Some Siegel modular standard L-values, and Shafarevich–Tate groups

AbstractWe explain how the Bloch–Kato conjecture leads us to the following conclusion: a large prime dividing a critical value of the L-function of a classical Hecke eigenform f of level 1, should often also divide certain ratios of critical values for the standard L-function of a related genus two (and in general vector-valued) Hecke eigenform F. The relation between f and F (Harderʼs conjecture in the vector-valued case) is a congruence involving Hecke eigenvalues, modulo the large prime. In the scalar-valued case we prove the divisibility, subject to weak conditions. In two instances in the vector-valued case, we confirm the divisibility using elaborate computations involving special differential operators. These computations do not depend for their validity on any unproved conjecture

Optic Flow Stimuli in and Near the Visual Field Centre: A Group fMRI Study of Motion Sensitive Regions

Motion stimuli in one visual hemifield activate human primary visual areas of the contralateral side, but suppress activity of the corresponding ipsilateral regions. While hemifield motion is rare in everyday life, motion in both hemifields occurs regularly whenever we move. Consequently, during motion primary visual regions should simultaneously receive excitatory and inhibitory inputs. A comparison of primary and higher visual cortex activations induced by bilateral and unilateral motion stimuli is missing up to now. Many motion studies focused on the MT+ complex in the parieto-occipito-temporal cortex. In single human subjects MT+ has been subdivided in area MT, which was activated by motion stimuli in the contralateral visual field, and area MST, which responded to motion in both the contra- and ipsilateral field. In this study we investigated the cortical activation when excitatory and inhibitory inputs interfere with each other in primary visual regions and we present for the first time group results of the MT+ subregions, allowing for comparisons with the group results of other motion processing studies. Using functional magnetic resonance imaging (fMRI), we investigated whole brain activations in a large group of healthy humans by applying optic flow stimuli in and near the visual field centre and performed a second level analysis. Primary visual areas were activated exclusively by motion in the contralateral field but to our surprise not by central flow fields. Inhibitory inputs to primary visual regions appear to cancel simultaneously occurring excitatory inputs during central flow field stimulation. Within MT+ we identified two subregions. Putative area MST (pMST) was activated by ipsi- and contralateral stimulation and located in the anterior part of MT+. The second subregion was located in the more posterior part of MT+ (putative area MT, pMT)

Long Range Magnetic Order and the Darwin Lagrangian

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.Comment: 5 figure

Does State Ownership Hurt or Help Minority Shareholders?

We argue that state ownership is a crucial policy instrument for alleviating what is perhaps the most important principal-principal (PP) agency problem around the globe: private benefits of control (PBC). Our results illustrate that states reduce PBC in the companies in which they acquire controlling ownership positions. We also examine how legal and political institutions influence the extent to which states accomplish this goal. Anti-self-dealing legal regulations make states more effective in their efforts to constrain PBC, while political constraints make them less effective. Regimes with high state capacity appear not to prioritize PBC reduction. We test and corroborate these ideas in a sample of 1,354 control transactions across 54 countries

Business Group Affiliation, Performance, Context, and Strategy: A Meta-analysis

Research on business groups—legally independent firms tied together in various formal and informal ways—is accelerating. Through meta-analytical techniques employed on a database of 141 studies covering 28 different countries, we synthesize this research and extend it by testing several new hypotheses. We find that affiliation diminishes firm performance in general, but also that affiliates are comparatively better off in contexts with underdeveloped financial and labor market institutions. We also trace reduced affiliate performance to specific strategic actions taken at the firm and group levels. Overall, our results indicate that affiliate performance reflects complex processes and motivations

Inhibition of polyploidization in Pten-deficient livers reduces steatosis

The tumour suppressor PTEN is a negative regulator of the PI3K/AKT signalling pathway. Liver-specific deletion of Pten in mice results in the hyper-activation PI3K/AKT signalling accompanied by enhanced genome duplication (polyploidization), marked lipid accumulation (steatosis) and formation of hepatocellular carcinomas. However, it is unknown whether polyploidization in this model has an impact on the development of steatosis and the progression towards liver cancer. Here, we used a liver-specific conditional knockout approach to delete Pten in combination with deletion of E2f7/8, known key inducers of polyploidization. As expected, Pten deletion caused severe steatosis and liver tumours accompanied by enhanced polyploidization. Additional deletion of E2f7/8 inhibited polyploidization, alleviated Pten-induced steatosis without affecting lipid species composition and accelerated liver tumour progression. Global transcriptomic analysis showed that inhibition of polyploidization in Pten-deficient livers resulted in reduced expression of genes involved in energy metabolism, including PPAR-gamma signalling. However, we find no evidence that deregulated genes in Pten-deficient livers are direct transcriptional targets of E2F7/8, supporting that reduction in steatosis and progression towards liver cancer are likely consequences of inhibiting polyploidization. Lastly, flow cytometry and image analysis on isolated primary wildtype mouse hepatocytes provided further support that polyploid cells can accumulate more lipid droplets than diploid hepatocytes. Collectively, we show that polyploidization promotes steatosis and function as an important barrier against liver tumour progression in Pten-deficient livers.</p

Weight Consistency Specifies Regularities of Macaque Cortical Networks

To what extent cortical pathways show significant weight differences and whether these differences are consistent across animals (thereby comprising robust connectivity profiles) is an important and unresolved neuroanatomical issue. Here we report a quantitative retrograde tracer analysis in the cynomolgus macaque monkey of the weight consistency of the afferents of cortical areas across brains via calculation of a weight index (fraction of labeled neurons, FLN). Injection in 8 cortical areas (3 occipital plus 5 in the other lobes) revealed a consistent pattern: small subcortical input (1.3% cumulative FLN), high local intrinsic connectivity (80% FLN), high-input form neighboring areas (15% cumulative FLN), and weak long-range corticocortical connectivity (3% cumulative FLN). Corticocortical FLN values of projections to areas V1, V2, and V4 showed heavy-tailed, lognormal distributions spanning 5 orders of magnitude that were consistent, demonstrating significant connectivity profiles. These results indicate that 1) connection weight heterogeneity plays an important role in determining cortical network specificity, 2) high investment in local projections highlights the importance of local processing, and 3) transmission of information across multiple hierarchy levels mainly involves pathways having low FLN values