Analysis of the Karmarkar-Karp Differencing Algorithm

The Karmarkar-Karp differencing algorithm is the best known polynomial time heuristic for the number partitioning problem, fundamental in both theoretical computer science and statistical physics. We analyze the performance of the differencing algorithm on random instances by mapping it to a nonlinear rate equation. Our analysis reveals strong finite size effects that explain why the precise asymptotics of the differencing solution is hard to establish by simulations. The asymptotic series emerging from the rate equation satisfies all known bounds on the Karmarkar-Karp algorithm and projects a scaling $n^{-c\ln n}$, where $c=1/(2\ln2)=0.7213...$. Our calculations reveal subtle relations between the algorithm and Fibonacci-like sequences, and we establish an explicit identity to that effect.Comment: 9 pages, 8 figures; minor change

Number partitioning as random energy model

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local random energy'' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.Comment: 8+2 pages, 9 figures, PDF onl

Diagnosis of Fanconi Anemia: Mutation Analysis by Next-Generation Sequencing

Fanconi anemia (FA) is a rare genetic instability syndrome characterized by developmental defects, bone marrow failure, and a high cancer risk. Fifteen genetic subtypes have been distinguished. The majority of patients (≈85%) belong to the subtypes A (≈60%), C (≈15%) or G (≈10%), while a minority (≈15%) is distributed over the remaining 12 subtypes. All subtypes seem to fit within the “classical” FA phenotype, except for D1 and N patients, who have more severe clinical symptoms. Since FA patients need special clinical management, the diagnosis should be firmly established, to exclude conditions with overlapping phenotypes. A valid FA diagnosis requires the detection of pathogenic mutations in a FA gene and/or a positive result from a chromosomal breakage test. Identification of the pathogenic mutations is also important for adequate genetic counselling and to facilitate prenatal or preimplantation genetic diagnosis. Here we describe and validate a comprehensive protocol for the molecular diagnosis of FA, based on massively parallel sequencing. We used this approach to identify BRCA2, FANCD2, FANCI and FANCL mutations in novel unclassified FA patients

The interrelation between clinical presentation and neurophysiology of posthypoxic myoclonus

ObjectivePosthypoxic myoclonus (PHM) in the first few days after resuscitation can be divided clinically into generalized and focal (uni- and multifocal) subtypes. The former is associated with a subcortical origin and poor prognosis in patients with postanoxic encephalopathy (PAE), and the latter with a cortical origin and better prognosis. However, use of PHM as prognosticator in PAE is hampered by the modest objectivity in its clinical assessment. Therefore, we aimed to obtain the anatomical origin of PHM with use of neurophysiological investigations, and relate these to its clinical presentation. MethodsThis study included 20 patients (56 18 y/o, 68% M, 2 survived, 1 excluded) with EEG-EMG-video recording. Three neurologists classified PHM into generalized or focal PHM. Anatomical origin (cortical/subcortical) was assessed with basic and advanced neurophysiology (Jerk-Locked Back Averaging, coherence analysis). ResultsClinically assessed origin of PHM did not match the result obtained with neurophysiology: cortical PHM was more likely present in generalized than in focal PHM. In addition, some cases demonstrated co-occurrence of cortical and subcortical myoclonus. Patients that recovered from PAE had cortical myoclonus (1 generalized, 1 focal). InterpretationHypoxic damage to variable cortical and subcortical areas in the brain may lead to mixed and varying clinical manifestations of myoclonus that differ of those patients with myoclonus generally encountered in the outpatient clinic. The current clinical classification of PHM is not adequately refined to play a pivotal role in guiding treatment decisions to withdraw care. Our neurophysiological characterization of PHM provides specific parameters to be used in designing future comprehensive studies addressing the potential role of PHM as prognosticator in PAE

Mixed gastric carcinomas show similar chromosomal aberrations in both their diffuse and glandular components

Gastric cancer is one of the most frequent malignancies in the world. Nonetheless, the knowledge of the molecular events involved in the development of gastric carcinoma is far from complete. One of the hallmarks of gastric cancer is chromosomal instability resulting in abnormal DNA copy number changes throughout the genome. Mixed gastric carcinomas constitute a rare histological entity, containing the two main histological phenotypes (diffuse and intestinal). Very little is known about the underlying mechanisms of phenotypic divergence in these mixed tumours. To the best of our knowledge only E-Cadherin mutations were implicated so far in the divergence of these tumours and nothing is known about the involvement of chromosome copy number changes in the two divergent histological components. In this study, we compared the DNA copy number changes, in the two different components (diffuse and intestinal) of mixed gastric carcinomas by microarray - comparative genomic hybridisation (array CGH). The analysis of 12 mixed gastric carcinomas showed no significant differences in array CGH profiles between the diffuse and intestinal components of mixed carcinomas. This supports the idea that the phenotypic divergence within mixed gastric carcinomas is not caused by DNA chromosomal aberrations.Portuguese Foundation for Science and Technology (FCT), grant POCTI/CBO/ 41179/2001 and by Dutch Cancer Society grant – KWF2004-305

Biogeochemie von Phosphat im Unterboden am Beispiel deutscher Dauerdüngungsversuche

Unterböden von Ackerstandorten verfügen über große Vorräte an Phosphat (P), allerdings ist nach wie vor unklar, ob, in welchem Umfang und unter welchen Bedingungen diese Nährstoffreserven im Unterboden zur Ernährung unserer Ackerkulturen beitragen. Wir vermuten, dass einerseits langjährige P-Limitierung dazu führen kann, dass mehr P aus dem Unterboden aufgenommen wird, dass aber andererseits die Zugänglichkeit zu P-Reserven im Unterboden auch abhängig ist von der Versorgung mit anderen Nährstoffen, wie z.B. Stickstoff (N) und Kalium (K). Um diese Hypothesen zu testen, beprobten wir unter anderem zwei Statische Nährstoffmangelversuche in Thyrow (Brandenburg) und Gießen (Hessen). Wir entnahmen Bodenproben bis in 100 cm Tiefe, aus Varianten, die seit über 60 Jahren entweder NPK, NK oder PK Düngung erhalten haben. Für diese Proben bestimmten wir die P Pools nach Hedley et al. (1), sowie die Sauerstoffisotopie des Phosphats nach Extraktion mit 1M HCl (δ18OHCl P), welches eine Differenzierung in primäre und sekundäre (d.h. nach vorherigem biologischem Cycling neu ausgefällte) P-Minerale ermöglicht. An beiden Standorten beobachteten wir, dass in den NK-gedüngten Varianten die Vorräte der labilen P Pools aus dem Hedley’schen Extraktionsschema im Unterboden (30 – 100 cm) 10 – 60% geringer waren als in den NPK-gedüngten Varianten. Die Vorräte an HCl P in den NK-Varianten waren jedoch v.a. in Thyrow bis zu 70% höher, während gleichzeitg die δ18OHCl P Werte deutlich niedriger waren als in den NPK-Varianten. Diese niedrigeren Isotopensignaturen deuten auf hauptsächlich primäre P-Minerale hin, sodass wir unsere Annahme von höherem P-Cycling im Unterboden bei Mangel im Oberboden widerrufen müssen. In den PK-gedüngten Varianten beobachteten wir, dass die Vorräte an labilem P im Unterboden 117% (Thyrow) und 22% (Gießen) größer waren als in der NPK-Variante. Dies stützt unsere zweite Annahme von einer Limitierung der P-Aufnahme aus dem Unterboden aufgrund des Mangels an anderen Nährstoffen, allerdings ergaben sich hier keine klaren Auswirkungen auf die δ18OHCl P Signatur des Phosphats. Im Folgenden sollen diese Beobachtungen nun an weiteren Standorten und unter weiteren Einflussparametern getestet werden. Zusammenfassend zeigen jedoch schon unsere bisherigen Ergebnisse, dass die effiziente Ausnutzung von P-Reserven im Unterboden nur unter optimaler Nährstoffversorgung im Oberboden erfolgt

High-resolution aCGH and expression profiling identifies a novel genomic subtype of ER negative breast cancer.

BACKGROUND: The characterization of copy number alteration patterns in breast cancer requires high-resolution genome-wide profiling of a large panel of tumor specimens. To date, most genome-wide array comparative genomic hybridization studies have used tumor panels of relatively large tumor size and high Nottingham Prognostic Index (NPI) that are not as representative of breast cancer demographics. RESULTS: We performed an oligo-array-based high-resolution analysis of copy number alterations in 171 primary breast tumors of relatively small size and low NPI, which was therefore more representative of breast cancer demographics. Hierarchical clustering over the common regions of alteration identified a novel subtype of high-grade estrogen receptor (ER)-negative breast cancer, characterized by a low genomic instability index. We were able to validate the existence of this genomic subtype in one external breast cancer cohort. Using matched array expression data we also identified the genomic regions showing the strongest coordinate expression changes ('hotspots'). We show that several of these hotspots are located in the phosphatome, kinome and chromatinome, and harbor members of the 122-breast cancer CAN-list. Furthermore, we identify frequently amplified hotspots on 8q22.3 (EDD1, WDSOF1), 8q24.11-13 (THRAP6, DCC1, SQLE, SPG8) and 11q14.1 (NDUFC2, ALG8, USP35) associated with significantly worse prognosis. Amplification of any of these regions identified 37 samples with significantly worse overall survival (hazard ratio (HR) = 2.3 (1.3-1.4) p = 0.003) and time to distant metastasis (HR = 2.6 (1.4-5.1) p = 0.004) independently of NPI. CONCLUSION: We present strong evidence for the existence of a novel subtype of high-grade ER-negative tumors that is characterized by a low genomic instability index. We also provide a genome-wide list of common copy number alteration regions in breast cancer that show strong coordinate aberrant expression, and further identify novel frequently amplified regions that correlate with poor prognosis. Many of the genes associated with these regions represent likely novel oncogenes or tumor suppressors.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Cerebral activations related to ballistic, stepwise interrupted and gradually modulated movements in parkinson patients

Patients with Parkinson's disease (PD) experience impaired initiation and inhibition of movements such as difficulty to start/stop walking. At single-joint level this is accompanied by reduced inhibition of antagonist muscle activity. While normal basal ganglia (BG) contributions to motor control include selecting appropriate muscles by inhibiting others, it is unclear how PD-related changes in BG function cause impaired movement initiation and inhibition at single-joint level. To further elucidate these changes we studied 4 right-hand movement tasks with fMRI, by dissociating activations related to abrupt movement initiation, inhibition and gradual movement modulation. Initiation and inhibition were inferred from ballistic and stepwise interrupted movement, respectively, while smooth wrist circumduction enabled the assessment of gradually modulated movement. Task-related activations were compared between PD patients (N = 12) and healthy subjects (N = 18). In healthy subjects, movement initiation was characterized by antero-ventral striatum, substantia nigra (SN) and premotor activations while inhibition was dominated by subthalamic nucleus (STN) and pallidal activations, in line with the known role of these areas in simple movement. Gradual movement mainly involved antero-dorsal putamen and pallidum. Compared to healthy subjects, patients showed reduced striatal/SN and increased pallidal activation for initiation, whereas for inhibition STN activation was reduced and striatal-thalamo-cortical activation increased. For gradual movement patients showed reduced pallidal and increased thalamo-cortical activation. We conclude that PD-related changes during movement initiation fit the (rather static) model of alterations in direct and indirect BG pathways. Reduced STN activation and regional cortical increased activation in PD during inhibition and gradual movement modulation are better explained by a dynamic model that also takes into account enhanced responsiveness to external stimuli in this disease and the effects of hyper-fluctuating cortical inputs to the striatum and STN in particular

A Conserved Mito-Cytosolic Translational Balance Links Two Longevity Pathways.

Slowing down translation in either the cytosol or the mitochondria is a conserved longevity mechanism. Here, we found a non-interventional natural correlation of mitochondrial and cytosolic ribosomal proteins (RPs) in mouse population genetics, suggesting a translational balance. Inhibiting mitochondrial translation in C. elegans through mrps-5 RNAi repressed cytosolic translation. Transcriptomics integrated with proteomics revealed that this inhibition specifically reduced translational efficiency of mRNAs required in growth pathways while increasing stress response mRNAs. The repression of cytosolic translation and extension of lifespan from mrps-5 RNAi were dependent on atf-5/ATF4 and independent from metabolic phenotypes. We found the translational balance to be conserved in mammalian cells upon inhibiting mitochondrial translation pharmacologically with doxycycline. Lastly, extending this in vivo, doxycycline repressed cytosolic translation in the livers of germ-free mice. These data demonstrate that inhibiting mitochondrial translation initiates an atf-5/ATF4-dependent cascade leading to coordinated repression of cytosolic translation, which could be targeted to promote longevity

Longitudinal characteristics of T2-FLAIR mismatch in IDH-mutant astrocytomas: Relation to grade, histopathology, and overall survival in the GLASS-NL cohort.

BACKGROUND: The T2-FLAIR mismatch sign is defined by signal loss of the T2-weighted hyperintense area with Fluid-Attenuated Inversion Recovery (FLAIR) on magnetic resonance imaging, causing a hypointense region on FLAIR. It is a highly specific diagnostic marker for IDH-mutant astrocytoma and is postulated to be caused by intercellular microcystic change in the tumor tissue. However, not all IDH-mutant astrocytomas show this mismatch sign and some show the phenomenon in only part of the lesion. The aim of the study is to determine whether the T2-FLAIR mismatch phenomenon has any prognostic value beyond initial noninvasive molecular diagnosis. METHODS: Patients initially diagnosed with histologically lower-grade (2 or 3) IDH-mutant astrocytoma and with at least 2 surgical resections were included in the GLASS-NL cohort. T2-FLAIR mismatch was determined, and the growth pattern of the recurrent tumor immediately before the second resection was annotated as invasive or expansive. The relation between the T2-FLAIR mismatch sign and tumor grade, microcystic change, overall survival (OS), and other clinical parameters was investigated both at first and second resection. RESULTS: The T2-FLAIR mismatch sign was significantly related to Grade 2 (80% vs 51%), longer post-resection median OS (8.3 vs 5.2 years), expansive growth, and lower age at second resection. At first resection, no relation was found between the mismatch sign and OS. Microcystic change was associated with areas of T2-FLAIR mismatch. CONCLUSIONS: T2-FLAIR mismatch in IDH-mutant astrocytomas is correlated with microcystic change in the tumor tissue, favorable prognosis, and Grade 2 tumors at the time of second resection