A unified convergence analysis for shuffling-type gradient methods

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many known variants such as randomized reshuffling, deterministic or randomized single permutation, and cyclic and incremental gradient schemes. We focus on two different settings: strongly convex and nonconvex problems, but also discuss the non-strongly convex case. Our main contribution consists of new non-asymptotic and asymptotic convergence rates for a wide class of shuffling-type gradient methods in both nonconvex and convex settings. We also study uniformly randomized shuffling variants with different learning rates and model assumptions. While our rate in the nonconvex case is new and significantly improved over existing works under standard assumptions, the rate on the strongly convex one matches the existing best-known rates prior to this paper up to a constant factor without imposing a bounded gradient condition. Finally, we empirically illustrate our theoretical results via two numerical examples: nonconvex logistic regression and neural network training examples. As byproducts, our results suggest some appropriate choices for diminishing learning rates in certain shuffling variants

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur

Faktor Penguat Pada Peningkatan Kinerja Karyawan PT. Gading Murni Surabaya

The purpose of this study is to determine which factors as an amplifier to improve the performance of employees of PT. Gading Murni Surabaya, between the leadership style and compensation received by employees. This study uses a survey approach by collecting data using a questionnaire of 50 respondents then analyzed using quantitative methods. The regession equation is Y = 8.009 + 0,223 X1 + 0,240 X2. The results of this study concluded that the leadership style and compensation variables had a corrected item total correlation value exceeding r table = 0.284 and the reliability test of the leadership style variable, and the alpha cronbach's compensation results exceeded 0.060, which means that the variable was valid and reliable. Leadership and compensation styles also simultaneously have a significant effect on employee performance. And the independent variable that has the largest beta coefficient is the compensation variable (X2) with a beta coefficient of 0.240.   Keywords : Leadership style, Compesation and Employee Performance

Finite-Sum Smooth Optimization with SARAH

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function F(w)=1n∑ni=1fi(w) has been proven to be at least Ω(n−−√/ϵ) for n≤O(ϵ−2) where ϵ denotes the attained accuracy E[∥∇F(w~)∥2]≤ϵ for the outputted approximation w~ (Fang et al., 2018). In this paper, we provide a convergence analysis for a slightly modified version of the SARAH algorithm (Nguyen et al., 2017a;b) and achieve total complexity that matches the lower-bound worst case complexity in (Fang et al., 2018) up to a constant factor when n≤O(ϵ−2) for nonconvex problems. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance

Molecular dynamics of photodissociation: towards more complex systems

We present a combined experimental and theoretical study of the photodissociation of thiophene mole-cule using energy-resolved electron-ion-ion coincidence technique and self-consistent charge density functional tight-binding theory combined with a statistical approach. The observed complex molecular dynamics with many internal-energy-dependent fragmentation pathways is successfully described by the theoretical simulation

Understanding the barriers to integrating maternal and mental health at primary health care in Vietnam

The prevalence of common perinatal mental disorders in Vietnam ranges from 16.9% to 39.9%, and substantial treatment gaps have been identified at all levels. This paper explores constraints to the integration of maternal and mental health services at the primary healthcare level and the implications for the health system’s responsiveness to the needs and expectations of pregnant women with mental health conditions in Vietnam. As part of the RESPONSE project, a three-phased realist evaluation study, we present Phase One findings which employed systematic and scoping literature reviews, and qualitative data collection (focus groups and interviews) with key health system actors, in Bac Giang province, Vietnam, to understand the barriers to maternal mental healthcare provision, utilisation, and integration strategies. A four-level framing of the barriers to integrating perinatal mental health services in Vietnam was used in reporting findings, which comprised individual, socio-cultural, organisational, and structural levels. At the socio-cultural and structural levels, these barriers included: cultural beliefs about the holistic notion of physical and mental health, stigma towards mental health, biomedical approach to healthcare services, absence of comprehensive mental health policy, and a lack of mental health workforce. At the organisational level, there was absence of clinical guidelines on the integration of mental health in routine antenatal visits, a shortage of staff, and poor health facilities. Finally, at the provider level, a lack of knowledge and training on mental health was identified. The integration of mental health into routine antenatal visits at the primary care level has the potential help to reduce stigma towards mental health and improve health system responsiveness by providing services closer to the local level, offering prompt attention, better choice of services, and better communication while ensuring privacy and confidentiality of services. This can improve the demand for mental health services and help reduce the delay of care-seeking

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Lagrange Duality in Set Optimization

Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum are obtained. In particular, a strong duality theorem, which includes the existence of the dual solution, is given under very weak assumptions: The ordering cone may have an empty interior or may not be pointed. "Saddle sets" replace the usual notion of saddle points for the Lagrangian, and this concept is proven to be sufficient to show the equivalence between the existence of primal/dual solutions and strong duality on the one hand and the existence of a saddle set for the Lagrangian on the other hand

School-based prevention for adolescent Internet addiction: prevention is the key. A systematic literature review

Adolescents’ media use represents a normative need for information, communication, recreation and functionality, yet problematic Internet use has increased. Given the arguably alarming prevalence rates worldwide and the increasingly problematic use of gaming and social media, the need for an integration of prevention efforts appears to be timely. The aim of this systematic literature review is (i) to identify school-based prevention programmes or protocols for Internet Addiction targeting adolescents within the school context and to examine the programmes’ effectiveness, and (ii) to highlight strengths, limitations, and best practices to inform the design of new initiatives, by capitalizing on these studies’ recommendations. The findings of the reviewed studies to date presented mixed outcomes and are in need of further empirical evidence. The current review identified the following needs to be addressed in future designs to: (i) define the clinical status of Internet Addiction more precisely, (ii) use more current psychometrically robust assessment tools for the measurement of effectiveness (based on the most recent empirical developments), (iii) reconsider the main outcome of Internet time reduction as it appears to be problematic, (iv) build methodologically sound evidence-based prevention programmes, (v) focus on skill enhancement and the use of protective and harm-reducing factors, and (vi) include IA as one of the risk behaviours in multi-risk behaviour interventions. These appear to be crucial factors in addressing future research designs and the formulation of new prevention initiatives. Validated findings could then inform promising strategies for IA and gaming prevention in public policy and education