The stochastic lot-sizing problem with quantity discounts

This paper addresses the stochastic lot-sizing problem with quantity discounts. In particular, we examine the uncapacitated finite-period economic lot-sizing problem in which the parameters in each period are random and discrete. When an order is placed, a fixed cost is incurred and an all-unit quantity discount is awarded based on the quantity ordered. The lead time is zero and the order is delivered immediately. First we study the case with overstocks by which the excess inventory incurs a holding cost. The objective in this case is to minimize the expected total cost including ordering and holding costs. The stochastic dynamics is modeled with a scenario tree. We characterize properties of the optimal policy and propose a polynomial time algorithm with complexity O ( n 3 ) for single discount level, where n is the number of nodes in the scenario tree. We extend the results to cases allowing stockout and multi-discount levels. Numerical experiments are conducted to evaluate the performance of the algorithm and to gain the man- agement insights

Global Slim Accretion Disk Solutions Revisited

We show that there exists a maximal possible accretion rate, beyond which global slim disk solutions cannot be constructed because in the vertical direction the gravitational force would be unable to balance the pressure force to gather the accreted matter. The principle for this restriction is the same as that for the Eddington luminosity and the corresponding critical accretion rate, which were derived for spherical accretion by considering the same force balance in the radial direction. If the assumption of hydrostatic equilibrium is waived and vertical motion is included, this restriction may become even more serious as the value of the maximal possible accretion rate becomes smaller. Previous understanding in the literature that global slim disk solutions could stand for any large accretion rates is due to the overestimation of the vertical gravitational force by using an approximate potential. For accretion flows with large accretion rates at large radii, outflows seem unavoidable in order for the accretion flow to reduce the accretion rate and follow a global solution till the central black hole.Comment: Accepted by Ap

BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/

Pulsating and Hydrodynamic Instabilities at Large Lewis Numbers

Abstract The dynamic behavior of freely propagating premixed flames with large Lewis numbers was computationally simulated using a sixth-order central difference scheme and non-reflective boundary conditions. Results in the linear stage of the instability growth show that the growth rate dramatically decreases with increasing Lewis number and that the large activation energy excites the pulsating instability and increases the growth rate of the hydrodynamic instability. In the nonlinear growth stage, there exist regimes of stable cell propagation, periodic pulsating cellular flames, and irregular pulsating cellular flames as the activation energy is increased. Characteristics of these regimes were further studied for the effects of Lewis number on the flame front structure in the stable cell propagation regime; the effects of flame pulsation on the flow and flame cell structures in the periodic pulsating cellular flame regime; and the complex pattern formation in the irregular pulsating cellular flame regime. It is further demonstrated that unsteady pulsating flames can propagate faster than the adiabatic flame when the local stretch rate is positive, implying that models based on quasi-steady flame propagation may not correctly predict the behavior of unsteady flames with large Lewis numbers

6-Hy­droxy-4-(pyridin-3-yl)-5-(2-thienyl­carbon­yl)-6-trifluoro­meth­yl-3,4,5,6-tetra­hydro­pyrimidin-2(1H)-one

In the title compound, C15H12F3N3O3S, the pyrimidine ring adopts a half-chair conformation with the mean plane formed by the ring atoms excluding the C atom bonded to thio­phene-2-carbonyl group lying nearly perpendicular to the pyridine and thio­phene rings, making dihedral angles of 84.91 (4) and 87.40 (5)°, respectively. The dihedral angle between the pyridine and thio­phene rings is 54.44 (5)°. The crystal structure is stabilized by inter­molecular O—H⋯O and N—H⋯N hydrogen bonds and weak C—H⋯O inter­actions further consolidate the structure

Cyclin D1 integrates G9a-mediated histone methylation.

Lysine methylation of histones and non-histone substrates by the SET domain containing protein lysine methyltransferase (KMT) G9a/EHMT2 governs transcription contributing to apoptosis, aberrant cell growth, and pluripotency. The positioning of chromosomes within the nuclear three-dimensional space involves interactions between nuclear lamina (NL) and the lamina-associated domains (LAD). Contact of individual LADs with the NL are dependent upon H3K9me2 introduced by G9a. The mechanisms governing the recruitment of G9a to distinct subcellular sites, into chromatin or to LAD, is not known. The cyclin D1 gene product encodes the regulatory subunit of the holoenzyme that phosphorylates pRB and NRF1 thereby governing cell-cycle progression and mitochondrial metabolism. Herein, we show that cyclin D1 enhanced H3K9 dimethylation though direct association with G9a. Endogenous cyclin D1 was required for the recruitment of G9a to target genes in chromatin, for G9a-induced H3K9me2 of histones, and for NL-LAD interaction. The finding that cyclin D1 is required for recruitment of G9a to target genes in chromatin and for H3K9 dimethylation, identifies a novel mechanism coordinating protein methylation

The effects of cavity on the etendue of a light source

The simulation proposes that the cylindrical cavity around a circular light source can decreases the divergence angle without changing the emission energy and source size. This result can provide a way to reduce the etendue of the light source by scrambling the rays inside the cavity with a lossless scattering surface. The experiment demonstrates that the metallic cavity around the surface source reduces the divergence angle. However, the metallic surface also absorbs quite a large portion of the light energy. The Lambertian nature of the sidewall surface changes the directions of the rays into horizontal directions. It increases the number of reflection inside the cavity and amplifies the small amount of absorption at a single reflection. The effect of the cavity on the etendue of the light source can contributes to providing more design flexibility in various lighting applications.Comment: 11 pages, 5 figure

Increases in solar conversion efficiencies of the ZrO2 nanofiber-doped TiO2 photoelectrode for dye-sensitized solar cells

In this paper, in order to improve the efficiency of dye-sensitized solar cells, we introduced zirconia [ZrO2] nanofibers into a mesoporous titania [TiO2] photoelectrode. The photoelectrode consists of a few weight percent of ZrO2 nanofibers and a mesoporous TiO2 powder. The mixed ZrO2 nanofibers and the mesoporous TiO2 powder possessed a larger surface area than the corresponding mesoporous TiO2 powder. The optimum ratio of the ZrO2 nanofiber was 5 wt.%. The 5 wt.% ZrO2-mixed device could get a short-circuit photocurrent density of 15.9 mA/cm2, an open-circuit photovoltage of 0.69 V, a fill factor of 0.60, and a light-to-electricity conversion efficiency of 6.5% under irradiation of AM 1.5 (100 mW/cm2)