Koszul modules and Green's conjecture

We prove a strong vanishing result for finite length Koszul modules, and use it to derive Green's conjecture for every g-cuspidal rational curve over an algebraically closed field k with char(k) = 0 or char(k) >= (g+2)/2. As a consequence, we deduce that the general canonical curve of genus g satisfies Green's conjecture in this range. Our results are new in positive characteristic, whereas in characteristic zero they provide a different proof for theorems first obtained in two landmark papers by Voisin. Our strategy involves establishing two key results of independent interest: (1) we describe an explicit, characteristic-independent version of Hermite reciprocity for sl_2-representations; (2) we completely characterize, in arbitrary characteristics, the (non-)vanishing behavior of the syzygies of the tangential variety to a rational normal curve.Comment: minor edits, 42 pages, to appear in Invent. Mat

Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?

Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their utility by linking to nodes with a higher/lower degree than their own. We interpret utility as an equivalent to energy in physical systems and discuss the temperature dependence of the emerging networks. We observe the existence of a critical temperature $T_c$ where total energy (utility) and network-architecture undergo radical changes. Along this topological transition we obtain scale-free networks with complex hierarchical topology. In contrast to models for scale-free networks introduced so far, the scale-free nature emerges within equilibrium, with a clearly defined microcanonical ensemble and the principle of detailed balance strictly fulfilled. This provides clear evidence that 'complex' networks may arise without irreversibility. The results presented here should find a wide variety of applications in socio-economic statistical systems.Comment: 4 pages, 5 figure

Unified model for network dynamics exhibiting nonextensive statistics

We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing networks, preferentially growing networks, and (preferentially) rewiring networks. Further, it exhibits a natural random graph limit. The proposed model generalizes network dynamics to rewiring and growth modes which depend on internal topology as well as on a metric imposed by the space they are embedded in. In all of the networks emerging from the presented model we find q-exponential degree distributions over a large parameter space. We comment on the parameter dependence of the corresponding entropic index q for the degree distributions, and on the behavior of the clustering coefficients and neighboring connectivity distributions.Comment: 11 pages 8 fig

More Growth through Higher Investment

While many countries in the euro area are deep in recession due to a debt and structural crisis, the German economy appears to have excelled compared to many other euro area countries. Unemployment has fallen to the lowest level since German reunification, economic output has grown by over eight percent since 2009, and public budgets have been consolidated, generating a surplus in 2012. But this is no cause for euphoria. On the contrary, if one looks at Germany's economic development from a more long-term perspective, we can see that the country is lagging behind in many areas compared to most EU member states and most euro area countries. Since 1999, the euro area countries have on average achieved more economic growth than Germany and this increase in competitiveness can be largely attributed to wage moderation rather than productivity growth. The rate of investment has been falling for a long time and is very low by international standards. The estimations in this study indicate that Germany has had an annual investment gap of three percent of GDP, on average, since 1999. This means that Germany needs to invest substantially more in order to reduce the investment backlog accumulated in recent years and also to ensure higher potential growth and prosperity in the long term

DX5+NKT cells display phenotypical and functional differences between spleen and liver as well as NK1.1-Balb/c and NK1.1+ C57Bl/6 mice

These results show that DX5+NKT cells are a heterogeneous population, depending on the dedicated organ and mouse strain, that has diverse functional capacity

Intestinal blood flow in patients with chronic heart failure: A link with bacterial growth, gastrointestinal symptoms, and cachexia

Background: Blood flow in the intestinal arteries is reduced in patients with stable heart failure (HF) and relates to gastrointestinal (GI) symptoms and cardiac cachexia. Objectives: The aims of this study were to measure arterial intestinal blood flow and assess its role in juxtamucosal bacterial growth, GI symptoms, and cachexia in patients with HF. Methods: A total of 65 patients and 25 controls were investigated. Twelve patients were cachectic. Intestinal blood flow and bowel wall thickness were measured using ultrasound. GI symptoms were documented. Bacteria in stool and juxtamucosal bacteria on biopsies taken during sigmoidoscopy were studied in a subgroup by fluorescence in situ hybridization. Serum lipopolysaccharide antibodies were measured. Results: Patients showed 30% to 43% reduced mean systolic blood flow in the superior and inferior mesenteric arteries and celiac trunk (CT) compared with controls (p < 0.007 for all). Cachectic patients had the lowest blood flow (p < 0.002). Lower blood flow in the superior mesenteric artery and CT was correlated with HF severity (p < 0.04 for all). Patients had more feelings of repletion, flatulence, intestinal murmurs, and burping (p < 0.04). Burping and nausea or vomiting were most severe in patients with cachexia (p < 0.05). Patients with lower CT blood flow had more abdominal discomfort and immunoglobulin A–antilipopolysaccharide (r = 0.76, p < 0.02). Antilipopolysaccharide response was correlated with increased growth of juxtamucosal but not stool bacteria. Patients with intestinal murmurs had greater bowel wall thickness of the sigmoid and descending colon, suggestive of edema contributing to GI symptoms (p < 0.05). In multivariate regression analysis, lower blood flow in the superior mesenteric artery, CT (p < 0.04), and inferior mesenteric artery (p = 0.056) was correlated with the presence of cardiac cachexia. Conclusions: Intestinal blood flow is reduced in patients with HF. This may contribute to juxtamucosal bacterial growth and GI symptoms in patients with advanced HF complicated by cachexia

Is Strain Elastography (IO-SE) sufficient for characterization of liver lesions before surgical resection, or is contrast enhanced ultrasound (CEUS) necessary?

Aim To evaluate the diagnostic accuracy of IO-SE in comparison to IO-CEUS for the differentiation between malignant and benign liver lesions. Material and Methods In a retrospective diagnostic study IO-CEUS and SE examinations of 49 liver lesions were evaluated and compared to histopathological examinations. Ultrasound was performed using a multifrequency linear probe (6–9 MHz). The loops of CEUS were evaluated up to 5 min. The qualitative characterization of IO-SE was based on a color coding system (blue = hard, red = soft). Stiffness of all lesions was quantified by a specific scaling of 0–6 (0 = low, 6 = high) using 7 ROIs (2 central, 5 peripheral). Results All malignant lesions displayed a characteristic portal venous washout and could be diagnosed correctly by IO-CEUS. 3/5 benign lesions could not be characterized properly either by IO-CEUS or IO-SE prior to resection. Thus for IO-CEUS sensitivity, specificity, positive and negative predictive value and accuracy were 100%, 40%, 94%, 100% and 94%. Lesion sizes were between 8 and 59 mm in diameter. Regarding the IO-SE, malignant lesions showed a marked variability. In qualitative analysis, 31 of the malignant lesions were blue colored denoting overall induration. Thirteen malignant lesions showed an inhomogenous color pattern with partial indurations. Two of the benign lesions also displayed overall induration. The other benign lesions showed an inhomogenous color mapping. Calculated sensitivity of the SE was 70.5%, specificity 60%, PPV 94%, NPV 18.75%, and accuracy 69%. Conclusion IO-CEUS is useful for localization and characterization of liver lesions prior to surgical resection whereas IO-SE provided correct characterization only for a limited number of lesions

Germany must invest more in its future

Shortly before the parliamentary election in 2013, Germany is riding on a wave of euphoria: hardly any other euro country has weathered the financial and debt crisis so well. Since 2009, GDP has grown by over eight percent and 1.2 million new jobs have been created. Public finances were consolidated and, in 2012, there was a fiscal surplus of 0.2 percent of GDP. An impressive financial position indeed for a country that, only ten years ago, was considered the sick man of Europe. But it is also a deceptive one. If one substitutes these for other comparative figures, then this image is seriously tarnished. Since 1999, Germany has achieved lower economic growth than the rest of the euro area. Real wages have barely increased since 1999 and real consumer spending has grown much more in the euro area on average than in Germany. In addition, German net public assets have contracted significantly. In 1999, net state assets were about 20 percent of GDP and, by 2011, they had declined to 0.5 percent of GDP and are, therefore, no longer available for future generations. In many areas, Germany has not really progressed at all and in some areas it has fallen significantly behind other countries. These arrears have not been balanced out by recent positive developments

Deutschland muss mehr in seine Zukunft investieren

Kurz vor der Bundestagswahl 2013 schwimmt Deutschland in den Augen der Ökonomen auf einer Welle der Euphorie: Kaum ein anderes Euroland hat die Finanz- und Schuldenkrise so gut gemeistert. Das deutsche Bruttoinlandsprodukt ist seit 2009 um mehr als acht Prozent gewachsen, es entstanden rund 1,2 Millionen neue Arbeitsplätze. Die öffentlichen Haushalte wurden konsolidiert, im Jahr 2012 gab es einen fiskalischen Überschuss von 0,2 Prozent des Bruttoinlandsprodukts. Eine glänzende Bilanz für ein Land, das vor zehn Jahren noch als der kranke Mann Europas galt - aber auch eine einseitige. Setzt man andere Vergleichsgrößen an, trübt sich das Bild erheblich ein: Seit 1999 hat Deutschland im Vergleich zum Euroraum ein niedrigeres Wirtschaftswachstum erzielt. Die Reallöhne sind seit 1999 kaum gestiegen, und die realen Konsumausgaben haben im Eurozonen-Durchschnitt deutlich kräftiger zugenommen als in Deutschland. Stark geschrumpft ist das deutsche Staatsvermögen: Lag es 1999 noch bei etwa 20 Prozent des Bruttoinlandsprodukts, so ist es bis 2011 auf 0,5 Prozent des Bruttoinlandsprodukts zusammengeschmolzen und steht damit für künftige Generationen nicht mehr zur Verfügung. In vielen Bereichen ist Deutschland nicht wirklich vorangekommen, in einigen deutlich hinter andere Länder zurückgefallen. Diese Rückstände sind durch die zuletzt gute Entwicklung nicht wieder aufgeholt worden