Polar Cremona Transformations and Monodromy of Polynomials

Consider the gradient map associated to any non-constant homogeneous polynomial f\in \C[x_0,...,x_n] of degree $d$, defined by \phi_f=grad(f): D(f)\to \CP^n, (x_0:...:x_n)\to (f_0(x):...:f_n(x)) where D(f)=\{x\in \CP^n; f(x)\neq 0\} is the principal open set associated to $f$ and $f_i=\frac{\partial f}{\partial x_i}$. This map corresponds to polar Cremona transformations. In Proposition \ref{p1} we give a new lower bound for the degree $d(f)$ of $\phi_f$ under the assumption that the projective hypersurface $V:f=0$ has only isolated singularities. When $d(f)=1$, Theorem \ref{t4} yields very strong conditions on the singularities of $V$.Comment: 8 page

A Brief Review on phytoconstituents and Ethnopharmacology of Scoparia dulcis Linn. (Scrophulariaceae)

Scoparia dulcis Linn.(S. dulcis)or sweet broom weed commonly known as Mithipatti and Bana Dhania in Western Orissa, it is also known as ‘GhodaTulsi’in Hindi. The present review attempts to narrate the chemical constituents of S.dulcis and their uses. S.dulcis is rich in flavones, terpenes and steroids. Main chemical constituents such as scoparic acid A-C, scopadulcic acid A and B, scopadulciol, scopadulin and ammelin have been shown to contribute to the observed medicinal effect of the plant. In this review we have composed the structure and functions of those active ingredients with their melting point and other physical properties individually.Some aspects of the several speculated pharmacological properties of S. dulcis have been validated by scientific research, which includes the presence of hypoglycaemic and anti-tumour promoting compound. It also has antimicrobial and antifungal effects as well as antihyperlipidemic action

Back to Massey: Impressively fast, scalable and tight security evaluation tools

None of the existing rank estimation algorithms can scale to large cryptographic keys, such as 4096-bit (512 bytes) RSA keys. In this paper, we present the first solution to estimate the guessing entropy of arbitrarily large keys, based on mathematical bounds, resulting in the fastest and most scalable security evaluation tool to date. Our bounds can be computed within a fraction of a second, with no memory overhead, and provide a margin of only a few bits for a full 128-bit AES key

Computing the everyday: social media as data platforms

We conceive social media platforms as sociotechnical entities that variously shape user platform involvement and participation. Such shaping develops along three fundamental data operations that we subsume under the terms of encoding, aggregation, and computation. Encoding entails the engineering of user platform participation along narrow and standardized activity types (e.g., tagging, liking, sharing, following). This heavily scripted platform participation serves as the basis for the procurement of discrete and calculable data tokens that are possible to aggregate and, subsequently, compute in a variety of ways. We expose these operations by investigating a social media platform for shopping. We contribute to the current debate on social media and digital platforms by describing social media as posttransactional spaces that are predominantly concerned with charting and profiling the online predispositions, habits, and opinions of their user base. Such an orientation sets social media platforms apart from other forms of mediating online interaction. In social media, we claim, platform participation is driven toward an endless online conversation that delivers the data footprint through which a computed sociality is made the source of value creation and monetization

The role of proteomics in depression research

Depression is a severe neuropsychiatric disorder affecting approximately 10% of the world population. Despite this, the molecular mechanisms underlying the disorder are still not understood. Novel technologies such as proteomic-based platforms are beginning to offer new insights into this devastating illness, beyond those provided by the standard targeted methodologies. Here, we will show the potential of proteome analyses as a tool to elucidate the pathophysiological mechanisms of depression as well as the discovery of potential diagnostic, therapeutic and disease course biomarkers

Signaling pathways responsible for the rapid antidepressant-like effects of a GluN2A-preferring NMDA receptor antagonist

In a previous study we found that the preferring GluN2A receptor antagonist, NVP-AAM077, elicited rapid antidepressant-like effects in the forced swim test that was related to the release of glutamate and serotonin in the medial prefrontal cortex. In the present work we sought to examine the duration of this behavioral effect as well as the molecular readouts involved. Our results showed that NVP-AAM077 reduced the immobility in the forced swim test 30?min and 24?h after its administration. However, this effect waned 7 days later. The rapid antidepressant-like response seems to be associated with increases in the GluA1 subunit of ?-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors, mammalian target of rapamycin (mTOR) signaling, glia markers such as glial fibrillary acidic protein (GFAP) and excitatory amino acid transporter 1 (EAAT1), and a rapid mobilization of intracellular stores of brain-derived neurotrophic factor (BDNF) in the medial prefrontal cortex.Acknowledgements: M.G.-S. was recipient of a contract from the Sistema Nacional de Garantía Juvenil co-funded by the European Social Fund. We also thank Novartis for the generous gift of NVP-AAM077. This work was supported by the Instituto de Salud Carlos III, Subdirección General del Evaluación y Fomento de la Investigación (FIS Grants PI13/00038 and PI16/00217) that were co-funded by the European Regional Development Fund (‘A way to build Europe’). Funding from the Centro de Investigación Biomédica en Red de Salud Mental (CIBERSAM), Instituto de Salud Carlos III is also acknowledged

Astrocyte pathology in the prefrontal cortex impairs the cognitive function of rats

Interest in astroglial cells is rising due to recent findings supporting dynamic neuron-astrocyte interactions. There is increasing evidence of astrocytic dysfunction in several brain disorders such as depression, schizophrenia or bipolar disorder; importantly these pathologies are characterized by the involvement of the prefrontal cortex and by significant cognitive impairments. Here, to model astrocyte pathology, we injected animals with the astrocyte specific toxin L-a-aminoadipate (L-AA) in the medial prefrontal cortex (mPFC); a behavioral and structural characterization two and six days after the injection was performed. Behavioral data shows that the astrocyte pathology in the mPFC affects the attentional set-shifting, the working memory and the reversal learning functions. Histological analysis of brain sections of the L-AA-injected animals revealed a pronounced loss of astrocytes in the targeted region. Interestingly, analysis of neurons in the lesion sites showed a progressive neuronal loss that was accompanied with dendritic atrophy in the surviving neurons. These results suggest that the L-AA-induced astrocytic loss in the mPFC triggers subsequent neuronal damage leading to cognitive impairment in tasks depending on the integrity of this brain region. These findings are of relevance to better understand the pathophysiological mechanisms underlying disorders that involve astrocytic loss/dysfunction in the PFC.This work was supported by the Marie Curie Fellowship FP7-PEOPLE-2010-IEF 273936, BIAL Foundation Grants 138/2008 and 61/2010, FEDER funds through Operational program for competitiveness factors-COMPETE -, ON2 Programa Operacional Regional do Norte (ON.2-O Novo Norte), QREN/FEDER, and by national funds through FCT-Foundation for Science and Technology-project (PTDC/SAU-NSC/118194/2010) and fellowships (SFRH/BPD/66151/2009 and SFRH/BD/89714/2012)

Resilient emotionality and molecular compensation in mice lacking the oligodendrocyte-specific gene Cnp1

Altered oligodendrocyte structure and function is implicated in major psychiatric illnesses, including low cell number and reduced oligodendrocyte-specific gene expression in major depressive disorder (MDD). These features are also observed in the unpredictable chronic mild stress (UCMS) rodent model of the illness, suggesting that they are consequential to environmental precipitants; however, whether oligodendrocyte changes contribute causally to low emotionality is unknown. Focusing on 2′-3′-cyclic nucleotide 3′-phosphodiesterase (Cnp1), a crucial component of axoglial communication dysregulated in the amygdala of MDD subjects and UCMS-exposed mice, we show that altered oligodendrocyte integrity can have an unexpected functional role in affect regulation. Mice lacking Cnp1 (knockout, KO) displayed decreased anxiety- and depressive-like symptoms (i.e., low emotionality) compared with wild-type animals, a phenotypic difference that increased with age (3–9 months). This phenotype was accompanied by increased motor activity, but was evident before neurodegenerative-associated motor coordination deficits (⩽9–12 months). Notably, Cnp1KO mice were less vulnerable to developing a depressive-like syndrome after either UCMS or chronic corticosterone exposure. Cnp1KO mice also displayed reduced fear expression during extinction, despite normal amygdala c-Fos induction after acute stress, together implicating dysfunction of an amygdala-related neural network, and consistent with proposed mechanisms for stress resiliency. However, the Cnp1KO behavioral phenotype was also accompanied by massive upregulation of oligodendrocyte- and immune-related genes in the basolateral amygdala, suggesting an attempt at functional compensation. Together, we demonstrate that the lack of oligodendrocyte-specific Cnp1 leads to resilient emotionality. However, combined with substantial molecular changes and late-onset neurodegeneration, these results suggest the low Cnp1 seen in MDD may cause unsustainable and maladaptive molecular compensations contributing to the disease pathophysiology