Chromosomal heteromorphisms and DNA polymorphisms have been utilized to identify the mechanisms that lead to formation of human ovarian teratomas and to construct a gene-centromere map of chromosome 1 by using those teratomas that arise by meiotic nondisjunction. Of 61 genetically informative ovarian teratomas, 21.3% arose by nondisjunction at meiosis I, and 39.3% arose by meiosis II nondisjunction. Eight polymorphic marker loci on chromosome 1p and one marker on 1q were used to estimate a gene-centromere map. The results show clear linkage of the most proximal 1p marker (NRAS) and the most proximal 1q marker (D1S61) to the centromere at a distance of 14 cm and 20 cm, respectively. Estimated gene-centromere distances suggest that, while recombination occurs normally in ovarian teratomas arising by meiosis II errors, ovarian teratomas arising by meiosis I nondisjunction have altered patterns of recombination. Furthermore, the estimated map demonstrates clear evidence of chiasma interference. Our ...

Feb 07, · On the left side, nondisjunction occurs during meiosis II. On the right side, nondisjunction occurs during meiosis I. Tweety / Creative Commons Attribution-Share Alike Nondisjunction Causes. Nondisjunction occurs when some aspect of the spindle assembly checkpoint (SAC) fails. The SAC is a molecular complex that holds a cell in anaphase until all of the chromosomes . May 16, · Sex chromosome aneuploidy is the term for an abnormal number of sex chromosomes. Normally, females have two X chromosomes, while males have one X and one Y. Nondisjunction can cause individuals to be born female with one X (Turner syndrome), female with three X chromosomes (Trisomy X), male with XXY (Klinefelter syndrome), or male with XYY (XYY.. Nondisjunction of sex chromosomes in meiosis in Weipa

Aneuploidy is the leading cause of pregnancy loss and birth defects in humans. At least 5% of all recognized pregnancies are aneuploid. Maternal meiosis is especially error-prone and the rate of chromosome missegregation increases exponentially with advancing maternal age. Despite its clinical significance, the mechanisms underlying maternal age-dependent segregation errors are not understood. One hypothesis is that cohesion deteriorates with advancing maternal age and homologous chromosomes that do not maintain chaismata segregate randomly during meiosis. With Drosophila as a model organism, I have used techniques developed in our laboratory to experimentally age oocytes. To accelerate loss of cohesion with age, I utilized mutant flies with slightly compromised meiotic cohesion. A standard genetic test was utilized to assess errors in meiotic chromosome segregation after oocytes were subjected to the aging regimen. My objective was to determine whether aging of oocytes with slightly compromised ...

Looking for Chromosomal nondisjunction? Find out information about Chromosomal nondisjunction. Failure of homologous chromosomes to separate symmetrically during cell division, with both ending up in the same daughter cell instead of in each daughter cell Explanation of Chromosomal nondisjunction

Recent Publications Subramanian, V.V. & S.E. Bickel. 2009 Heterochromatin-mediated association of achiasmate chromosomes declines with age when cohesion is compromised. Genetics 2009 Apr;181(4):1207-18. Subramanian VV, Bickel SE. Aging predisposes oocytes to meiotic nondisjunction when the cohesin subunit SMC1 is reduced. PLoS Genet. 2008 Nov;4(11):e1000263. Epub 2008 Nov 14.. Page SL, Khetani RS, Lake CM, Nielsen RJ, Jeffress JK, Warren WD, Bickel SE, Hawley RS. Corona is required for higher-order assembly of transverse filaments into full-length synaptonemal complex in Drosophila oocytes. PLoS Genet. 2008 Sep 19;4(9):e1000194.. Gause, M., Webber, H.A., Misulovin, Z., Haller, G., Rollins, R.A., Eissenberg, J.C., Bickel S.E. and Dorsett, D. Functional links between Drosophila Nipped-B and cohesin in somatic and meiotic cells. Chromosoma (2008) 117:51-66.. Khetani, R.S. and Bickel, S.E. Regulation of meiotic cohesion and chromosome core morphogenesis during pachytene in Drosophila oocytes. J Cell ...

Attempts to identify genetic contributors to human meiotic nondisjunction have met with little, if any, success. Thus, recent reports linking Down syndrome to maternal polymorphisms at either of two folate metabolism enzymes, methylenetetrahydrofolate reductase (MTHFR) and methionine synthase reduct …

We report on a fetus with 47,XX,+15 chromosome abnormality detected on chorionic villus sampling (CVS). The pregnancy was terminated at 15.5 weeks of gestation and chromosome analysis done on amniocytes and fetal tissues showed a karyotype 46,XX/47,XX,+15. Autopsy showed multiple abnormalities. Short-arm polymorphisms of the three number 15 chromosomes were highly informative in the delineation of parental origin and the stage of meiotic error. Using fluorescent in situ hybridization (FISH) with D15Z1 and a chromosome 15 painting probe, in addition to DA/DAPI and G-banding, we were able to show that the trisomic conceptus was derived through maternal meiosis I error. The trisomic state was then partially corrected by the loss of one of the two maternal 15s resulting in mosaicism without uniparental disomy (UPD). Striking differences in the proportion of trisomic cells in kidneys, blood, intestine, and skin, and lower proportions of trisomic cells in transformed and frozen than in fresh tissues, ...

What are Non-Disjunction Disorders?! Non-disjunction is a failure of chromosomes to separate properly (i.e there is an imbalance of genetic information) Occurs when: Homologous chromosomes fail to separate properly in Anaphase I Sister chromatids fail to separate properly during Anaphase II Having abnormal amounts of karyotypes will overload the cells, which may result in: The death of the zygote A person with a non-disjunction disorder being born

We have analyzed the origin, in a patient with 49,XXXXY, of the four X-chromosomes by means of recombinant DNA techniques. We found a maternal origin of the four X-chromosomes due to non-disjunctions in the first and second meiotic divisions.

Notice the number of chromosomes in each gamete. Notice the difference in what is occuring with the spindle. How does non-disjunction in meiosis I differ from non-disjunction in meiosis II?. ...

Wu, S.; Scheible, W.-R.; Schindelasch, D.; van Den Daele, H.; de Veylder, L.; Baskin, T. I.: A conditional mutation in Arabidopsis thaliana separase induces chromosome non-disjunction, aberrant morphogenesis and cyclin B1;1 stability. Development 137 (6), pp. 953 - 961 (2010 ...

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Looking for online definition of nondisjunction in the Medical Dictionary? nondisjunction explanation free. What is nondisjunction? Meaning of nondisjunction medical term. What does nondisjunction mean?

Aneuploidy denotes an abnormal number of chromosomes in cells. The presence of 3 homologous chromosomes in a cell, rather than the normal pair, is termed trisomy. Monosomy is the presence of only 1 member of any pair of autosomes or only 1 sex chromosome. The absence of a single autosome is almost always lethal to the embryo; an extra autosome is often catastrophic to surviving embryos. Aneuploidy of sex chromosomes (eg, X, XXX, XXY, and XYY) is less disastrous. Monosomies and trisomies are generally caused by mechanical accidents that increase or decrease the number of chromosomes in the gametes. The most common type of accident, meiotic nondisjunction, results from a disruption of chromosome movement during meiosis (see Fig 6-5).. Trisomy 21 syndrome, or Down syndrome, is the most common chromosomal syndrome in humans; it has an overall incidence of 1:800 live births. Clinical features of this syndrome have been well known since John Langdon Down originally described them in 1866.. The most ...

This pretty muffin is waiting for her family! She is healthy, with no heart condition noted in her records. She has brown hair and hazel eyes, and is already up and learning to walk! Her records indicate meiotic nondisjunction, but this is just a fancy word for what happens to create Down syndrome genetically. She is considered higher functioning and is really doing well. She is an orphanage favorite, and the director has asked for a family to save her from the institution. ...

Frequency and distribution of chromosome abnormalities in human oocytes[10] It was previously shown that more than half of the human oocytes obtained from IVF patients of advanced reproductive age are aneuploid, due to meiosis I and meiosis II errors. The present paper further confirms that 61.8% of the oocytes tested by fluorescent probes specific for chromosomes 13, 16, 18, 21 and 22 are abnormal, representing predominantly chromatid errors, which are the major source of aneuploidy in the resulting embryos. Almost half of the oocytes with meiosis I errors (49.3%) are prone to sequential meiosis II errors, which may lead to aneuploidy rescue in 30.8% of the cases. Half of the detected aneuploidies (49.8%) are of complex nature with involvement of two or more chromosomes, or the same chromosome in both meiotic divisions. The aneuploidy rates for individual chromosomes are different, with a higher prevalence of chromosome 21 and 22 errors. The origin of aneuploidy for the individual chromosomes ...

Frequency and distribution of chromosome abnormalities in human oocytes[10] It was previously shown that more than half of the human oocytes obtained from IVF patients of advanced reproductive age are aneuploid, due to meiosis I and meiosis II errors. The present paper further confirms that 61.8% of the oocytes tested by fluorescent probes specific for chromosomes 13, 16, 18, 21 and 22 are abnormal, representing predominantly chromatid errors, which are the major source of aneuploidy in the resulting embryos. Almost half of the oocytes with meiosis I errors (49.3%) are prone to sequential meiosis II errors, which may lead to aneuploidy rescue in 30.8% of the cases. Half of the detected aneuploidies (49.8%) are of complex nature with involvement of two or more chromosomes, or the same chromosome in both meiotic divisions. The aneuploidy rates for individual chromosomes are different, with a higher prevalence of chromosome 21 and 22 errors. The origin of aneuploidy for the individual chromosomes ...

Examples of recessive X-linked diseases are hemophilia, Fragile X, and Duchenne muscular dystrophy.. In contrast, dominant X-linked diseases are transmitted by affected women to 50% of their daughters and sons, but affected males do not transmit it to their sons. Examples of diseases linked dominant X are Rett syndrome, incontinentia pigmenti, pseudohyperparathyroidism, and vitamin D-resistant rachitism.. As an example of Y-linked disorders, there are some AZF region microdeleted in the long arm of the Y-chromosome. In this case, the only option to avoid transmission to the offspring is female sex selection.. 2) Chromosome rearrangements - constitutional chromosomal abnormalities are present in up to 0.9% in newborns, and are associated with 50-60% of first trimester miscarriages. Most of these aneuploidies are a result of a meiotic non-disjunction event, but about 1/500 individuals carry a balanced structural rearrangement as reciprocal and Robertsonian translocations. Although most present ...

Thirteen X-linked mutants have been isolated in Drosophila melanogaster which render male and homozygous female larvae sensitive to the mutagen methyl methanesulfonate. Their characterization and preliminary assignment to functional groups is described. Four of these mutants are alleles of mei-41 (Baker and Carpenter 1972). Like previously isolated alleles of this locus, these mutants reduce fertility and increase loss and nondisjunction of the X-chromosome in homozygous females. The remaining mutants have been tentatively assigned to six functional groups (two mutants to the mus(1)101 locus, two to mus(1)102, two to mus(1)103, and one each to mus(1)104, mus(1)105, and mus(1)106). Several of the complementation groups can be distinguished on the basis of nondisjunction and cross sensitivity to mutagens. Females homozygous for the mei-41, mus(1)101 and mus(1)102 mutants exhibit elevated levels of nondisjunction. Mutants belonging to complementation groups mei-41, mus(1)101, and mus(1)104 are ...

THE processes of meiotic pairing, synapsis, and recombination are essential for progression through the first meiotic division and the formation of haploid gametes. Unpaired, asynapsed chromatin is transcriptionally silenced (Shiu et al. 2001; Baarends et al. 2005), and the aberrant repression of key genes regulating meiotic progression can cause premature arrest of the meiotic cell cycle (Turner et al. 2005; Burgoyne et al. 2009). A minimum of one crossover per bivalent is needed to ensure its stable orientation at the metaphase plate (Mather 1938; Nicklas 1974), and homologous chromosome pairs that lack an obligate crossover are susceptible to nondisjunction at the first meiotic division (Hawley et al. 1994; Lamb et al. 1996; Ross et al. 1996). As a consequence, meiotic pairing, synapsis, and recombination defects are directly linked to infertility and chromosome aneuploidy (Hassold and Hunt 2001; Cohen et al. 2006; Burgoyne et al. 2009; Handel and Schimenti 2010), outcomes with severe ...

Posted by Tricia on December 01, 2003 at 00:21:29:. In Reply to: Re: Thread on Down Syndrome posted by Cheyenne on November 30, 2003 at 21:49:16:. Okay, in an attempt to get the true facts as they are known out here, I am going to list information from the National Down Syndrome Societys web page on the causes of Down syndrome. These are the people that know guys, not some misinformed doctor telling a mom she caused Ds with poor prenatal care, or someone talking about research that is so secret she can not reveal its source. If you think for a minute that there are not doctors out there who are misinformed about Down syndrome....I am here to tell you that any mom I know (and I am one) of a child with Ds knows more about the issue than their own OBGYN or pediatrician. The only doctors I see that know more than I about my sons conditions are the developmental pediatrician. Here is the info from the site;. Nondisjunction. Nondisjunction is a faulty cell division which results in an embryo with ...

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This is the first report that adaptive mutagenesis can arise by chromosomal nondisjunction, a phenomenon previously associated exclusively with DNA

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RanGTP is important for chromosome‐dependent spindle assembly in Xenopus extracts. Here we report on experiments to determine the role of the Ran pathway on microtubule dynamics in Drosophila oocytes and embryos. Females expressing a dominant‐negative form of Ran have fertility defects, suggesting that RanGTP is required for normal fertility. This is not, however, because of a defect in acentrosomal meiotic spindle assembly. Therefore, RanGTP does not appear to be essential or sufficient for the formation of the acentrosomal spindle. Instead, the most important function of the Ran pathway in spindle assembly appears to be in the tapering of microtubules at the spindle poles, which might be through regulation of proteins such as TACC and the HURP homolog, Mars. One consequence of this spindle organization defect is an increase in the nondisjunction of achiasmate chromosomes. However, the meiotic defects are not severe enough to cause the decreased fertility. Reductions in fertility occur ...

RanGTP is important for chromosome-dependent spindle assembly in Xenopus extracts. Here we report on experiments to determine the role of the Ran pathway on microtubule dynamics in Drosophila oocytes and embryos. Females expressing a dominant-negative form of Ran have fertility defects, suggesting that RanGTP is required for normal fertility. This is not, however, because of a defect in acentrosomal meiotic spindle assembly. Therefore, RanGTP does not appear to be essential or sufficient for the formation of the acentrosomal spindle. Instead, the most important function of the Ran pathway in spindle assembly appears to be in the tapering of microtubules at the spindle poles, which might be through regulation of proteins such as TACC and the HURP homolog, Mars. One consequence of this spindle organization defect is an increase in the nondisjunction of achiasmate chromosomes. However, the meiotic defects are not severe enough to cause the decreased fertility. Reductions in fertility occur because ...

FZR1 is an anaphase-promoting complex (APC) activator best known for its role in the mitotic cell cycle at M-phase exit, in G1, and in maintaining genome integrity. Previous studies also established that it prevents meiotic resumption, equivalent to the G2/M transition. Here we report that mouse oocytes lacking FZR1 undergo passage through meiosis I that is accelerated by ∼1 h, and this is due to an earlier onset of spindle assembly checkpoint (SAC) satisfaction and APCCDC20 activity. However, loss of FZR1 did not compromise SAC functionality; instead, earlier SAC satisfaction was achieved because the bipolar meiotic spindle was assembled more quickly in the absence of FZR1. This novel regulation of spindle assembly by FZR1 led to premature bivalent attachment to microtubules and loss of kinetochore-bound MAD2. Bivalents, however, were observed to congress poorly, leading to nondisjunction rates of 25%. We conclude that in mouse oocytes FZR1 controls the timing of assembly of the bipolar ...

Down syndrome may be understood best as a syndrome complex of genetic and epigenetic origin with several characteristic neurodevelopmental manifestations. DS is a chromosomal disorder. Majority of cases result from complete trisomy of chromosome 21 due to nondisjunction during meiosis. A region on chromosome 21 proximal to 21q22.3, known as down syndrome critical region, is considered responsible for pathogenesis of DS. In approximately 95% of cases of trisomy 21, the nondisjunction is of maternal origin; which occurs randomly during meiosis. Rarely, in about 1% of cases, nondisjunction may occur after fertilization is complete, resulting in two different cell lines, and this is referred to as mosaicism. Approximately 4% of the time, DS results from complete or partial translocation of chromosome 21 to another chromosome. This so called Robertsonian translocations occurs when the long arms of two acrocentric chromosomes fuse at the centromere. The two short arms get lost as a result. Although ...

Patau syndrome is a syndrome caused by a chromosomal abnormality, in which some or all of the cells of the body contain extra genetic material from chromosome 13. The extra genetic material disrupts normal development, causing multiple and complex organ defects. This can occur either because each cell contains a full extra copy of chromosome 13 (a disorder known as trisomy 13 or trisomy D), or because each cell contains an extra partial copy of the chromosome (i.e., Robertsonian translocation) or because of mosaic Patau syndrome. Full trisomy 13 is caused by nondisjunction of chromosomes during meiosis (the mosaic form is caused by nondisjunction during mitosis). Like all nondisjunction conditions (such as Down syndrome and Edwards syndrome), the risk of this syndrome in the offspring increases with maternal age at pregnancy, with about 31 years being the average. Patau syndrome affects somewhere between 1 in 10,000 and 1 in 21,700 live births. Of those fetuses that do survive to gestation and ...

Down syndrome (DS) is a main cause of human prenatal and postnatal morbidity and mortality, and a leading cause of birth defects and mental retardation. There is increasing evidence that maternal meiosis is an error prone process that is most sensitive to the effect of exogenous factors at the time of chromosomal segregation, which is around conception. In addition to environmental factors, various genetic factors have been described which seem to influence the nondisjunction rate during meiosis. The first data of DS in the Oman yielded a high prevalence among live births. The birth prevalence of Trisomy 21 in Oman with 1:454 newborns is, perhaps, the highest reported so far. We have performed a case control study based on a structured questionnaire, which covers socio demographics, family history and potential risk factors. We identified increased maternal age as one factor for the birth of a DS child. The sex ratio among Down Syndrome children showed a predominance of boys of 1.37:1 (m:f ) as ...

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Fact #2: Down syndrome is not a disease; it is a genetic condition. You cant catch Down syndrome. A baby has Down syndrome the minute the sperm meets the egg. Its not something a woman can develop during pregnancy because it is present at the moment of conception; as soon as the cells divide. The most common type of Down syndrome is Nondisjunction Trisomy 21 or T21; it occurs because of incorrect chromosome division during meiosis. It results in the fertilized egg having three 21st chromosomes instead of two. The other types of Down syndrome are Translocation T21, Mosaicism (Mosaic Down Syndrome), and Partial Trisomy 21. ...

Summary: None of these properties applies to division. Most commonly, this refers to the property of multiplication distributing over addition or subtraction, such that \(x(a+b) = xa + xb\). The distributive property of multiplication over addition formula explains the distributive law in a simple manner and click on the link below the formula to use the distributive law calculator. If I have 21 of something and I take 8 of them away, Im left with 13 of that something. So, those are going to simplify to 13y. Division math trivia, Adding Lesson Plan 1st grade, tuturial distributive property 6th grade, difference quotient calculator, pre-algebra collecting like terms, free online maths test for year 10. The distributive property does not apply to division in the same since as it does with multiplication, but the idea of distributing or breaking apart can be used in division. So, this whole thing simplified, using a little bit of distributive property and combining similar or … What is the ...

Premise (1) is true. Conclusion (3) sounds false. There are a couple of things that one can do about this odd argument. One can embrace the conclusion but insist that the conditional is only used materially, and is trivially true because the antecedent is false. One can-and I think this is going to be the most common reaction among philosophers-reject the inference of (3) from (2). But a lot of ordinary people will balk at (2)-the disjunction introduction step, where from p, we conclude p or q for any q.. Denying disjunction introduction neatly undercuts the above argument, as well as removing the oddity that everything can be proved from a contradiction.. But blocking disjunction introduction is a mistake, because we need disjunction introduction. Suppose that we say ...

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TY - JOUR. T1 - Recurrent triploidy of maternal origin. AU - Pergament, Eugene. AU - Confino, Edmond. AU - Zhang, John Xingqi. AU - Roscetti, Liza. AU - Chen, Pei Xien. AU - Wellman, David. N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.. PY - 2000. Y1 - 2000. N2 - We report the occurrence of triploid preimplantation embryos following in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) in a woman with two previously-identified triploid conceptuses which spontaneously underwent fetal demise at 10 and 23 weeks gestation. An error in maternal meiosis II is proposed as the most likely cause. Copyright (C) 2000 John Wiley and Sons, Ltd.. AB - We report the occurrence of triploid preimplantation embryos following in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) in a woman with two previously-identified triploid conceptuses which spontaneously underwent fetal demise at 10 and 23 weeks gestation. An error in maternal meiosis II is ...

Meiosis is a reductional division that produces haploid gametes or spores from diploid progenitor cells. Ploidy reduction is achieved by one round of DNA replication, followed by two consecutive nuclear divisions (Meiosis I and II), producing four daughter cells (Roeder 1997). Crossovers promote the formation of chiasma which serves as a physical linkage between two homologs and opposes the spindle generated forces that pull apart the homolog pairs. This opposing set of forces provides the tension necessary to promote proper disjunction of homolog pairs at Meiosis I (Petronczki et al. 2003). Failure to maintain at least one crossover per homolog pair increases the probability of nondisjunction, resulting in aneuploid gametes (Serrentino and Borde 2012). Although crossovers are important for chromosome segregation, nonexchange chromosomes have been observed to segregate accurately forming viable gametes (Hawley et al. 1992; Davis and Smith 2003; Kemp et al. 2004; Newnham et al. 2010; ...

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Author Summary For traits with complex genetic inheritance it has generally proven very difficult to identify the majority of the specific causative variants involved. A range of hypotheses have been put forward to explain this so-called

It has been known for more than half a century that the risk of conceiving a child with trisomy increases with advanced maternal age However the origin of the high susceptibility to nondisjunction of whole chromosomes and precocious separation of sister chromatids leading to aneuploidy in aged oocytes and embryos derived from them cannot be traced back to a single disturbance and mechanism Instead analysis of recombination patterns of meiotic chromosomes of spread oocytes from embryonal ovary and of origins and exchange patterns of extra chromosomes in trisomies as well as morphological and molecular studies of oocytes and somatic cells from young and aged females show chromosome specific risk patterns and cellular aberrations related to the chronological age of the female In addition analysis of the function of meiotic and cell cycle regulating genes in oogenesis and the study of the spindle and chromosomal status of maturing oocytes suggest that several events contribute synergistically to ...

Occurring in approximately 1 in 700 live births, trisomy 21 is by far the most common trisomy. In 94% of patients, it is caused by nondisjunction, with 3 copies of chromosome 21 present in all cells. In 4.5% of patients, the extra chromosome 21 is part of a translocation, the most common of which involves chromosomes 14 and 21.. Although most children with trisomy 21 have normal birthweight and birth length, they have a characteristic facial appearance, which includes brachycephaly, a flattened occiput, a depressed nasal bridge, upslanting palpebral fissures, epicanthal folds, and a large protruding tongue. Other features include short, broad hands, often with a transverse palmar crease, and a wide gap between the first and second toes. Hypotonia may be severe enough to cause significant feeding problems, with some infants requiring nasogastric feeding. Individuals with trisomy 21 have many health issues. In the newborn period, concerns include the following:. ...

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Notice the number of chromosomes in each gamete. Notice the difference in what is occuring with the spindle. How does non-disjunction in meiosis I differ from non-disjunction in meiosis II?. ...

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An extra chromosome also called trisomy can cause a wide range of developmental disorders. Learn about trisomy conditions in babies.

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Benchmade. The 535 Bugout has become one of the most popular knives in Benchmades line up and to celebrate, theyve created a new Gold Class version full of upgrades. Munin pattern Damasteel and ghost carbon fiber handles are coupled with smoked gray PVD coated liners, pocket clip, and hardware. Blue anodized titanium thumb studs and barrel spacers round out this Unlimited Limited Gold Class model. A Bugout of this caliber is sure to be a bright spot in anyones collection ...

Amended 8-9-1977 by Ord. No. 77-12; 12-14-1977 by Ord. No. 77-20; 4-13-1982 by Ord. No. 82-6; 11-27-1984 by Ord. No. 84-16; 11-27-1984 by Ord. No. 84-17; 2-23-1988 by Ord. No. 88-2; 6-12-1990 by Ord. No. 90-10; 11-12-1991 by Ord. No. 91-24; 3-9-1993 by Ord. No. 93-7; 5-25-1993 by Ord. No. 93-20; 5-9-1995 by Ord. No. 95-18; 12-19-1995 by Ord. No. 95-49; 11-28-2001 by Ord. No. 2001-45; 8-27-2002 by Ord. No. 2002-27; 7-22-2003 by Ord. No. 2003-12; 4-27-2004 by Ord. No. 2004-10; 10-27-2006 by Ord. No. 2006-46; 2-13-2007 by Ord. No. 2007-01; 2-26-2008 by Ord. No. 2008-01; 11-10-2008 by Ord. No. 2008-40; 2-23-2010 by Ord. No. 2010-01; 4-24-2012 by Ord. No. 2012-18; 12-18-2012 by Ord. No. 2012-34; 3-11-2014 by Ord. No. 2014-02; 12-22-2014 by Ord. No. 2014-20 ...

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how to simplifying algebraic expressions using the Distributive Property, examples and step by step solutions, Intermediate Algebra

Zero knowledge proofs are an important building block in many cryptographic applications. Unfortunately, when the proof statements become very large, existing zero-knowledge proof systems easily reach their limits: either the computational overhead, the memory footprint, or the required bandwidth exceed levels that would be tolerable in practice. We present an interactive zero-knowledge proof system for boolean and arithmetic circuits, called MacnCheese, with a focus on supporting large circuits. Our work follows the commit-and-prove paradigm instantiated using information-theoretic MACs based on vector oblivious linear evaluation to achieve high efficiency. We additionally show how to optimize disjunctions, with a general OR transformation for proving the disjunction of $m$ statements that has communication complexity proportional to the longest statement (plus an additive term logarithmic in $m$). These disjunctions can further be \emph{nested}, allowing efficient proofs about complex ...

Die Universität zu Köln ist eine Exzellenzuniversität mit dem klassischen Fächerspektrum einer Volluniversität. Als eine der größen Hochschulen Europas arbeitet sie in Forschung und Lehre auch international auf höchstem Niveau.