A set of qubit channels has a classical representation when it is isomorphic to the convex closure of a group of classical channels. From Crowder and Martin (Proceedings of Quantum Physics and Logic, Electronic Notes in Theoretical Computer Science, 2009), we know that up to isomorphism there are five such sets, each corresponding to either a subgroup of the alternating group on four letters, or a subgroup of the symmetric group on three letters. In this paper, we show that (...) the classical representation of a qubit channel also carries its information theoretic data—in particular, both the Holevo capacity and the scope of a unital qubit channel can be completely calculated from a systematically determined classical channel. (shrink)

In this paper we prove the space of unital qubit channels is a Scott domain. In the process we provide a simple protocol to achieve Holevo capacity for these channels.

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρj] that originate from a set of four linearly independent “test” states ρj (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly (...) independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel. (shrink)

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, (...) we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence. (shrink)

Recent work has shown how to use the laws of quantum mechanics to keep classical and quantum bits secret in a number of different circumstances. Among the examples are private quantum channels, quantum secret sharing and quantum data hiding. In this paper we show that a method for keeping two classical bits hidden in any such scenario can be used to construct a method for keeping one quantum bit hidden, and vice–versa. In the realm of quantum data hiding, this allows (...) us to construct bipartite and multipartite hiding schemes for qubits from the previously known constructions for hiding bits. (shrink)

“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and for wave-particle (...) dualism. Its meaning:- mathematically: a ratio of two measures (of sets), which are not collinear; physically: the ratio of the measurements of two physical quantities, which are not simultaneously measurable. The main innovation is in the mapping between phase and Hilbert space, since both are sums. Phase space is a sum of cells, and Hilbert space is a sum of qubits. The mapping is reduced to the mapping of a cell into a qubit and vice versa. Negative probability helps quantum mechanics to be represented quasi-statistically by quasi-probabilistic distributions. Pure states of negative probability cannot exist, but they, where the conditions for their expression exists, decrease the sum probability of the integrally positive regions of the distributions. They reflect the immediate interaction (interference) of probabilities common in quantum mechanics. (shrink)

In 1738, Jacques Vaucanson unveiled his masterpiece before the court of Louis XV: a gilded copper duck that ate, drank, quacked, flapped its wings, splashed about, and, most astonishing of all, digested its food and excreted the remains. The imitation of life by technology fascinated Vaucanson's contemporaries. Today our technology is more powerful, but our fascination is tempered with apprehension. Artificial intelligence and genetic engineering, to name just two areas, raise profoundly disturbing ethical issues that undermine our most fundamental beliefs (...) about what it means to be human. In The Vital Machine, David Channell examines the history of our relationship with technology and argues that, while the resolution of these issues may not be imminent, a philosophical framework for dealing with them is already in place. The source of our fears, he suggests, lies in an outmoded distinction between organic life and machines, a distinction rooted in the two world-views that have defined and guided Western civilization: the mechanical and the organic. The mechanical view holds that the universe is basically a machine--we can understand it by breaking it down into its smallest components. Even organisms are machines. The organic view claims that there is something more, some vital, directive force. The whole is more than just the sum of its parts. Even machines are organisms. Channell presents these polar views in a fascinating chronicle of human thought and achievement, ranging over the discoveries of Galileo, Copernicus, Newton, and Einstein, the philosophies of Plato, Descartes, Kant, and Marx, the fields of alchemy, physics, astrology, and biology. We see not only how the two views progressed independently, but also how they influenced each other, not only how they persisted, but also how they changed. Most fascinating of all, we follow the emergence of a third, all-embracing world view as developments in genetics, relativity, quantum mechanics, and computer intelligence force both science and philosophy to come to a more complex understanding of the universe. As a central metaphor for this third view Channell proposes "the vital machine." And in this stimulating work by the same name, he reveals how this new metaphor may provide us with the philosophical understanding we need to address the ethical issues our science has created. (shrink)

IntroductionApproaches to improve heart rate variability and reduce stress such as breathing retraining are more frequently being integrated into psychotherapy but little research on their effectiveness has been done to date. Specifically, no studies to date have directly compared using a breathing pacer at 6 breaths per minute with compassion focused soothing rhythm breathing.Current StudyIn this randomized controlled experiment, 6 breaths per minute breathing using a pacer was compared with compassion focused soothing rhythm breathing, with a nature video being used (...) as a control group condition.MethodsHeart rate variability measures were assessed via electrocardiogram and respiration belt, and an automated blood pressure machine was used to measure systolic diastolic blood pressure, and heart rate. A total of 96 participants were randomized into the three conditions. Following a 5-min baseline, participants engaged in either 6 breath per minute breathing, soothing rhythm breathing, or watched a nature video for 10 min. To induce a stressful state, participants then wrote for 5 min about a time they felt intensely self-critical. Participants then wrote for 5 min about a time they felt self-compassionate, and the experiment ended with a 10-min recovery period.ResultsConditions did not significantly differ at baseline. Overall, HRV, as measured by standard deviation of NN intervals, low frequency HRV, and LF/HF ratio, increased during the intervention period, decreased during self-critical writing, and then returned to baseline levels during the recovery period. High frequency HRV was not impacted by any of the interventions. The participants in the 6 breath per minute pacer condition were unable to consistently breathe at that rate and averaged about 12 breaths per minute. Time by Condition analyses revealed that both the 6 breaths per minute pacer and soothing breathing rhythm conditions lead to significantly higher SDNN than the nature video condition during breathing practice but there were no significant differences between conditions in response to the self-critical and self-compassionate writing or recovery periods. The 6 breath per minute pacer condition demonstrated a higher LF HRV and LF/HF ratio than the soothing rhythm breathing condition, and both intervention conditions had a higher LF HRV and LF/HF ratio than the nature video.ConclusionsAlthough the 6 breath per minute pacer condition participants were not able to breath consistently at the low pace, both the participants attempting to breathe at 6 breaths per minute as well as those in the soothing rhythm breathing condition effectively increased HR variability as measured by SDNN, and attempting to breathe at 6 breaths per minute led to the highest LF HRV and LF/HF ratio. Both breathing approaches impacted HRV more than watching a relaxing nature video and can potentially be used as key adjuncts in psychotherapy to aid in regulating physiological functioning, although it appears that consistent breathing practice would be needed. (shrink)

This article argues that the (epi)genetic, cultural, symbolic, and environmental transmission channels are insufficient to explain the structure of modern human societies. Economic exchange of knowledge embodied in goods and services constitutes an additional transmission channel that makes more efficient use of limited human cognitive capacity. Economic exchange results in a gradual shift in societies from task-based division of labor to cognitive specialization. This shifts scarce cognitive resources away from production and into learning. It accelerates learning and reinforces the (...) drive towards specialization. Cognitive specialization may constitute another “major transition” towards a higher level of aggregation in human societies, with properties that differ from symbolic transmission. Collective control of individual market-based exchange is ensured by means of economic institutions that put a constraint on individual behavior. (shrink)

Applications of quantum mechanics in the computational and information processing tasks is a recent research interest among the researchers. Certain operations which are impossible to achieve in the description of quantum mechanics are known as no-go theorems. One such theorem is no-splitting theorem of quantum states. The no-splitting theorem states that the information in an unknown quantum bit is an inseparable entity and cannot be split into two complementary qubits. In this work, we try to find out the class of (...) operators for which the splitting is possible in a probabilistic way. The work also aims to find the connection between the unitary operators and probabilistic splitting. (shrink)

The developmental properties of organisms play important roles in the generation of variation necessary for evolutionary change. But how can individual development steer the course of evolution? To answer this question, we introduce developmental channeling as a disposition of individual organisms that shapes their possible developmental trajectories and evolutionary dappling as an evolutionary outcome in which the space of possible organismic forms is dappled—it is only partially filled. We then trace out the implications of the channeling-dappling framework for contemporary debates (...) in the philosophy of evolution, including evolvability, reciprocal causation, and the extended evolutionary synthesis. (shrink)

Ion channels mediate ion flux across biological membranes and regulate important organellar and cellular tasks. A recent study revealed the presence of four new proteins, the MIM complex (composed by Mim1 and Mim2), Ayr1, OMC7, and OMC8, that are able to form ion‐conducting channels in the outer mitochondria membrane (OMM). These findings strongly indicate that the OMM is endowed with many solute‐specific channels, in addition to porins and known channels mediating protein import into mitochondria. These solute‐specific channels provide essential pathways (...) for the controlled transport of ions and metabolites and may thus add a further layer of specificity to the regulation of mitochondrial function at the organelle‐cytosol and/or inter‐organellar interface. Future studies will be required to fully understand the way(s) of regulation of these new channels and to integrate them into signaling pathways within the cells. (shrink)

Of John Wheeler’s ‘Really Big Questions’, the one on which the most progress has been made is It From Bit? – does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other Questions, such as How Come Existence?, because it does not necessarily require a metaphysical answer. And unlike, say, Why The Quantum?, it does not require the discovery of new laws of nature: there was room for hope that it (...) might be answered through a better understanding of the laws as we currently know them, particularly those of quantum physics. And this is what has happened: the better understanding is the quantum theory of information and computation. (shrink)

Associated with the sharing economy, collaborative consumption behaviors often take place among customers. Different from the traditional consumption that customers purchase the product and own it, in the sharing economy, customers can access the product only for a particular period and the ownership of the product also belongs to the firm. In this paper, we develop a theoretical analysis model, and investigate the intrinsic connection between collaborative consumption and the sharing channel strategy. Adopting the sharing channel strategy, the (...) firm has a chance to expand the market demand and improve its profit. In addition, we examine the impacts of other influential factors on a firm’s decisions, such as the unit product cost, surplus-value, and service capability coefficient. (shrink)

With the development of wireless technology, two basic wireless network models that are commonly used, known as infrastructure and wireless ad hoc networks, have been developed. In the literature, it has been observed that channel contention is one of the main reasons for packet drop in WANETs. To handle this problem, this paper presents a routing protocol named CCBR. CCBR tries to determine a least contended path between the endpoints to increase packet delivery ratio and to reduce packet delay (...) and normalized routing overhead. Moreover, throughout the active data section, each intermediate node computes its channel contention value. If an intermediate node detects an increase in channel contention, it notifies the source node. Then the source node determines another least contended route for transmission. The advantages of CCBR are verified in our NS2-based performance study, and the results show that CCBR outperforms ad hoc on-demand distance vector in terms of packet delivery ratio, end-to-end delay, and routing overhead by 4% to 9%. (shrink)

Chloride channels are probably found in every cell, from bacteria to mammals. Their physiological tasks range from cell volume regulation to stabilization of the membrane potential, signal transduction, transepithelial transport and acidification of intracellular organelles. These different functions require the presence of many distinct chloride channels, which are differentially expressed and regulated by various stimuli. These include various intracellular messengers (like calcium and cyclic AMP), pH, extracellular ligands and transmembrane voltage. Three major structural classes of chloride channels are known to (...) date, but there may be others not yet identified. After an overview of the general functions of chloride channels, this review will focus on these cloned chloride channels: the CLC chloride channel family, which includes voltage‐gated chloride channels, and the cystic fibrosis transmembrane regulator (CFTR), which performs other functions in addition to being a chloride channel. Finally, a short section deals with GABA and glycine receptors. Diseases resulting from chloride channel defects will be specially emphasized, together with the somewhat limited information about how these proteins work at the molecular level. (shrink)

Analysis of three kinds of flow of viscous, incompressible, electrically conducting fluids in high-aspect-ration rectangular channels subjected to transverse magnetic fields: turbulent flow in the presence of a d-c magnetic field, and both laminar and turbulent induction-driven flows.

The identification of additional subunits of the cGMP-gated cation channel suggests exciting questions about their regulatory roles and about structure/functional relationships. How do the different subunits interact? How is the complex assembled into the plasma membrane? Divalent cations have been implicated in the regulation of adaptation. One often overlooked cation is magnesium. Could this ion play a role in phototransduction?

The cyclic GMP-gated channel responds to changes in free intracellular cGMP, and as a result, it plays a central role in the phototransduction process in rod and cone photoreceptor cells. Recent biochemical, immunochemical, and molecular biology studies indicate that this channel consists of a complex of two distinct subunits and one or more associated proteins. Primary structural analysis indicates that the a and (3 subunits contain a cGMP-binding domain, an even number of membrane-spanning segments, a voltage sensor motif (...) and a pore region. The latter two features are found in voltage-gated channels and suggest that these two classes of channels have evolved from the same ancestral channel protein. A working model for the membrane topography of the channel subunits is proposed based on immunogold labeling studies and sequence analysis. Recent studies also indicate that calmodulin binds to the 240 kDa protein of the channel complex and modulates the sensitivity of the channel for cGMP in a Ca2+-dependent manner. The molecular properties of the channel complex and the possible role of Ca2+-calmodulin modulation of the channel during photoactivation and photorecovery are discussed in relation to the current mechanism of phototransduction in photoreceptor cells. (shrink)

A session-based recommendation system is designed to predict the user’s next click behavior based on an ongoing session. Existing session-based recommendation systems usually model a session into a sequence and extract sequence features through recurrent neural network. Although the performance is greatly improved, these procedures ignore the relationships between items that contain rich information. In order to obtain rich items embeddings, we propose a novel Recommendation Model based on Multi-channel Convolutional Neural Network for session-based recommendation, RMMCNN for brevity. Specifically, (...) we capture items' internal features from three dimensions through multi-channel convolutional neural network firstly. Next, we merge the internal features with external features obtained by a GRU unit. Then, both internal features and external features are merged by an attention mechanism together as the input of the transformation function. Finally, the probability distribution is taken as the output after the softmax function. Experiments on various datasets show that our method's precision and recommendation performance are better than those of other state-of-the-art approaches. (shrink)

An increasing number of studies indicate that changes in cytosolic free Ca2+ ([Ca2+]c) mediate specific types of signal transduction in plant cells. Modulation of [Ca2+]c is likely to be achieved through changes in the activity of Ca2+ channels, which catalyse passive influx of Ca2+ to the cytosol from extracellular and intracellular compartments. Voltage‐sensitive Ca2+ channels have been detected in the plasma membranes of algae, where they control membrane electrical properties and cell turgor. These channels are sensitive to 1,4‐dihydropyridines, which in (...) animal cells specifically affect one class of voltage‐regulated plasma membrane Ca2+ channel. Ca2+‐permeable channels with different pharmacological properties have been found in the plasma membrane of higher plants. Recent evidence suggests the existence of two discrete classes of Ca2+ channel co‐resident in the vacuolar membrane (tonoplast) of higher plants. The first is gated by inositol 1,4,5‐trisphosphate, and bears a number of similarities to its animal counterpart which is located in the endoplasmic reticulum (ER). The second tonoplast Ca2+ channel is voltage‐operated. However, the specific roles of these tonoplast channels in signal transduction have yet to be elucidated. (shrink)

SummaryMuch excitement surrounded the proposal that a family of endo‐lysosomal channels, the two‐pore channels (TPCs) were the long sought after targets of the Ca2+‐mobilising messenger, nicotinic acid adenine dinucleotide phosphate (NAADP). However, the role of TPCs in NAADP signalling may be more complex than originally envisaged. First, NAADP may not bind directly to TPCs but via an accessory protein. Second, two papers recently challenged the notion that TPCs are NAADP‐regulated Ca2+ channels by suggesting that they are highly selective Na+ channels (...) regulated by the lipid phosphatidylinositol 3,5‐bisphosphate and by ATP. This paper aims critically to evaluate the evidence for TPCs as NAADP targets and to discuss how the new findings fit in with what we know about endo‐lysosomal Ca2+ stores. (shrink)

Media critics invariably disparage the quality of programming produced by the U.S. television industry. But why the industry produces what it does is a question largely unasked. It is this question, at the crux of American popular culture, that Switching Channels explores.

Electrical signaling by neurons depends on the precisely ordered distribution of a wide variety of ion channels on the neuronal surface. The mechanisms underlying the targeting of particular classes of ion channels to specific subcellular sites are poorly understood. Recent studies have identified a new class of protein‐protein interaction mediated by PDZ domains, protein binding modules that recognize specific sequences at the C terminus of membrane proteins. The PDZ domains of a family of synaptic cytoskeleton‐associated proteins, typified by PSD‐95, bind (...) to the intracellular C‐terminal tails of NMDA receptors and Shaker‐type K+ channels. This interaction appears to be important in the clustering and localization of these ion channels at synaptic sites. Recognition of specific C‐terminal peptide sequences by different PDZ domain‐containing proteins may be a general mechanism for differential targeting of proteins to a variety of subcellular locations. (shrink)

The use of cross-media and transmedia-based art installation has generated new ways for the audience to appreciate, understand and experience art. Transmedia, the integration of multiple media forms to augment a single narrative, has not only been largely used in commercial films, but has also been used by artists to communicate their message more effectively. In this article, we explore some remarkable multi-channel video installations and transmedia artworks to highlight how this technology has shaped new uses of technology as (...) a new medium to express artistic concepts. We discuss one artwork, an experimental collaboration between artists and scientists, entitled Reefs on the Edge, which communicates valuable information about climate change to a general audience. (shrink)

Marketing in the social network environment integrates current advanced internet and information technologies. This marketing method not only broadens marketing channels and builds a network communication platform but also meets the purchase needs of customers in the entire market and shortens customer purchases. The process is also an inevitable product of the development of the times. However, when companies use social networks for product marketing, they usually face the impact of multiple realistic factors. This article takes the maximization of influence (...) as the main idea to find seed users for product information dissemination and also considers the users’ interest preferences. The target users can influence the product, and the company should control marketing costs to obtain a larger marginal benefit. Based on this, this paper considers factors such as the scale of information diffusion, user interest preferences, and corporate budgets, takes the influence maximization model as a multiobjective optimization problem, and proposes a multiobjective maximization of influence model. To solve the NP-hard problem of maximizing influence, this paper uses Monte Carlo sampling to calculate high-influence users. Next, a seed user selection algorithm based on NSGA-II is proposed to optimize the above three objective functions and find the optimal solution. We use real social network data to verify the performance of models and methods. Experiments show that the proposed model can generate appropriate seed sets and can meet different purposes of information dissemination. Sensitivity analysis proves that our model is robust under different actual conditions. (shrink)

In special application scenarios, such as portable anesthesia depth monitoring, portable emotional state recognition and portable sleep monitoring, electroencephalogram (EEG) signal acquisition equipment is required to be convenient and easy to use. It is difficult to remove electrooculogram (EOG) artifacts when the number of EEG acquisition channels is small, especially when the number of observed signals is less than that of the source signals, and the overcomplete problem will arise. The independent component analysis (ICA) algorithm commonly used for artifact removal (...) requires the number of basis vectors to be smaller than the dimension of the input data due to a set of standard orthonormal bases learned during the convergence process, so it cannot be used to solve the overcomplete problem. The empirical mode decomposition method decomposes the signal into several independent intrinsic mode functions so that the number of observed signals is more than that of the source signals, solving the overcomplete problem. However, when using this method to solve overcompleteness, the modal aliasing problem will arise, which is caused by abnormal events such as sharp signals, impulse interference, and noise. Aiming at the above problems, we propose a novel EEG artifact removal method based on discrete wavelet transform, complete empirical mode decomposition for adaptive noise (CEEMDAN) and ICA in this paper. First, the input signals are transformed by discrete wavelet (DWT), and then CEEMDAN is used to solve the overcomplete and mode aliasing problems, meeting the a priori conditions of the ICA algorithm. Finally, the components belonging to EOG artifacts are removed according to the sample entropy value of each independent component. Experiments show that this method can effectively remove EOG artifacts while solving the overcomplete and modal aliasing problems. (shrink)

To improve the accuracy of the multiple channel integration quality evaluation, this paper proposes a comprehensive evaluation method using the nonlinear autoregressive exogenous model and constructs an index system. First, the entropy method is used to determine the objective weight of each indicator. The indicators used in this paper are process consistency, information consistency, emotional value, procedural value, service structure transparency, online result value, business relevance, and online purchase intention. Second, an improved gray relational analysis algorithm is used to (...) obtain the comprehensive gray relational degree between the above eight indicators’ standard samples and the tested samples. Then, this study uses the dataset preprocessed with the GRA algorithm for training the NARX model. Then, this study uses the trained model to evaluate the quality of multiple channel integration comprehensively. Next, this study uses standardized methods to quantify the evaluation results to provide new ideas and theoretical guidance for teaching traditional retailers to use the advantages of multiple channels to expand their online business. This paper uses 50,000 consecutive samples of a product for 3 months as a dataset in the experimental part. Through the GRA method and the NARX model, the comprehensive gray relational degree between the test sample and the ideal sample is obtained, and the results are quantified. Experiments show that, compared with the GRA method, this paper’s method has a higher degree of fit between the output value and the target value. (shrink)

Culture and social structure may affect the testosterone–behavior link by shaping the way we construe events; by muting, channelling, or amplifying the drives that testosterone produces; and by affecting the distribution and level of testosterone in various parts of the population. Research on testosterone, culture, and social class has produced suggestive results, opening broad areas for research.

When eighteenth-century revolutionary elites set about designing new political orders, they drew on commonplace theoretical understandings of “democracy” as highly undesirable. They therefore designed government institutions in which popular participation was to be extremely limited. The new political constructions, in both France and the United States, never worked as planned. The mobilizations of the revolutionary era did not vanish as the constitutional designers hoped. More profoundly, challenging social movements were unintentionally woven into the fabric of modern democracy due to the (...) confluence of three processes: The legitimacy claims of democratic powerholders also legitimate protest; the institutional architecture of modern democracy, especially the allocation of office through elections, provides structural support for social movements as well; and the practices of democracy recurrently trigger politically powerful emotions that energize protest. Understanding democracy therefore demands a theory of the interplay of social movements and governing institutions from the foundational moment. (shrink)

Rebate has long been a crucial tool that has attracted researchers from a diverse range of fields including marketing and supply chain management. When a manufacturer uses a retailer for reaching end customers, the rebate strategy undertakes an additional dimension. Here we show whether the two rebate strategies, manufacturer rebate and channel rebate, can be the optimal choice for the manufacturer and the retailer. And we aim at full coordination with rebate. Game theory is exploited to identify the equilibrium (...) rebate decisions, which are fully characterized with two rebate strategies considering rebate sensitivity. Furthermore, we demonstrate how the decisions depend on parameters, such as market size, rebate redemption rate, and competition intensity in monopoly and duopoly supply chain systems. Our work also coordinates the supply chain with two coordination policies and examines if they can achieve full coordination. Counterintuitive findings suggest that the channel rebate with sensitivity and discrimination is not effective and the manufacturer rebate is the unique optimal option. Besides, the coordination can be realized with a centralized rebate in monopoly setting when the manufacturer forgoes her own interest. Then full coordination can be achieved in duopoly setting with a new coordination policy, rebate combination, given the redemption rate for the channel rebate is lower compared with the manufacturer rebate. Managerial insights are suggested that offering rebates with discrimination can have significant inventory and coordination policy implications and can lead to a double win under a well-controlled redemption rate. (shrink)