The Iwasawa decomposition and the Bruhat decomposition of the automorphism group on certain exceptional Jordan algebra

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_{\epsilon}-$Iwasawa decomposition, the Matsuki decomposition, and the Bruhat and Gauss decompositions.Comment: v3, 30 pages, 1 figure, major changes from v2 by separating section 9--14, reformatted, and the title changed to appear in Tsukuba J. of Mat

Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge

We envision a mobile edge computing (MEC) framework for machine learning (ML) technologies, which leverages distributed client data and computation resources for training high-performance ML models while preserving client privacy. Toward this future goal, this work aims to extend Federated Learning (FL), a decentralized learning framework that enables privacy-preserving training of models, to work with heterogeneous clients in a practical cellular network. The FL protocol iteratively asks random clients to download a trainable model from a server, update it with own data, and upload the updated model to the server, while asking the server to aggregate multiple client updates to further improve the model. While clients in this protocol are free from disclosing own private data, the overall training process can become inefficient when some clients are with limited computational resources (i.e. requiring longer update time) or under poor wireless channel conditions (longer upload time). Our new FL protocol, which we refer to as FedCS, mitigates this problem and performs FL efficiently while actively managing clients based on their resource conditions. Specifically, FedCS solves a client selection problem with resource constraints, which allows the server to aggregate as many client updates as possible and to accelerate performance improvement in ML models. We conducted an experimental evaluation using publicly-available large-scale image datasets to train deep neural networks on MEC environment simulations. The experimental results show that FedCS is able to complete its training process in a significantly shorter time compared to the original FL protocol

Investigating Generalized Parton Distribution in Gravity Dual

Generalized parton distribution (GPD) contains rich information of partons in a hadron, including transverse profile, and is also non-perturbative information necessary in describing a variety of hard processes, such as meson leptoproduction and double deeply virtual Compton scattering (DDVCS). In order to unveil non-perturbative aspects of GPD, we study DDVCS at small $x$ in gravitational dual description. Using the complex spin $j$-plane representation of DDVCS amplitude, we show that GPD is well-defined and can be extracted from the amplitude even in the strong coupling regime. It also turns out that the saddle point value in the $j$-plane representation plays an important role; there are two phases in the imaginary part of the amplitude of DDVCS and GPD, depending on relative position of the saddle point and the leading pole in the $j$-plane, and crossover between them is induced by the change of the kinematical variables. The saddle point value also directly controls kinematical variable dependence of many observables in one of the two phases, and indeed the dependence is qualitatively in nice agreement with HERA measurements. Such observation that the gravity dual shares basic properties of the real world QCD suggests that information from BFKL theory might be used to reduce error in the gravity dual predictions of the form factor and of GPD. This article also serves as a brief summery of a preprint arXiv:1105.2999

Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control

In this paper we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment or by non Hermitian measurements, there is no need for feedback control to accomplish the task. Constructive necessary and sufficient conditions on the form of the open-loop controller can be provided in this case. When open-loop control is not sufficient, filtering-based feedback control laws steering the evolution towards a target pure state are provided, which generalize those available in the literature