Enumeration of set-theoretic solutions to the Yang-Baxter equation

We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang-Baxter equation of small size. We show that there are 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.Comment: 11 pages, 8 table

Enumeration of set-theoretic solutions to the Yang-Baxter equation

Funding: The second author is partially supported by PICT 2018-3511 and is also a Junior Associate of the ICTP. The third author acknowledges support of NYU-ECNU Institute of Mathematical Sciences at NYU–Shanghai and he is supported in part by PICT 2016-2481 and UBACyT 20020170100256BA.We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang-Baxter equation of small size. We show that there are 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.PostprintPeer reviewe

Economic activity and congenital anomalies: An ecologic study in Argentina

In this study, we analyze the association between industrial activity and the occurrence of 34 congenital anomalies. We selected 21 counties in Argentina during 1982-1994 and examined a total of 614,796 births in these counties in consecutive series. We used the International Standard Industrial Classification of All Economic Activities as an indicator of exposure to 80 specific industrial activities. Incidence rate ratios for each congenital anomaly were adjusted by the socioeconomic level of the county according to a census index of social deprivation. For a given exposure/anomaly association to be considered as significant and relevant, the exposure had to be a statistically significant risk for the occurrence of the anomaly and an increase in the birth prevalence rate of the congenital anomaly type involved had to be observed in those counties where the putative causal activity was being performed. Significant associations (p < 0.01) were identified between textile industry and anencephaly, and between the manufacture of engines and turbines and microcephaly. These observations are consistent with previous reports on occupational exposure, and their further investigation by means of case-control studies is recommended.Instituto Multidisciplinario de Biología Celula

Aquaporin 5 Interacts with Fluoride and Possibly Protects Against Caries

Aquaporins (AQP) are water channel proteins and the genes coding for AQP2, AQP5, and AQP6 are clustered in 12q13. Since AQP5 is expressed in serous acinar cells of salivary glands, we investigated its involvement in caries. DNA samples from 1,383 individuals from six groups were studied. Genotypes of eight single nucleotide polymorphisms covering the aquaporin locus were tested for association with caries experience. Interaction with genes involved in enamel formation was tested. The association between enamel microhardness at baseline, after creation of artificial caries lesion, and after exposure to fluoride and the genetic markers in AQP5 was tested. Finally, AQP5 expression in human whole saliva, after exposure to fluoride in a mammary gland cell line, which is known to express AQP5, and in Wistar rats was also verified. Nominal associations were found between caries experience and markers in the AQP5 locus. Since these associations suggested that AQP5 may be inhibited by levels of fluoride in the drinking water that cause fluorosis, we showed that fluoride levels above optimal levels change AQP5 expression in humans, cell lines, and rats. We have shown that AQP5 is involved in the pathogenesis of caries and likely interact with fluoride.Fil: Anjomshoaa, Ida. University of Pittsburgh; Estados UnidosFil: Briseño Ruiz, Jessica. University of Pittsburgh; Estados UnidosFil: Deeley, Kathleen. University of Pittsburgh; Estados UnidosFil: Poletta, Fernando Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; ArgentinaFil: Mereb, Juan C.. Provincia de Río Negro. Ministerio de Salud. Hospital de Área El Bolsón ; ArgentinaFil: Leite, Aline L.. Universidade de Sao Paulo; BrasilFil: Barreta, Priscila A. T.. Universidade de Sao Paulo; BrasilFil: Silva, Thelma L.. Universidade de Sao Paulo; BrasilFil: Dizak, Piper. University of Pittsburgh; Estados UnidosFil: Ruff, Timothy. University of Pittsburgh; Estados UnidosFil: Patir, Asli. İstanbul Medipol Üniversitesi; TurquíaFil: Koruyucu, Mine. İstanbul Üniversitesi; TurquíaFil: Abbasoğlu, Zerrin. Yeditepe Üniversitesi; TurquíaFil: Casado, Priscila L.. Universidade Federal Fluminense; BrasilFil: Brown, Andrew. University of Pittsburgh; Estados UnidosFil: Zaky, Samer H.. University of Pittsburgh; Estados UnidosFil: Bayram, Merve. İstanbul Medipol Üniversitesi; TurquíaFil: Küchler, Erika C.. University of Pittsburgh; Estados UnidosFil: Cooper, Margaret E.. University of Pittsburgh; Estados UnidosFil: Liu, Kai. University of Pittsburgh; Estados UnidosFil: Marazita, Mary L.. University of Pittsburgh; Estados UnidosFil: Tanboğa, İlknur. Marmara Üniversitesi; TurquíaFil: Granjeiro, José M.. Universidade Federal Fluminense; Brasil. Instituto Nacional de Metrologia, Qualidade e Tecnologia; BrasilFil: Seymen, Figen. İstanbul Üniversitesi; TurquíaFil: Castilla, Eduardo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; Argentina. Fundación Oswaldo Cruz; BrasilFil: Orioli, Iêda M.. Universidade Federal do Rio de Janeiro; BrasilFil: Sfeir, Charles. University of Pittsburgh; Estados UnidosFil: Owyang, Hongjiao. Marmara Üniversitesi; TurquíaFil: Rabelo Buzalaf, Marilia Afonso. Universidade de Sao Paulo; BrasilFil: Vieira, Alexandre R.. University of Pittsburgh; Estados Unido

Economic activity and congenital anomalies: An ecologic study in Argentina

In this study, we analyze the association between industrial activity and the occurrence of 34 congenital anomalies. We selected 21 counties in Argentina during 1982-1994 and examined a total of 614,796 births in these counties in consecutive series. We used the International Standard Industrial Classification of All Economic Activities as an indicator of exposure to 80 specific industrial activities. Incidence rate ratios for each congenital anomaly were adjusted by the socioeconomic level of the county according to a census index of social deprivation. For a given exposure/anomaly association to be considered as significant and relevant, the exposure had to be a statistically significant risk for the occurrence of the anomaly and an increase in the birth prevalence rate of the congenital anomaly type involved had to be observed in those counties where the putative causal activity was being performed. Significant associations (p < 0.01) were identified between textile industry and anencephaly, and between the manufacture of engines and turbines and microcephaly. These observations are consistent with previous reports on occupational exposure, and their further investigation by means of case-control studies is recommended.Instituto Multidisciplinario de Biología Celula

Role of estrogen related receptor beta (ESRRB) in DFN35B hearing impairment and dental decay

BACKGROUND: Congenital forms of hearing impairment can be caused by mutations in the estrogen related receptor beta (ESRRB) gene. Our initial linkage studies suggested the ESRRB locus is linked to high caries experience in humans. METHODS: We tested for association between the ESRRB locus and dental caries in 1,731 subjects, if ESRRB was expressed in whole saliva, if ESRRB was associated with the microhardness of the dental enamel, and if ESRRB was expressed during enamel development of mice. RESULTS: Two families with recessive ESRRB mutations and DFNB35 hearing impairment showed more extensive dental destruction by caries. Expression levels of ESRRB in whole saliva samples showed differences depending on sex and dental caries experience. CONCLUSIONS: The common etiology of dental caries and hearing impairment provides a venue to assist in the identification of individuals at risk to either condition and provides options for the development of new caries prevention strategies, if the associated ESRRB genetic variants are correlated with efficacy.Fil: Weber, Megan L.. University of Pittsburgh; Estados UnidosFil: Hsin, Hong Yuan. University of Pittsburgh; Estados UnidosFil: Kalay, Ersan. Karadeniz Technical University; TurquíaFil: Brožková, Dana Š. Charles University; República Checa. University Hospital Motol; República ChecaFil: Shimizu, Takehiko. Nihon University. School of Dentistry; JapónFil: Bayram, Merve. Medipol Istanbul University; TurquíaFil: Deeley, Kathleen. University of Pittsburgh; Estados UnidosFil: Küchler, Erika C.. University of Pittsburgh; Estados UnidosFil: Forella, Jessalyn. University of Pittsburgh; Estados UnidosFil: Ruff, Timothy D.. University of Pittsburgh; Estados UnidosFil: Trombetta, Vanessa M.. University of Pittsburgh; Estados UnidosFil: Sencak, Regina C.. University of Pittsburgh; Estados UnidosFil: Hummel, Michael. University of Pittsburgh; Estados UnidosFil: Briseño Ruiz, Jessica. University of Pittsburgh; Estados UnidosFil: Revu, Shankar K.. University of Pittsburgh; Estados UnidosFil: Granjeiro, José M.. Universidade Federal Fluminense; BrasilFil: Antunes, Leonardo S.. Universidade Federal Fluminense; BrasilFil: Antunes, Livia A.. Universidade Federal Fluminense; BrasilFil: Abreu, Fernanda V.. Universidade Federal Fluminense; BrasilFil: Costabel, Marcelo C.. Universidade Federal do Rio de Janeiro; BrasilFil: Tannure, Patricia N.. Veiga de Almeida University; Brasil. Salgado de Oliveira University; BrasilFil: Koruyucu, Mine. Istanbul University; TurquíaFil: Patir, Asli. Medipol Istanbul University; TurquíaFil: Poletta, Fernando Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas ; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mereb, Juan C.. Estudio Colaborativo Latino Americano de Malformaciones Congénitas; ArgentinaFil: Castilla, Eduardo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas ; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Orioli, Iêda M.. Universidade Federal do Rio de Janeiro; BrasilFil: Marazita, Mary L.. University of Pittsburgh; Estados UnidosFil: Ouyang, Hongjiao. University of Pittsburgh; Estados UnidosFil: Jayaraman, Thottala. University of Pittsburgh; Estados UnidosFil: Seymen, Figen. Istanbul University; TurquíaFil: Vieira, Alexandre R.. University of Pittsburgh; Estados Unido

Women are more susceptible to caries but individuals born with clefts are not

The identification of individuals at a higher risk of developing caries is of great interest. Isolated forms of cleft lip and palate are among the most common craniofacial congenital anomalies in humans. Historically, several reports suggest that individuals born with clefts have a higher risk for caries. Caries continues to be the most common infectious noncontagious disease worldwide and a great burden to any health system. The identification of individuals of higher susceptibility to caries is of great interest. In this paper, we assessed caries experience of 1,593 individuals from three distinct populations. The study included individuals born with clefts, their unaffected relatives, and unrelated unaffected controls that were recruited from areas with similar cultural pressures and limited access to dental care. DMFT/dmft scores were obtained, and caries experience rates were compared among the three groups in each geographic area. Individuals born with clefts did not present higher caries experience in comparison to their unaffected relatives or unrelated unaffected controls. Women tend to present higher caries rates in comparison to men. Our work provides strong evidence that individuals born with clefts are not at higher risk to caries; however, women tend to have more severe caries experience.Instituto Multidisciplinario de Biología Celula

Women Are More Susceptible to Caries but Individuals Born with Clefts Are Not

The identification of individuals at a higher risk of developing caries is of great interest. Isolated forms of cleft lip and palate are among the most common craniofacial congenital anomalies in humans. Historically, several reports suggest that individuals born with clefts have a higher risk for caries. Caries continues to be the most common infectious noncontagious disease worldwide and a great burden to any health system. The identification of individuals of higher susceptibility to caries is of great interest. In this paper, we assessed caries experience of 1,593 individuals from three distinct populations. The study included individuals born with clefts, their unaffected relatives, and unrelated unaffected controls that were recruited from areas with similar cultural pressures and limited access to dental care. DMFT/dmft scores were obtained, and caries experience rates were compared among the three groups in each geographic area. Individuals born with clefts did not present higher caries experience in comparison to their unaffected relatives or unrelated unaffected controls. Women tend to present higher caries rates in comparison to men. Our work provides strong evidence that individuals born with clefts are not at higher risk to caries; however, women tend to have more severe caries experience

Fine-mapping of 5q12.1-13.3 unveils new genetic contributors to caries

Caries is a multifactorial disease and little is still known about the host genetic factors influencing susceptibility. Our previous genome-wide linkage scan has identified the interval 5q12.1–5q13.3 as linked to low caries susceptibility in Filipino families. Here we fine-mapped this region in order to identify genetic contributors to caries susceptibility. Four hundred and seventy-seven subjects from 72 pedigrees with similar cultural and behavioral habits and limited access to dental care living in the Philippines were studied. DMFT scores and genotype data of 75 single-nucleotide polymorphisms were evaluated in the Filipino families with the Family-Based Association Test. For replication purposes, a total 1,467 independent subjects from five different populations were analyzed in a case-control format. In the Filipino cohort, statistically significant and borderline associations were found between low caries experience and four genes spanning 13 million base pairs (PART1, ZSWIM6, CCNB1, and BTF3). We were able to replicate these results in some of the populations studied. We detected PART1 and BTF3 expression in whole saliva, and the expression of BTF3 was associated with caries experience. Our results suggest BTF3 may have a functional role in protecting against caries.Fil: Shimizu, T.. Nihon University of Dentistry; JapónFil: Deeley, K.. University of Pittsburgh; Estados UnidosFil: Briseño Ruiz, J.. University of Pittsburgh; Estados UnidosFil: Faraco Junior, I. M.. University of Pittsburgh; Estados UnidosFil: Poletta, Fernando Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; ArgentinaFil: Brancher, J. A.. Pontifical Catholic University of Paraná; BrasilFil: Pecharki, G. D.. Pontifical Catholic University of Paraná; BrasilFil: Küchler, E. C.. Universidade Federal Fluminense; BrasilFil: Tannure, P. N.. Universidade Federal do Rio de Janeiro; BrasilFil: Lips, A.. Universidade Federal do Rio de Janeiro; BrasilFil: Vieira, T. C. S.. Universidade Federal Fluminense; BrasilFil: Patir, A.. Istanbul Medipol Universit; TurquíaFil: Yildirim, M.. Istanbul University; TurquíaFil: Mereb, J. C.. Centro de Educación Médica e Investigaciones Clínicas “Norberto Quirno”; ArgentinaFil: Resick, J. M.. University of Pittsburgh; Estados UnidosFil: Brandon, C. A.. University of Pittsburgh; Estados UnidosFil: Cooper, M. E.. University of Pittsburgh; Estados UnidosFil: Seymen, F.. Istanbul University; TurquíaFil: Costa, M. C.. Universidade Federal do Rio de Janeiro; BrasilFil: Granjeiro, J. M.. Universidade Federal Fluminense; BrasilFil: Trevilatto, P. C.. Pontifical Catholic University of Paraná; BrasilFil: Orioli, I. M.. Universidade Federal do Rio de Janeiro; Brasil. Centro de Educación Médica e Investigaciones Clínicas “Norberto Quirno”; ArgentinaFil: Castilla, Eduardo Enrique. Instituto Oswaldo Cruz; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; ArgentinaFil: Marazita, M. L.. University of Pittsburgh; Estados UnidosFil: Vieira, A. R.. University of Pittsburgh; Estados Unido

Enamel Formation Genes Influence Enamel Microhardness Before and After Cariogenic Challenge

There is evidence for a genetic component in caries susceptibility, and studies in humans have suggested that variation in enamel formation genes may contribute to caries. For the present study, we used DNA samples collected from 1,831 individuals from various population data sets. Single nucleotide polymorphism markers were genotyped in selected genes (ameloblastin, amelogenin, enamelin, tuftelin, and tuftelin interacting protein 11) that influence enamel formation. Allele and genotype frequencies were compared between groups with distinct caries experience. Associations with caries experience can be detected but they are not necessarily replicated in all population groups and the most expressive results was for a marker in AMELX (p = 0.0007). To help interpret these results, we evaluated if enamel microhardness changes under simulated cariogenic challenges are associated with genetic variations in these same genes. After creating an artificial caries lesion, associations could be seen between genetic variation in TUFT1 (p = 0.006) and TUIP11 (p = 0.0006) with enamel microhardness. Our results suggest that the influence of genetic variation of enamel formation genes may influence the dynamic interactions between the enamel surface and the oral cavity. © 2012 Shimizu et al