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The Foundations of Probability with Black Swans
Graciela Chichilnisky
Journal of Probability and Statistics , 2010, DOI: 10.1155/2010/838240
Abstract: We extend the foundation of probability in samples with rare events that are potentially catastrophic, called black swans, such as natural hazards, market crashes, catastrophic climate change, and species extinction. Such events are generally treated as ‘‘outliers’’ and disregarded. We propose a new axiomatization of probability requiring equal treatment in the measurement of rare and frequent events—the Swan Axiom—and characterize the subjective probabilities that the axioms imply: these are neither finitely additive nor countably additive but a combination of both. They exclude countably additive probabilities as in De Groot (1970) and Arrow (1971) and are a strict subset of Savage (1954) probabilities that are finitely additive measures. Our subjective probabilities are standard distributions when the sample has no black swans. The finitely additive part assigns however more weight to rare events than do standard distributions and in that sense explains the persistent observation of ‘‘power laws’’ and ‘‘heavy tails’’ that eludes classic theory. The axioms extend earlier work by Chichilnisky (1996, 2000, 2002, 2009) to encompass the foundation of subjective probability and axiomatic treatments of subjective probability by Villegas (1964), De Groot (1963), Dubins and Savage (1965), Dubins (1975) Purves and Sudderth (1976) and of choice under uncertainty by Arrow (1971). 1. Introduction Black swans are rare events with important consequences, such as market crashes, natural hazards, global warming, and major episodes of extinction. This article is about the foundations of probability when catastrophic events are at stake. It provides a new axiomatic foundation for probability requiring sensitivity both to rare and frequent events. The study culminates in Theorem 6.1, that proves existence and representation of a probability satisfying three axioms. The last of these axioms requires sensitivity to rare events, a property that is desirable but not respected by standard probabilities. The article shows the connection between those axioms and the Axiom of Choice at the foundation of Mathematics. It defines a new type of probabilities that coincide with standard distributions when the sample is populated only by relatively frequent events. Generally, however, they are a mixture of countable and finitely additive measures, assigning more weight to black swans than do normal distributions, and predicting more realistically the incidence of “outliers,” “power laws,” and “heavy tails” [1, 2]. The article refines and extends the formulation of probability in an
Quality control in the nucleus
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050329-02
Abstract: Protein quality control systems, which fix or rid the cell of unfolded, misfolded, or improperly modified proteins, have long been known to exist both in prokaryotes and eukaryotes. But they have been found only in compartments where protein synthesis occurs: the cytoplasm, the endoplasmic reticulum, and the mitochondria, senior author Dan Gottschling, of Seattle's Fred Hutchinson Cancer Research Center, told The Scientist."It largely has been thought that as proteins are being made, they're being sampled and destroyed right during the process of folding and assembly," said Gottschling. "We wanted to find a place where proteins that become old could be recognized and degraded, and the nucleus is the only compartment in which that could potentially happen, because there's no protein synthesis there."The team conducted what they called a "virtual genetic screen." It means that we didn't do anything except read the literature," joked Gottschling.Their approach was a rather smart one, according to Christian Hirsch of the Max-Delbrück Center for Molecular Medicine, who coauthored a related preview in the same issue of Cell. "They looked at screens that had found suppressors of temperature-sensitive mutant proteins that are functional in the cell, but that are degraded because they are recognized by a quality control system," Hirsch told The Scientist. Those results pointed to a gene that was an excellent candidate for a component of a degradation system of misfolded proteins."First we looked for nuclear proteins in yeast that were temperature sensitive," said Gottschling. "Then we looked at the subset in which there had been a suppressor screened, and we looked for a common gene that was a suppressor of all these different temperature-sensitive mutations. We found one gene, and that was SAN1, which turned out to be a ubiquitin-ligase." The team later discovered that San1 only targets aberrant proteins - not wildtype ones - and that it only functions in the nucleus."The m
Transcription factor moonlights
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050527-01
Abstract: "Here, we show for the first time that a transcription factor has a function in the DNA damage response that is completely independent of its transcriptional activity," Ze'ev Ronai, of the Burnham Institute in La Jolla, Calif., told The Scientist.For its transcriptional regulatory roles, ATF2 is activated by phosphorylation via the JNK/p38 pathway. The group found alternate phosphorylation sites at serines 490 and 498 that are generally recognized by the kinase ataxia telangiectasia mutated (ATM), which is implicated in double-strand break (DSB) repair. They found ATF2 phosphorylated at those serines localizing at irradiation-induced DSB repair foci. When they inhibited JNK/p38 or disrupted transcriptional regulatory activity of ATF2, the protein continued to show up at these DSBs and maintained proper S-phase checkpoint, indicating that its role in DNA damage response is uncoupled from its transcriptional activities.Using antibodies to ATF2 and RNA interference, Ronai and colleagues studied ATF2 in cultured mammalian cells subjected to ionizing radiation and in ATF2 mutant mice. The results showed that ATF2 is phosphorylated by ATM and that ATF2 plays an important role in the double-strand break repair process.In the last decade, evidence supporting the idea that certain proteins - so-called moonlighting proteins - can perform multiple jobs has mounted. The novelty of this paper is that it demonstrates that the two functions of ATF2 are uncoupled."ATF2 doesn't need its transcriptional activity to participate in the DNA damage response," said Dan Mercola at the Sidney Kimmel Cancer Center, San Diego, Calif., who was not involved in the study. "The authors show that a nontranscriptionally active form appears to be aggregating at DNA damage sites. The studies are very beautiful, and the data are very convincing."William Bonner at the National Cancer Institute's Center for Cancer Research, who did not participate in the research, said the paper was an interesting devel
MicroRNAs linked to cancer
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050610-01
Abstract: Todd Golub at the Dana-Farber Cancer Institute and the Broad Institute of the Massachusetts Institute of Technology and Harvard and coauthors report that they could accurately classify human cancers with an novel assay that they say could become a powerful diagnostic tool. In a second paper, the groups of Gregory Hannon at Cold Spring Harbor and Scott Hammond at the University of North Carolina describe elevated levels of miRNAs in human lymphoma samples and cell lines. Experimental overexpression of those miRNAs caused cancer in a mouse model.The highly conserved miRNAs and their link to cancer has been in people's minds for many years, Paul Meltzer at the National Human Genome Research Institute told The Scientist. "Previous works have reported changes in miRNA expression associated with cancer, but this new constellation of papers provides very strong support for that idea. Golub's paper provides a very nice database in terms of the pattern of expression of the 217 annotated miRNAs in human cancers," said Meltzer, who wrote an accompanying News and Views commentary.A third paper by Joshua Mendell at The Johns Hopkins University School of Medicine and colleagues unravels the connection between miRNA and c-Myc, a transcription regulator known to be overexpressed in human cancers. Most importantly, they identify an elusive miRNA target.To study miRNAs expression, Golub and his colleagues developed a bead-based flow cytometric profiling assay that first amplifies the miRNAs in the cell and then captures them on fluorescently labeled beads. "This method enabled us to measure the expression of a great number of miRNAs from samples including several human cancers," Golub told The Scientist. "We found a highly informative pattern of miRNA expression that varied across tumor types and reflected the developmental lineage as well as the differentiation state of the tumors. The patterns of which miRNAs are turned on and off in a cell can be diagnostic for whether that cell i
Zinc finger nucleases correct genes
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050404-01
Abstract: Michael Holmes and his colleagues at Richmond, Ca. - based Sangamo Biosciences corrected a defective version of the IL2R-gamma receptor gene, which is mutant in children with X-linked severe combined immunodeficiency. Sangamo had used zinc-finger proteins before in several instances, among them, to inhibit specific single gene expression in vivo."With our technology platform here at Sangamo, we can basically engineer zinc-finger proteins to recognize virtually any sequence," Holmes, the senior author of the study, told The Scientist. "Here, we show that gene correction can be done at a specific site of the genome, where a mutation occurs, and at high frequency."The authors report that more than 18% of the cells were correctly modified without selection, of which 7% acquired the desired modification in both chromosomes."This is the highest level of gene targeting I've seen," said Dana Carroll of the University of Utah, who described the paper as "terrific." Recent estimates have found an absolute rate of gene targeting in human cells of 3 to 5%.According to Carroll, the key for the researchers' success was their ability to introduce a break in the desired gene. "Normally, gene targeting is done by isolating and manipulating a segment of the gene in the laboratory, and then putting it back into cells, hoping that homologous recombination will lead to the replacement of the endogenous gene with this manipulated gene," explained Carroll. "The problem is that the frequency of that sort of gene targeting is typically quite low - about one in a million cells gets the targeting event."Sangamo's strategy built upon two fundamental observations previously made by other researchers: that a double-strand break stimulates homologous recombination at a target and that such breaks can be made with designed zinc-finger nucleases.Although other researchers had been successful at targeting specific sequences, no one had designed the zinc-finger protein nucleases from scratch, Sriniva
E. coli ages
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050204-02
Abstract: "Until recently, people thought that bacteria cannot age," said Martin Ackermann, of the ETH Zentrum, who was not involved in the study. "Then, we published this paper showing aging in bacteria with asymmetric division. The next question was if a visible morphological asymmetry was necessary or whether all bacteria could age. This new paper suggests that aging can actually be found in all bacterial cells, maybe in all living cells."In the PLoS study, Eric Stewart, of INSERM and Paris 5 René Descartes University, and his colleagues used automated time-lapse microscopy to follow individual bacteria throughout nine subsequent cycles of reproduction and measured several physical parameters in over 35,000 cells. They found that daughter cells that inherited the "old pole" of a dividing parent cell - a pole coming from the previous generation in contrast to one newly formed - had a reduced rate of growth, a reduced rate of offspring formation, and an increased risk of dying, compared to cells inheriting new poles.The team also discovered that although division in E. coli does not show morphological asymmetries, it is characterized by functional asymmetries, which has not been described in this species before. That could be how the organism satisfies one of the requirements of the established hypothesis of aging: only organisms that undergo asymmetric division, and produce offspring that are smaller than the parents and thus need to grow and develop before reproducing themselves, can age. E. coli, however, does not have smaller offspring, nor does it undergo a juvenile phase.Thomas Nystr?m, of G?teborg University, acknowledged that the paper casts some doubt on the idea that E. coli divides in a perfectly symmetrical fashion so that the daughter cells display equal fitness. "However, it appears a bit early to announce that E. coli belongs to organisms exhibiting mandatory replicative aging and that immortality is too costly or mechanistically impossible in natural organism
Sperm fusion protein identified
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050314-01
Abstract: Masaru Okabe of Osaka University and coworkers used the fusion-inhibiting monoclonal antibody OBF13 and gene-cloning techniques to identify an antigen on mice sperm involved in fusion. "The antigen Izumo is a novel protein of the immunoglobulin superfamily," Okabe, the senior author of the study, told The Scientist. Proteins belonging to this family are membrane-anchored, and are usually involved in cell-cell adhesion.Okabe has been seeking the sperm protein since 1987, when his group reported that OBF13 bound to an unknown molecule on the sperm head. Further studies revealed that the antibody did not prevent sperm binding, but did inhibit fertilization. This gave the researchers a clue as to the protein's involvement in fusion. "For the next ten years, I tried very hard to find the antigen [that OBF13 bound], but I couldn't clone the gene," explained Okabe. "Then, I rested for five years, until Noakazu Inoue, the first author of the paper, joined our group. Inoue tried the procedure again, with newer and more sensitive techniques, and succeeded."In recent years, Okabe and his team have also studied egg proteins. In 2000 they published a paper in Science, reporting that CD9—a protein on the egg surface—was essential for sperm-egg fusion. A group in France also published a report presenting similar results in the same issue. "We had this egg protein involved in fusion, but on the sperm side, nothing was clear," said Okabe. "With the discovery of Izumo, the mechanism of sperm-egg fusion is now ready to be examined."In their latest paper, the researchers established the role of Izumo in fertilization by producing a knockout mouse line. The experiments rendered unambiguous results. The mice were healthy, but the males were sterile. Their sperm bound to, and penetrated the zona pellucida but could not fuse with the egg.Paul Primakoff of the University of California at Davis, who was not involved in the research, welcomed the paper, which deals with a field in which there
Fast track to longevity
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050308-01
Abstract: Pere Puigserver of Johns Hopkins University and colleagues found that fasting signals induce the SIRT1 protein in the liver. This protein is one of the mammalian homologues of Sir2, known to extend lifespan in yeast and worms. SIRT1 then interacts with the coactivator PGC-1alpha, which, in turn, triggers glucose production, a key metabolic change associated with extended lifespan."Our work provides a novel connection between PGC-1alpha, a protein involved in the food-deprivation response, and SIRT1, a protein linked to aging in lower organisms," Puigserver told The Scientist.SIRT1, which is an NAD+-dependent histone deacetylase, had already been associated with calorie restriction and longevity in mammals. Induced by food deprivation, it inhibits stress-induced apoptotic cell death in vitro and promotes fat mobilization in vitro and in vivo. However, it was unclear how SIRT1 might be involved in pathways such as gluconeogenesis and glycolysis, which are directly affected by calorie restriction in mammals.In the Nature paper, the research team provides a connection between SIRT1 and these pathways. Moreover, they show that SIRT1 acts as a sensor of food deprivation."During starvation, there is an increase in pyruvate, a nutrient signal that induces translation of SIRT1, and an increase in NAD+, which functions as a substrate and as an activator of SIRT1. The active SIRT1 interacts with PGC-1alpha, deacetylates it, and keeps it active, promoting glucose production in the liver," explained Puigserver. With these results, the researchers showed that besides the hormonal control of PGC-1 through glucocorticoids and glucagon during fasting, there is a nutrient control as well, which targets SIRT1.Marc Tatar of Brown University, who did not participate in the research, found the role of SIRT1 in nutrient sensing impressive. "There are hormonal inputs for sensing nutrients that are released systemically and circulate throughout the body," Tatar told The Scientist. "But what
Science retracts highly cited paper
Graciela Flores
Genome Biology , 2005, DOI: 10.1186/gb-spotlight-20050617-01
Abstract: The research, which had been cited 227 times, reported evidence for one of the two prevalent hypotheses explaining the molecular correlates of Cockayne syndrome, a disorder that leads to death in early childhood.The suggestion is that one of the underlying causes of Cockayne syndrome is the cell's inability to perform transcription-coupled repair of oxidative damage, according to first author Priscilla Cooper of the Lawrence Berkeley National Laboratory. The alternative hypothesis states that the proteins involved in transcription-coupled repair are also important for efficient basal transcription in the absence of any kind of DNA damage."There is some evidence on both sides of that question," said Cooper, "but data from my and other labs suggest that the main conclusions of the paper are probably correct. However, the field as a whole, and certainly my laboratory, has to go back and reinvestigate the whole issue."This is not the first time that a paper by Leadon has been withdrawn from publication. In March 2003, Leadon himself retracted a 1998 Mutation Research/DNA Repair paper, taking sole responsibility for what he called a "systemic error that could have influenced, if not accounted for," some of the findings. That month, Leadon resigned from his position as director of radiobiology at the University of North Carolina at Chapel Hill after an investigating committee found that a 1998 Sciencepaper–also later retracted–had contained results that he had fabricated and falsified. Leadon appealed the committee's findings to the Office of Research Integrity (ORI) at the US Department of Health and Human Services.It was Leadon who suggested retracting the 1998 Science paper, according to Katrina Kelner of Science. "Although he was appealing the committee's findings, he still felt that it was appropriate to retract it." Leadon could not be reached for comment for this article.This week's retraction, which Leadon declined to sign, comes after the committee issued new cha
Rat olfaction molded early
Graciela Flores
Genome Biology , 2004, DOI: 10.1186/gb-spotlight-20050708-01
Abstract: Kevin Franks and Jeffry Isaacson of the University of California, San Diego, found that in newborn rats, early olfactory experiences caused changes in the relative amounts of two types of glutamate receptors in lateral olfactory tract fibers. Specifically, they observed a decrease in the number of NMDA receptors, which are believed to be important in synaptic plasticity and long-term changes, relative to AMPA receptors, which mediate fast synaptic transmission. The researchers suggest this phenomenon might be associated with "olfactory imprinting," the strong attachment to maternal odors that occurs early in mammalian development."The ability of the animal to smell caused downregulation in the number of NMDA receptors," Isaacson told The Scientist. "Very early in rat development, there is quite robust NMDA receptor-mediated, long-term potentiation from the sensory synapses into the cortex, but later in life, after the animal has had time to smell, the loss of NMDA receptors makes it difficult to induce any long-term changes in the strength of the synaptic transmission."To study the synaptic modifications that occur during development, the authors took advantage of the layered architecture of the rat's olfactory cortex. "The stratification makes this a nice experimental model to use," said Kurt Illig of the University of Virginia, who did not participate in the research. "The authors were able to selectively stimulate different types of cells and look at the development of the responses for each of those layers independently in an in vitro preparation. The loss of NMDA receptors they observed could be a mechanism by which early olfactory experience shapes the cortex to respond to particular odors."To test for the role of sensory experience in the synaptic changes, the authors occluded one of the nostrils in newborn rats, depriving one side of the brain of olfactory stimulation, and compared the two sides of the brain in each animal. "This is a great technique because
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