Suppose that  is a finite group. Then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . Suppose that . Then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if  is a group such that , where , then . Here  denotes the family of Suzuk...

Synthetic biology holds promise as both a framework for rationally engineering biological systems and a way to revolutionize how we fundamentally understand them. Essential to realizing this promise is the development of strategies and tools to reliably and predictably control and characterize sophisticated patterns of gene expression. Here we review the role that RNA can play towards this goal...

An interactive proof system is called doubly-efficient if the prescribed prover strategy can be implemented in polynomial-time and the verifier’s strategy can be implemented in almost-linear-time. Such proof systems, introduced by Goldwasser, Kalai, and Rothblum (JACM, 2015), make the benefits of interactive proof system available to real-life agents who are restricted to polynomial-time comput...

While the spread of some neurodegenerative disease-associated proteinopathies, such as tau and α-synuclein, is well studied and clearly implicates transsynaptic pathology transmission, research into the progressive spread of amyloid-β pathology has been less clear. In fact, prior analyses of transregional amyloid-β pathology spread have implicated both transsynaptic and other intracellular- as ...

This paper presents an approach for engineering time-constrained systems which must operate in dynamic environments. Systems which operate in such environments may have unknown worst-case scenarios, may have large variances in the sizes of the data and event sets that they process (and thus, have large variances in execution latencies and resource requirements), and may not be statically charac...

We consider the Rosenfeld–Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M(F) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld–Gröbner algorithm, in whic...

Bovet, Crescenzi, and Silvestri ( 1992, 1995), and independently Vereshchagin ( 1994), showed that many complexity classes in the polynomial time setting are leaf language classes, i.e. classes which are determined by two disjoint languages. They gave many examples but they did not characterize the set of leaf language classes. This will be done in &his paper. It will be shown that the set of l...

We have built two tools for dynamically verifying MPI programs – one called ISP and the other called DMA. Both these tools are aimed at formally analyzing the executions of an MPI programs by running executions, analyzing the actual MPI operation dependencies that manifest, and rerunning executions to cover the dependency space. ISP implements an MPI-specific dynamic partial order reduction alg...

The fundamental limits for detection and characterization of fluorescent (phosphorescent) inhomogeneities embedded in tissuelike highly scattering turbid media are investigated. The absorption and fluorescence contrast introduced by exogenous fluorophores are also compared. Both analyses are based on practical signal-to-noise ratio considerations. For an object with fivefold fluorophore concent...

Launched before the atomic hypothesis took hold, elasticity theory is a spectacular achievement. A continuum-level description, it provides a powerful toolkit for determining how architecturally simple solids such as crystals respond macroscopically to stress, whilst encoding microscopic, atomic-realm details parsimoniously, via a few parameters. Solids that are architecturally complex at the a...