Residue Formulas for the Large k Asymptotics of Witten's Invariants of Seifert Manifolds. The Case of SU(2)

We derive the large k asymptotics of the surgery formula for SU(2) Witten's invariants of general Seifert manifolds. The contributions of connected components of the moduli space of flat connections are identified. The contributions of irreducible connections are presented in a residue form. This form is similar to the one used by A. Szenes, L. Jeffrey and F. Kirwan. This similarity allows us to express the contributions of irreducible connections in terms of intersection numbers on their moduli spaces.Comment: 39 pages, no figures, LaTe

Über die blutzuckersteigernde Wirkung des menschlichen Speichels

Eine Stunde nach i. v. Zufuhr von menschlichem Speichel wird ein bedeutender Blutzuckeranstieg bei Kaninchen beobachtet. 2. Die durch Insulinzufuhr verursachte Hypoglykämie und auch die hypoglykämischen allgemeinen Symptome lassen sich durch i. v. Speichelinjektion gut beeinflussen. 3. Die gleichzeitig verabreichten Insulin- und Speichelinjektionen scheinen einander nicht einfach zu paralysieren. 4. Scheint die nach Speichelinjektionen beobachtete stärke Muskelschwäche und Hinfälligkeit der Tiere durch Muskelglykolyse bedingt zu sein. 5. Können nach Speichelinjektion und Muskelexcisionen außerordentlich hohe Blutzuckerwerte festgestellt werden, welche jedoch bedeutend größer sind als durch Addition jener Werte erhalten wird, welche die beiden getrennten Eingriffe an sich verursachen würden

On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Crater formation by fast ions: comparison of experiment with Molecular Dynamics simulations

An incident fast ion in the electronic stopping regime produces a track of excitations which can lead to particle ejection and cratering. Molecular Dynamics simulations of the evolution of the deposited energy were used to study the resulting crater morphology as a function of the excitation density in a cylindrical track for large angle of incidence with respect to the surface normal. Surprisingly, the overall behavior is shown to be similar to that seen in the experimental data for crater formation in polymers. However, the simulations give greater insight into the cratering process. The threshold for crater formation occurs when the excitation density approaches the cohesive energy density, and a crater rim is formed at about six times that energy density. The crater length scales roughly as the square root of the electronic stopping power, and the crater width and depth seem to saturate for the largest energy densities considered here. The number of ejected particles, the sputtering yield, is shown to be much smaller than simple estimates based on crater size unless the full crater morphology is considered. Therefore, crater size can not easily be used to estimate the sputtering yield.Comment: LaTeX, 7 pages, 5 EPS figures. For related figures/movies, see: http://dirac.ms.virginia.edu/~emb3t/craters/craters.html New version uploaded 5/16/01, with minor text changes + new figure

Comparative study on the uniform energy deposition achievable via optimized plasmonic nanoresonator distributions

Plasmonic nanoresonators of core-shell composition and nanorod shape were optimized to tune their absorption cross-section maximum to the central wavelength of a short pulse. Their distribution along a pulse-length scaled target was optimized to maximize the absorptance with the criterion of minimal absorption difference in between neighbouring layers. Successive approximation of layer distributions made it possible to ensure almost uniform deposited energy distribution up until the maximal overlap of two counter-propagating pulses. Based on the larger absorptance and smaller uncertainty in absorptance and energy distribution core-shell nanoresonators override the nanorods. However, optimization of both nanoresonator distributions has potential applications, where efficient and uniform energy deposition is crucial, including phase transitions and even fusion

(0,2) Deformations of Linear Sigma Models

We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear sigma model these correspond to some of the holomorphic deformations of the tangent bundle on the hypersurface. Combinatorial formulas are given for the number of these deformations, and we show that these numbers are exchanged by mirror symmetry in a subclass of the models.Comment: 35 pages; uses xy-fig; typos fixed, acknowledgments adde

Kindlin-3 maintains marginal zone B cells but confines follicular B cell activation and differentiation

Integrin-mediated interactions between hematopoietic cells and their microenvironment are important for the development and function of immune cells. Here, the role of the integrin adaptor Kindlin-3 in B cell homeostasis is studied. Comparing the individual steps of B cell development in B cell-specific Kindlin-3 or alpha4 integrin knockout mice, we found in both conditions a phenotype of reduced late immature, mature, and recirculating B cells in the bone marrow. In the spleen, constitutive B cell-specific Kindlin-3 knockout caused a loss of marginal zone B cells and an unexpected expansion of follicular B cells. Alpha4 integrin deficiency did not induce this phenotype. In Kindlin-3 knockout B cells VLA-4 as well as LFA-1-mediated adhesion was abrogated, and short-term homing of these cells in vivo was redirected to the spleen. Upon inducible Kindlin-3 knockout, marginal zone B cells were lost due to defective retention within 2 weeks, while follicular B cell numbers were unaltered. Kindlin-3 deficient follicular B cells displayed higher IgD, CD40, CD44, CXCR5, and EBI2 levels, and elevated PI3K signaling upon CXCR5 stimulation. They also showed transcriptional signatures of spontaneous follicular B cell activation. This activation manifested in scattered germinal centers in situ, early plasmablasts differentiation, and signs of IgG class switch

A topologically twisted index for three-dimensional supersymmetric theories

We provide a general formula for the partition function of three-dimensional (formula presented) gauge theories placed on S2 7S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to \u3a9-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 7 T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants

Molecular dynamics simulations of non-equilibrium systems

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