Given a graph F , let st(F ) be the number of subdivisions of F , each with a different vertex set, which one can guarantee in a graph G in which every edge lies in at least t copies of F . In 1990, Tuza asked for which graphs F and large t, one has that st(F ) is exponential in a power of t. We show that, somewhat surprisingly, the only such F are complete graphs, and for every F which is not ...

The supersymmetric “shining” of free massive chiral superfields in extra dimensions from a distant source brane can trigger exponentially small supersymmetry breaking on our brane of order e−2πR, where R is the radius of the extra dimensions. This supersymmetry breaking can be transmitted to the superpartners in a number of ways, for instance by gravity or via the standard model gauge interacti...

It is proved that CTL+ is exponentially more succinct than CTL. More precisely, it is shown that every CTL formula (and every modal -calculus formula) equivalent to the CTL+ formula E(Fp0 ^ ^ Fpn 1) is of length at least n dn=2e , which is (2n=pn). This matches almost the upper bound provided by Emerson and Halpern, which says that for every CTL+ formula of length n there exists an equivalent C...

We study implicit systems of linear time-varying (LTV) difference equations with rational coefficients of arbitrary order and their solution spaces, called discrete LTV-behaviors. The signals are sequences, i.e. functions from the discrete time set of natural numbers into the complex numbers. The difference field of rational functions with complex coefficients gives rise to a noncommutative ske...

The overarching goal of this paper is to derive excess risk bounds for learning from expconcave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management. In batch setting, we obtai...

In this paper we propose new method for simultaneous generating multiple quantiles corresponding to given probability levels from data streams and massive data sets. This method provides a basis for development of single-pass low-storage quantile estimation algorithms, which differ in complexity, storage requirement and accuracy. We demonstrate that such algorithms may perform well even for hea...

We show that for a single neuron with the logistic function as the transfer function the number of local minima of the error function based on the square loss can grow exponentially in the dimension.

We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. More precisely, for every D and C , there exists α=α(D,C ) > 0 such that for any graph G , with n vertices and maximal degree D , the probability that a simple random walk, started anywhere in G , will visit every vertex of G in its first C n steps is at most e−αn ...

Historical records show that culture can increase exponentially in time, e.g., in number of poems, musical works, scientific discoveries. We model how human capacities for creativity and cultural transmission may make such an increase possible, suggesting that: (1) creativity played a major role at the origin of human culture and for its accumulation throughout history, because cultural transmi...

We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase-space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate 2l2, where l2 is a generalized Lyapunov exponent. As a result, for example, the dephasing time for classically chaotic systems goes to infinity logarithmically w...