Diassociative algebras and Milnor's invariants for tangles

We extend Milnor's mu-invariants of link homotopy to ordered (classical or virtual) tangles. Simple combinatorial formulas for mu-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves corresponds to axioms of Loday's diassociative algebra. The relation of tangles to diassociative algebras is formulated in terms of a morphism of corresponding operads.Comment: 17 pages, many figures; v2: several typos correcte

On homotopies with triple points of classical knots

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point $p$ of the cylinder is called {\em coherent} if all three branches intersect at $p$ pairwise with the same index. A {\em triple unknotting} of a classical knot $K$ is a homotopy which connects $K$ with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant $v_2(K)$ by using triple unknottings. As a corollary we obtain a very simple proof of the fact that passing a coherent triple point always changes the knot type. As another corollary we show that there are triple unknottings which are not homotopic as triple unknottings even if we allow more complicated singularities to appear in the homotopy of the homotopy.Comment: 10 pages, 13 figures, bugs in figures correcte

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective function; convex or strongly convex objective and constraint; deterministic or randomized information about the objective and constraint. We hope that it is convenient for a reader to have all the methods for different settings in one place. Described methods are based on Mirror Descent algorithm and switching subgradient scheme. One of our focus is to propose, for the listed different settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule. This means that neither stepsize nor stopping rule require to know the Lipschitz constant of the objective or constraint. We also construct Mirror Descent for problems with objective function, which is not Lipschitz continuous, e.g. is a quadratic function. Besides that, we address the problem of recovering the solution of the dual problem

East African HIV care: depression and HIV outcomes.

Importance:Depression is a common co-morbidity for people living with HIV (PLWH) and is associated with elevated plasma HIV RNA levels. While depression correlates with deficits in antiretroviral (ARV) adherence, little data exist to inform the relationship between depression and HIV vial load more broadly. Objective:To examine the relationship between depression and viral load in the African Cohort Study (AFRICOS) independently of ARV adherence. Design:PLWH in Kenya, Uganda and Tanzania underwent screening for depression using the Center for Epidemiologic Studies Depression Scale (CESD) upon enrollment at AFRICOS HIV care sites. Setting:AFRICOS is an ongoing prospective longitudinal cohort study enrolling HIV-infected adults at HIV care centers including sites in Kenya, Tanzania and Uganda. These sites are administered by President's Emergency Plan For AIDS Relief programs. Participants:HIV+ individuals were eligible if they were at least 18 years old, receiving HIV care at the enrolling clinic and consented to data and specimen collection. Main outcome measure:CESD. Results:Among 2307 participants, 18-25% met the CESD threshold for depression. Depression was associated with decreased ARV adherence (OR 0.59, p =  0.01). Higher scores on three CESD items were significantly associated with 209-282% higher viral load, independently of ARV adherence among participants on ARVs ⩾6 months. Conclusions:PLWH had high prevalence of depression on the CESD. Diverse depression symptoms were independently associated with increases in viral load, underscoring the need for comprehensive treatment of depression

Structural Optimization Using the Newton Modified Barrier Method

The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program

Ultrafast Photoinduced Dynamics of 1,3-Cyclohexadiene Using XMS-CASPT2 Surface Hopping

A full-dimensional simulation of the photodissociation of 1,3-cyclohexadiene in the manifold of three electronic states was performed via nonadiabatic surface hopping dynamics using extended multistate complete active space second-order perturbation (XMS-CASPT2) electronic structure theory with fully analytic nonadiabatic couplings. With the 47 ± 8% product quantum yield calculated from the 136 trajectories, generally 400 fs-long, and an estimated excited lifetime of 89 ± 9 fs, our calculations provide a detailed description of the nonadiabatic deactivation mechanism, showing the existence of an extended conical intersection seam along the reaction coordinate. The nature of the preferred reaction pathways on the ground state is discussed and extensive comparison to the previously published full dimensional dynamics calculations is provided

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201

Analysis of trans-resveratrol in oilseeds by high-performance liquid chromatography

Oilseeds are very popular edibles that are often used to enhance the fibre content of baked goods, and specific types are used for preserving and seasoning. Polyphenol-related researches have been receiving growing attention in the last 20 years, especially the ones concentrating on stilbenoids. In previous studies, resveratrol concentrations have been determined from oilseeds such as peanut.The aim of our research was to define the composition of oilseeds with a focus on the bioactive compounds, more specifically the resveratrol.Research took place in 2010–2011 at the University of Pécs, Medical School, using non-random, convenience sampling. Oilseeds studied in the research were: sunflower seed, roasted peanut, un-roasted peanut, sesame seed, pumpkin seed, almond, linseed, bio white mustard seed, bio black mustard seed, mustard seed of foreign provenance, and wild black mustard seed. All of these oilseeds can be purchased from trade. Samples used in the research were obtained from the producers and collectors. High Performance Liquid Chromatography (HPLC) was used for the measurements.Summarising our results, it can be stated that each type of oilseed analysed in our research can be regarded as good sources of resveratrol. The highest level of resveratrol was detected in the sunflower seeds (0.00398±0.0001 mg g−1), almonds (0.00176±0.00021 mg g−1), roasted peanut (0.00206±0.00013 mg g−1), and wild black mustard seeds (0.0023±0.0007 mg g−1)