A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

Update on Hemicrania Continua

Hemicrania continua (HC) is a rare primary headache syndrome, characterized by unilateral pain and an absolute response to indometacin. Since the term was first coined in 1984, more than 100 cases have been described worldwide. Most recently, detailed case series that provide more detailed information concerning the sometimes complex clinical presentation of HC have been reported. Functional imaging studies suggest a unique pattern of subcortical involvement in HC: contralateral to the pain posterior hypothalamic region, ipsilateral dorsal pons and ipsilateral ventral midbrain, which, along with the particular effect of indometacin, probably justifies its classification as a unique entity. Increasing the awareness of this primary headache form among clinicians will aid in its diagnosis while further work is being undertaken to characterize the syndrome

Social Isolation-Induced Aggression Potentiates Anxiety and Depressive-Like Behavior in Male Mice Subjected to Unpredictable Chronic Mild Stress

Accumulating epidemiological evidence shows that life event stressors are major vulnerability factors for psychiatric diseases such as major depression. It is also well known that social isolation in male mice results in aggressive behavior. However, it is not known how social isolation-induced aggression affects anxiety and depressive-like behavior in isolated male mice subjected to unpredictable chronic mild stress (CMS), an animal model of depression.C57/B6 male mice were divided into 3 groups; non-stressed controls, in Group I; isolated mice subjected to the CMS protocol in Group II and aggression by physical contact in socially isolated mice subjected to the CMS protocol in Group III. In the sucrose intake test, ingestion of a 1% sucrose solution by mice in Groups II and III was significantly lower than in Group I. Furthermore, intake of this solution in Group III mice was significantly lower than in Group II mice. In the open field test, mice in Group III, showed reduced locomotor activity and reduced entry and retention time in the central zone, compared to Groups I and II mice. Moreover, the distances moved in 1 hour by Group III mice did not differ between night and morning. In the light/black box test, Groups II and III animals spent significantly less time in the light box compared to Group I animals. In the tail suspension test (TST) and forced swimming test (FST), the immobility times of Group II and Group III mice were significantly longer than in Group I mice. In addition, immobility times in the FST were significantly longer in Group III than in Group II mice.These findings show that social isolation-induced aggression could potentiate anxiety and depressive-like behaviors in isolated male mice subjected to CMS

Comparative study of T84 and T84SF human colon carcinoma cells: in vitro and in vivo ultrastructural and functional characterization of cell culture and metastasis

To better understand the relationship between tumor heterogeneity, differentiation, and metastasis, suitable experimental models permitting in vitro and in vivo studies are necessary. A new variant cell line (T84SF) exhibiting an altered phenotype was recently selected from a colon cancer cell line (T84) by repetitive plating on TNF-alpha treated human endothelial cells and subsequent selection for adherent cells. The matched pair of cell lines provides a useful system to investigate the extravasation step of the metastatic cascade. Since analysis of morphological differences can be instructive to the understanding of metastatic potential of tumor cells, we compared the ultrastructural and functional phenotype of T84 and T84SF cells in vitro and in vivo. The reported ultrastructural features evidence differences between the two cell lines; selected cells showed a marked pleomorphism of cell size and nuclei, shape, and greater surface complexity. These morphological differences were also coupled with biochemical data showing a distinct tyrosine phosphorylation-based signaling, an altered localization of beta-catenin, MAPK, and AKT activation, as well as an increased expression in T84SF cells of Bcl-X-L, a major regulator of apoptosis. Therefore, these cell lines represent a step forward in the development of appropriate models in vitro and in vivo to investigate colon cancer progression

Prognostic significance of urokinase plasminogen activator and plasminogen activator inhibitor-1 mRNA expression in lymph node- and hormone receptor-positive breast cancer

BACKGROUND: One of the most thoroughly studied systems in relation to its prognostic relevance in patients with breast cancer, is the plasminogen activation system that comprises of, among others, the urokinase Plasminogen Activator (uPA) and its main inhibitor, the Plasminogen Activator Inhibitor-1 (PAI-1). In this study, we investigated the prognostic value of uPA and PAI-1 at the mRNA level in lymph node- and hormone receptor-positive breast cancer. METHODS: The study included a retrospective series of 87 patients with hormone-receptor positive and axillary lymph node-positive breast cancer. All patients received radiotherapy, adjuvant anthracycline-based chemotherapy and five years of tamoxifen treatment. The median patient age was 54 and the median follow-up time was 79 months. Distant relapse occurred in 30 patients and 22 patients died from breast cancer during follow-up. We investigated the prognostic value of uPA and PAI-1 at the mRNA level as measured by real-time quantitative RT-PCR. RESULTS: uPA and PAI-1 gene expression was not found to be correlated with any of the established clinical and pathological factors. Metastasis-free Survival (MFS) and Breast Cancer specific Survival (BCS) were significantly shorter in patients expressing high levels of PAI-1 mRNA (p < 0.0001; p < 0.0001; respectively). In Cox multivariate analysis, the level of PAI-1 mRNA appeared to be the strongest prognostic factor for MFS (Hazard Ratio (HR) = 10.12; p = 0.0002) and for BCS (HR = 13.17; p = 0.0003). Furthermore, uPA gene expression was not significantly associated neither with MFS (p = 0.41) nor with BCS (p = 0.19). In a Cox-multivariate regression analysis, uPA expression did not demonstrate significant independent prognostic value. CONCLUSION: These findings indicate that high PAI-1 mRNA expression represents a strong and independent unfavorable prognostic factor for the development of metastases and for breast cancer specific survival in a population of hormone receptor- and lymph node-positive breast cancer patients

An immune dysfunction score for stratification of patients with acute infection based on whole-blood gene expression

Dysregulated host responses to infection can lead to organ dysfunction and sepsis, causing millions of global deaths each year. To alleviate this burden, improved prognostication and biomarkers of response are urgently needed. We investigated the use of whole-blood transcriptomics for stratification of patients with severe infection by integrating data from 3149 samples from patients with sepsis due to community-acquired pneumonia or fecal peritonitis admitted to intensive care and healthy individuals into a gene expression reference map. We used this map to derive a quantitative sepsis response signature (SRSq) score reflective of immune dysfunction and predictive of clinical outcomes, which can be estimated using a 7- or 12-gene signature. Last, we built a machine learning framework, SepstratifieR, to deploy SRSq in adult and pediatric bacterial and viral sepsis, H1N1 influenza, and COVID-19, demonstrating clinically relevant stratification across diseases and revealing some of the physiological alterations linking immune dysregulation to mortality. Our method enables early identification of individuals with dysfunctional immune profiles, bringing us closer to precision medicine in infection

An immune dysfunction score for stratification of patients with acute infection based on whole-blood gene expression.

Dysregulated host responses to infection can lead to organ dysfunction and sepsis, causing millions of global deaths each year. To alleviate this burden, improved prognostication and biomarkers of response are urgently needed. We investigated the use of whole-blood transcriptomics for stratification of patients with severe infection by integrating data from 3149 samples from patients with sepsis due to community-acquired pneumonia or fecal peritonitis admitted to intensive care and healthy individuals into a gene expression reference map. We used this map to derive a quantitative sepsis response signature (SRSq) score reflective of immune dysfunction and predictive of clinical outcomes, which can be estimated using a 7- or 12-gene signature. Last, we built a machine learning framework, SepstratifieR, to deploy SRSq in adult and pediatric bacterial and viral sepsis, H1N1 influenza, and COVID-19, demonstrating clinically relevant stratification across diseases and revealing some of the physiological alterations linking immune dysregulation to mortality. Our method enables early identification of individuals with dysfunctional immune profiles, bringing us closer to precision medicine in infection

Biologic markers of risk in nipple aspirate fluid are associated with residual cancer and tumour size

We previously demonstrated that nipple aspirate fluid (NAF) can be obtained from virtually all non-Asian women between the ages of 30 and 72. The focus of this report is to (1) determine the association of candidate markers of breast cancer risk in NAF obtained from fresh mastectomy specimens with residual breast carcinoma, and (2) evaluate the association of the markers with breast tumour progression. Nipple aspiration was performed on 97 specimens. Cytology, DNA index (including % hypertetraploid cells), cell cycle parameters (S phase fraction, % cells in G2/M), prostate-specific antigen (PSA), epidermal growth factor (EGF), testosterone, carcinoembryonic antigen (CEA) and prostaglandin D synthase (PGDS) were evaluated in NAF for their association with (1) residual ductal carcinoma in situ (DCIS) or invasive cancer, and (2) pathologic tumour size. NAF was obtained from 99% (96/97) of specimens. Atypical and malignant NAF cytology were significantly associated with residual DCIS or invasive cancer (P = 0.001) and with larger tumours (P = 0.004). One hundred per cent and 88% of subjects with malignant and atypical NAF cytology, respectively, had residual carcinoma. The percentage of cells in G2/M and DNA index were associated both with risk of residual carcinoma (P = 0.01 for each) and larger tumour size (DNA index, P = 0.03; G2/M, P = 0.05), although neither biomarker improved the ability of NAF cytology, to predict residual breast cancer. Higher DNA index was associated with atypical cytology (P = 0.0001). In summary, atypical and malignant NAF cytology are associated with larger tumour size, and are highly predictive of residual carcinoma after needle or excisional biopsy of the breast. © 1999 Cancer Research Campaig