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Communications in Mathematical Physics 2022The derived categories of toric varieties admit semi-orthogonal decompositions coming from wall-crossing in GIT. We prove that these decompositions satisfy a...
The derived categories of toric varieties admit semi-orthogonal decompositions coming from wall-crossing in GIT. We prove that these decompositions satisfy a Jordan-Hölder property: the subcategories that appear, and their multiplicities, are independent of the choices made. For Calabi-Yau toric varieties wall-crossing instead gives derived equivalences and autoequivalences, and mirror symmetry relates these to monodromy around the GKZ discriminant locus. We formulate a conjecture equating intersection multiplicities in the discriminant with the multiplicities appearing in certain semi-orthogonal decompositions. We then prove this conjecture in some cases.
PubMed: 35250038
DOI: 10.1007/s00220-021-04298-2 -
BMC Medical Genomics Jun 2011With the advent of whole-genome analysis for profiling tumor tissue, a pressing need has emerged for principled methods of organizing the large amounts of resulting...
BACKGROUND
With the advent of whole-genome analysis for profiling tumor tissue, a pressing need has emerged for principled methods of organizing the large amounts of resulting genomic information. We propose the concept of multiplicity measures on cancer and gene networks to organize the information in a clinically meaningful manner. Multiplicity applied in this context extends Fearon and Vogelstein's multi-hit genetic model of colorectal carcinoma across multiple cancers.
METHODS
Using the Catalogue of Somatic Mutations in Cancer (COSMIC), we construct networks of interacting cancers and genes. Multiplicity is calculated by evaluating the number of cancers and genes linked by the measurement of a somatic mutation. The Kamada-Kawai algorithm is used to find a two-dimensional minimum energy solution with multiplicity as an input similarity measure. Cancers and genes are positioned in two dimensions according to this similarity. A third dimension is added to the network by assigning a maximal multiplicity to each cancer or gene. Hierarchical clustering within this three-dimensional network is used to identify similar clusters in somatic mutation patterns across cancer types.
RESULTS
The clustering of genes in a three-dimensional network reveals a similarity in acquired mutations across different cancer types. Surprisingly, the clusters separate known causal mutations. The multiplicity clustering technique identifies a set of causal genes with an area under the ROC curve of 0.84 versus 0.57 when clustering on gene mutation rate alone. The cluster multiplicity value and number of causal genes are positively correlated via Spearman's Rank Order correlation (rs(8) = 0.894, Spearman's t = 17.48, p < 0.05). A clustering analysis of cancer types segregates different types of cancer. All blood tumors cluster together, and the cluster multiplicity values differ significantly (Kruskal-Wallis, H = 16.98, df = 2, p < 0.05).
CONCLUSION
We demonstrate the principle of multiplicity for organizing somatic mutations and cancers in clinically relevant clusters. These clusters of cancers and mutations provide representations that identify segregations of cancer and genes driving cancer progression.
Topics: Algorithms; Cluster Analysis; Humans; Mutation; Neoplasms
PubMed: 21714919
DOI: 10.1186/1755-8794-4-52 -
Birth Defects Research Jul 2022Conjoined triplets are among the rarest of human malformations, as are asymmetric or parasitic conjoined twins. Based on a very modest corpus of recent literature, we... (Review)
Review
Conjoined triplets are among the rarest of human malformations, as are asymmetric or parasitic conjoined twins. Based on a very modest corpus of recent literature, we applied the embryonic disk model of conjoined twinning to 10 previously reported cases involving asymmetric anatomical multiplications to determine whether they concerned conjoined twins or conjoined triplets. In spite of their phenotypic similarities, we diagnosed four of these cases as conjoined twins and three of them as conjoined triplets. In the remaining three cases, no definite diagnosis could be made, as essential information was lacking from the reports. We conclude that it is not necessarily the expected duplication or triplication of structures that points to the correct diagnosis in these cases, but the number and mutual position of the hearts they presented with. Considering their rarity we stress to thoroughly investigate and describe internal (dys)morphology in novel cases of (asymmetric) conjoined twins and triplets to further unravel their pathogenicity and come to the correct diagnoses.
Topics: Heart; Humans; Twins, Conjoined
PubMed: 35766259
DOI: 10.1002/bdr2.2066 -
Genes Jun 2021The process of non-allelic gene conversion acts on homologous sequences during recombination, replacing parts of one with the other to make them uniform. Such concerted...
The process of non-allelic gene conversion acts on homologous sequences during recombination, replacing parts of one with the other to make them uniform. Such concerted evolution is best described as paralogous ribosomal RNA gene unification that serves to preserve the essential house-keeping functions of the converted genes. Transposed elements (TE), especially short interspersed elements (SINE) that have more than a million copies in primate genomes, are a significant source of homologous units and a verified target of gene conversion. The consequences of such a recombination-based process are diverse, including multiplications of functional TE internal binding domains and, for evolutionists, confusing divergent annotations of orthologous transposable elements in related species. We systematically extracted and compared 68,097 insertions in various primates looking for potential events of TE gene conversion and discovered 98 clear cases of - gene conversion, including 64 cases for which the direction of conversion was identified (e.g., S conversion to Y). Gene conversion also does not necessarily affect the entire homologous sequence, and we detected 69 cases of partial gene conversion that resulted in virtual hybrids of two elements. Phylogenetic screening of gene-converted s revealed three clear hotspots of the process in the ancestors of Catarrhini, Hominoidea, and gibbons. In general, our systematic screening of orthologous primate loci for gene-converted TEs provides a new strategy and view of a post-integrative process that changes the identities of such elements.
Topics: Alu Elements; Animals; Evolution, Molecular; Gene Conversion; Humans; Primates
PubMed: 34208107
DOI: 10.3390/genes12060905 -
Cellular and Molecular Life Sciences :... Sep 2007alpha-Synuclein belongs to a small group of natively unfolded proteins that can transiently bind to lipid membranes and acquire a partial alpha-helical conformation.... (Review)
Review
alpha-Synuclein belongs to a small group of natively unfolded proteins that can transiently bind to lipid membranes and acquire a partial alpha-helical conformation. Under certain pathogenic conditions, alpha-synuclein aggregates to form oligomers and insoluble fibrils with increased ss-sheet configuration. Although genetic mutations and multiplications of the gene have been found in familial cases, the mechanism by which this protein aggregates in sporadic cases of Parkinson's disease, dementia with Lewy bodies and multisystem atrophy is not fully understood. Here we review the function of alpha-synuclein and recent insight into the mechanisms by which it aggregates.
Topics: Humans; Lewy Bodies; Parkinson Disease; Protein Processing, Post-Translational; Protein Structure, Tertiary; alpha-Synuclein
PubMed: 17605001
DOI: 10.1007/s00018-007-7217-5 -
Multimedia Tools and Applications 2022The traditional method for learning the multiplication tables is a repetitive and boring task. Teachers try to find new methods to motivate children in this tedious...
The traditional method for learning the multiplication tables is a repetitive and boring task. Teachers try to find new methods to motivate children in this tedious duty, and one of the lines to consider is to integrate en- tertainment into educational processes. This work presents a new multimedia interaction approach in order to allow children to practice these math opera- tions and have fun. The learning process has been gamified by means of two mini-games designed for mobile platforms, based on meromictic or repetitive learning. The genre of these mini-games have been selected according to chil- dren preferences: one turn-based fighting and other throwing-objects game. A series of proposed multiplications have to be solved during the play to per- form the player actions. Moreover, in order to support learning engagement, both have been visualized through Augmented Reality, combining real and virtual reality. This paper discusses the good results of mixing entertainment with some learning tasks, due to the engagement of the children to the mobile based games. A pilot study has been performed in order to evaluate the learn- ing effectiveness and usability of the proposal. Results support that playing the video games makes this tedious multiplication practice more enjoyable and attractive for children so they improve their math skills.
PubMed: 33814967
DOI: 10.1007/s11042-021-10821-3 -
Science Bulletin Nov 2021Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant...
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solutions of linear systems of equations and matrix-vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on the variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansätz for efficiently finding the ground state, and show the solution verification. Our algorithms are especially suitable for linear algebra problems with sparse matrices, and have wide applications in machine learning and optimisation problems. The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation. We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations. We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.
PubMed: 36654109
DOI: 10.1016/j.scib.2021.06.023 -
International Journal of Molecular... Aug 2023Parkinson's disease (PD) pathology is characterized by the loss of dopaminergic neurons of the nigrostriatal system and accumulation of Lewy bodies (LB) and Lewy...
Parkinson's disease (PD) pathology is characterized by the loss of dopaminergic neurons of the nigrostriatal system and accumulation of Lewy bodies (LB) and Lewy neurites (LN), inclusions mainly composed of alpha-synuclein (α-Syn) fibrils. Studies linking the occurrence of mutations and multiplications of the α-Syn gene () to the onset of PD support that α-Syn deposition may play a causal role in the disease, in line with the hypothesis that disease progression may correlate with the spreading of LB pathology in the brain. Interestingly, LB accumulate posttranslationally modified forms of α-Syn, suggesting that α-Syn posttranslational modifications impinge on α-Syn aggregation and/or toxicity. Here, we aimed at investigating changes in α-Syn phosphorylation, nitration and acetylation in mice subjected to nigral stereotaxic injections of adeno-associated viral vectors inducing overexpression of human α-Syn (AAV-hα-Syn), that model genetic PD with multiplications. We detected a mild increase of serine (Ser) 129 phosphorylated α-Syn in the substantia nigra (SN) of AAV-hα-Syn-injected mice in spite of the previously described marked accumulation of this PTM in the striatum. Following AAV-hα-Syn injection, tyrosine (Tyr) 125/136 nitrated α-Syn accumulation in the absence of general 3-nitrotirosine (3NT) or nitrated-Tyr39 α-Syn changes and augmented protein acetylation abundantly overlapping with α-Syn immunopositivity were also detected.
Topics: Animals; Humans; Mice; alpha-Synuclein; Disease Models, Animal; Lewy Bodies; Parkinson Disease; Phosphorylation; Protein Processing, Post-Translational
PubMed: 37686236
DOI: 10.3390/ijms241713435 -
Viruses Jul 2019Knowledge of the time of HIV-1 infection and the multiplicity of viruses that establish HIV-1 infection is crucial for the in-depth analysis of clinical prevention...
Knowledge of the time of HIV-1 infection and the multiplicity of viruses that establish HIV-1 infection is crucial for the in-depth analysis of clinical prevention efficacy trial outcomes. Better estimation methods would improve the ability to characterize immunological and genetic sequence correlates of efficacy within preventive efficacy trials of HIV-1 vaccines and monoclonal antibodies. We developed new methods for infection timing and multiplicity estimation using maximum likelihood estimators that shift and scale (calibrate) estimates by fitting true infection times and founder virus multiplicities to a linear regression model with independent variables defined by data on HIV-1 sequences, viral load, diagnostics, and sequence alignment statistics. Using Poisson models of measured mutation counts and phylogenetic trees, we analyzed longitudinal HIV-1 sequence data together with diagnostic and viral load data from the RV217 and CAPRISA 002 acute HIV-1 infection cohort studies. We used leave-one-out cross validation to evaluate the prediction error of these calibrated estimators versus that of existing estimators and found that both infection time and founder multiplicity can be estimated with improved accuracy and precision by calibration. Calibration considerably improved all estimators of time since HIV-1 infection, in terms of reducing bias to near zero and reducing root mean squared error (RMSE) to 5-10 days for sequences collected 1-2 months after infection. The calibration of multiplicity assessments yielded strong improvements with accurate predictions (ROC-AUC above 0.85) in all cases. These results have not yet been validated on external data, and the best-fitting models are likely to be less robust than simpler models to variation in sequencing conditions. For all evaluated models, these results demonstrate the value of calibration for improved estimation of founder multiplicity and of time since HIV-1 infection.
Topics: AIDS Vaccines; Evolution, Molecular; Genetic Variation; HIV Infections; HIV-1; Humans; Models, Statistical; Mutation; Phylogeny; Sequence Analysis; Time Factors; Viral Load
PubMed: 31277299
DOI: 10.3390/v11070607 -
Optics Express Apr 2016In this paper, we show fast signal reconstruction for compressive holography using a graphics processing unit (GPU). We implemented a fast iterative...
In this paper, we show fast signal reconstruction for compressive holography using a graphics processing unit (GPU). We implemented a fast iterative shrinkage-thresholding algorithm on a GPU to solve the ℓ and total variation (TV) regularized problems that are typically used in compressive holography. Since the algorithm is highly parallel, GPUs can compute it efficiently by data-parallel computing. For better performance, our implementation exploits the structure of the measurement matrix to compute the matrix multiplications. The results show that GPU-based implementation is about 20 times faster than CPU-based implementation.
PubMed: 27137282
DOI: 10.1364/OE.24.008437