Bubble Divergences from Cellular Cohomology

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang–Mills theory, the Ponzano–Regge model of 3d quantum gravity and discrete BF theory, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined in general, because of a phenomenon called ‘bubble divergences’. A common expectation is that the degree of these divergences is given by the number of ‘bubbles’ of the 2-complex. In this note, we show that this expectation, although not realistic in general, is met in some special cases: when the 2-complex is simply connected, or when the structure group is Abelian – in both cases, the divergence degree is given by the second Betti number of the 2-complex.     

Impaired neurogenesis, learning and memory and low seizure threshold associated with loss of neural precursor cell survivin

Background

Survivin is a unique member of the inhibitor of apoptosis protein (IAP) family in that it exhibits antiapoptotic properties and also promotes the cell cycle and mediates mitosis as a chromosome passenger protein. Survivin is highly expressed in neural precursor cells in the brain, yet its function there has not been elucidated.

Results

To examine the role of neural precursor cell survivin, we first showed that survivin is normally expressed in periventricular neurogenic regions in the embryo, becoming restricted postnatally to proliferating and migrating NPCs in the key neurogenic sites, the subventricular zone (SVZ) and the subgranular zone (SGZ). We then used a conditional gene inactivation strategy to delete the survivin gene prenatally in those neurogenic regions. Lack of embryonic NPC survivin results in viable, fertile mice (Survivin ^Camcre ) with reduced numbers of SVZ NPCs, absent rostral migratory stream, and olfactory bulb hypoplasia. The phenotype can be partially rescued, as intracerebroventricular gene delivery of survivin during embryonic development increases olfactory bulb neurogenesis, detected postnatally. Survivin ^Camcre brains have fewer cortical inhibitory interneurons, contributing to enhanced sensitivity to seizures, and profound deficits in memory and learning.

Conclusions

The findings highlight the critical role that survivin plays during neural development, deficiencies of which dramatically impact on postnatal neural function.     

Integrability and Linear Stability of Nonlinear Waves

It is well known that the linear stability of solutions of \(1+1\) partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general \(N\times N\) matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for \(N=3\) for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.     

On the use of intersection cuts for bilevel optimization

We address a generic mixed-integer bilevel linear program (MIBLP), i.e., a bilevel optimization problem where all objective functions and constraints are linear, and some/all variables are required to take integer values. We first propose necessary modifications needed to turn a standard branch-and-bound MILP solver into an exact and finitely-convergent MIBLP solver, also addressing MIBLP unboundedness and infeasibility. As in other approaches from the literature, our scheme is finitely-convergent in case both the leader and the follower problems are pure integer. In addition, it is capable of dealing with continuous variables both in the leader and in follower problems—provided that the leader variables influencing follower’s decisions are integer and bounded. We then introduce new classes of linear inequalities to be embedded in this branch-and-bound framework, some of which are intersection cuts based on feasible-free convex sets. We present a computational study on various classes of benchmark instances available from the literature, in which we demonstrate that our approach outperforms alternative state-of-the-art MIBLP methods.     

On the Euler–Lagrange equation for a variational problem: the general case II

In this paper we study the existence of a solution in ${L^\infty_{\rm loc}(\Omega)}In this paper we study the existence of a solution in L^￥_loc(W){L^\infty_{\rm loc}(\Omega)} to the Euler–Lagrange equation for the variational problem

inf[`(u)] + W1,￥0(W) òW (ID(?u) + g(u)) dx,                   (0.1)\inf_{\bar u + W^{1,\infty}_0(\Omega)} \int\limits_{\Omega} ({\bf I}_D(\nabla u) + g(u)) dx,\quad \quad \quad \quad \quad(0.1)      998. Locality of the perimeter in Carnot groups and chain rule      Luigi Ambrosio  Matteo Scienza 《Annali di Matematica Pura ed Applicata》2010,189(4):661-678 In the class of Carnot groups, we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio–Kleiner–Le Donne, we show that the perimeter measure is local, i.e., that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. This solves a question left open in Ambrosio et al. (Calculus of variations: topics from mathematical heritage of Ennio De Giorgi. Quad Mat). As a consequence, we prove a general chain rule for BV functions in this setting.      999. Locally Lipschitz vector optimization with inequality and equality constraints      Ivan Ginchev  Angelo Guerraggio  Matteo Rocca 《Applications of Mathematics》2010,55(1):77-88 The present paper studies the following constrained vector optimization problem: \(\mathop {\min }\limits_C f(x),g(x) \in - K,h(x) = 0\), where f: ? n → ? m , g: ? n → ? p are locally Lipschitz functions, h: ? n → ? q is C 1 function, and C ? ? m and K ? ? p are closed convex cones. Two types of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x 0 to be a w-minimizer and first-order sufficient conditions for x 0 to be an i-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done.      1000. Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation      Matteo Bonforte  Juan Luis Vázquez 《Advances in Mathematics》2010,224(5):2151-2215 We study qualitative and quantitative properties of local weak solutions of the fast p-Laplacian equation, t∂u=Δpu, with 1<p<2. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of Rn×[0,T]. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion range, that is when 1<p?2n/(n+1). The boundedness results may be also extended to the limit case p=1, while the positivity estimates cannot.We prove the existence as well as sharp asymptotic estimates for the so-called large solutions for any 1<p<2, and point out their main properties.We also prove a new local energy inequality for suitable norms of the gradients of the solutions. As a consequence, we prove that bounded local weak solutions are indeed local strong solutions, more precisely .      [首页] « 上一页 [95] [96] [97] [98] [99] 100 下一页 » 末  页»

Locality of the perimeter in Carnot groups and chain rule

In the class of Carnot groups, we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio–Kleiner–Le Donne, we show that the perimeter measure is local, i.e., that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. This solves a question left open in Ambrosio et al. (Calculus of variations: topics from mathematical heritage of Ennio De Giorgi. Quad Mat). As a consequence, we prove a general chain rule for BV functions in this setting.     

Locally Lipschitz vector optimization with inequality and equality constraints

The present paper studies the following constrained vector optimization problem: \(\mathop {\min }\limits_C f(x),g(x) \in - K,h(x) = 0\), where f: ? ⁿ → ? ^m , g: ? ⁿ → ? ^p are locally Lipschitz functions, h: ? ⁿ → ? ^q is C ¹ function, and C ? ? ^m and K ? ? ^p are closed convex cones. Two types of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x ⁰ to be a w-minimizer and first-order sufficient conditions for x ⁰ to be an i-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done.     

Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation

We study qualitative and quantitative properties of local weak solutions of the fast p-Laplacian equation, t_∂u=Δpu, with 1<p<2. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of Rn×[0,T]. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion range, that is when 1<p?2n/(n+1). The boundedness results may be also extended to the limit case p=1, while the positivity estimates cannot.We prove the existence as well as sharp asymptotic estimates for the so-called large solutions for any 1<p<2, and point out their main properties.We also prove a new local energy inequality for suitable norms of the gradients of the solutions. As a consequence, we prove that bounded local weak solutions are indeed local strong solutions, more precisely .