SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.     

Complexity and intransitivity in technological development

This paper investigates the existence of a fundamental link between two disciplines that emerged during last few decades： complexity science and advanced engineering. During this time many industries, especially those related to the high-tech end of technological development, have faced the problem of increasing complexity of design, production and operation. Industrial projects have grown to become multidisciplinary, tightly interconnected, costly and difficult to control and predict. Two trends can be identified in this respect： one is the consistent effort of systems engineering in reducing the uncertainties of complex industrial operations and the other is the effort undertaken in complexity studies to account for uncertainties present in the real world.
In this work, we provide a brief overview of recent developments in advanced engineering and give a consistent interpretation of technological evolution from the perspective of complexity science in general and complex competitive systems （CCS） in particular. CCS is a general framework that was recently developed for analysis of complex systems involving competition. Transitivity of the decision-making process and the cyclic nature of technological progress are considered. Correctness of intransitive decisions is inherently relativistic： the same decisions can be seen as correct or incorrect when considered from different perspectives. When treated simplistically, intransitivity may seem to be illogical but, nevertheless, it is common in nature and needs to be studied. CCS provides a formalised scientific framework for analysis of intransitivity and establishes the existence of an important connection linking complexity and uncertainty with intransitivity. Implications of intransitivity for engineering decision-making and strategic planning are considered in the context of CCS. A working example of intransitivity in competition between major car mantifacturers is presented.     

含镍磁黄铁矿尾矿氧化动力学及机理研究

X-ray powder diffraction, scanning electron microscopy, energy dispersive spectroscopy, thermogravimetry, differential scanning calorimetry, and mass spectrometry have been used to study the products of nickel-containing pyrrhotite tailings oxidation by oxygen in the air. The kinetic triplets of oxidation, namely, activation energy (E_a), pre-exponential factor (A), and reaction model (f(α)) being a function of the conversion degree (α), were adjusted by regression analysis. In case of a two-stage process representation, the first step proceeds under autocatalysis control and ends at α = 0.42. The kinetic triplet in the first step is E_a = 262.2 kJ/mol, lg A = 14.53 s?1, and f(α) = (1 – α)4.11(1 + 1.51 × 10–4α). For the second step, the process is controlled by the two-dimensional diffusion of the reactants in the layer of oxidation products. The kinetic triplet in the second step is Е_a = 215.0 kJ/mol, lg A = 10.28 s?1, and f(α) = (–ln(1 – α))–1. The obtained empirical formulae for the rate of pyrrhotite tailings oxidation reliably describe the macro-mechanism of the process and can be used to design automatization systems for roasting these materials.     

Genetic risk and a primary role for cell-mediated immune mechanisms in multiple sclerosis

Multiple sclerosis is a common disease of the central nervous system in which the interplay between inflammatory and neurodegenerative processes typically results in intermittent neurological disturbance followed by progressive accumulation of disability. Epidemiological studies have shown that genetic factors are primarily responsible for the substantially increased frequency of the disease seen in the relatives of affected individuals, and systematic attempts to identify linkage in multiplex families have confirmed that variation within the major histocompatibility complex (MHC) exerts the greatest individual effect on risk. Modestly powered genome-wide association studies (GWAS) have enabled more than 20 additional risk loci to be identified and have shown that multiple variants exerting modest individual effects have a key role in disease susceptibility. Most of the genetic architecture underlying susceptibility to the disease remains to be defined and is anticipated to require the analysis of sample sizes that are beyond the numbers currently available to individual research groups. In a collaborative GWAS involving 9,772 cases of European descent collected by 23 research groups working in 15 different countries, we have replicated almost all of the previously suggested associations and identified at least a further 29 novel susceptibility loci. Within the MHC we have refined the identity of the HLA-DRB1 risk alleles and confirmed that variation in the HLA-A gene underlies the independent protective effect attributable to the class I region. Immunologically relevant genes are significantly overrepresented among those mapping close to the identified loci and particularly implicate T-helper-cell differentiation in the pathogenesis of multiple sclerosis.     

A young source for the Hawaiian plume

Recycling of oceanic crust through subduction, mantle upwelling, and remelting in mantle plumes is a widely accepted mechanism to explain ocean island volcanism. The timescale of this recycling is important to our understanding of mantle circulation rates. Correlations of uranogenic lead isotopes in lavas from ocean islands such as Hawaii or Iceland, when interpreted as model isochrons, have yielded source differentiation ages between 1 and 2.5?billion years (Gyr). However, if such correlations are produced by mixing of unrelated mantle components they will have no direct age significance. Re-Os decay model ages take into account the mixing of sources with different histories, but they depend on the assumed initial Re/Os ratio of the subducted crust, which is poorly constrained because of the high mobility of rhenium during subduction. Here we report the first data on (87)Sr/(86)Sr ratios for 138 melt inclusions in olivine phenocrysts from lavas of Mauna Loa shield volcano, Hawaii, indicating enormous mantle source heterogeneity. We show that highly radiogenic strontium in severely rubidium-depleted melt inclusions matches the isotopic composition of 200-650-Myr-old sea water. We infer that such sea water must have contaminated the Mauna Loa source rock, before subduction, imparting a unique 'time stamp' on this source. Small amounts of seawater-derived strontium in plume sources may be common but can be identified clearly only in ultra-depleted melts originating from generally highly (incompatible-element) depleted source components. The presence of 200-650-Myr-old oceanic crust in the source of Hawaiian lavas implies a timescale of general mantle circulation with an average rate of about 2 (±1)?cm?yr(-1), much faster than previously thought.     

Ephrin Bs are essential components of the Reelin pathway to regulate neuronal migration

Coordinated migration of neurons in the developing and adult brain is essential for its proper function. The secreted glycoprotein Reelin (also known as RELN) guides migration of neurons by binding to two lipoprotein receptors, the very-low-density lipoprotein receptor (VLDLR) and apolipoprotein E receptor 2 (ApoER2, also known as LRP8). Loss of Reelin function in humans results in the severe developmental disorder lissencephaly and it has also been associated with other neurological disorders such as epilepsy, schizophrenia and Alzheimer's disease. The molecular mechanisms by which Reelin activates its receptors and controls cellular functions are largely unknown. Here we show that the neuronal guidance cues ephrin B proteins are essential for Reelin signalling during the development of laminated structures in the brain. We show that ephrin Bs genetically interact with Reelin. Notably, compound mouse mutants (Reln(+/-); Efnb3(-/-) or Reln(+/-); Efnb2(-/-)) and triple ephrin B1, B2, B3 knockouts show neuronal migration defects that recapitulate the ones observed in the neocortex, hippocampus and cerebellum of the reeler mouse. Mechanistically, we show that Reelin binds to the extracellular domain of ephrin Bs, which associate at the membrane with VLDLR and ApoER2 in neurons. Clustering of ephrin Bs leads to the recruitment and phosphorylation of Dab1 which is necessary for Reelin signalling. Conversely, loss of function of ephrin Bs severely impairs Reelin-induced Dab1 phosphorylation. Importantly, activation of ephrin Bs can rescue the reeler neuronal migration defects in the absence of Reelin protein. Together, our results identify ephrin Bs as essential components of the Reelin receptor/signalling pathway to control neuronal migration during the development of the nervous system.     

Linking mantle plumes, large igneous provinces and environmental catastrophes

Large igneous provinces (LIPs) are known for their rapid production of enormous volumes of magma (up to several million cubic kilometres in less than a million years), for marked thinning of the lithosphere, often ending with a continental break-up, and for their links to global environmental catastrophes. Despite the importance of LIPs, controversy surrounds even the basic idea that they form through melting in the heads of thermal mantle plumes. The Permo-Triassic Siberian Traps--the type example and the largest continental LIP--is located on thick cratonic lithosphere and was synchronous with the largest known mass-extinction event. However, there is no evidence of pre-magmatic uplift or of a large lithospheric stretching, as predicted above a plume head. Moreover, estimates of magmatic CO(2) degassing from the Siberian Traps are considered insufficient to trigger climatic crises, leading to the hypothesis that the release of thermogenic gases from the sediment pile caused the mass extinction. Here we present petrological evidence for a large amount (15?wt%) of dense recycled oceanic crust in the head of the plume and develop a thermomechanical model that predicts no pre-magmatic uplift and requires no lithospheric extension. The model implies extensive plume melting and heterogeneous erosion of the thick cratonic lithosphere over the course of a few hundred thousand years. The model suggests that massive degassing of CO(2) and HCl, mostly from the recycled crust in the plume head, could alone trigger a mass extinction and predicts it happening before the main volcanic phase, in agreement with stratigraphic and geochronological data for the Siberian Traps and other LIPs.