For that purpose, we set up experiments specially designed to measure infant mortality. In particular, we two species commonly used as model species in biological laboratories, namely the zebrafish Danio rerio and the rotifer Brachionus plicatilis. For the second, whose number of cells is about hundred times smaller than for the first, we find as expected that the screening effect of the infant phase is of much smaller amplitude. Our analysis also raises a number of challenging questions for which further investigation is necessary. For instance, why is the infant death rate of beetles and mollusks falling off exponentially rather than as a power law as observed for most other species? A possible research agenda is discussed in the conclusion of the paper., Comment: 31 pages, 16 figures

In earlier centuries kings and governments employed astrologists to help them take the best decisions. Present-day governments no longer employ astrologists but still have no clear analytical tool to replace them. Over the past two decades we have developed a methodology for the scientific investigation of recurrent historical events. It consists in two steps. (i) Identification and comparison of historical episodes driven by a common mechanism. (ii) Under the reasonable assumption that what has happened several times in the past is likely to happen again, one then derives testable predictions. This of course is nothing other than the protocol used in experimental science when exploring new phenomena. We believe such a tool can give decision makers much better insight. In the present paper we illustrate this analysis by considering challenges, that span more than a century, to US hegemony in the Pacific. The outcomes suggest that it is only through the sidelining of one of the contenders that the confrontation will end. At the time of writing (late 2018) early evidence of this confrontation is already visible at three levels. (i) Growing US concerns for domestic security that are leading to a new form of McCarthyism. (ii) Political instability due to China-US polarization in several Asian countries as well as in the countries participating in the Belt and Road Initiative. (iii) Tension and sanctions in procurement and trade., Comment: 38 pages, 5 figures

The aim of the plsRglm package is to deal with complete and incomplete datasets through several new techniques or, at least, some which were not yet implemented in R. Indeed, not only does it make available the extension of the PLS regression to the generalized linear regression models, but also bootstrap techniques, leave-one-out and repeated $k$-fold cross-validation. In addition, graphical displays help the user to assess the significance of the predictors when using bootstrap techniques. Biplots (Fig. 4) can be used to delve into the relationship between individuals and variables., Comment: 11 pages, 8 figures

We designed a completely automated Maple ($\geqslant 15$) worksheet for deriving Edgeworth and Cornish-Fisher expansions as well as the acceleration constant of the bootstrap bias-corrected and accelerated technique. It is valid for non-parametric or parametric bootstrap, of any (studentized) statistics that is -a regular enough- function of the mean of an iid sample of an absolutely continuous distribution. This worksheet allowed us to point out one error in the second-order Cornish-Fisher expansion of the studentized mean stated in Theorem 13.5 by Das Gupta in [8, p. 194] as well as lay the stress on the influence of the slight change of the normalizing constant when computing the second-order Edgeworth and Cornish-Fisher expansions of the t-distribution as stated in Theorem 11.4.2 by Lehman and Romano in [14, p. 460]. In addition, we successfully applied the worksheet to a complex maximum likelihood estimator as a first step to derive more accurate confidence intervals in order to enhance quality controls. The worksheet also features export of Maple results into R code. In addition, we provide R code to plot these expansions as well as their increasing rearrangements. All these supplemental materials are available upon request., Comment: 20 pages, 8 figures, code snippet

Investigating the ``physics'' of food crises consists in identifying features which are common to all large-scale food crises. One element which stands out is the fact that during a food crisis there is not only a surge in deaths but also a correlative temporary decline in conceptions and subsequent births. As a matter of fact, birth reduction may even start several months before the death surge and can therefore serve as an early warning signal of an impending crisis. This scenario is studied in three cases of large-scale food crises. Finland (1868), India (1867--1907), China (1960--1961). It turns out that between the regional amplitudes of death spikes and birth troughs there is a power law relationship. This confirms what was already observed for the epidemic of 1918 in the United States (Richmond et al. 2018b). In a second part of the paper we explain how this relationship can be used for the investigation of mass-mortality episodes in cases where direct death data are either uncertain or nonexistent., Comment: 29 pages, 11 figures

Herteliu et al. (2015) have elsewhere analyzed the impact of religious festivals on births in Romania. Here we broaden the analysis (i) by studying the effect of Lent on marriages as well as births (ii) by analyzing a number of other countries which allows a comparison with non-Orthodox countries. We also introduce a new methodology which treats the data in a way that frees the analysis from bias related to seasonal patterns of births and marriages. The comparison between the effects on marriages and conceptions appears of particular interest for it permits to assess the respective weighs of social pressure on one hand and personal leanings on the other hand. Our analysis reveals a strong effect of Lent on marriages with a reduction by 80% in Orthodox countries and 40% in West European Catholic and Protestant countries. Since the influence of Lent on conceptions is independent of any form of direct social control one might expect the effect to be much smaller. In percentage terms it is roughly 10 times smaller than the effect on marriage. The present methodology opens the way to the accurate investigation of the impact of other mobile religious periods (e.g. Ramadan) on various social phenomena (e.g. suicide)., Comment: 16 pages, 7 figures

In the same way as tree rings give us useful information about the climate many decades ago (or even centuries ago in the case of big trees), population pyramids allow us to know birth or death rates several decades earlier. Naturally, they can fulfill such promises only if they have been recorded accurately. That is why we start this study by listing a number of pitfalls that may occur in the process of taking censuses. In this paper our main goal is to show how it is possible to "read" population pyramids. Sudden changes in birth rate give rise to the clearest signatures. This indicator reveals that major tragedies like famines, wars, or epidemics are generally accompanied by a fall in birth rates. Thanks to this observation, population pyramids can be used to identify and gauge the blows suffered by populations and nations. As an illustration of how this works, we compare the population pyramids of North and South Korea. This allows us, among other things, to gauge the scale of the food shortage that North Korea experienced at the end of the 1990s., Comment: 17 pages, 10 figures

Investigations of a possible connection between population density and the propagation and magnitude of epidemics have so far led to mixed and unconvincing results. There are three reasons for that. (i) Previous studies did not focus on the appropriate density interval. (ii) For the density to be a meaningful variable the population must be distributed as uniformly as possible. If an area has towns and cities where a majority of the population is concentrated its average density is meaningless. (iii) In the propagation of an epidemic the initial proportion of susceptibles (that is to say persons who have not developed an immunity) is an essential, yet usually unknown, factor. The assumption that most of the population is susceptible holds only for new strain of diseases. It will be shown that when these requirements are taken care of, the size of epidemics is indeed closely connected with the population density. This empirical observation comes as a welcome confirmation of the classical KMK (Kermack-McKendrick 1927) model. Indeed, one of its key predictions is that the size of the epidemic increases strongly (and in a non linear way) with the initial density of susceptibles. An interesting consequence is that, contrary to common beliefs, in sparsely populated territories, like Alaska, Australia or the west coast of the United states the size of epidemics among native populations must have been limited by the low density even for diseases for which the natives had no immunity (i.e., were susceptibles)., Comment: 16 pages, 7 figures

Here the term "high frequency" refers to daily, weekly or monthly birth data. The fluctuations of daily birth numbers show a succession of spikes and dips which, at least at first sight, looks almost as random as white noise. However in recent times several studies were published, including by the present authors, which have given better insight into how birth is affected by exogenous factors. One of them concerns the way adverse conditions (e.g. famines, diseases, earthquakes, heat waves) temporarily affect the conception capacity of populations, thus producing birth rate troughs 9 months after mortality waves. In addition, religious interdicts (e.g. during the Lent period) lead to reduced conceptions. These as well as other effects raise the hope that we will soon be able to "read" and interpret birth rate patterns just as the Egyptologist Jean-Francois Champollion managed to decipher many (though not all) hieroglyphs., Comment: 23 pages, 10 figures

In a general way at all ages and for almost all diseases, male death rates are higher than female death rates. Here we report a case in which the opposite holds, namely for tuberculosis (TB) mortality between the ages of 5 and 25, female death rates are about two times higher than male rates. What makes this observation of interest is that it occurs in all countries for which data are available (e.g. Britain, Switzerland and United States), and in all years from the end of the 19th century up to the time in the 1960s when TB became a very rare disease in all developed countries. The fact that this regularity holds despite a drastic reduction in the number of deaths is also noteworthy. What is the practical usefulness of this investigation? So far, the reason of this anomaly remains an open question but the effect is so accurate that it can be used for probing the reliability and accuracy of mortality records. This will be explained in the case of developing countries. For instance, it turns out that in South African TB death data as published (and revised) by the "World Health Organization", female deaths were certainly under-estimated by a factor of two., Comment: 13 pages, 4 figures

In 2015 in the United States 612,000 persons died from cancer whereas only 470 died from tuberculosis (TB), a disease which was the main cause of death around 1900. How can one explain such a key discrepancy in treatment progress? A statistical comparison between TB and cancer will give some clues. However, TB and cancer also share several important features. Both TB and cancer can affect several organs, e.g. lungs, brain, bones, intestines, skin. What in cancer is called malignant neoplasm (tumor) is called granuloma in TB. By isolating malignant cells (versus bacteria) from the rest of the body, such clusters protect the host's organism but at the same time they are "secure beachheads" from where malignant cells (versus infected macrophages) can wander off to new locations. Thus, metastatic tumors have a TB parallel in the form of secondary granulomas. In order to investigate more closely this parallel we use the age-specific response of organs. Called spectrometric analysis in a previous paper (Berrut et al. 2017), this method provides information about how fast tumors develop and how serious they become. A convenient characterization of the response to TB of organ j is given by the following (age-dependent) death ratio: Tj(t)=(death by TB of type j)/(all TB deaths) The development of cancer tumors can be described by a similar function Cj(t). We compare the organs' responses in all cases for which specific death data are available. It appears that for the same organ Tj(t) is similar in shape to Cj(t). For instance, with regard to brain tumors, both TB and cancer mortality peak around the age of 10. Such observations may bring to light vulnerabilities in the way the immune system provides protection to various organs., Comment: 22p, 8 figures. An old version was replaced by a new one which is about twice as long. At first the new version was submitted as a new paper, but at the request of the administration a replacement seemed a more appropriate solution

In part 1 we identified a new coupling between death spikes and birth dips that occurs following catastrophic events such as influenza pandemics and earthquakes. Here we seek to characterize some of the key features. We introduce a transfer function defined as the amplitude of the birth trough (the output) divided by the amplitude of the death spike (the input). This has two features: it is always smaller than one so is an attenuation factor and as a function of the amplitude of the death spike, it may be characterized by a power law with exponent close to unity. Since many countries do not publish monthly data, merely annual data, we attempt to extend the analysis to cover such data and how to identify the death-birth coupling. Finally we compare the response to unexpected death spikes and regular seasonal death peaks, such as winter death peaks which occur annually in many countries., Comment: 16 pages, 4 figures

In the wake of the influenza pandemic of 1889-1890 Jacques Bertillon, a pioneer of medical statistics, noticed that after the massive death spike there was a dip in birth numbers around 9 months later which was significantly larger than that which could be explained by the population change as a result of excess deaths. In addition it can be noticed that this dip was followed by a birth rebound a few months later. However having made this observation, Bertillon did not explore it further. Since that time the phenomenon was not revisited in spite of the fact that in the meanwhile there have been several new cases of massive death spikes. The aim here is to analyze these new cases to get a better understanding of this death-birth coupling phenomenon. The largest death spikes occurred in the wake of more recent influenza pandemics in 1918 and 1920, others were triggered by the 1923 earthquakes in Tokyo and the Twin Tower attack on September 11, 2001. We shall see that the first of these events indeed produced an extra dip in births whereas the 9/11 event did not. This disparity highlights the pivotal role of collateral sufferers. In the last section it is shown how the present coupling leads to predictions; it can explain in a unified way effects which so far have been studied separately, as for instance the impact on birth rates of heat waves. Thus, it appears that behind the random appearance of birth rate fluctuations there are in fact hidden explanatory factors., Comment: 27 pages, 13 figures

Separatism is examined in a long-run perspective. Accordingly, many political or economic factors which may be crucial in dealing with short-term episodes can be safely disregarded. Extending an approach pioneered by J. Jenkins, the paper assesses the role of spatial and historical factors. It shows that the means used to stage a separatist struggle are to a notable extent borrowed from former historical episodes, an analysis which supports and illustrates Charles Tilly's thesis of restricted repertoires of action. The purpose of the present paper is to introduce the model, to make it plausible and to demonstrate its potential usefulness by examining a number of critical examples. A more systematic analysis is carried out in a follow-up paper by using a data set that includes about 40 cases of separatist struggles., Comment: 28 pages, 3 figures

In part 1 we have discussed the role played by geographical and historical conditions. Here we wish to test our model and to estimate its parameters. Ti this effect two indexes are introduced. The geographical index is aimed at characterizing the degree of separateness of a given region with respect to the national state to which it belongs. This index turns out to be closely connected to the number of minority-speakers; it is also correlated with the level of separatist disturbances, at least for samples having the same historical background. The purpose of the second index is precisely to specify the role of past episodes in shaping current separatist outbreaks. To a large extent, current episodes are modeled on former ones; typically this process of semi-replication appears to be characterized by a "memory" that extends over at least one and a half century. Note that this study concentrates on the occurrence and forms of separatist struggles rather than on their short-term political causes. In so doing, it follows a methodological track that has been pioneered by Stanley Lieberson (1985, the "stardom" paradigm) and Charles Tilly (1993, the "traffic jam" paradigm)., Comment: 26 pages, 9 figures