Compact Formulation Research Articles

Improved oral delivery of clonazepam through liquisolid powder compact formulations: In-vitro and ex-vivo characterization

The liquisolid powder compacts (LSPCs) proved to be the potential solubility improvement strategy for efficient oral delivery of BCS class II and IV drugs. Henceforth, an attempt was made to improve the oral delivery of BCS class II drug clonazepam (CLZ) by formulating into a novel LSPCs. Solubility studies were conducted in different liquid vehicles, namely propylene glycol, span 20 and span 80. The LSPCs were formulated using propylene glycol as non volatile solvent. The effect of different formulation variables on LSPCs performance was evaluated using 32 factorial design. The selected independent variables were % of clonazepam in propylene glycol (X1) and % of sodium starch glycolate (X2) and dependent variables were disintegration time (YDT) and % cumulative drug release at 15th minute (YQ15). LSPCs of CLZ formulated with propylene glycol at optimum drug concentration produced high dissolution profile with acceptable tablet properties. Fourier transform infra-red spectroscopy (FTIR) studies revealed that there was no interaction between drug and polymers, differential scanning calorimetry (DSC) and X-Ray Diffraction (XRD) indicated conversion of crystalline to amorphous form of the CLZ. Further the permeation studies carried out in isolated rat intestine revealed that potential of LSPCs for enhanced permeation of CLZ across rat intestinal barrier. The increase in permeation of clonazepam from LSPCs formulation across rat intestine suggests the potential of LSPC formulation for improved oral delivery of CLZ.

Smallest compact formulation for the permutahedron

In this note, we consider the permutahedron, the convex hull of all permutations of $$\{1,2\ldots ,n\}$$ . We show how to obtain an extended formulation for this polytope from any sorting network. By using the optimal Ajtai–Komlós–Szemerédi sorting network, this extended formulation has $$\varTheta (n\log n)$$ variables and inequalities. Furthermore, from basic polyhedral arguments, we show that this is best possible (up to a multiplicative constant) since any extended formulation has at least $$\varOmega (n \log n)$$ inequalities. The results easily extend to the generalized permutahedron.

Lagrangian relaxation based decomposition for well scheduling in shale-gas systems

Suppressing the effects of liquid loading is a key issue for efficient utilization of mid and late-life wells in shale-gas systems. This state of the wells can be prevented by performing short shut-ins when the gas rate falls below the minimum rate needed to avoid liquid loading. In this paper, we present a Lagrangian relaxation scheme for shut-in scheduling of distributed shale multi-well systems. The scheme optimizes shut-in times and a reference rate for each multi-well pad, such that the total produced rate tracks a given short-term gas demand for the field. By using simple, frequency-tuned well proxy models, we obtain a compact mixed-integer formulation which by Lagrangian relaxation renders a decomposable structure. A set of computational tests demonstrates the merits of the proposed scheme. This study indicates that the method is capable of solving large field-wide scheduling problems by producing good solutions in reasonable computation times.

Multi-way PLS for discrimination: Compact form equivalent to the tri-linear PLS2 procedure and its monotony convergence

This paper focuses on multi-way PLS for discrimination. Emphasis was placed on the computation of parameters (so-called scores and loadings) using an iterative procedure called tri-linear PLS2. In the context of discrimination, this algorithm is applied to a dummy matrix representing group membership, and according to its specific formalism, the tri-linear PLS2 procedure offers the possibility of simplification. The purpose of this paper is to introduce a compact formulation of the tri-linear PLS2 procedure adapted for a discrimination setting. A property of this variant that allows formally establishing its convergence and, by extension, the convergence of the tri-linear PLS2 will be demonstrated. The potential of this compact form will be illustrated with simulated examples.

Mathematical Programming Formulations and Algorithms for Discrete k-Median Clustering of Time-Series Data

Discrete k-median (DKM) clustering problems arise in many real-life applications that involve time-series data sets, in which nondiscrete clustering methods may not represent the problem domain adequately. In this study, we propose mathematical programming formulations and solution methods to efficiently solve the DKM clustering problem. We develop approximation algorithms from a bilinear formulation of the discrete k-median problem using an uncoupled bilinear program algorithm. This approximation algorithm, which we refer to as DKM-L, is composed of two alternating linear programs, where one can be solved in linear time and the other is a minimum cost assignment problem. We then modify this algorithm by replacing the assignment problem with an efficient sequential algorithm for a faster approximation, which we call DKM-S. We also propose a compact exact integer formulation, DKM-I, and a more efficient network design-based exact mixed-integer formulation, DKM-M. All of our methods use arbitrary pairwise distance matrices as input. We apply our methods to simulated single-variate and multivariate random walk time-series data. We report comparative clustering performances using normalized mutual information (NMI) and solution speeds among the DKM methods we propose. We also compare our methods to other clustering algorithms that can operate with distance matrices, such as hierarchical cluster trees (HCT) and partition around medoids (PAM). We present NMI scores and classification accuracies of our DKM algorithms compared to HCT and PAM using five different distance measures on simluated data, as well as public benchmark and real-life neural time-series data sets. We show that DKM-S is much faster than HCT, PAM, and all other DKM methods and produces consistently good clustering results on all data sets.

A Branch-and-Price-and-Cut Approach for Sustainable Crop Rotation Planning

In this paper, we study a multi-periodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received increased attention in the literature in recent years. Crop cultivation and fallow periods must be scheduled on land plots over a given time horizon so as to minimize the total surface area of land used, while satisfying crop demands every period. This problem is proven strongly NP-hard. We propose a 0-1 linear programming compact formulation based on crop-sequence graphs. An extended formulation is then provided with a polynomial-time pricing problem, and a Branch-and-Price-and-Cut (BPC) algorithm is presented with adapted branching rules and cutting planes. The numerical experiments on instances varying the number of crops, periods and plots show the e ffectiveness of the BPC for the extended formulation compared to solving the compact formulation, even though these two formulations have the same linear relaxation bound.

Compact Formulation of Redox Systems According to GATES/GEB Principles

The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were obtained according to Approach II to GEB, i.e., on the basis of the equation 2?f(O) ? f(H) obtained from elemental balances: f(H) for H, and f(O) for O. Equivalency of the Approach II and the Approach I to GEB was proved for an aqueous solution and a binary-solvent system. On this basis, a compact form of GEB was derived.

High-order methods for computational fluid dynamics: A brief review of compact differential formulations on unstructured grids

Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD) include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) methods. The recently proposed Flux Reconstruction (FR) approach or Correction Procedure using Reconstruction (CPR) is based on a differential formulation and provides a unifying framework for these high-order schemes. Here we present a brief review of recent progress in FR/CPR research as well as some pacing items and future challenges.

On connected dominating sets of restricted diameter

A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no more than s leading to the concept of a dominating s-club. We prove that for any fixed positive integer s it is NP-complete to determine if a graph has a dominating s-club, even when the graph has diameter s+1. As a special case it is NP-complete to determine if a graph of diameter two has a dominating clique. We then propose a compact integer programming formulation for the related minimization problem, enhance the approach with variable fixing rules and valid inequalities, and present computational results.

Social exchange networks with distant bargaining

Network bargaining is a natural extension of the classical, 2-player Nash bargaining solution to the network setting. Here one is given an exchange network G connecting a set of players V in which edges correspond to potential contracts between their endpoints. In the standard model, a player may engage in at most one contract, and feasible outcomes therefore correspond to matchings in the underlying graph. Kleinberg and Tardos [STOC'08] recently proposed this model, and introduced the concepts of stability and balance for feasible outcomes. The authors characterized the class of instances that admit such solutions, and presented a polynomial-time algorithm to compute them.In this paper, we generalize the work of Kleinberg and Tardos by allowing agents to engage into more complex contracts that span more than two agents. We provide suitable generalizations of the above stability and balance notions, and show that many of the previously known results for the matching case extend to our new setting. In particular, we can show that a given instance admits a stable outcome only if it also admits a balanced one. Like Bateni et al. [ICALP'10] we exploit connections to cooperative games. We fully characterize the core of these games, and show that checking its non-emptiness is NP-complete. On the other hand, we provide efficient algorithms to compute core elements for several special cases of the problem, making use of compact linear programming formulations.

Spectral dualities in XXZ spin chains and five dimensional gauge theories

Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for q-->1, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.

Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem

This paper presents a mixed-integer linear programming (MILP) reformulation of the thermal unit commitment (UC) problem. The proposed formulation is simultaneously tight and compact. The tighter characteristic reduces the search space and the more compact characteristic increases the searching speed with which solvers explore that reduced space. Therefore, as a natural consequence, the proposed formulation significantly reduces the computational burden in comparison with analogous MILP-based UC formulations. We provide computational results comparing the proposed formulation with two others which have been recognized as computationally efficient in the literature. The experiments were carried out on 40 different power system mixes and sizes, running from 28 to 1870 generating units.

A service flow model for the liner shipping network design problem

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The formulation alleviates issues faced by arc flow formulations with regards to handling multiple calls to the same port. A problem which has not been fully dealt with earlier by LSNDP formulations. Multiple calls are handled by introducing service nodes, together with port nodes in a graph representation of the problem, and by introducing numbered arcs between a port and a novel service node. An arc from a port node to a service node indicate whether a service is calling the port or not. This representation allows recurrent calls of a service to a port, which previously could not be handled by LSNDP models. The model ensures strictly weekly frequencies of services, ensures that port-vessel draft capabilities are not violated, respects vessel capacities and the number of vessels available. The profit of the generated network is maximized, i.e. the revenue of flowed cargo subtracted operational costs of the network and a penalty for not flowed cargo. The model can be used to design liner shipping networks to utilize a container carrier’s assets efficiently and to investigate possible scenarios of changed market conditions. The model is solved as a Mixed Integer Program. Results are presented for the two smallest instances of the benchmark suite LINER-LIB-2012 presented in Brouer, Alvarez, Plum, Pisinger, and Sigurd (2013).

A Lifted Compact Formulation for the Daily Aircraft Maintenance Routing Problem

Given a set of flights for a specific fleet type, the aircraft routing problem (ARP) determines the flying sequence for each individual aircraft while incorporating specific considerations of minimum turn time, maintenance checks, as well as restrictions on the total accumulated flying time, the total number of takeoffs, and the total number of days between two consecutive maintenances. This stage is significant to airline companies as it directly assigns operational routes and maintenance breaks for each aircraft in service. Most approaches related to the problem adopt set partitioning formulations that include exponentially many variables, which requires the design of specialized column generation or branch-and-price algorithms and codes. In this paper, we present a compact polynomial-sized representation for the ARP, which is then linearized and lifted using the reformulation-linearization technique. In addition, we propose two root-node strategies for further augmenting the model formulation. The resulting formulations remain polynomial in size, and we show that they can be solved very efficiently by commercial software without complicated algorithmic implementations. The numerical experiments demonstrate high-quality solutions and significant savings in computational time.

A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

Abstract In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O ( k 2 + h 4 ) based on non-polynomial tension spline approximation in r -direction and finite difference approximation in t -direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

Compact YORP formulation and stability analysis

We present a concise analytical formulation of the YORP effect, with exact formulae for torques on convex bodies and motion-averaged components applicable to any shapes. We analyze the main features of the secular torques for zero and nonzero thermal inertia that are function series dependent on only a few coefficients. Using these, we investigate the stability of the YORP effect against shape perturbations with analytical and numerical estimates. We define a quantity describing the YORP capacity of any shape, and estimate YORP stability with it.

New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates

We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

Methodology for the design of a thermal distortion compensation for large machine tools based in state-space representation with Kalman filter

A methodology for the design of a thermal distortion compensation system is presented which will assist the manufacturing processes to reach higher levels of accuracy when working with large machines in common shop floor environments. A parametric state-space representation was selected as model architecture, providing multiple inputs and outputs capability and a compact formulation that takes into account previous thermal states of the machine. Inputs for the model are spindle speed and temperatures of main motor gearbox and room air. Outputs are the estimations of the thermal drift of the machine tool centre point along the three axes in different positions within the working volume. Model parameters were numerically identified with initial experimental tests performed in a large gantry-type milling machine, measuring mentioned variables and also thermal distortion values using a reference artifact along with non-contact proximity sensors. Proposed model was finally verified with a new validation measurement in the machine. Obtained results revealed 80% of error reduction in the vertical axis which comprised 70% of total thermal effects and 50% in the longitudinal X axis which comprised 25% of total thermal effects. Also it was concluded that the model benefits from using valuable information about the machine state from previous spindle speed register instead of using only temperature values. Proposed methodology benefits from providing a feasible implementation in real shop floor conditions without the necessity of including additional temperature sensors or probing systems in the machine.

MoReeSC: A Framework for the Simulation and Analysis of Sound Production in Reed and Brass Instruments

This paper presents a free and open-source numerical framework for the simulation and the analysis of the sound production in reed and brass instruments. This tool is developed using the freely distributed Python language and libraries, making it available for acoustics student, engineers and researchers involved in musical acoustics. It relies on the modal expansion of the acoustic resonator (the bore of the instrument), the dynamics of the valve (the cane reed or the lips) and of the jet, to provide a compact continuous-time formulation of the sound production mechanism, modelling the bore as a series association of Helmholtz resonators. The computation of the self-sustained oscillations is controlled by time-varying parameters, including the mouth pressure and the player's embouchure, but the reed and acoustic resonator are also able to evolve during the simulation in order to allow the investigation of transient or non-stationary phenomena. Some examples are given (code is provided within the framework) to show the main features of this tool, such as the ability to handle bifurcations, like oscillation onset or change of regime, and to simulate musical effects.

Branch-and-price algorithm for the Resilient Multi-level Hop-constrained Network Design

In this work, we investigate the Resilient Multi-level Hop-constrained Network Design (RMHND) problem, which consists of designing hierarchical telecommunication networks, assuring resilience against random failures and maximum delay guarantees in the communication. Three mathematical formulations are proposed and algorithms based on the proposed formulations are evaluated. A Branch-and-price algorithm, which is based on a delayed column generation approach within a Branch-and-bound framework, is proven to work well, finding optimal solutions for practical telecommunication scenarios within reasonable time. Computational results show that algorithms based on the compact formulations are able to prove optimality for instances of limited size in the scenarios of interest while the proposed Branch-and-price algorithm exhibits a much better performance.