Littérature scientifique sur le sujet « H¨older continuity »

"We study the distortion features of homeomorphisms of Sobolev class $W^{1,1}_{\rm loc}$ admitting integrability for $p$-outer dilatation. We show that such mappings belong to $W^{1,n-1}_{\rm loc},$ are differentiable almost everywhere and possess absolute continuity in measure. In addition, such mappings are both ring and lower $Q$-homeomorphisms with appropriate measurable functions $Q.$ This allows us to derive various distortion results like Lipschitz, H\""older, logarithmic H\""older continuity, etc. We also establish a weak bounded variation property for such class of homeomorphisms."

Abstract This symposium co-sponsored by the Disasters and Older Adults and the Technology and Aging special interest groups of GSA aims to highlight the promise of, and barriers to, the use of telehealth to support continuity of care in the face of disasters and crises, such as the ongoing COVID-19 pandemic. M. Mattos will showcase a home-based medical care (HBPC) program to address chronically ill and homebound persons living with dementia and caregivers’ needs during the pandemic. T. Wyte-Lake will present the results of a national survey on how changes were made to the Department of Veterans Affairs (VA) HBPC programs in response to the pandemic. G. Demiris describes a large caregiver study in which problem solving therapy and positive appraisal theory interventions designed specifically to support family caregivers of hospice patients during the COVID-19 pandemic were implemented via telehealth. D. Lindeman will specifically discuss challenges and implementation strategies for telehealth solutions applied to low-income older adults living in affordable housing communities. Finally, H. Xu will present the results of an analysis examining the effectiveness of telehealth in reducing readmissions among heart failure patients during the COVID-19 pandemic. While the COVID-19 pandemic has especially impacted older adults and those who care for them, these talks highlight the potential of telehealth services and interventions to provide support and facilitate the continuity of care during times of crisis.

Canada’s successful space-based earth-observation (EO) radar program has earned widespread and expanding user acceptance following the launch of RADARSAT-1 in 1995. RADARSAT-2, launched in 2007, while providing data continuity for its predecessor’s imaging capabilities, added new polarimetric modes. Canada’s follow-up program, the RADARSAT Constellation Mission (RCM), launched in 2019, while providing continuity for its two predecessors, includes an innovative suite of polarimetric modes. In an effort to make polarimetry accessible to a wide range of operational users, RCM uses a new method called hybrid compact polarization (HCP). There are two essential elements to this approach: (1) transmit only one polarization, circular; and (2) receive two orthogonal polarizations, for which RCM uses H and V. This configuration overcomes the conventional dual and full polarimetric system limitations, which are lacking enough polarimetric information and having a small swath width, respectively. Thus, HCP data can be considered as dual-pol data, while the resulting polarimetric classifications of features in an observed scene are of comparable accuracy as those derived from the traditional fully polarimetric (FP) approach. At the same time, RCM’s HCP methodology is applicable to all imaging modes, including wide swath and ScanSAR, thus overcoming critical limitations of traditional imaging radar polarimetry for operational use. The primary image data products from an HCP radar are different from those of a traditional polarimetric radar. Because the HCP modes transmit circularly polarized signals, the data processing to extract polarimetric information requires different approaches than those used for conventional linearly polarized polarimetric data. Operational users, as well as researchers and students, are most likely to achieve disappointing results if they work with traditional polarimetric processing tools. New tools are required. Existing tutorials, older seminar notes, and reference papers are not sufficient, and if left unrevised, could succeed in discouraging further use of RCM polarimetric data. This paper is designed to provide an initial response to that need. A systematic review of studies that used HCP SAR data for environmental monitoring is also provided. Based on this review, HCP SAR data have been employed in oil spill monitoring, target detection, sea ice monitoring, agriculture, wetland classification, and other land cover applications.

BackgroundIntegrated care is an approach to health care based on multidisciplinary working and the continuity and coordination of different levels of care (1). In an integrated care setting, health services are designed to go beyond fragmentation and isolation and delivered in response to chronic patient health needs. Integrated care has been proved to enhance patients’ quality of life (2), as well as reduce hospital admission rates and length of stay (3). Furthermore, integrated care favors patients’ access to care and improves their satisfaction (4). To evaluate the application and benefits of integrated care, patient experiences should be measured (5). However, while the patient experiences of integrated care have been documented for various chronic diseases, little is known in the context of rheumatic and musculoskeletal diseases (RMDs).ObjectivesThis study aims at providing an overview of the patient experience of integrated care of RMDs patients in Italy and defining the experience profiles and priorities of different patient subgroups.MethodsA cross-sectional online self-administered survey formulated following a scoping review of the literature was administered to a purposive sample of Italian RMDs patients (n=433). Respondents were asked to evaluate their patient experience and the importance attributed to different aspects of integrated care. Explorative factor analysis (EFA) was performed to determine the dimensions of integrated care investigated by the survey. The differences in the responses provided by different subgroups of the sample were assessed using the non-parametric versions of ANOVA and ANCOVA statistical tests with Scheffe’s adjustment for multiple comparisons.ResultsTwo factors (“person-centered care” and “health service delivery”) were extracted in the EFA. Respondents attributed high importance to both of them. However, an overall positive experience was reported only for the dimension of person-centered care. The delivery of integrated care services was evaluated poorly, especially for digital ones. Women described both dimensions of integrated care as more important compared to men (H(1)=45.292, p<.001 and H(1)=6.998, p=.008). However, their experience of integrated care services was significantly worse (H(1)=20.201, p<.001). Older participants reported poorer health service delivery compared to younger ones (H(3)=73.203, p=.009), especially for digital and outpatient services. Person-centered care was especially important for patients with comorbidities (F(1,431)=4.944, p=.027). However, this subgroup reported markedly worse experiences of integrated care services (F=(1,431)=4.187, p=.041).ConclusionItalian RMDs patients identified integrated care as something important to them. They reported receiving positive person-centered care but the delivery of integrated care services was evaluated poorly. Different patient subgroups described different experience profiles and priorities. This diversification can inform the design of tailored interventions to address the specific concerns and needs of each patient subgroup.References[1]Goodwin N. Understanding Integrated Care. Int J Integr Care 2016; 16: 1–4[2]Flanagan S, Damery S, Combes G. The effectiveness of integrated care interventions in improving patient quality of life (QoL) for patients with chronic conditions. An overview of the systematic review evidence. Health Qual Life Outcomes 2017; 15: 1–11[3]Liljas AEM, Brattström F, Burström B, et al. Impact of Integrated Care on Patient-Related Outcomes Among Older People – A Systematic Review. Int J Integr Care 2019; 19: 1–16[4]Baxter S, Johnson M, Chambers D, et al. The effects of integrated care: A systematic review of UK and international evidence. BMC Health Serv Res 2018; 18: 1–13[5]Rijken M, Lette M, Baan CA, et al. Assigning a Prominent Role to “ The Patient Experience ” in Assessing the Quality of Integrated Care for Populations with Multiple Chronic Conditions. Int J Integr Care 2019; 19: 1–5AcknowledgementsThe authors would like to thank all the patients who made this research possible.Disclosure of InterestsNone declared

We have previously shown that Swiss 3T3 cells located in the first part of G1 (post-mitotic G1 cells younger than 4.0 h or G1pm cells) were arrested after 9–10 h in the cell cycle by a short (1-8 h) exposure to serum-free medium or by a short (2-4 h) exposure to low doses of the protein synthesis inhibitor cycloheximide (CH). Kinetic data indicate that such G1pm cells rapidly return to G0 during this brief treatment and thereafter require a preparatory period of 8 h before continuing to G1. Cells older than 4 h, i.e. cells in mid or late G1 are already committed to DNA synthesis (presynthesis or G1ps cells). These cells as well as S and G2 cells were consequently unaffected by the brief serum starvation or the brief treatment with cycloheximide. In the present paper we show that the 10-h intermitotic delay that follows a 1–2 h exposure to serum-free medium can be completely counteracted by the presence of any one of the purified growth factors, epidermal growth factor (EGF), insulin or platelet-derived growth factor (PDGF). In contrast, the intermitotic delay following a longer exposure (8 h) to serum-free medium could no longer be counteracted by EGF or insulin. However, PDGF was still active in this respect. Most interestingly, the 12 h gross intermitotic delay induced by a 4h exposure to CH could be efficiently counteracted by EGF, PDGF or insulin. However, this effect on CH-treated cells could be counteracted by the growth factor only in the presence of 10% serum. This indicates the existence of a cooperative effect between PDGF, EGF or insulin and an unidentified serum factor. The effects on the cell cycle time of brief serum starvation and exposure to CH were compared with the effects on rate of protein synthesis and degradation. Although the effects of serum starvation on protein synthesis and degradation were found to be partially normalized by growth factors, we suggest that growth factors prevent cells from leaving the cell cycle by another mechanism and not merely by affecting the level of overall protein accumulation.

Magnesium Sulfate for Neuroprotection After Traumatic Brain Injury: A Randomised Controlled Trial. Temkin NR, Anderson GD, Winn HR, Ellenbogen RG, Britz GW, Schuster J, Lucas T, Newell DW, Mansfield PN, Machamer JE, Barber J, Dikmen SS. Lancet Neurol 2007;6(1):29–38. BACKGROUND: Traumatic brain injuries represent an important and costly health problem. Supplemental magnesium positively affects many of the processes involved in secondary injury after traumatic brain injury and consistently improves outcome in animal models. We aimed to test whether treatment with magnesium favourably affects outcome in head-injured patients. METHODS: In a double-blind trial, 499 patients aged 14 years or older admitted to a level 1 regional trauma centre between August, 1998, and October, 2004, with moderate or severe traumatic brain injury were randomly assigned one of two doses of magnesium or placebo within 8 h of injury and continuing for 5 days. Magnesium doses were targeted to achieve serum magnesium ranges of 1 0–1·85 mmol/L or 1·25–2·5 mmol/L. The primary outcome was a composite of mortality, seizures, functional measures, and neuropsychological tests assessed up to 6 months after injury. Analyses were done according to the intention-to-treat principle. This trial is registered with Clinicaltrials.gov, number NCT00004730. FINDINGS: Magnesium showed no significant positive effect on the composite primary outcome measure at the higher dose (mean = 55 average percentile ranking on magnesium vs. 52 on placebo, 95% CI for difference – 7 to 14; p = 0·70). Those randomly assigned magnesium at the lower dose did significantly worse than those assigned placebo (48 vs. 54, 95% CI −10·5 to −2; p = 0007). Furthermore, there was higher mortality with the higher magnesium dose than with placebo. Other major medical complications were similar between groups, except for a slight excess of pulmonary oedema and respiratory failure in the lower magnesium target group. No subgroups were identified in which magnesium had a significantly positive effect. INTERPRETATION: Continuous infusions of magnesium for 5 days given to patients within 8 h of moderate or severe traumatic brain injury were not neuroprotective and might even have a negative effect in the treatment of significant head injury.

Abstract Purpose: The threat of childhood obesity has never been greater. Behavior changes implemented during childhood and adolescence are believed to be the most successful means of thwarting the progression of this epidemic. The American Academy of Pediatrics has developed a public health campaign that promotes awareness of clinical guidelines for nutrition and physical activity. The campaign is based on a concept developed by the Maine Center for Public Health referred to as “5-2-1-0 Healthy”. The simple clear message of this concept outlines steps families can take to help prevent and treat childhood obesity. The purpose of the present study is to determine the current level of compliance and health education needs of a middle school population related to the “5-2-1-0” concept. Methods: A modified version of the 2010 National Youth Physical Activity and Nutrition Survey (developed by the Centers for Disease Control and Prevention) was distributed to students at a private, nonsectarian, middle school in New York City. The school is located in the borough of Manhattan, but includes youngsters from all five boroughs of the city. The questions were grouped and analyzed according to “5-2-1-0” categories. Surveys were scored, and the association between targeted questionnaire items and demographic variables (i.e., sex and grade) was examined. Results: All 140 students completed the survey, and there was great variability in their responses to both the nutrition and physical activity questions. Of all students, 65% reported eating one cup or more of fruit daily, and 38% reported eating one cup or more of vegetables daily. There was no statistically significant difference reported in consumption of fruits or vegetables by gender or grade. Over 60% of students indicated <2 h of DVD/video or computer/video game time per day, while 10% indicated more than 3 h per day for each. A significant difference existed in the screen time reported between grades (more screen time by the older students) and a statistically significant difference also existed in the amount of physical activity reported by gender and grade (more physical activity by males and younger students). There was no difference in the reported consumption of sugar-sweetened beverages by gender or grade. Conclusion: In a cohort of middle school students in New York City, there was great variability in compliance with the principles represented by the “5-2-1-0” concept. Changes in health behaviors were noted as students went from 6th to 7th to 8th grade, with physical activity decreasing and screen time increasing. Consequently, health curriculum topics for middle school students should focus on physical activity and screen time, while continuing to emphasize the need for proper nutrition.

Beginning in 2006 and continuing into 2009, an apparently new disease of strawberry (Fragaria × ananassa) affected commercial plantings (cvs. Albion, Camarosa, and others) in coastal (Ventura and Santa Barbara counties) California. Symptoms consisted of wilting of foliage, drying and withering of older leaves, stunting of plants, and reduced fruit production. Plants eventually collapsed and died. Internal vascular and cortical tissues of plant crowns showed a brown-to-orange-brown discoloration. Differences in cultivar susceptibility were not recorded. Internal crown and petiole tissues, when placed on acidified corn meal agar, consistently yielded Fusarium isolates having similar colony morphologies. No other pathogens were isolated. The Fusarium isolates were subcultured on carnation leaf agar and observed to be producing macroconidia and microconidiophores that are diagnostic of Fusarium oxysporum (1). For two of these isolates, the internal transcribed spacer region comprising ITS1, ITS2, and 5.8S rRNA was amplified using primers ITS-1 and ITS-4 (3). On the basis of a comparison of 515 bp, both isolates had the identical sequence, which was a 100% match for 30 accessions of F. oxysporum in GenBank. This comparison included several formae speciales of F. oxysporum, but F. oxysporum f. sp. fragariae, a previously described pathogen of strawberry (4), was not included. The isolates are archived in the Department of Plant Pathology at UC Davis and are available on request. Both sequenced isolates plus four others were tested for pathogenicity on strawberries. For these tests, spore suspensions of 1 × 105 conidia/ml were prepared separately for six isolates. Roots of strawberry transplants (12 plants of cv. Camino Real) were cut and soaked in spore suspensions for 10 min. Plants were potted in soilless, peat moss-based medium in containers. Control strawberry plants were soaked in water prior to planting. All plants were then grown in a shadehouse. After 8 weeks, inoculated plants began to show wilting and decline of foliage and internal crown tissue was lightly discolored. F. oxysporum was isolated from all inoculated plants. Control plants did not exhibit any disease symptoms and crown tissue was symptomless. To our knowledge, this is the first report of Fusarium wilt of strawberry in California. This disease has been reported from a number of other countries including Argentina, Australia, China, South Korea, Spain, and Japan (2). Since 2006, Fusarium wilt of strawberry has increased in incidence and severity in California. Initial problems in 2006 consisted of multiple small patches (2 to 4 beds wide × 3 to 10 m long) of diseased plants; in these patches disease incidence could range from 80 to 100%. By 2009, in some fields, the disease affected large sections that ran the length of the field. References: (1) P. E. Nelson et al. Fusarium Species: An Illustrated Manual for Identification. Pennsylvania State University Press, University Park, 1983. (2) H. S. Okamoto et al. Plant Prot. 24:231, 1970. (3) T. J. White et al. Page 315 in: PCR Protocols: A Guide to Methods and Application. Academic Press, NY, 1993. (4) B. L. Winks and Y. N. Williams. Qld. J. Agric. Anim. Sci. 22:475, 1966.

This research is aimed to discover the interrelation between marital satisfaction, religiouscommitment and marital commitment globally and based on its types, personal, moral, andstructural. The sampling of the research is 315 persons, with age 20 until 58 years old. The resultof the research shows there is a significant correlation between marital satisfaction and maritalcommitment, religious commitment and marital commitment, marital satisfaction together withreligious commitment and marital commitment. It is also discovers that marital commitmentinfluences personal commitment and moral commitment, while religious commitment influencespersonal commitment, moral commitment, and structural commitment.Keywords: marital satisfaction, religious commitment, marital commitment Abstrak Penelitian ini bertujuan untuk mengetahui hubungan antara kepuasan pernikahan, komitmen beragama, dan komitmen pernikahan secara global dan menurut tipenya, komitmen personal, moral, dan struktural. Partisipan penelitian ini adalah berjumlah 315 orang, berusia 20 hingga 58 tahun. Hasil penelitian ini menunjukan bahwa terdapat hubungan signifikan antara kepuasan pernikahan dan komitmen pernikahan, komitmen beragama dan komitmen pernikahan, kepuasan pernikahan bersama dengan komitmen beragama dan komitmen pernikahan. Juga diketahui bahwa kepuasan pernikahan memiliki pengaruh terhadap komitmen personal dan komitmen moral. Sementara komitmen beragama memiliki pengaruh terhadap komitmen personal, komitmen moral, dan komitmen struktural. Kata kunci: kepuasan pernikahan, komitmen beragama, komitmen pernikahan References Abbott, D., Berry, M. and Meredith, W. (1990). Religious Belief and Practice: A Potential Assetin Helping Families. Family Relations, 39(4), p.443.Adams, J. M. & Jones, W. H. (1999). Interpersonal commitment in historichal perspectives. InHandbook of Interpersonal Commitment and Relationship Stability. New York: SpringerScience+Business Media.Agnew, H. (2009). Commitment, Theories and Typologies. Department of PsychologicalSciences Faculty Publications. Diunduh dari: http://docs.lib.purdue.edu/psychpubs/28Allgood, S. M., Harris, S.,Skogrand, L., & Lee, T.R. (2008). Marital commitment andreligiosity in a religiously homogenous population. Marriage & Family Review, 45(1),52-67. doi: 10.1080/01494920802537472.Amato, P. R. 2010. Research on divorce: continuing developments and newtrends. Journal ofMarriage and Family 72(3): 650-666. doi:10.1111/j.1741-3737.2010.00723.xAmato, P. and Sobolewski, J. (2001). The Effects of Divorce and Marital Discordon AdultChildren's Psychological Well-Being. American SociologicalReview, 66(6), p.900.Andrea, S.G. (2014). Hubungan antara religiositas dan komitmen pernikahan pada individuyang menikah melalui ta’aruf. Skripsi. Depok: Fakultas Psikologi Universitas Indonesia.Argue, A., Johnson, D. and White, L. (1999). Age and Religiosity: Evidence froma Three-WavePanel Analysis. Journal for the Scientific Study of Religion, 38(3), p.423.Aron, A., Aron, E. and Smollan, D. (1992). Inclusion of Other in the Self Scaleand the structureof interpersonal closeness. Journal of Personality and Social Psychology, 63(4), pp.596- 612.Arriaga, X. and Agnew, C. (2001). Being Committed: Affective, Cognitive, and ConativeComponents of Relationship Commitment. Personality and Social Psychology Bulletin, 27(9), pp.1190-1203.Benokraitis, N. (1996). Marriages and families. Upper Saddle River, N.J.: Prentice Hall.Beveridge, A., Campbell, A., Converse, P. and Rodgers, W. (1976). The Quality of AmericanLife: Perceptions, Evaluations, and Satisfactions. Political Science Quarterly, 91(3),p.529.Bilqisthi, H. (2014). Hubungan antara komitmen pernikahan dengan kepuasanpernikahan padaindividu yang menikah melalui ta’aruf. Skripsi. Depok: Fakultas Psikologi UniversitasIndonesia.Bimas Islam Dalam Angka. (2012). Kementerian Agama Republik Indonesia.www.bimasislam.kemenag.go.idBKKBN (2011, Desember). Policy brief pusat penelitian dan pengembangan kependudukan.20 Februari 2015. http://www.bkkbn.go.id/ViewBerita.aspx?BeritaID=967Badan Pusat Statistik. (2010). Survey agama berdasarkan provinsi di Indonesia. www.bps.go.idBurpee, L. and Langer, E. (2005). Mindfulness and Marital Satisfaction. Journalof AdultDevelopment, 12(1), pp.43-51.Carp, F. and Carp, A. (1982). Test of a Model of Domain Satisfactions and WellBeing: EquityConsiderations. Research on Aging, 4(4), pp.503-522. Cho, D. W. (2014). The influence of religiosity and adult attachment style on maritalsatisfaction among Korean Christian couples living in South Korea. A Dissertation. Liberty University.Chomeya, R. (2010). Quality of psychology test between likert scale 5 and points. Journal ofSocial Sciences, 6 (3), 399-403.Chung, R. H. (2008). Religiosity as predictor of marital commitment andsatisfaction in KoreanAmerican couples. University of Southern CaliforniaClements, R. and Swensen, C. (2000). Commitment to one’s spouse as a predictorof maritalquality among older couples. Curr Psychol, 19(2), pp.110-119.DeGenova, M. and Rice, F. (2005). Intimate relationships, marriages, andfamilies. New York:McGraw-Hill.DeGenova, M. (2008). Intimate relationships, marriages & families. Boston, MA: McGrawHill.Diener, E. (1984). Subjective well-being. Psychological Bulletin, 95(3), pp.542575.Duvall, E. and Miller, B. (1985). Marriage and family development. New York: Harper & Row.Fowers, B. and Olson, D. (1993). ENRICH Marital Satisfaction Scale: A brief research andclinical tool. Journal of Family Psychology, 7(2), pp.176-185.Gravetter, F.J. & Forzano, L.B. (2009). Research methods for the behavioral sciences (Edisike-3). Belmont, CA: Wadsworth.Goltz, J.W. (1987). Correlates in marital commitment. Disertasi Doktoral.Kanada: UniversitasAlberta.Hansen, D., Kelley, H. and Thibaut, J. (1982). Interpersonal Relations: A Theory ofInterdependence. Journal of Marriage and the Family, 44(1), p.246.Hassan, R. (2007). On Being Religious: Patterns of Religious Commitment in MuslimSocieties. The Muslim World, 97(3), pp.437-478.Hatch, R., James, D. and Schumm, W. (1986). Spiritual Intimacy and MaritalSatisfaction. Family Relations, 35(4), p.539.Harris, S. S. (2005). Marital commitment and religiosity in a sample of adults in Utah. AllGraduate Theses and Dissertations. Paper 2851. http://digitalcommons.usu.edu/etd/2851Haseley, J. and Riggs, S. (2006). Marital satisfaction among newly married couples. Denton:University of North Texas.Hawkins, M. (1981). Care of the dying. BMJ, 282(6280), pp.1969-1969.Heaton, T. and Albrecht, S. (1991). Stable Unhappy Marriages. Journal of Marriage and theFamily, 53(3), p.747.Heaton, T., Albrecht, S. and Martin, T. (1985). The Timing of Divorce. Journal of Marriageand the Family, 47(3), p.631.Hoge, D. and Hoge, J. (1984). Period Effects and Specific Age Effects Influencing Values ofAlumni in the Decade after College. Social Forces, 62(4), p.941Impett, E., Beals, K. and Peplau, L. (2001). Testing the investment model of relationshipcommitment and stability in a longitudinal study of married couples. Curr Psychol, 20(4),pp.312-326.Johnson, M. P. (1973). Commitment: A conceptual structure and empirical application. TheSociological Quarterly, 14(3), 395-406.

Abstract Background: Triple negative breast cancers (TNBC) are characterized by the absence of estrogen receptors, progesterone receptors, and HER2 receptors on immunohistochemical analysis (IHC). This subtype of breast cancer has been traditionally associated with unfavorable prognosis. TNBC includes morphologically diverse mammary carcinomas including apocrine, metaplastic, medullary and other less common variants with heterogeneous clinical behavior and outcome. Despite previous efforts to further characterize TNBC with genomic and transcriptomic techniques, there is no specific targeted therapy for TNBC. Cytotoxic chemotherapy remains the mainstay of systemic treatment for these patients. DNA methylation has proved to be a promising tool in classifying a variety of cancers. In this study, we aim to analyze TNBC using comprehensive DNA methylation profiling. Method: DNA methylation profiling was performed in TNBC cases from a single academic institution using Illumina Infinium MethylationEPIC Kit. The tumors were obtained from formalin-fixed paraffin-embedded tissue from surgical specimens. Unsupervised clustering analysis based on the methylation profile was performed. Clinical, pathological, and genetic features were analyzed between the clusters. Results: We analyzed 44 cases (all female; median age 61 years) with treatment naïve TNBC diagnosed from March 2011 to April 2018. Median follow-up time was 58 months. Thirty-four (77%) patients were identified as white with the remaining 10 (23%) as non-white. Thirty-four tumors (77%) were classified as invasive ductal carcinoma of no special type, six (14%) as apocrine carcinoma, and four (9%) as metaplastic carcinoma. Six tumors (14%) were grade 2 and 38 (86%) were grade 3. Lymphovascular invasion was noted in 7 patients (16%). Tumor size ranged from 4 to 45 mm (median: 20 mm). Lymph node involvement was identified in 8 (18%) patients. Eleven (25%) patients harbored germline BRCA1/2 mutations. During the follow up period, 7 patients developed recurrent disease: 3 had local recurrences, 4 patients were found to have metastatic disease, and 1 patient had both local and distant recurrence. At last follow-up, 34 patients (77%) showed no evidence of disease, while 4 (9%) were alive with disease and 5 (11%) had died of disease. In this cohort, we identified three distinct DNA methylation clusters. In Cluster 1 (n=9), the patients were significantly older (mean age: 72 years; p=0.008) and tumors were more likely to be of apocrine morphology (56%, p= 0.001), of lower grade (55% were grade 3; p=0.009), and showed lower proliferation index (mean ki-67: 32%; p= 0.002). Cluster 3 (n=28) included younger patients (mean: 55 years) and tumors with higher grade (92% were grade 3) and proliferation index (mean ki-67: 75%). Cluster 2 (n=7) represented cases with intermediate features between Clusters 1 and 3. All patients in Cluster 1 were white, while Clusters 2 and 3 included non-white women. Cluster 1 included a significantly higher percentage of HER2-low tumors (HER2 1+ or 2+ by IHC and negative fluorescence in situ hybridization) (p=0.03; cluster 1: 89%, cluster 2: 28%, cluster 3: 46%). The vast majority of patients with germline BRCA1/2 mutation were found in Cluster 3 (67% of patients with genetic testing in Cluster 3 had germline BRCA1/2 mutation). There was no difference between the clusters in relation to stage, recurrence, and outcome. Conclusion: DNA methylation profiling is a promising tool to classify TNBC patients into clinicopathologically relevant groups, and we are continuing to expand this cohort. Classification by DNA methylation profile may result in better risk stratification for TNBC patients, which can inform their system therapy. In addition, specific methylation profiles have the potential to lead to the development of specific targeted therapies to improve the prognosis and survival for these patients. Citation Format: Lawrence H. Lin, Ivy Tran, Yiying Yang, Paolo Cotzia, Daniel Roses, Freya Schnabel, Farbod Darvishian, Matija Snuderl. DNA Methylation Analysis of Triple Negative Breast Cancers [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr P2-23-07.

We prove a Harnack inequality for non-negative solutions of a parabolic equation having an anisotropic slow diffusion. We study the propagation of support of solutions, through an iterative technique reminiscent of De Giorgi’s method and through the investigation of particular embeddings in anisotropic Sobolev spaces. At this point, we make an analysis of the natural scaling of the equation to reduce the problem to a Fokker-Planck equation and construct a self-similar Barenblatt solution thanks to finite speed of propagation. Then we exploit translation invariance to obtain positivity near the origin via a self-iteration method and deduce a sharp anisotropic expansion of positivity. This eventually yields a scale-invariant Harnack inequality in an anisotropic intrinsic geometry, dictated by the powers of the diffusion coefficients. Finally we show some consequences as H¨older continuity of solutions, Liouville-type theorems and we formulate some open problems.