Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Improvement of Hyperthermia Properties of Iron Oxide Nanoparticles by Surface Coating

Magnetic hyperthermia is an oncological therapy that exploits magnetic nanoparticles activated by radiofrequency magnetic fields to produce a controlled temperature increase in a diseased tissue. The specific loss power (SLP) of magnetic nanoparticles or the capability to release heat can be improved using surface treatments, which can reduce agglomeration effects, thus impacting on local magnetostatic interactions. In this work, Fe3O4 nanoparticles are synthesized via a coprecipitation reaction and fully characterized in terms of structural, morphological, dimensional, magnetic, and hyperthermia properties (under the Hergt–Dutz limit). Different types of surface coatings are tested, comparing their impact on the heating efficacy and colloidal stability, resulting that sodium citrate leads to a doubling of the SLP with a substantial improvement in dispersion and stability in solution over time; an SLP value of around 170 W/g is obtained in this case for a 100 kHz and 48 kA/m magnetic field

An EPTAS for Scheduling on Unrelated Machines of Few Different Types

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than $1.5$ unless P$=$NP. We consider the case that there are only a constant number $K$ of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $K=1$. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $\varepsilon > 0$ an assignment with makespan of length at most $(1+\varepsilon)$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $1/\varepsilon$. In particular we achieve a running time of $2^{\mathcal{O}(K\log(K) \frac{1}{\varepsilon}\log^4 \frac{1}{\varepsilon})}+\mathrm{poly}(|I|)$, where $|I|$ denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques

Analysis of an Artificial Hormone System

The increased complexity of modern networks and the increasingly dynamic access patterns in multimedia consumption have led to new challenges for content delivery. Dynamic networks and dynamic access patterns result in a complex system. To deliver content efficiently we introduced an artificial hormone system that is capable of handling the dynamics, is self-organizing, robust and adaptive. The content placement problem is NP complete and is closely related to several hard problems including edge-disjoint path routing, scheduling and the bin packing problem. The evaluation of self-organizing algorithms brings also a real challenge. For a first evaluation we created and ILP model of the problem. It is applied to get the exact optimum that serves as a bound in the evaluation of the solution algorithms. In this paper, we examine the convergence of the algorithm and found that the hormone levels converge to a limit at each node in the typical cases. We form a series of theorems on convergence with different conditions by starting with a specific base case and then we consider more general, practically relevant cases. The theorems can be proved by exploiting the analogy between the Markov chains and the artificial hormone system

Learning programs by learning from failures

We describe an inductive logic programming (ILP) approach called learning from failures. In this approach, an ILP system (the learner) decomposes the learning problem into three separate stages: generate, test, and constrain. In the generate stage, the learner generates a hypothesis (a logic program) that satisfies a set of hypothesis constraints (constraints on the syntactic form of hypotheses). In the test stage, the learner tests the hypothesis against training examples. A hypothesis fails when it does not entail all the positive examples or entails a negative example. If a hypothesis fails, then, in the constrain stage, the learner learns constraints from the failed hypothesis to prune the hypothesis space, i.e. to constrain subsequent hypothesis generation. For instance, if a hypothesis is too general (entails a negative example), the constraints prune generalisations of the hypothesis. If a hypothesis is too specific (does not entail all the positive examples), the constraints prune specialisations of the hypothesis. This loop repeats until either (i) the learner finds a hypothesis that entails all the positive and none of the negative examples, or (ii) there are no more hypotheses to test. We introduce Popper, an ILP system that implements this approach by combining answer set programming and Prolog. Popper supports infinite problem domains, reasoning about lists and numbers, learning textually minimal programs, and learning recursive programs. Our experimental results on three domains (toy game problems, robot strategies, and list transformations) show that (i) constraints drastically improve learning performance, and (ii) Popper can outperform existing ILP systems, both in terms of predictive accuracies and learning times.Comment: Accepted for the machine learning journa

Learning MDL logic programs from noisy data

Many inductive logic programming approaches struggle to learn programs from noisy data. To overcome this limitation, we introduce an approach that learns minimal description length programs from noisy data, including recursive programs. Our experiments on several domains, including drug design, game playing, and program synthesis, show that our approach can outperform existing approaches in terms of predictive accuracies and scale to moderate amounts of noise

Adiponectin affects the mechanical responses in strips from the mouse gastric fundus

AIMTo investigate whether the adipocytes derived hormone adiponectin (ADPN) affects the mechanical responses in strips from the mouse gastric fundus.METHODSFor functional experiments, gastric strips from the fundal region were cut in the direction of the longitudinal muscle layer and placed in organ baths containing Krebs-Henseleit solution. Mechanical responses were recorded via force-displacement transducers, which were coupled to a polygraph for continuous recording of isometric tension. Electrical field stimulation (EFS) was applied via two platinum wire rings through which the preparation was threaded. The effects of ADPN were investigated on the neurally-induced contractile and relaxant responses elicited by EFS. The expression of ADPN receptors, Adipo-R1 and Adipo-R2, was also evaluated by touchdown-PCR analysis.RESULTSIn the functional experiments, EFS (4-16 Hz) elicited tetrodotoxin (TTX)-sensitive contractile responses. Addition of ADPN to the bath medium caused a reduction in amplitude of the neurally-induced contractile responses (P < 0.05). The effects of ADPN were no longer observed in the presence of the nitric oxide (NO) synthesis inhibitor L-N-G-nitro arginine (L-NNA) (P > 0.05). The direct smooth muscle response to methacholine was not influenced by ADPN (P > 0.05). In carbachol precontracted strips and in the presence of guanethidine, EFS induced relaxant responses. Addition of ADPN to the bath medium, other than causing a slight and progressive decay of the basal tension, increased the amplitude of the neurally-induced relaxant responses (P < 0.05). Touchdown-PCR analysis revealed the expression of both Adipo-R1 and Adipo-R2 in the gastric fundus.CONCLUSIONThe results indicate for the first time that ADPN is able to influence the mechanical responses in strips from the mouse gastric fundus

A Multilingual Study of Multi-Sentence Compression using Word Vertex-Labeled Graphs and Integer Linear Programming

Multi-Sentence Compression (MSC) aims to generate a short sentence with the key information from a cluster of similar sentences. MSC enables summarization and question-answering systems to generate outputs combining fully formed sentences from one or several documents. This paper describes an Integer Linear Programming method for MSC using a vertex-labeled graph to select different keywords, with the goal of generating more informative sentences while maintaining their grammaticality. Our system is of good quality and outperforms the state of the art for evaluations led on news datasets in three languages: French, Portuguese and Spanish. We led both automatic and manual evaluations to determine the informativeness and the grammaticality of compressions for each dataset. In additional tests, which take advantage of the fact that the length of compressions can be modulated, we still improve ROUGE scores with shorter output sentences.Comment: Preprint versio