It is known that there exists a quasi-projective coarse moduli space for nonsingular n-dimensional varieties X with ample canonical divisor KX and given Hilbert function H(l) = χ(X,O(lKX)) (e.g. see [Vie]). The starting point in the construction of this moduli space is Matsusaka’s big theorem [Mat1] which states that the class of these varieties is bounded: there exists an integer ν0 > 0, indep...

Crawling of eukaryotic cells on flat surfaces is underlain by the protrusion of the actin network, the contractile activity of myosin II motors, and graded adhesion to the substrate regulated by complex biochemical networks. Some crawling cells, such as fish keratocytes, maintain a roughly constant shape and velocity. Here we use moving-boundary simulations to explore four different minimal mec...

We provide a new topological obstruction for complete stable minimal hypersurfaces in IRn+1. For n ≥ 3, we prove that a complete orientable stable minimal hypersurface in IRn+1 cannot have more than one end by showing the existence of a bounded harmonic function based on the Sobolev inequality for minimal submanifolds [MS] and by applying the Liouville theorem for harmonic functions due to Scho...

We are interested in a well-known problem in Computer Science and Economics, the Stable Marriage Problem (SM). Considering two communities in which each member has some preferences on the potential partners, the goal is to make pairs taking into account their preferences. This abstract problem has many applications. From a multiagent approach, the seminal Gale-Shapley algorithm [2] solves the S...

A proof of the statement in the title is given.

We present two solutions to the firing synchronization problem on the ring, an 8-state minimal-time solution and a 6-state non-minimal-time solution. Both solutions use fewer states than the previous best-known minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We ...

the main goal of this note is to introduce another second-order differenceequation where every nontrivial solution is of minimal period 5, namelythe difference equation:xn+1 =1 + xn−1xnxn−1 − 1, n = 1, 2, 3, . . .with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

In this paper, we pursue our analysis of the W1+∞ symmetry of the lowenergy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1 + 1)-dimensional effective field theories, which are built by representations of the W1+∞ algebra. Generic W1+∞ theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular cla...

Let C be a smooth projective curve of genus g ≥ 2 and L be a line bundle on C of degree d. Assume that r ≥ 2 is an integer coprime with d. Let M := UC(r,L) be the moduli space of stable vector bundles on C of rank r and with the fixed determinant L. It is well-known that M is a smooth projective Fano variety with Picard number 1. For any projective curve in M , we can define its degree with res...

The paper describes a new algorithm to generate minimal, stable, and symbolic corrections to an input that will cause a neural network with ReLU neurons to change its output. We argue that such a correction is a useful way to provide feedback to a user when the neural network produces an output that is different from a desired output. Our algorithm generates such a correction by solving a serie...