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In this paper, we propose a Riemannian version of the difference of convex algorithm (DCA) to solve a minimization problem involving the difference of convex (DC) function. The equivalence between the classical and simplified Riemannian versions of the DCA is established. We also prove that under mild assumptions the Riemannian version of the DCA is well defined and every cluster point of the sequence generated by the proposed method, if any, is a critical point of the objective DC function. Some duality relations between the DC problem and its dual are also established. To illustrate the algorithm's effectiveness, some numerical experiments are presented. [ABSTRACT FROM AUTHOR]

DC (difference of convex functions) programming and DC algorithm (DCA) are powerful tools for nonsmooth nonconvex optimization. This field was created in 1985 by Pham Dinh Tao in its preliminary state, then the intensive research of the authors of this paper has led to decisive developments since 1993, and has now become classic and increasingly popular worldwide. For 35 years from their birthday, these theoretical and algorithmic tools have been greatly enriched, thanks to a lot of their applications, by researchers and practitioners in the world, to model and solve nonconvex programs from many fields of applied sciences. This paper is devoted to key open issues, recent advances and trends in the development of these tools to meet the growing need for nonconvex programming and global optimization. We first give an outline in foundations of DC programming and DCA which permits us to highlight the philosophy of these tools, discuss key issues, formulate open problems, and bring relevant answers. After outlining key open issues that require deeper and more appropriate investigations, we will present recent advances and ongoing works in these issues. They turn around novel solution techniques in order to improve DCA's efficiency and scalability, a new generation of algorithms beyond the standard framework of DC programming and DCA for large-dimensional DC programs and DC learning with Big data, as well as for broader classes of nonconvex problems beyond DC programs. [ABSTRACT FROM AUTHOR]

Extreme learning machine (ELM) is a machine learning technique with simple structure, fast learning speed, and excellent generalization ability, which has received a lot of attention since it was proposed. In order to further improve the sparsity of output weights and the robustness of the model, this paper proposes a sparse and robust ELM based on zero-norm regularization and a non-convex quadratic loss function. The zero-norm regularization obtains sparse hidden nodes automatically, and the introduced non-convex quadratic loss function enhances the robustness by setting constant penalties to outliers. The optimization problem can be formulated as the difference of convex functions (DC) programming. This DC programming is solved by using the DC algorithm (DCA) in this paper. The experiments on the artificial and Benchmark datasets verify that the proposed method has promising robustness while reducing the number of hidden nodes, especially on the datasets with higher outliers level. [ABSTRACT FROM AUTHOR]

In this study, the semi-aromatic poly (decamethylene terephthalamide) acid (PA10T) and an array of PA10T/1010 with various copolymerization content of the third monomer 1,10-decanedioic acid (DCA) were synthesized using a productive one-step melt polycondensation method. Importantly, the addition of DCA's effect for PA10T on crystallization behaviors, thermal properties, and mechanical performances were extensively investigated. Additionally, the results of DSC demonstrate that all the melting temperature of PA10T/1010 copolyamides are significantly lower than PA10T by introducing the third monomer DCA, and the heat stability has been not significantly affected according to the results of TGA, suggesting the improvement of processing properties. Besides, compared with PA10T, the bending modulus, breaking elongation, tensile strength, and izod impact strength of PA10T/1010-1 all increase obviously, when the feed ratio of DCA and terephthalic acid (PTA) is 10:90. Thus, introducing bio-based DCA for copolymerization is a promising method to enhance both the processing and mechanical properties of PA10T. [ABSTRACT FROM AUTHOR]

Background The primary objective of the research was to develop a method using radiomics-based computed tomography (CT) to predict muscle invasion in bladder cancer (BCa) before surgery. Methods A total of 269 patients with bladder cancer were divided into two groups; training group (n = 188 cases) and validation group (n = 81 cases). Radiomics characteristics were determined by analyzing the CT images of each patient. The least absolute shrinkage and selection operator (LASSO) technique was used for developing a radiomics signature. Furthermore, logistic regression (LR), the support vector machine (SVM), decision tree (DT), and Artificial Neural Network (ANN) models were applied to differentiate between non-muscle-invasive bladder cancer (NMIBC) and muscle-invasive bladder cancer (MIBC). Their performance was determined using the area under the receiver operating characteristic curve (AUC-ROC). In addition, accuracy, specificity, and sensitivity evaluations were also conducted. Results The radiomics signature was found to be successful in its prediction. A total of 1036 radiomics features were found in the 269 patients, and out of those, 16 were selected as the best predictors of radiomics features. The results revealed that the ANN classifier had the best performance, with a validation set accuracy of 0.950. Conclusions The current work used machine learning and radiomics techniques to successfully construct a prediction model for muscle invasion in bladder cancer. The ANN model produced significant outcomes that may be used in clinical diagnosis or therapy. [ABSTRACT FROM AUTHOR]

The second part of our study is devoted to a detailed convergence analysis of two extensions of the well-known DCA method for solving DC (Difference of Convex functions) optimization problems to the case of general cone constrained DC optimization problems. We study the global convergence of the DCA for cone constrained problems and present a comprehensive analysis of a version of the DCA utilizing exact penalty functions. In particular, we study the exactness property of the penalized convex subproblems and provide two types of sufficient conditions for the convergence of the exact penalty method to a feasible and critical point of a cone constrained DC optimization problem from an infeasible starting point. In the numerical section of this work, the exact penalty DCA is applied to the problem of computing compressed modes for variational problems and the sphere packing problem on Grassmannian. [ABSTRACT FROM AUTHOR]

Background: Commensal bacteria secrete metabolites that reach distant cancer cells through the circulation and influence cancer behavior. Deoxycholic acid (DCA), a hormone-like metabolite, is a secondary bile acid specifically synthesized by intestinal microbes. DCA may have both pro- and antineoplastic effects in cancers. Methods and results: The pancreatic adenocarcinoma cell lines, Capan-2 and BxPC-3, were treated with 0.7 µM DCA, which corresponds to the reference concentration of DCA in human serum. DCA influenced the expression of epithelial to mesenchymal transition (EMT)-related genes, significantly decreased the expression level of the mesenchymal markers, transcription factor 7- like 2 (TCF7L2), snail family transcriptional repressor 2 (SLUG), CLAUDIN-1, and increased the expression of the epithelial genes, zona occludens 1 (ZO-1) and E-CADHERIN, as shown by real-time PCR and Western blotting. Consequently, DCA reduced the invasion capacity of pancreatic adenocarcinoma cells in Boyden chamber experiments. DCA induced the protein expression of oxidative/nitrosative stress markers. Moreover, DCA reduced aldehyde dehydrogenase 1 (ALDH1) activity in an Aldefluor assay and ALDH1 protein level, suggesting that DCA reduced stemness in pancreatic adenocarcinoma. In Seahorse experiments, DCA induced all fractions of mitochondrial respiration and glycolytic flux. The ratio of mitochondrial oxidation and glycolysis did not change after DCA treatment, suggesting that cells became hypermetabolic. Conclusion: DCA induced antineoplastic effects in pancreatic adenocarcinoma cells by inhibiting EMT, reducing cancer stemness, and inducing oxidative/nitrosative stress and procarcinogenic effects such as hypermetabolic bioenergetics. [ABSTRACT FROM AUTHOR]

This paper addresses the emerging practical requirement that wireless information and power transfer are employed simultaneously in a multiple-input single-output (MISO) secrecy channel. Transmit beamforming without artificial noise and that with artificial noise are considered. In addition, perfect and imperfect channel state information of both the legitimate receivers and eavesdroppers are investigated. These four scenarios correspond to four optimization problems. The considered problems aim to maximize the secrecy rate with constraints on the transmit power and the harvested energy at each receiver. Since these optimization problems are nonconvex, we propose the efficient algorithms based on Difference of Convex (DC) functions programming and DC Algorithm (DCA)—an innovative approach in nonconvex optimization. Exploiting the special structure of these problems, we utilize the semidefinite relaxation technique and S-procedure to reformulate them as general DC programs. The efficient algorithms based on general DCA are developed to solve the corresponding general DC programs. Numerical results are presented which illustrate the effectiveness of our proposed algorithms, they outperform the existing approaches in terms of both quality and rapidity. [ABSTRACT FROM AUTHOR]

A single trusted entity known as a Key Server is in charge of key generation, distribution, and management in centralized key management schemes. To prevent eavesdropping and protect the exchange content, a group key is used to encrypt the group communication. This management mechanism is typically based on a binary tree structure. When the membership of a group changes dynamically, the group key must be changed, triggering a certain updated cost. This paper addresses an important problem in centralized dynamic group key management. It consists in finding a set of leaf nodes in a binary key tree to insert new members with minimal insertion cost and keeping the tree as balanced as possible. The two mentioned important objectives are combined into a unified (deterministic) optimization model whose objective function contains discontinuous step functions with binary variables, which is known to be NP-hard. We then reformulate the problem as a combinatorial optimization program with continuous objective by introducing new binary variables. Applying penalty techniques, it results in a standard DC (Difference of Convex functions) program that can be solved efficiently by DCA (DC algorithm). Besides, the insertion nodes must be the leaf nodes, we introduce a two-step algorithm to reduce the model complexity: the first is to find the set of leaf nodes, while the second is to solve the simplified optimization problem. Numerical experiments have been studied intensively to justify the merit of our proposed model as well as the corresponding DCA. [ABSTRACT FROM AUTHOR]

We study a challenging problem in machine learning that is the reduced-rank multitask linear regression with covariance matrix estimation. The objective is to build a linear relationship between multiple output variables and input variables of a multitask learning process, taking into account the general covariance structure for the errors of the regression model in one hand, and reduced-rank regression model in another hand. The problem is formulated as minimizing a nonconvex function in two joint matrix variables (X,Θ) under the low-rank constraint on X and positive definiteness constraint on Θ. It has a double difficulty due to the non-convexity of the objective function as well as the low-rank constraint. We investigate a nonconvex, nonsmooth optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for this hard problem. A penalty reformulation is considered which takes the form of a partial DC program. An alternating DCA and its inexact version are developed, both algorithms converge to a weak critical point of the considered problem. Numerical experiments are performed on several synthetic and benchmark real multitask linear regression datasets. The numerical results show the performance of the proposed algorithms and their superiority compared with three classical alternating/joint methods. [ABSTRACT FROM AUTHOR]

Dichloroacetate (DCA), a pyruvate dehydrogenase kinase inhibitor, is often used to treat lactic acidosis and malignant tumors. Increasing studies have shown that DCA has neuroprotective effects. Here, we explored the role and mechanism of DCA in Sepsis associated encephalopathy (SAE). Single-cell analysis was used to determine the important role of PDK4 in SAE and identify the cell type. GO and GSEA analysis were used to determine the correlation between DCA and pyroptosis. Through LPS + ATP stimulation, a microglia pyroptosis model was established to observe the expression level of intracellular pyroptosis-related proteins under DCA intervention, and further detect the changes in intracellular ROS and JC-1. Additionally, a co-culture environment of microglia and neuron was simply constructed to evaluate the effect of DCA on activated microglia-mediated neuronal apoptosis. Finally, Novel object recognition test and the Morris water maze were used to explore the effect of DCA on cognitive function in mice from different groups after intervention. Based on the above experiments, this study concludes that DCA can improve the ratio of peripheral and central M1 macrophages, inhibit NLRP3-mediated pyroptosis through ROS and mitochondrial membrane potential (MMP). DCA can reduce neuron death caused by SAE and improve cognitive function in LPS mice. In SAE, DCA may be a potential candidate drug for the treatment of microglia-mediated neuroinflammation.Graphical Abstract: Dichloroacetate (DCA), a pyruvate dehydrogenase kinase inhibitor, is often used to treat lactic acidosis and malignant tumors. Increasing studies have shown that DCA has neuroprotective effects. Here, we explored the role and mechanism of DCA in Sepsis associated encephalopathy (SAE). Single-cell analysis was used to determine the important role of PDK4 in SAE and identify the cell type. GO and GSEA analysis were used to determine the correlation between DCA and pyroptosis. Through LPS + ATP stimulation, a microglia pyroptosis model was established to observe the expression level of intracellular pyroptosis-related proteins under DCA intervention, and further detect the changes in intracellular ROS and JC-1. Additionally, a co-culture environment of microglia and neuron was simply constructed to evaluate the effect of DCA on activated microglia-mediated neuronal apoptosis. Finally, Novel object recognition test and the Morris water maze were used to explore the effect of DCA on cognitive function in mice from different groups after intervention. Based on the above experiments, this study concludes that DCA can improve the ratio of peripheral and central M1 macrophages, inhibit NLRP3-mediated pyroptosis through ROS and mitochondrial membrane potential (MMP). DCA can reduce neuron death caused by SAE and improve cognitive function in LPS mice. In SAE, DCA may be a potential candidate drug for the treatment of microglia-mediated neuroinflammation. [ABSTRACT FROM AUTHOR]

Bile acids are soluble derivatives of cholesterol produced in the liver that subsequently undergo bacterial transformation yielding a diverse array of metabolites. The bulk of bile acid synthesis takes place in the liver yielding primary bile acids; however, other tissues have also the capacity to generate bile acids (e.g. ovaries). Hepatic bile acids are then transported to bile and are subsequently released into the intestines. In the large intestine, a fraction of primary bile acids is converted to secondary bile acids by gut bacteria. The majority of the intestinal bile acids undergo reuptake and return to the liver. A small fraction of secondary and primary bile acids remains in the circulation and exert receptor-mediated and pure chemical effects (e.g. acidic bile in oesophageal cancer) on cancer cells. In this review, we assess how changes to bile acid biosynthesis, bile acid flux and local bile acid concentration modulate the behavior of different cancers. Here, we present in-depth the involvement of bile acids in oesophageal, gastric, hepatocellular, pancreatic, colorectal, breast, prostate, ovarian cancer. Previous studies often used bile acids in supraphysiological concentration, sometimes in concentrations 1000 times higher than the highest reported tissue or serum concentrations likely eliciting unspecific effects, a practice that we advocate against in this review. Furthermore, we show that, although bile acids were classically considered as pro-carcinogenic agents (e.g. oesophageal cancer), the dogma that switch, as lower concentrations of bile acids that correspond to their serum or tissue reference concentration possess anticancer activity in a subset of cancers. Differences in the response of cancers to bile acids lie in the differential expression of bile acid receptors between cancers (e.g. FXR vs. TGR5). UDCA, a bile acid that is sold as a generic medication against cholestasis or biliary surge, and its conjugates were identified with almost purely anticancer features suggesting a possibility for drug repurposing. Taken together, bile acids were considered as tumor inducers or tumor promoter molecules; nevertheless, in certain cancers, like breast cancer, bile acids in their reference concentrations may act as tumor suppressors suggesting a Janus-faced nature of bile acids in carcinogenesis. [ABSTRACT FROM AUTHOR]

DC (Difference of Convex functions) programming and DCA (DC Algorithm) play a key role in nonconvex programming framework. These tools have a rich and successful history of thirty five years of development, and the research in recent years is being increasingly explored to new trends in the development of DCA: design novel DCA variants to improve standard DCA, to deal with the scalability and with broader classes than DC programs. Following these trends, we address in this paper the two wide classes of nonconvex problems, called partial DC programs and generalized partial DC programs, and investigate an alternating approach based on DCA for them. A partial DC program in two variables (x , y) ∈ R n × R m takes the form of a standard DC program in each variable while fixing other variable. A so-named alternating DCA and its inexact/generalized versions are developed. The convergence properties of these algorithms are established: both exact and inexact alternating DCA converge to a weak critical point of the considered problem, in particular, when the Kurdyka–Łojasiewicz inequality property is satisfied, the algorithms furnish a Fréchet/Clarke critical point. The proposed algorithms are implemented on the problem of finding an intersection point of two nonconvex sets. Numerical experiments are performed on an important application that is robust principal component analysis. Numerical results show the efficiency and the superiority of the alternating DCA comparing with the standard DCA as well as a well known alternating projection algorithm. [ABSTRACT FROM AUTHOR]

Universum data that do not belong to any class of a classification problem can be exploited to utilize prior knowledge to improve generalization performance. In this paper, we design a novel parametric ν-support vector machine with universum data (U Par-ν-SVM). Unlabeled samples can be integrated into supervised learning by means of U Par-ν-SVM. We propose a fast method to solve the suggested problem of U Par-ν-SVM. The primal problem of U Par-ν-SVM, which is a nonconvex optimization problem, is transformed into an unconstrained optimization problem so that the objective function can be treated as a difference of two convex functions (DC). To solve this unconstrained problem, a boosted difference of convex functions algorithm (BDCA) based on a generalized Newton method is suggested (named DC- U Par-ν-SVM). We examined our approach on UCI benchmark data sets, NDC data sets, a handwritten digit recognition data set, and a landmine detection data set. The experimental results confirmed the effectiveness and superiority of the proposed method for solving classification problems in comparison with other methods. [ABSTRACT FROM AUTHOR]

Human Activity Recognition (HAR) in videos using convolution neural network become the preferred choice for researcher due to the tremendous success of deep learning models for visual recognition applications. After the invention of the low-cost depth sensor, multiple modalities based activity recognition systems were successfully developed in the past decade. Although it is always challenging to recognize the complex human activities in videos. In this work, we proposed a deep bottleneck multimodal feature fusion (D-BMFF) framework that fused three different modalities of RGB, RGB-D(depth) and 3D coordinates information for activity classification. It helps to better recognize and make full use of information available simultaneously from a depth sensor. During the training process RGB and depth, frames are fed at regular intervals for an activity video while 3D coordinates are first converted into single RGB skeleton motion history image (RGB-SklMHI). We have extracted the features from multimodal data inputs using the latest deep pre-trained network architecture. The multimodal feature obtained from bottleneck layers before the top layer is fused by using multiset discriminant correlation analysis (M-DCA), which allows for robust visual action modeling. Finally, using a linear multiclass support vector machine (SVM) method, the fused features are categorized. The proposed approach is evaluated over four standard RGB-D datasets: UT-Kinect, CAD-60, Florence 3D and SBU Interaction. Our framework produces outstanding results and outperformed the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Sentence compression is an important problem in natural language processing with wide applications in text summarization, search engine and human–AI interaction system etc. In this paper, we design a hybrid extractive sentence compression model combining a probability language model and a parse tree language model for compressing sentences by guaranteeing the syntax correctness of the compression results. Our compression model is formulated as an integer linear programming problem, which can be rewritten as a difference-of-convex (DC) programming problem based on the exact penalty technique. We use a well-known efficient DC algorithm—DCA to handle the penalized problem for local optimal solutions. Then a hybrid global optimization algorithm combining DCA with a parallel branch-and-bound framework, namely PDCABB, is used for finding global optimal solutions. Numerical results demonstrate that our sentence compression model can provide excellent compression results evaluated by F-score, and indicate that PDCABB is a promising algorithm for solving our sentence compression model. [ABSTRACT FROM AUTHOR]

Studying the effect of altitude on species distribution may help us to predict the response of species to future climate changes, which will likely cause upward migration of vegetation zones. In this study, we aimed to analyze distribution and abundance patterns of Potamogetonaceae along an altitudinal gradient and to determine the species characterizing a priori defined five altitudinal groups. We included 294 sampling for 19 species from 141 wetlands across Turkey with an elevation gradient of 2700 m. Analysis of similarities (ANOSIM) found significant differences in species assemblages only between some altitudinal groups. Seven species were found in either high or low altitudes. Stuckenia pectinata had the highest contribution to all groups except one in analysis of similarity percentages. Detrended correspondence analysis revealed a clear altitudinal gradient by placing species under six clusters. Even widespread species occurring in all altitudes showed a tendency of altitudinal preference. The results were inferred from our physicochemical measurements for the species and relevant literature. Exclusively highland species were found in waters with similar physical and chemical properties (i.e. low electrical conductivity, salinity, and ammonium concentrations). However, lowland species were sampled from very diverse aquatic habitats. Among the lowland species Potamogeton acutifolius was found under low values for the above-mentioned physicochemical water parameters but Althenia orientalis showed extremely high values, as well as Potamogeton coloratus and Potamogeton nodosus. Understanding elevational distribution of macrophytes is especially important due to difficulties in their upward migration and availability of suitable aquatic habitats. [ABSTRACT FROM AUTHOR]

Biometric system has been widely adopted for human verification or identification, so inherently it requires the characteristics like high security, accuracy and acceptability. However, most of existing unimodal biometric systems provide low-middle security and are vulnerable to attacks. Therefore, multimodal biometric system fuses information from multiple modalities to break these limitations. This paper presents a novel hybrid fusion model for a multimodal biometric system. The hybrid fusion model includes an improved feature fusion algorithm and a novel weighting vote strategy. It captures canonical characteristics with multi-set structure and utilizes score distribution information to help guiding decision-making. The system was examined on databases from CASIA, PolyU and SDU respectively, which provided high precision and strong robustness over previous work. Experimental results showed that the proposed approach achieved an average accuracy of 99.33%, which outperformed other fusion strategies in multimodal biometric systems. [ABSTRACT FROM AUTHOR]

Estimation of fluid and rock properties of a hydrocarbon reservoir is always a challenging matter; especially, it is true for heterogeneous carbonate reservoirs. Petrophysical logs and laboratory activities are common methods for characterizing a hydrocarbon reservoir. This method in conjunction with geostatistical methods is applied to relatively homogeneous sandstone reservoirs or matrix media of dual-porosity heterogeneous carbonate reservoirs. To estimate properties of fracture system of a dual-media carbonate reservoir, outcrop properties, electrical borehole scans, fractal discrete fracture network and analogy with other reservoirs are common methods. Results which obtained from these methods describe the reservoir in a static way and could be relied on them for very small portion of the reservoir. In this paper, a dynamic procedure for describing reservoir features is proposed in order to enhance the conventional reservoir characterization methods. This method utilizes the reported production data for a specific period of time in conjunction with rock and fluid properties to estimate drainage radius of the well and matrix block height, porosity and width of fracture in the estimated drainage radius. The presented method is elaborated through its application in a real case. By this method, one can generate maps of matrix block size and fracture width and porosity throughout the reservoir. Also, it could be a powerful tool for estimation of effectiveness of acid/hydraulic fracturing activity. [ABSTRACT FROM AUTHOR]

As a development of ν-support vector machine (ν-SVM), parametric-margin ν-support vector machine (Par-ν-SVM) can be useful in many cases, especially heteroscedastic noise classification problems. The present article proposes a novel and fast method to solve the primal problem of Par-ν-SVM (named as DC-Par-ν-SVM), while Par-ν-SVM maximizes the parametric-margin by solving a dual quadratic programming problem. In fact, the primal non-convex problem is converted into an unconstrained problem to express the objective function as the difference of convex functions (DC). The DC-Algorithm (DCA) based on generalized Newton's method is proposed to solve the unconstrained problem cited. Numerical experiments performed on several artificial, real-life, UCI and NDC data sets showed the superiority of the DC-Par-ν-SVM in terms of both accuracy and learning speed. [ABSTRACT FROM AUTHOR]

The feeding habits of brown trout (age 2+ and 3+ years) in the small Orzega River (Lake Onega basin) are analyzed with an autumn decrease in the number of accessible food items. Along with the previously determined mechanisms for compensating for this phenomenon (feeding directly from the bottom and consumption of large items), a sharp increase in the variability of the individual feeding habits of sea trout in October is revealed both by the composition of the contents of its stomachs and by the amount of consumed feed. The food differentiation of individuals makes it possible to expand the food supply of the brown trout population in the river and effectively use the food resources of the small watercourse, which is particularly important during the period of low availability. [ABSTRACT FROM AUTHOR]

We evaluated the structural responses of marine sponge assemblages to different substrates as well as their positioning around Ilha Grande, a local hotspot of marine biodiversity sheltered in a bay area off Southeast Brazil. Sampling sites were distributed between sides of the island facing the continent (North) and ocean (South) across two depth-dependent substrates. As proved by ordination and permutation analyses, these two factors accounted for nearly half the variation observed among assemblages, either with species abundance or coverage area data. Out of 46 OTUs surveyed (~ 3000 individuals), Tedania (Tedania) ignis, Scopalina ruetzleri, and Iotrochota arenosa dominated the community, even though most of the dissimilarity detected among assemblages relied on 20% of the OTUs. The northern side was proved as more diverse, and the south-facing side held more unspecific, putatively new OTUs. Assemblages dwelling on rocky-to-sandy interface bottoms were meager in species number, although they mainly included Dragmacidon reticulatum and the endemic Brazilian sponge Polymastia janeirensis. By highlighting structuring factors operating on Ilha Grande's sponge assemblage, we hope to support future monitoring surveys on an environment increasingly impacted by human activities over the years. [ABSTRACT FROM AUTHOR]

We propose a local regularization of elliptic optimal control problems which involves the nonconvex L q quasi-norm penalization in the cost function. The proposed Huber type regularization allows us to formulate the PDE constrained optimization instance as a DC programming problem (difference of convex functions) that is useful to obtain necessary optimality conditions and tackle its numerical solution by applying the well known DC algorithm used in nonconvex optimization problems. By this procedure we approximate the original problem in terms of a consistent family of parameterized nonsmooth problems for which there are efficient numerical methods available. Finally, we present numerical experiments to illustrate our theory with different configurations associated to the parameters of the problem. [ABSTRACT FROM AUTHOR]

We investigate a powerful nonconvex optimization approach based on Difference of Convex functions (DC) programming and DC Algorithm (DCA) for reinforcement learning, a general class of machine learning techniques which aims to estimate the optimal learning policy in a dynamic environment typically formulated as a Markov decision process (with an incomplete model). The problem is tackled as finding the zero of the so-called optimal Bellman residual via the linear value-function approximation for which two optimization models are proposed: minimizing the ℓp-norm of a vector-valued convex function, and minimizing a concave function under linear constraints. They are all formulated as DC programs for which attractive DCA schemes are developed. Numerical experiments on various examples of the two benchmarks of Markov decision process problems—Garnet and Gridworld problems, show the efficiency of our approaches in comparison with two existing DCA based algorithms and two state-of-the-art reinforcement learning algorithms. [ABSTRACT FROM AUTHOR]

The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmic tools. The survey is comprised of three parts. In the first part we present a brief history of the field, while in the second we summarize the state-of-the-art results and recent advances. We focus on main theoretical results and DCA solvers for important classes of difficult nonconvex optimization problems, and then give an overview of real-world applications whose solution methods are based on DCA. The third part is devoted to new trends and important open issues, as well as suggestions for future developments. [ABSTRACT FROM AUTHOR]

We propose a DC (Difference of two Convex functions) formulation approach for sparse optimization problems having a cardinality or rank constraint. With the largest-k norm, an exact DC representation of the cardinality constraint is provided. We then transform the cardinality-constrained problem into a penalty function form and derive exact penalty parameter values for some optimization problems, especially for quadratic minimization problems which often appear in practice. A DC Algorithm (DCA) is presented, where the dual step at each iteration can be efficiently carried out due to the accessible subgradient of the largest-k norm. Furthermore, we can solve each DCA subproblem in linear time via a soft thresholding operation if there are no additional constraints. The framework is extended to the rank-constrained problem as well as the cardinality- and the rank-minimization problems. Numerical experiments demonstrate the efficiency of the proposed DCA in comparison with existing methods which have other penalty terms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel approach in the nonconvex optimization framework for image restoration via a Markov random field (MRF) model. While image restoration is elegantly expressed in the language of MRF's, the resulting energy minimization problem was widely viewed as intractable: it exhibits a highly nonsmooth nonconvex energy function with many local minima, and is known to be NP-hard. The main goal of this paper is to develop fast and scalable approximation optimization approaches to a nonsmooth nonconvex MRF model which corresponds to an MRF with a truncated quadratic (also known as half-quadratic) prior. For this aim, we use the difference of convex functions (DC) programming and DC algorithm (DCA), a fast and robust approach in smooth/nonsmooth nonconvex programming, which have been successfully applied in various fields in recent years. We propose two DC formulations and investigate the two corresponding versions of DCA. Numerical simulations show the efficiency, reliability and robustness of our customized DCAs with respect to the standard GNC algorithm and the Graph-Cut based method-a more recent and efficient approach to image analysis. [ABSTRACT FROM AUTHOR]

We consider the supervised pattern classification in the high-dimensional setting, in which the number of features is much larger than the number of observations. We present a novel approach to the sparse Fisher linear discriminant problem using the $$\ell _0$$ -norm. The resulting optimization problem is nonconvex, discontinuous and very hard to solve. We overcome the discontinuity by using appropriate approximations to the $$\ell _0$$ -norm such that the resulting problems can be formulated as difference of convex functions (DC) programs to which DC programming and DC Algorithms (DCA) are investigated. The experimental results on both simulated and real datasets demonstrate the efficiency of the proposed algorithms compared to some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

An understory vegetation survey of the Pinus wallichiana-dominated temperate forests of Swat District was carried out to inspect the structure, composition and ecological associations of the forest vegetation. A quadrat method of sampling was used to record the floristic and phytosociological data necessary for the analysis using 300 quadrats of 10 × 10 m each. Some vegetation parameters viz. frequency and density for trees (overstory vegetation) as well as for the understory vegetation were recorded. The results revealed that in total, 92 species belonging to 77 different genera and 45 families existed in the area. The largest families were Asteraceae, Rosaceae and Lamiaceae with 12, ten and nine species, respectively. Ward's agglomerative cluster analysis for tree species resulted in three floristically and ecologically distinct community types along different topographic and soil variables. Importance value indices (IVI) were also calculated for understory vegetation and were subjected to ordination techniques, i.e. canonical correspondence analysis (CCA) and detrended correspondence analysis (DCA). DCA bi-plots for stands show that most of the stands were scattered around the centre of the DCA bi-plot, identified by two slightly scattered clusters. DCA for species bi-plot clearly identified three clusters of species revealing three types of understory communities in the study area. Results of the CCA were somewhat different from the DCA showing the impact of environmental variables on the understory species. CCA results reveal that three environmental variables, i.e. altitude, slope and P (mg/kg), have a strong influence on distribution of stands and species. Impact of tree species on the understory vegetation was also tested by CCA which showed that four tree species, i.e. P. wallichiana A.B. Jackson, Juglans regia Linn., Quercus dilatata Lindl. ex Royle and Cedrus deodara (Roxb. ex Lamb.) G. Don, have strong influences on associated understory vegetation. It is therefore concluded that Swat District has various microclimatic zones with suitable environmental variables to support distinct flora. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of feature selection for Multi-class Support Vector Machines. Two models involving the $$\ell _{0}$$ (the zero norm) and the $$\ell _{2}$$ - $$\ell _{0}$$ regularizations are considered for which two continuous approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) are investigated. The first is DC approximation via several sparse inducing functions and the second is an exact reformulation approach using penalty techniques. Twelve versions of DCA based algorithms are developed on which empirical computational experiments are fully performed. Numerical results on real-world datasets show the efficiency and the superiority of our methods versus one of the best standard algorithms on both feature selection and classification. [ABSTRACT FROM AUTHOR]

For solving a class of ℓ - ℓ - regularized problems we convexify the nonconvex ℓ - ℓ term with the help of its biconjugate function. The resulting convex program is explicitly given which possesses a very simple structure and can be handled by convex optimization tools and standard softwares. Furthermore, to exploit simultaneously the advantage of convex and nonconvex approximation approaches, we propose a two phases algorithm in which the convex relaxation is used for the first phase and in the second phase an efficient DCA (Difference of Convex functions Algorithm) based algorithm is performed from the solution given by Phase 1. Applications in the context of feature selection in support vector machine learning are presented with experiments on several synthetic and real-world datasets. Comparative numerical results with standard algorithms show the efficiency the potential of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a difference of convex algorithm (DCA) to deal with a non-convex data fidelity term, proposed by Aubert and Aujol referred to as the AA model. The AA model was adopted in many subsequent works for multiplicative noise removal, most of which focused on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Noting that the AA model can be naturally split into a difference of two convex functions, we apply the DCA to solve the original AA model. Compared to the gradient projection algorithm considered by Aubert and Aujol, the DCA often converges faster and leads to a better solution. We prove that the DCA sequence converges to a stationary point, which satisfies the first order optimality condition. In the experiments, we consider two applications, image denoising and deblurring, both of which involve multiplicative Gamma noise. Numerical results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for multiplicative noise removal. [ABSTRACT FROM AUTHOR]

Construction of big dams on rivers develops artificial lakes or water reservoirs which conceive alterations in soil properties of the upstream catchment area. An undulating topography and freckly soil properties cause ups and downs in tree diversity, composition and distribution. The study aimed to evaluate the effect of Gobind Sagar reservoir on soil properties relative to the distance from it and aßsess its effect on tree diversity, evenness and their distribution in tropical and subtropical forests. Based on data analysis it was found that the soil moisture and organic carbon decreased along with increasing distance from the reservoir. It played a significant role in varying tree diversity. The sites distributed within 0-2 km showed significantly higher a and β-diversity indices. Tree species richness and diversity indices showed a strong correlation ( p < 0.05) with soil moisture and organic carbon content. Simpson's and McIntosh evenness indices showed a strong negative correlation with soil bulk density. Indirect Detrended Correspondence Analysis (DCA) identified soil moisture and soil organic carbon as two major environmental gradients that influenced tree diversity and their distribution in five tropical and four subtropical forests in an upstream catchment of the reservoir. Mixed forests inhabited moist sites and Acacia-Pinus forests showed an inclination to dry areas. Canonical Correspondence Analysis (CCA) revealed that the tree species in tropical forests were mainly affected by driving forces such as soil moisture, organic carbon and bulk density whereas, in subtropical forest tree species were influenced by elevation, soil pH, EC and clay content. [ABSTRACT FROM AUTHOR]

The paper investigates DC programming and DCA for both modeling discrete portfolio optimization under concave transaction costs as DC programs, and their solution. DC reformulations are established by using penalty techniques in DC programming. A suitable global optimization branch and bound technique is also developed where a DC relaxation technique is used for lower bounding. Numerical simulations are reported that show the efficiency of DCA and the globality of its computed solutions, compared to standard algorithms for nonconvex nonlinear integer programs. [ABSTRACT FROM AUTHOR]

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algorithm for quadratic problems with box constraints (the DCA for QB), a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods. Graphical Abstract: Although the first-order parameter perturbation method (FM) is effective for solving the static response problem of structures with interval parameters with small uncertainties, the method may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, a new approach (the proposed method:PM) is presented based on the second-order Taylor series expansion and the DCA for QB(the difference of convex functions algorithm for quadratic problems with box constraints). [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

We develop an exact penalty approach for feature selection in machine learning via the zero-norm $$\ell _{0}$$ -regularization problem. Using a new result on exact penalty techniques we reformulate equivalently the original problem as a Difference of Convex (DC) functions program. This approach permits us to consider all the existing convex and nonconvex approximation approaches to treat the zero-norm in a unified view within DC programming and DCA framework. An efficient DCA scheme is investigated for the resulting DC program. The algorithm is implemented for feature selection in SVM, that requires solving one linear program at each iteration and enjoys interesting convergence properties. We perform an empirical comparison with some nonconvex approximation approaches, and show using several datasets from the UCI database/Challenging NIPS 2003 that the proposed algorithm is efficient in both feature selection and classification. [ABSTRACT FROM AUTHOR]

Introduction: Lung cancer is the leading cause of cancer death. Radiation therapy plays a key role in its treatment. Ionizing radiation induces cell death through chromosomal aberrations, which trigger mitotic catastrophe and apoptosis. However, many lung cancer patients show resistance to radiation. Dichloroacetate (DCA) is a small molecule that can promote mitochondrial activation by increasing the influx of pyruvate. Here, we tested whether DCA may increase the sensitivity of non-small cell lung cancer (NSCLC) cells to radiation through this mechanism. Methods: Two representative NSCLC cell lines (A549 and H1299) were tested for their sensitivity to radiation with and without pre-exposure to DCA. The treatment efficacy was evaluated using a clonogenic survival assay. An extracellular flux analyzer was used to assess the effect of DCA on cellular oxygen consumption as a surrogate marker for mitochondrial activity. Results: We found that DCA increases the oxygen consumption rate in both A549 and H1299 cells by 60 % ( p = 0.0037) and 20 % ( p = 0.0039), respectively. Pre-exposure to DCA one hour before radiation increased the cytotoxic death rate 4-fold in A549 cells (55 to 13 %, p = 0.004) and 2-fold in H1299 cells (35 to 17 %, p = 0.28) respectively, compared to radiation alone. Conclusion: Mitochondrial induction by DCA may serve as a radio-sensitizer in non-small cell lung cancer. [ABSTRACT FROM AUTHOR]

Coastal sand dune vegetation in Central Black Sea Region of Turkey was investigated by numerical methods. Eight plant associations were determined according to two-way indicator species analysis (TWINSPAN) and detrended correspondence analysis (DCA). Plant associations were also classified according to NATURA 2000 and European Nature Information System. Coastal dune ecosystems in the Central Black Sea Region include eight habitat types. Eight plant associations belonging to four classes, order and alliances are described and five of them are new associations. TWINSPAN revealed the existence of a gradient from drift line to the inner parts. These have been separated into shifting dunes and fixed dunes. DCA allowed determining the plant associations in shifting dunes along the shoreline as well as the annual vegetation of drift line and embryonic shifting dunes and of fixed coastal dunes with herbaceous vegetation. The syntaxonomical classification is given in the following: [ABSTRACT FROM AUTHOR]

This article uses document co-citation analysis to objectively explore the underlying structure of the intellectual property research domain, taken from a managerial and strategic standpoint. The goal of this study is identifying its main research areas, understanding its current state of development and suggesting potential future directions, by analyzing the co-citations from 181 papers published between 1992 and 2011 in the most influential academic journals. Five main clusters have been identified, mapped, and labeled as follows: Economics of patent system, technological and institutional capabilities, university patenting, intellectual property exploitation, and division of labor. Their most active areas on this topic, and the most influential and co-cited papers have been identified and described. Also, intra- and inter-cluster knowledge base diversity has been assessed by using indicators stemming from the domains of information theory and biology. A t test has been performed to assess the significance of the inter-cluster diversity. The knowledge bases of these five clusters are significantly diverse, this meaning that they are five co-existing paradigms. [ABSTRACT FROM AUTHOR]

In the last years many techniques in bioinformatics have been developed for the central and complex problem of optimally aligning biological sequences. In this paper we propose a new optimization approach based on DC (Difference of Convex functions) programming and DC Algorithm (DCA) for the multiple sequence alignment in its equivalent binary linear program, called 'Maximum Weight Trace' problem. This problem is beforehand recast as a polyhedral DC program with the help of exact penalty techniques in DC programming. Our customized DCA, requiring solution of a few linear programs, is original because it converges after finitely many iterations to a binary solution while it works in a continuous domain. To scale-up large-scale (MSA), a constraint generation technique is introduced in DCA. Preliminary computational experiments on benchmark data show the efficiency of the proposed algorithm DCAMSA, which generally outperforms some standard algorithms. [ABSTRACT FROM AUTHOR]

We offer an efficient approach based on difference of convex functions (DC) optimization for self-organizing maps (SOM). We consider SOM as an optimization problem with a nonsmooth, nonconvex energy function and investigated DC programming and DC algorithm (DCA), an innovative approach in nonconvex optimization framework to effectively solve this problem. Furthermore an appropriate training version of this algorithm is proposed. The numerical results on many real-world datasets show the efficiency of the proposed DCA based algorithms on both quality of solutions and topographic maps. [ABSTRACT FROM AUTHOR]