A generalized FKKM theorem and variational inequality

We present a generalized FKKM Theorem and it's application to the existence of solution for the variationals inequalities using a generalized coercivity type condition for correspondences defined in L-space.L-structure, L-spaces, L-KKM correspondences, L-coercing family and variational inequality.

Algebraic constructions in the category of vector bundles

The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that any vector subbundle of the pullback vector bundle of a generalized Lie algebroid is called interior differential system (IDS) for that generalized Lie algebroid, a theorem of Cartan type is obtained. Extending the classical notion of exterior differential system (EDS) to generalized Lie algebroids, a theorem of Cartan type is obtained. Using the theory of linear connections of Ehresmann type presented in the paper [1], the identities of Cartan and Bianchi type are presented.Comment: 29 page

On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems

Minimum cost spanning extension problems are generalizations of minimum cost spanning tree problems in which an existing network has to be extended to connect users to a source. This paper generalizes the definition of irreducible core to minimum cost spanning extension problems and introduces an algorithm generating all elements of the irreducible core. Moreover, the equal remaining obligations rule, a one-point refinement of the irreducible core ispresented. Finally, the paper characterizes these solutions axiomatically. The classical Bird tree allocation of minimum cost spanning tree problems is obtained as a particular case in our algorithm for the irreducible core.Networks;Cost Allocation;costs and cost price

Neoadjuvant eribulin mesylate following anthracycline and taxane in triple negative breast cancer: Results from the HOPE study

Background Eribulin mesylate (E) is indicated for metastatic breast cancer patients previously treated with anthracycline and taxane. We argued that E could also benefit patients eligible for neoadjuvant chemotherapy. Methods Patients with primary triple negative breast cancer 2 cm received doxorubicin 60 mg/m2 and paclitaxel 200 mg/m2 x 4 cycles (AT) followed by E 1.4 mg/m2 x 4 cycles. Primary endpoint was pathological complete response (pCR) rate; secondary and explorative endpoints included clinical/metabolic response rates and safety, and biomarker analysis, respectively. Using a two-stage Simon design, 43 patients were to be included provided that 4 of 13 patients had achieved pCR in the first stage of the study. Results In stage I of the study 13 women were enrolled, median age 43 years, tumor size 2–5 cm in 9/13 (69%), positive nodal status in 8/13 (61%). Main grade 3 adverse event was neutropenia (related to AT and E in 4 and 2 cases, respectively). AT followed by E induced clinical complete + partial responses in 11/13 patients (85%), pCR in 3/13 (23%). Median measurements of maximum standardized uptake value (SUVmax) resulted 13, 3, and 1.9 at baseline, after AT and E, respectively. Complete metabolic response (CMR) occurred after AT and after E in 2 and 3 cases, respectively. Notably, 2 of the 5 (40%) patients with CMR achieved pCR at surgery. Immunostaining of paired pre-/post-treatment tumor specimens showed a reduction of β-catenin, CyclinD1, Zeb-1, and c-myc expression, in the absence of N-cadherin modulation. The study was interrupted at stage I due to the lack of the required patients with pCR. Conclusions Despite the early study closure, preoperative E following AT showed clinical and biological activity in triple negative breast cancer patients. Furthermore, the modulation of β-catenin pathway core proteins, supposedly outside the domain of epithelial–mesenchymal transition, claims for further investigation. Trial registration EU Clinical Trial Register, EudraCT number 2012-004956-12

Trade-throughs in European cross-traded equities after transaction costs – empirical evidence for the EURO STOXX 50

This paper investigates the accuracy and heterogeneity of output growth and inflation forecasts during the current and the four preceding NBER-dated U.S. recessions. We generate forecasts from six different models of the U.S. economy and compare them to professional forecasts from the Federal Reserve’s Greenbook and the Survey of Professional Forecasters (SPF). The model parameters and model forecasts are derived from historical data vintages so as to ensure comparability to historical forecasts by professionals. The mean model forecast comes surprisingly close to the mean SPF and Greenbook forecasts in terms of accuracy even though the models only make use of a small number of data series. Model forecasts compare particularly well to professional forecasts at a horizon of three to four quarters and during recoveries. The extent of forecast heterogeneity is similar for model and professional forecasts but varies substantially over time. Thus, forecast heterogeneity constitutes a potentially important source of economic fluctuations. While the particular reasons for diversity in professional forecasts are not observable, the diversity in model forecasts can be traced to different modeling assumptions, information sets and parameter estimates. JEL Classification: G14, G15, G2

Do the Kontsevich tetrahedral flows preserve or destroy the space of Poisson bi-vectors?

From the paper "Formality Conjecture" (Ascona 1996): "I am aware of only one such a class, it corresponds to simplest good graph, the complete graph with $4$ vertices $($and $6$ edges$)$. This class gives a remarkable vector field on the space of bi-vector fields on $\mathbb{R}^{d}$. The evolution with respect to the time $t$ is described by the following non-linear partial differential equation: ..., where $\alpha=\sum_{i,j}\alpha_{ij} {\partial}/{\partial x_{i}}\wedge {\partial}/{\partial x_{j}}$ is a bi-vector field on $\mathbb{R}^d$. It follows from general properties of cohomology that $1)$ this evolution preserves the class of $($real-analytic$)$ Poisson structures}, ... In fact, I cheated a little bit. In the formula for the vector field on the space of bivector fields which one get from the tetrahedron graph, an additional term is present. ... It is possible to prove formally that if $\alpha$ is a Poisson bracket, i.e. if $[{\alpha,\alpha}]=0\in T^2(\mathbb{R}^d)$, then the additional term shown above vanishes." By using twelve Poisson structures with high-degree polynomial coefficients as explicit counterexamples, we show that both the above claims are false: neither does the first flow preserve the property of bi-vectors to be Poisson nor does the second flow vanish identically at Poisson bi-vectors. The counterexamples at hand suggest a correction to the formula for the "exotic" flow on the space of Poisson bi-vectors; in fact, this flow is encoded by the balanced sum involving both the Kontsevich tetrahedral graphs (that give rise to the flows mentioned above). We reveal that it is only the balance $1:6$ for which the flow does preserve the space of Poisson bi-vectors.Comment: Talks given in parallel by A.B. at GADEIS VIII workshop (12--16 June 2016, Larnaca, Cyprus) and A.K. at ISQS'24 conference (13--19 June 2016, CVUT Prague, Czech Republic), 10 pages, 2 figures, 4 table

Information Guide: Germania. January 2015

Una guida alle fonti d’ informazione sulla Repubblica Federale Tedesca, con collegamenti ipertestuali a informazioni presenti su European Sources Online e altri siti esterni. (For other language versions of this record click on the original url

Interlacing eigenvalues and graphs

We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a maximal (co)clique, the chromatic number, the diameter and the bandwidth in terms of the eigenvalues of the standard adjacency matrix or the Laplacian matrix. We also deal with inequalities and regularity results concerning the structure of graphs and block designs.Graphs;Eigenvalues;mathematics