The affine Grassmannian and the Springer resolution in positive characteristic

An important result of Arkhipov-Bezrukavnikov-Ginzburg relates constructible sheaves on the affine Grassmannian to coherent sheaves on the dual Springer resolution. In this paper, we prove a positive-characteristic analogue of this statement, using the framework of "mixed modular sheaves" recently developed by the first author and Riche. As an application, we deduce a relationship between parity sheaves on the affine Grassmannian and Bezrukavnikov's "exotic t-structure" on the Springer resolution.Comment: 50 pages; with an appendix joint with Simon Riche. v2: minor correction

Parity sheaves on the affine Grassmannian and the Mirkovi\'c-Vilonen conjecture

We prove the Mirkovi\'c-Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau-Mautner-Williamson theory of parity sheaves.Comment: 27 pages. v4: added details to Section 2 and an appendix on sheaf functors on non-locally compact space

Dinah Dodds and Pam Allen-Thompson, eds.: The Wall in My Backyard: East German Women in Transition

Amherst: University of Massachusetts Press, 1994. 178 p

Helga Schubert: Die Andersdenkende

Munich: dtv, 1994. 241 p

Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch

A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles “stabilization of chaos by chaos,” i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively

Deterministic coherence resonance in a ring of coupled chaotic oscillators

We study synchronization three unidirectionally Rössler oscillator the presence small mismatch between their natural frequencies w1< w2< w3. The forward (1 - 2 - 3 - 1) backward coupling directions are considered. As strength increases, common route to both configurations is intermittent phase imperfect perfect almost synchronization. difference scenario two only occurs couplings regime characterized with time-averaged dominant frequency power spectrum linear approximated slope dependent phases oscillators. Although more easily achieved configuration, results significant enhancement which within narrow range strengths as soon oscillators synchronize phases

Obese Subjects Show Sex-Specific Differences in Right Ventricular Hypertrophy

As right ventricular (RV) remodeling in obesity remains underinvestigated, and the impact of left ventricular (LV) diastolic dysfunction on RV hypertrophy is unknown, we aimed to investigate whether (1) sex-specific patterns of RV remodeling exist in obesity and (2) LV diastolic dysfunction in obesity is related to RV hypertrophy.Seven hundred thirty-nine subjects (women, n=345; men, n=394) without identifiable cardiovascular risk factors (body mass index [BMI], 15.3-59.2 kg/m2) underwent cardiovascular magnetic resonance (1.5 T) to measure RV mass (g), RV end-diastolic volume (mL), RV mass/volume ratio, and LV diastolic peak filling rate (mL/s). All subjects were normotensive (average, 119±11/73±8 mm Hg), normoglycaemic (4.8±0.5 mmol/L), and normocholesterolaemic (4.8±0.9 mmol/L) at the time of scanning. Across both sexes, there was a moderately strong positive correlation between BMI and RV mass (men, +0.8 g per BMI point increase; women, +1.0 g per BMI point increase; both P&lt;0.001). Whereas women exhibited RV cavity dilatation (RV end-diastolic volume, +1.0 mL per BMI point increase; P&lt;0.001), BMI was not correlated with RV end-diastolic volume in men (R=0.04; P=0.51). Concentric RV remodeling was present in both sexes, with RV mass/volume ratio being positively correlated to BMI (men, R=0.41; women, R=0.51; both P&lt;0.001). Irrespective of sex, the LV peak filling rate was negatively correlated with both RV mass (men, R=-0.43; women, R=-0.44; both P&lt;0.001) and RV mass/volume ratio (men, R=-0.37; women, R=-0.35; both P&lt;0.001).A sex difference in RV remodeling exists in obesity. Whereas men exhibit concentric RV remodeling, women exhibit a mixed pattern of eccentric and concentric remodeling. Regardless of sex, reduced LV diastolic function is associated with concentric RV remodeling