Relaxations and Duality for Multiobjective Integer Programming

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point

Sea level Projections with Machine Learning using Altimetry and Climate Model ensembles

Satellite altimeter observations retrieved since 1993 show that the global mean sea level is rising at an unprecedented rate (3.4mm/year). With almost three decades of observations, we can now investigate the contributions of anthropogenic climate-change signals such as greenhouse gases, aerosols, and biomass burning in this rising sea level. We use machine learning (ML) to investigate future patterns of sea level change. To understand the extent of contributions from the climate-change signals, and to help in forecasting sea level change in the future, we turn to climate model simulations. This work presents a machine learning framework that exploits both satellite observations and climate model simulations to generate sea level rise projections at a 2-degree resolution spatial grid, 30 years into the future. We train fully connected neural networks (FCNNs) to predict altimeter values through a non-linear fusion of the climate model hindcasts (for 1993-2019). The learned FCNNs are then applied to future climate model projections to predict future sea level patterns. We propose segmenting our spatial dataset into meaningful clusters and show that clustering helps to improve predictions of our ML model

Impact of Carica papaya L. Fruit juice on plasma variables and tissue glycogen of induced hyperglycemic albino rats

It was aimed at to evaluate the activity of Carica papaya fruit juice on induced diabetic rats (Rattus norvegicus) with a view of proposing a management scheme. Animals were sacrificed after treatment with unripe and ripe papaya juice. The plasma glucose, cholesterol, protein and tissue glycogen concentrations were estimated. Feeding of papaya juice raised the levels of these parameters more than the controlled value throughout the work. The results showed that the concentrations of these parameters were significantly increased (p<0.05). The rise was more with unripe papaya when compared to ripe papaya. However, papaya intake must be with caution since its consumption increases blood glucose concentration.Keywords: Papaya, Fruit juice, Albino rats, Plasma variables, Hyperglycemia, Diabete

Temporal Expression Profiling Identifies Pathways Mediating Effect of Causal Variant on Phenotype

Even with identification of multiple causal genetic variants for common human diseases, understanding the molecular processes mediating the causal variants' effect on the disease remains a challenge. This understanding is crucial for the development of therapeutic strategies to prevent and treat disease. While static profiling of gene expression is primarily used to get insights into the biological bases of diseases, it makes differentiating the causative from the correlative effects difficult, as the dynamics of the underlying biological processes are not monitored. Using yeast as a model, we studied genome-wide gene expression dynamics in the presence of a causal variant as the sole genetic determinant, and performed allele-specific functional validation to delineate the causal effects of the genetic variant on the phenotype. Here, we characterized the precise genetic effects of a functional MKT1 allelic variant in sporulation efficiency variation. A mathematical model describing meiotic landmark events and conditional activation of MKT1 expression during sporulation specified an early meiotic role of this variant. By analyzing the early meiotic genome-wide transcriptional response, we demonstrate an MKT1-dependent role of novel modulators, namely, RTG1/3, regulators of mitochondrial retrograde signaling, and DAL82, regulator of nitrogen starvation, in additively effecting sporulation efficiency. In the presence of functional MKT1 allele, better respiration during early sporulation was observed, which was dependent on the mitochondrial retrograde regulator, RTG3. Furthermore, our approach showed that MKT1 contributes to sporulation independent of Puf3, an RNA-binding protein that steady-state transcription profiling studies have suggested to mediate MKT1-pleiotropic effects during mitotic growth. These results uncover interesting regulatory links between meiosis and mitochondrial retrograde signaling. In this study, we highlight the advantage of analyzing allele-specific transcriptional dynamics of mediating genes. Applications in higher eukaryotes can be valuable for inferring causal molecular pathways underlying complex dynamic processes, such as development, physiology and disease progression

Can Avalanche Deposits be Effectively Detected by Deep Learning on Sentinel-1 Satellite SAR Images?

International audienceAchieving reliable observations of avalanche debris is crucial for many applications including avalanche forecasting. The ability to continuously monitor the avalanche activity, in space and time, would provide indicators on the potential instability of the snowpack and would allow a better characterization of avalanche risk periods and zones. In this work, we use Sentinel-1 SAR (synthetic aperture radar) data and an independent in-situ avalanche inventory (ground truth) to automatically detect avalanche debris in the French Alps during the remarkable winter season 2017-18. Convolutional neural networks are applied on SAR image patches to locate avalanche debris signatures. We are able to successfully locate new avalanche deposits with as much as 77% confidence on the most susceptible mountain zone (compared to 53% with a baseline method). One of the challenges of this study is to make an efficient use of remote sensing measurements on a complex terrain. It explores the following questions: to what extent can deep learning methods improve the detection of avalanche deposits and help us to derive relevant avalanche activity statistics at different scales (in time and space) that could be useful for a large number of users (researchers, forecasters, government operators)

Meiotic Interactors of a Mitotic Gene TAO3 Revealed by Functional Analysis of its Rare Variant

Studying the molecular consequences of rare genetic variants has the potential to identify novel and hitherto uncharacterized pathways causally contributing to phenotypic variation. Here, we characterize the functional consequences of a rare coding variant of TAO3, previously reported to contribute significantly to sporulation efficiency variation in Saccharomyces cerevisiae. During mitosis, the common TAO3 allele interacts with CBK1-a conserved NDR kinase. Both TAO3 and CBK1 are components of the RAM signaling network that regulates cell separation and polarization during mitosis. We demonstrate that the role of the rare allele TAO3(4477C) in meiosis is distinct from its role in mitosis by being independent of ACE2-a RAM network target gene. By quantitatively measuring cell morphological dynamics, and expressing the TAO3(4477C) allele conditionally during sporulation, we show that TAO3 has an early role in meiosis. This early role of TAO3 coincides with entry of cells into meiotic division. Time-resolved transcriptome analyses during early sporulation identified regulators of carbon and lipid metabolic pathways as candidate mediators. We show experimentally that, during sporulation, the TAO3(4477C) allele interacts genetically with ERT1 and PIP2, regulators of the tricarboxylic acid cycle and gluconeogenesis metabolic pathways, respectively. We thus uncover a meiotic functional role for TAO3, and identify ERT1 and PIP2 as novel regulators of sporulation efficiency. Our results demonstrate that studying the causal effects of genetic variation on the underlying molecular network has the potential to provide a more extensive understanding of the pathways driving a complex trait

Robust dynamic optimization: theory and applications

Thesis (Ph.D.)--University of Washington, 2018Many applications in decision-making use a dynamic optimization framework to model a system evolving uncertainly in discrete time, and an agent who chooses actions/controls from a set of available choices in order to minimize a suitable cost function. An important aspect of model formulation is the choice of input parameters. These are traditionally estimated from historical data and prior domain knowledge, and treated as known quantities in the decision-making process. This approach ignores any estimation errors or misspecification in the problem data, leading to potentially suboptimal solutions. Robust optimization addresses this issue by treating the parameters themselves as unknown quantities, known only to lie within some set of plausible values called the ‘uncertainty set’. The decision-maker then follows a conservative approach and minimizes a ‘worst-case’ cost over all possible values of the parameter. Problems of this nature are the subject of this dissertation. The first chapter provides a background on infinite-horizon Markov decision processes (MDPs) and the Newsvendor model. MDPs are sequential decision-making problems with infinitely many decision epochs. At the end of every epoch, the next state of the system is prescribed via a transition probability depending on the current state and the action cho- sen. The robust formulation allows for these transition probabilities to be unknown, and the decision-maker minimizes the maximum expected total discounted cost. A detailed analytical treatment of robust MDPs with bounded immediate costs, along with robust versions of the the standard solution methods of value iteration and policy iteration, is available in the literature. However, these methods cannot be implemented when the state-space is countable. Further, no theoretical framework is available for the case when costs are unbounded. These issues are addressed in Chapters 2 to 4. The Newsvendor model is a classical framework for inventory management over a finite horizon under demand ambiguity, and a robust formulation described in Chapter 5 circumvents the issue of assuming distributional information on this demand. Robust nonstationary MDPs: In the second chapter, I consider an infinite-horizon robust MDP for which immediate costs are time-dependent but uniformly bounded, and the uncertainty sets vary with time. The state- and action-spaces are assumed to be finite. The optimal value function can be obtained from the robust Bellman equations [28], but the non- stationarity of the data results in an infinite system of equations to be solved. I provide a policy iteration algorithm which uses finite-dimensional approximations to policy evaluation and policy improvement, so that each step of the algorithm requires a finite amount of memory and computation, and as such, can be used in practice. These approximations are chosen adaptively to guarantee that the algorithm achieves sufficient improvement in each iteration, so that the values of the policies generated by the algorithm monotonically converge pointwise to the optimal. The policies converge subsequentially to an optimal policy. Robust countable-state MDPs with bounded costs: In the third chapter, I generalize the above setup to solve robust stationary MDPs with countable state-spaces. Im- mediate costs as well as the uncertainty sets are time-invariant in this case. The costs are non-negative and bounded, and the action-spaces are finite. In this case as well, an as-is execution of the existing policy iteration method is not possible, owing to three main reasons. The first issue arises due to the countable nature of the state-space that necessitates the solution of an infinite system of equations, and is addressed via state-space truncation. The other two complications arise from the nonlinearity of the robust evaluation operator and the need for solving the so-called inner problems to arbitrary accuracy. These are addressed by successive approximation and a careful selection of uncertainty sets. Thus, I present an approximate policy iteration algorithm that can be used in practice. Value functions of the policies generated by the algorithm converge to the optimal, while the policies themselves converge subsequentially to an optimal policy. Robust MDPs with interval uncertainty sets, robust MDPs with bounded state-transitions, and a robust equipment replacement model are presented as examples where the algorithm can be implemented. Robust countable-state MDPs with unbounded costs: The third chapter further widens the scope by allowing the immediate cost functions to be unbounded. A theoretical treatment of these MDPs is not available in the literature, and I develop such a framework here. Standard assumptions for unbounded-cost MDPs are generalized to the robust case. The robust Bellman operator is shown to be a J-step contraction mapping, which guarantees the existence of a unique solution to the robust Bellman equations. Optimality of the robust Bellman equations is also established. A robust multi-period newsvendor model with inventory balance constraints: In the fourth chapter, I study a different approach to dynamic optimization by means of an application in inventory control. A seller managing the inventory of a single product over multiple periods must determine the optimal order quantity per period in the face of uncertain demand. This problem is solved via a newsvendor model, and the optimal solution is a function of the purchase, shortage and holding costs as well as the revenue earned per unit. Here, I formulate a robust multi-period newsvendor model to address the ambiguity in demand, and the seller maximizes his ‘worst-case’ total profit. Closed-form expressions for robust optimal order quantities are provided, and their relationship with various cost parameters is analyzed. Explicit optimal solutions to the inner-problems are obtained for a large class of uncertainty sets. Additionally, a numerical comparison of the robust model with a stochastic one is presented for benchmarking

Comparing Risks and Benefits for Value Enhancement of Online Purchase

In a developing economy, the acceptability of e–retailing is not very new, but the potential of online marketing in market research and analysis is still largely unexplored. This article is an attempt to understand the psyche of Indian online consumers. As consumers have their own preconceived notions toward this growing purchasing environment, it becomes important for e-retailers to understand the consumers’ perceptions and attitudes toward online purchases. This paper integrates the dimensions of the risks and benefits with the Theory of Planned Behavior (TPB) to understand how consumers adopt their online purchase processes. Four hundred and sixty-eight valid responses were analyzed using structural equation modeling on AMOS 21 to identify the relationship between the different factors and the intention to purchase online. The paper concludes that consumers’ purchase intentions are jointly determined by their attitude towards online purchases and the subjective norm. Furthermore, their attitude is determined by the sub-dimensions of perceived benefits (hedonic benefit, convenience benefit, economic benefit and variety) and the sub-dimensions of perceived risk (product risk and financial risk)

Fundamental principles governing sporulation efficiency: A network theory approach

Integrating network theory approaches over time-resolved genome-wide gene expression data, we proposed a network-based framework, which considered intricate dynamic regulatory relationships of transcription factors and target genes, for assessing the molecular underpinnings underlying extreme phenotypic differences between two strains of the yeast, Saccharomyces cerevisiae. Using network attributes which have demonstrated tremendous success in understanding and predicting behaviors in a wide range of complex biological and social systems, we identified factors and candidate genes that acted as crucial regulators of sporulation in the highly sporulating SK1 strain. We then carried out independent network-based investigations of S288c gene expression profiles and identified the molecular events that occur in SK1 strain but fail to occur in S288c strain, which eventually lead to low sporulation efficiency of S288c. Results suggested that late appearance of known early sporulation regulators and a delay in crosstalk between functional modules can be construed as the prime reasons behind low sporulation efficiency of the S288c. Revelation of meiosis-associated genes for SK1 and mitotic genes for S288c through weak ties analysis and late appearance of hierarchical modularity were further indications of delay in regulatory activities essential to initiate sporulation in S288c. Our results demonstrate the potential of this framework in identifying candidate nodes contributing to phenotypic diversity of developmental processes in natural populations