Collaborative Competitive filtering II: Optimal Recommendation and Collaborative Games

Recommender systems have emerged as a new weapon to help online firms to realize many of their strategic goals (e.g., to improve sales, revenue, customer experience etc.). However, many existing techniques commonly approach these goals by seeking to recover preference (e.g., estimating ratings) in a matrix completion framework. This paper aims to bridge this significant gap between the clearly-defined strategic objectives and the not-so-well-justified proxy. We show it is advantageous to think of a recommender system as an analogy to a monopoly economic market with the system as the sole seller, users as the buyers and items as the goods. This new perspective motivates a game-theoretic formulation for recommendation that enables us to identify the optimal recommendation policy by explicit optimizing certain strategic goals. In this paper, we revisit and extend our prior work, the Collaborative-Competitive Filtering preference model, towards a game-theoretic framework. The proposed framework consists of two components. First, a conditional preference model that characterizes how a user would respond to a recommendation action; Second, knowing in advance how the user would respond, how a recommender system should act (i.e., recommend) strategically to maximize its goals. We show how objectives such as click-through rate, sales revenue and consumption diversity can be optimized explicitly in this framework. Experiments are conducted on a commercial recommender system and demonstrate promising results.Comment: 10 pages, 5 figures; Recommender system, Collaborative filterin

Local Optimality of User Choices and Collaborative Competitive Filtering

While a user's preference is directly reflected in the interactive choice process between her and the recommender, this wealth of information was not fully exploited for learning recommender models. In particular, existing collaborative filtering (CF) approaches take into account only the binary events of user actions but totally disregard the contexts in which users' decisions are made. In this paper, we propose Collaborative Competitive Filtering (CCF), a framework for learning user preferences by modeling the choice process in recommender systems. CCF employs a multiplicative latent factor model to characterize the dyadic utility function. But unlike CF, CCF models the user behavior of choices by encoding a local competition effect. In this way, CCF allows us to leverage dyadic data that was previously lumped together with missing data in existing CF models. We present two formulations and an efficient large scale optimization algorithm. Experiments on three real-world recommendation data sets demonstrate that CCF significantly outperforms standard CF approaches in both offline and online evaluations.Comment: 27 pages, 4 figur

Achieving proportional fairness with a control theoretic approach in error-prone 802.11e WLANs

This letter proposes a control theoretic approach to achieve proportional fairness amongst access categories (ACs) in an error-prone EDCA WLAN for provision of distinct QoS requirements and priority parameters. The approach adaptively adjusts the minimum contention window of each AC to derive the station attempt probability to its optimum which leads to a proportional fair allocation of station throughputs. Evaluation results demonstrate that the proposed control approach has high accuracy performance and fast convergence speed for general network scenarios

Image Reconstruction Image reconstruction by using local inverse for full field of view

The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact inverse from an approximate inverse with a few iterations. The IRM has been used in CT image reconstruction to lower the radiation dose. The IRM utilize the errors between the original measured data and the recalculated data to correct the reconstructed images. However if it is not smooth inside the object, there often is an over-correction along the boundary of the organs in the reconstructed images. The over-correction increase the noises especially on the edges inside the image. One solution to reduce the above mentioned noises is using some kind of filters. Filtering the noise before/after/between the image reconstruction processing. However filtering the noises also means reduce the resolution of the reconstructed images. The filtered image is often applied to the image automation for examples image segmentation or image registration but diagnosis. For diagnosis, doctor would prefer the original images without filtering process. In the time these authors of this manuscript did the work of interior image reconstruction with local inverse method, they noticed that the local inverse method does not only reduced the truncation artifacts but also reduced the artifacts and noise introduced from filtered back-projection method without truncation. This discovery lead them to develop the sub-regional iterative refinement (SIRM) image reconstruction method. The SIRM did good job to reduce the artifacts and noises in the reconstructed images. The SIRM divide the image to many small sub-regions. To each small sub-region the principle of local inverse method is applied.Comment: 39 pages, 9 figure

The modified Poynting theorem and the concept of mutual energy

The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the retarded potential and advanced potential, time-offset field. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Mixed mutual energy theorem is derived. We derive the mutual energy from Fourier domain. We obtain the time-reversed mutual energy theorem and the mutual energy theorem. Then we derive the mutual energy theorem in time-domain. The instantaneous modified mutual energy theorem is derived. Applying time-offset transform and time integral to the instantaneous modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are two electromagnetic fields one is retarded potential and one is advanced potential, the convolution reciprocity theorem can be derived. Corresponding to the modified time-correlation mutual energy theorem and the time-convolution reciprocity theorem in Fourier domain, there is the modified mutual energy theorem and the Lorentz reciprocity theorem. Hence all mutual energy theorem and the reciprocity theorems are put in one frame of the concept of the mutual energy. 3 new Complementary theorems are derived. The inner product is introduced for two different electromagnetic fields in both time domain and Fourier domain for the application of the wave expansion.Comment: Derivation of the mutual energy theorem from Fourier domain is added. Time-reversed transform, time-reversed mutual energy theorem, time reversed reciprocity theorem, mixed mutual energy theorem are added, Complementary theorems are adde

Orbit Tracking Control of Quantum Systems

The orbit tracking of free-evolutionary target system in closed quantum systems is studied in this paper. Based on the concept of system control theory, the unitary transformation is applied to change the time-dependent target function into a stationary target state so that the orbit tracking problem is changed into the state transfer one. A Lyapunov function with virtual mechanical quantity P is employed to design a control law for such a state transferring. The target states in density matrix are grouped into two classes: diagonal and non-diagonal. The specific convergent conditions for target state of diagonal mixed-states are derived. In the case that the target state is a non-diagonal superposition state, we propose a non-diagonal P construction method; if the target state is a non-diagonal mixed-state we use a unitary transformation to change it into a diagonal state and design a diagonal P. In such a way, the orbit tracking problem with arbitrary initial state is properly solved. The explicit expressions of P are derived to obtain a convergent control law. At last, the system simulation experiments are performed on a two-level quantum system and the tracking process is illustrated on the Bloch sphere.Comment: 20 pages, 5 figure

A gradient estimate for positive functions on graphs

We derive a gradient estimate for positive functions, in particular for positive solutions to the heat equation, on finite or locally finite graphs. Unlike the well known Li-Yau estimate, which is based on the maximum principle, our estimate follows from the graph structure of the gradient form and the Laplacian operator. Though our assumption on graphs is slightly stronger than that of Bauer, Horn, Lin, Lippner, Mangoubi, and Yau (J. Differential Geom. 99 (2015) 359-405), our estimate can be easily applied to nonlinear differential equations, as well as differential inequalities. As applications, we estimate the greatest lower bound of Cheng's eigenvalue and an upper bound of the minimal heat kernel, which is recently studied by Bauer, Hua and Yau (Preprint, 2015) by the Li-Yau estimate. Moreover, generalizing an earlier result of Lin and Yau (Math. Res. Lett. 17 (2010) 343-356), we derive a lower bound of nonzero eigenvalues by our gradient estimate.Comment: 11 page

The principle of the mutual energy

Advanced potential solution of Maxwell equations isn't often accepted. We have proven if without advanced potential, it is not possible to satisfy the Maxwell equations. We also shown that it is not the Poynting vector related energy current transferring energy in the space and it is the mutual energy really did that. A important result of the mutual energy theorem is that the advanced potential can suck energy from the transmitter. This energy is equal to the energy received at the receiver. Hence a transmitter can not send any energy out without the receiver. For two remote objects, the energy is transferred only can by the mutual energy of a retarded potential from the source together with an advanced potential from the sink. If the sucked energy is discrete, the summation of mutual energy current of the infinite background atoms or currents, which can be seen as receivers, is a random process. This means that the photon energy sent by the transmitter is actually grabbed by the receiver. Hence the photon from very beginning knows their destination. This receiver send advanced potential to the transmitter. This explanation also avoided the wave function collapse. The retarded potential first reached the receiver, cause the current in the receiver, the current of receiver send a advanced potential to the transmitter with a reversed time, in the same time, a photon minus-time-instantly runs from receiver to transmitter. In our normal feeling, the photon is still runs from the transmitter to the receiver with a positive time. How to transfer superluminal signal using advanced potential is also discussed.Maxwell equations as principle of the theory of the electromagnetic fields is replaced by the mutual energy principle.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0200

Contour-Variable Model of Constitutive Equations for Polymer Melts

Based on a modified expression of the rate of the convective constraint release, we present a new contour-variable model of constitutive equations in which the non-uniform segmental stretch and the non-Gaussian chain statistical treatment of the single chain are considered to describe the polymer chain dynamics and the rheological behavior of an entangled system composed of linear polymer chains. The constitutive equations are solved numerically in the cases of steady shear and transient start-up of steady shear. The results indicate that the orientation and stretch, as well as the tube survival probability, have strong dependence on the chain contour variable, especially in the high-shear-rate region. However, the inclusion of the non-uniform features in the constitutive models has little modification comparing with the uniform models in determining the rheological properties both qualitatively and quantitatively.Comment: 26 pages, 13 figure

Global gradient estimate on graph and its applications

Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, it can be used to get an upper bound and a lower bound of the heat kernel on locally finite graphs. These global gradient estimates can be compared with the Li-Yau inequality on graphs contributed by Bauer, Horn, Lin, Lipper, Mangoubi and Yau (J. Differential Geom. 99 (2015) 359-409). In many topics, such as eigenvalue estimate and heat kernel estimate (not including the Liouville type theorems), replacing the Li-Yau inequality by the global gradient estimate, we can get similar results.Comment: 7 page