相关论文: Concentration effects of BV gradients have gradien…
We propose an implementation of a valley selective electronic Veselago lens in bilayer graphene. We demonstrate that in the presence of an appropriately oriented potential step, low-energy electrons radiating from a point source can be…
We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the underlying space.
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
We consider the gradient method with variable step size for minimizing functions that are definable in o-minimal structures on the real field and differentiable with locally Lipschitz gradients. We prove that global convergence holds if…
Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the…
In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev…
Notions of weak and uniformly weak mixing (to zero) are defined for bounded sequences in arbitrary Banach spaces. Uniformly weak mixing for vector sequences is characterized by mean ergodic convergence properties. For bounded sequences,…
The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties…
We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
It is well known that besides oscillations, sequences bounded only in $L^1$ can also develop concentrations, and if the latter occurs, we can at most hope for weak$^*$ convergence in the sense of measures. Here we derive a new tool to…
The presence of defects such as vacancies in solids has prominent effects on their mechanical properties. It not only modifies the stiffness and strength of materials, but also changes their morphologies. The latter effect is extremely…
Modulation of electronic states in two-dimensional (2D) materials can be achieved by using in-plane variations of the band gap or the average potential in lateral quantum structures. In the atomic configurations with hexagonal symmetry,…
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we…
Motivated by problems where jumps across lower dimensional subsets and sharp transitions across interfaces are of interest, this paper studies the properties of fractional bounded variation ($BV$)-type spaces. Two different natural…
We have derived that on certain Banach spaces having a graph structure $G$, the iterations for asymptotically $G$-nonexpansive map will converge weakly towards a fixed point. This result unifies and extends several theorems on fixed points…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
A number of different mechanisms exist which can produce vector perturbations to the metric. One might think that such perturbations could deflect light rays from distant sources, producing observable effects. Indeed, this is expected to be…
We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering…