The Role of Edge Offload for Hardware - Accelerated Mobile Devices

This position paper examines a spectrum of approaches to overcoming the limited computing power of mobile devices caused by their need to be small, lightweight and energy efficient. At one extreme is offloading of compute-intensive operations to a cloudlet nearby. At the other extreme is the use of fixed-function hardware accelerators on mobile devices. Between these endpoints lie various configurations of programmable hardware accelerators. We explore the strengths and weaknesses of these approaches and conclude that they are, in fact, complementary. Based on this insight, we advocate a softwarehardware co-evolution path that combines their strengths.

On rough convergence in amenable semigroups and some properties

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIMrf of a fixed function f ∈ G on varying parameter r.

The Fake News about Fake News

It is widely believed that we are facing a problem, caused by something called ‘fake news’. Governments and other powerful institutions around the world have adopted a variety of measures to restrict the reporting and dissemination of claims they deem to be fake news. Many of these measures are clear breaches of fundamental rights, including freedom of speech and freedom of the press. This chapter arsgues that, contrary to common opinion, there is no new or growing problem of fake news. There is instead a new and growing problem caused by the term ‘fake news’. Although this term has no fixed meaning it does have a fixed function. It functions to restrict permissible public speech and opinion in ways that serve the interests of powerful people and institutions.

The spectral decomposition of $$|\theta |^2$$

Let $$\theta $$ θ be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for $$\langle |\theta |^2, \varphi \rangle $$ ⟨ | θ | 2 , φ ⟩ as $$\varphi $$ φ traverses a sequence of Hecke-translates of a nice enough fixed function. The subtlety is that typically $$|\theta |^2 \notin L^2$$ | θ | 2 ∉ L 2 . Applications to the subconvexity, quantum variance and 4-norm problems We determine all pairs $$(A_{f,g},A_{g,h})$$ ( A f , g , A g , h ) of generalized weighted quasi-arithmetic means being square iterative roots of $$(A_{F,G},A_{G,H})$$ ( A F , G , A G , H ) , that is, the equation $$( A_{f,g},A_{g,h}) \circ ( A_{f,g},A_{g,h}) =(A_{F,G},A_{G,H}),$$ ( A f , g , A g , h ) ∘ ( A f , g , A g , h ) = ( A F , G , A G , H ) , is solved under three times differentiability of the functions f, g, h, F, G, H. As an application, some special cases are presented. are indicated.

Equivalent symmetric kernels of determinantal point processes

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point process. It is well known that there are different kernels that induce the same correlation functions. We classify all the possible transformations of a kernel that leave the induced correlation functions invariant, restricting to the case of symmetric kernels.

Higher differentiability of solutions to a class of obstacle problems under non-standard growth conditions

We establish the higher differentiability of integer order of solutions to a class of obstacle problems assuming that the gradient of the obstacle possesses an extra integer differentiability property. We deal with the case in which the solutions to the obstacle problems satisfy a variational inequality of the form\int_{\Omega}\langle\mathcal{A}(x,Du),D(\varphi-u)\rangle\,dx\geq 0\quad\text{% for all }\varphi\in\mathcal{K}_{\psi}(\Omega).The main novelty is that the operator {\mathcal{A}} satisfies the so-called {p,q}-growth conditions with p and q linked by the relation\frac{q}{p}<1+\frac{1}{n}-\frac{1}{r},for {r>n}. Here {\psi\in W^{1,p}(\Omega)} is a fixed function, called obstacle, for which we assume {D\psi\in W^{1,2q-p}_{\mathrm{loc}}(\Omega)}, and {\mathcal{K}_{\psi}=\{w\in W^{1,p}(\Omega):w\geq\psi\text{ a.e. in }\Omega\}} is the class of admissible functions. We require for the partial map {x\mapsto\mathcal{A}(x,\xi\/)} a higher differentiability of Sobolev order in the space {W^{1,r}}, with {r>n} satisfying the condition above.