Source author record

Yuan Zhong

Yuan Zhong appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record

Catalog footprint

What is connected

40works
15topics
4close collaborators

Actions

Connect this record

Log in to claim

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

40 published item(s)

preprint2026arXiv

A Cascaded Generative Approach for e-Commerce Recommendations

Personalized storefronts in large e-commerce marketplaces are often assembled from many independent components: static themes per page section ("placement"), retrieval systems to fetch eligible products per placement, and pointwise rankers to order content. While effective in optimizing for aggregate preferences, this paradigm is rigid and can limit personalization and semantic cohesion across the page. This makes it poorly suited to support dynamic objectives and merchandising requirements over time. To address this, we introduce a cascaded merchandising framework that decomposes storefront construction into two generative tasks: (i) placement-level theme generation and (ii) constrained keyword generation per placement to power product retrieval. Teacher-student fine-tuning is leveraged to improve scalability of this framework under production latency and cost constraints. Fine-tuned model ablations are shown to approach closed-weight LLM performance. We further contribute frameworks for AI-driven content evaluation and quality filtering, enabling safe and automated deployment of dynamic content at scale. Generative output is fused with traditional ranking models to preserve hybrid infrastructure. In online experiments, this framework yields an estimated +2.7% lift in cart adds per page view over a strong baseline.

preprint2026arXiv

Quaternion optical computing chip for parallel high-dimensional data processing

Optical computing chips have emerged as a transformative computing technology due to their high computational density, low energy consumption, and compact footprint. While real- and complex-valued computing chips have been well developed, their fundamental limitations in representing high-dimensional data significantly constrain their applicability in modern signal processing. Quaternions enable direct operations on three- and four-dimensional data, powering high-dimensional processing in data analytics and artificial intelligence. Here we demonstrate a quaternion optical computing chip (QOCC) for the first time and benchmark its performance in several typical application scenarios: three-dimensional point cloud processing, RGB chromatic transformation, and quaternion convolutional neural network for color image recognition. The QOCC harnesses high parallelism of light by wavelength-division multiplexing, processing high-dimensional data simultaneously through multiple optical wavelength channels. Compared to the electronic computing counterpart, our QOCC achieves higher computational fidelity (root mean square error < 0.035) and substantially reduced computational load (2/3 lower). It paves the way towards next-generation optical computing, overcoming the limitations of traditional computing systems in high-dimensional data processing.

preprint2022arXiv

A BMS-invariant free scalar model

The BMS (Bondi-van der Burg-Metzner-Sachs) symmetry arises as the asymptotic symmetry of flat spacetime at null infinity. In particular, the BMS algebra for three dimensional flat spacetime (BMS$_3$) is generated by the super-rotation generators which form a Virasoro sub-algebra with central charge $c_L$, together with mutually-commuting super-translation generators. The super-rotation and super-translation generators have non-trivial commutation relations with another central charge $c_M$. In this paper, we study a free scalar theory in two dimensions exhibiting BMS$_3$ symmetry, which can also be understood as the ultra-relativistic limit of a free scalar CFT$_2$. Upon canonical quantization on the highest weight vacuum, the central charges are found to be $c_L=2$ and $c_M=0$. Because of the vanishing central charge $c_M=0$, the theory features novel properties: there exist primary states which form a multiplet, and the Hilbert space can be organized by an enlarged version of BMS modules dubbed the staggered modules. We further calculate correlation functions and the torus partition function, the later of which is also shown explicitly to be modular invariant.

preprint2022arXiv

Analytical Shaping Method for Low-Thrust Rendezvous Trajectory Using Cubic Spline Functions

Preliminary mission design requires an efficient and accurate approximation to the low-thrust rendezvous trajectories, which might be generally three-dimensional and involve multiple revolutions. In this paper, a new shaping method using cubic spline functions is developed for the analytical approximation, which shows advantages in the optimality and computational efficiency. The rendezvous constraints on the boundary states and transfer time are all satisfied analytically, under the assumption that the boundary conditions and segment numbers of cubic spline functions are designated in advance. Two specific shapes are then formulated according to whether they have free optimization parameters. The shape without free parameters provides an efficient and robust estimation, while the other one allows a subsequent optimization for the satisfaction of additional constraints such as the constraint on the thrust magnitude. Applications of the proposed method in combination with the particle swarm optimization algorithm are discussed through two typical interplanetary rendezvous missions, that is, an inclined multi-revolution trajectory from the Earth to asteroid Dionysus and a multi-rendezvous trajectory of sample return. Simulation examples show that the proposed method is superior to existing methods in terms of providing good estimation for the global search and generating suitable initial guess for the subsequent trajectory optimization.

preprint2022arXiv

Bayesian learning of COVID-19 Vaccine safety while incorporating Adverse Events ontology

While vaccines are crucial to end the COVID-19 pandemic, public confidence in vaccine safety has always been vulnerable. Many statistical methods have been applied to VAERS (Vaccine Adverse Event Reporting System) database to study the safety of COVID-19 vaccines. However, all these methods ignored the adverse event (AE) ontology. AEs are naturally related; for example, events of retching, dysphagia, and reflux are all related to an abnormal digestive system. Explicitly bringing AE relationships into the model can aid in the detection of true AE signals amid the noise while reducing false positives. We propose a Bayesian graphical model to estimate all AEs while incorporating the AE ontology simultaneously. We proposed strategies to construct conjugate forms leading to an efficient Gibbs sampler. Built upon the posterior distributions, we proposed a negative control approach to mitigate reporting bias and an enrichment approach to detect AE groups of concern. The proposed methods were evaluated using simulation studies and were further illustrated on studying the safety of COVID-19 vaccines. The proposed methods were implemented in R package \textit{BGrass} and source code are available at https://github.com/BangyaoZhao/BGrass.

preprint2022arXiv

Kink-antikink collision in a Lorentz-violating $ϕ^4$ model

In this work, kink-antikink collision in a two-dimensional Lorentz-violating $ϕ^4$ model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum of the standard $ϕ^4$ model, and thus there exists only one vibrational mode. The Lorentz-violating term impacts, however, the frequency and spatial wave function of the vibrational mode. As a consequence, the well-known results on $ϕ^4$ kink-antikink collision will also change. Collisions of kink-antikink pairs with different values of initial velocities and Lorentz-violating parameters are simulated using the Fourier spectral method. Our results indicate that models with larger Lorentz-violating parameters would have smaller critical velocities $v_c$ and smaller widths of bounce windows. Interesting fractal structures existing in the curves of maximal energy densities of the scalar field are also found.

preprint2022arXiv

Scalar perturbation of gravitating double-kink solutions

In this letter, a two-dimensional (2D) gravity-scalar model is studied. This model supports interesting double-kink solutions, and the corresponding metric solutions can be derived analytically. Depending on a tunable parameter $c$, the metric can be symmetric or asymmetric. The Schrödinger-like equation for normal modes of the physical linear perturbation is derived. As $c$ varies, the effective potential can have one or two singular barriers. If $c$ is larger than a critical value, the zero mode will be normalizable, despite of the appearance of a strong repulsive singularity. The double-kink solution is always stable against linear perturbations.

preprint2021arXiv

Normal modes for two-dimensional gravitating kinks

We study small perturbations around an arbitrary static kink solution of a two-dimensional (2D) gravity-scalar system, where the gravity part is described by a subclass of 2D dilaton gravity theory, and the scalar matter field has generalized dynamics. We expand the action around an arbitrary static solution and keep terms up to the second order of the perturbations. After variation the linear-order action leads to background field equations, as expected. The quadratic action of the normal modes are obtained after fixing the gauge and using the constraint equation. The linear perturbation equations obtained from the quadratic action are consistent with those obtained by linearizing the field equations under the dilaton gauge. All the calculations are assisted by a Mathematica code, which is also provided as a supplementary material.

preprint2020arXiv

Collision of two kinks with inner structure

In this work, we study kink collisions in a scalar field model with scalar-kinetic coupling. This model supports kink/antikink solutions with inner structure in the energy density. The collision of two such kinks is simulated by using the Fourier spectral method. We numerically calculate how the critical velocity and the widths of the first three two bounce windows vary with the model parameters. After that, we report some interesting collision results including two-bion escape final states, kink-bion-antikink intermediate states and kink or antikink intertwined final states. These results show that kinks with inner structure in the energy density have similar properties as those of the double kinks.

preprint2020arXiv

Kaluza-Klein modes of $U(1)$ gauge vector field on brane with codimension-$d$

From the paper [JHEP 01 (2019) 021], it is known that the effective action of a massless $U(1)$ gauge vector field on a codimension-2 brane is gauge invariant due to the coupling between the vector Kaluza-Klein (KK) modes with two types of scalar KK modes. It is interesting to generalize this result to a brane world model with an arbitrary number of extra dimensions. In this work, we first investigate the case with three extra dimensions. After KK decomposition, there are three types of scalar KK modes. In addition to the mutual coupling between these scalar modes, there are also coupling between the scalar and the vector KK modes. The coupling constants are not all independent. The relationships between the coupling constants enable us to obtain a gauge invariant effective action, from which we can see that the masses of the vector KK modes depend on all the three extra dimensions. The masses of the scalar modes, however, depend only on two of the three extra dimensions. Then we generalize the results into branes with codimension $d$ ($d=1, 2...$), and find that $d$ will directly affect the masses of the KK modes. But there is always a gauge invariant effective action for the massive vector KK modes.

preprint2020arXiv

Modular Hamiltonians in flat holography and (W)AdS/WCFT

We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS$_3$ or AdS$_3$ backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on "modular chaos" introduced recently in the context of the AdS/CFT correspondence.

preprint2020arXiv

Time-based Sequence Model for Personalization and Recommendation Systems

In this paper we develop a novel recommendation model that explicitly incorporates time information. The model relies on an embedding layer and TSL attention-like mechanism with inner products in different vector spaces, that can be thought of as a modification of multi-headed attention. This mechanism allows the model to efficiently treat sequences of user behavior of different length. We study the properties of our state-of-the-art model on statistically designed data set. Also, we show that it outperforms more complex models with longer sequence length on the Taobao User Behavior dataset.

preprint2018arXiv

$U(1)$ gauge vector field on a codimension-2 brane

In this paper, we obtain a gauge invariant effective action for a bulk massless $U(1)$ gauge vector field on a brane with codimension two by using a general Kaluza-Klein (KK) decomposition for the field. It suggests that there exist two types of scalar KK modes to keep the gauge invariance of the action for the massive vector KK modes. Both the vector and scalar KK modes can be massive. The masses of the vector KK modes $m^{(n)}$ contain two parts, $m_{1}^{(n)}$ and $m_{2}^{(n)}$, due to the existence of the two extra dimensions. The masses of the two types of scalar KK modes $m_ϕ^{(n)}$ and $m_φ^{(n)}$ are related to the vector ones, i.e., $m_ϕ^{(n)}=m_{1}^{(n)}$ and $m_φ^{(n)}=m_{2}^{(n)}$. Moreover, we derive two Schrödinger-like equations for the vector KK modes, for which the effective potentials are just the functions of the warp factor.

preprint2016arXiv

Experimental Analysis of Algorithms for Coflow Scheduling

Modern data centers face new scheduling challenges in optimizing job-level performance objectives, where a significant challenge is the scheduling of highly parallel data flows with a common performance goal (e.g., the shuffle operations in MapReduce applications). Chowdhury and Stoica introduced the coflow abstraction to capture these parallel communication patterns, and Chowdhury et al. proposed effective heuristics to schedule coflows efficiently. In our previous paper, we considered the strongly NP-hard problem of minimizing the total weighted completion time of coflows with release dates, and developed the first polynomial-time scheduling algorithms with O(1)-approximation ratios. In this paper, we carry out a comprehensive experimental analysis on a Facebook trace and extensive simulated instances to evaluate the practical performance of several algorithms for coflow scheduling, including the approximation algorithms developed in our previous paper. Our experiments suggest that simple algorithms provide effective approximations of the optimal, and that the performance of our approximation algorithms is relatively robust, near optimal, and always among the best compared with the other algorithms, in both the offline and online settings.

preprint2016arXiv

Gravitational resonances on $f(R)$-brane

In this paper, we investigate various $f(R)$-brane models and compare their gravitational resonance structures with the corresponding general relativity (GR)-branes. {Starting from some known GR-brane solutions}, we derive thick $f(R)$-brane solutions such that the metric, scalar field, and scalar potential coincide with those of the corresponding GR-branes. {We find that for branes generated by a single or several canonical scalar fields, there is no obvious distinction between the GR-branes and corresponding $f(R)$-branes in terms of gravitational resonance structure.} Then we discuss the branes generated by K-fields. In this case, there could exist huge differences between GR-branes and $f(R)$-branes.

preprint2016arXiv

Localization and mass spectrum of $q-$form fields on branes

In this paper, we investigate localization of a bulk massless q-form field on codimension-one brane by using a new Kaluza-Klein (KK) decomposition, for which there are two types of KK modes for the bulk q-form field, the q-form and (q-1)-form modes. The first modes may be massive or massless while the second ones are all masselss. These two types fo KK modes satisfy twy Schrodinger-like equations. For a five-dimensional brane model with a finite dimension, the spectrum of a bulk 3-form field on the brane consists of some massive bound 3-form KK modes as well as some massless bound 2-form ones with different configuration along the extra dimension. These 2-form modes are different form those obtained from a bulk 2-form field. For a five-dimensional degenerated Bloch brane model with an infinite extra dimension, some massive 3-form resonant KK modes and corresponding massless 2-form resonant ones are obtained for a bulk 3-form field.

preprint2016arXiv

Pure geometric thick $f(R)$-branes: stability and localization of gravity

We study two exactly solvable five-dimensional thick brane world models in pure metric $f(R)$ gravity. Working in the Einstein frame, we show that these solutions are stable against small linear perturbations, including the tensor, vector, and scalar modes. For both models, the corresponding gravitational zero mode is localized on the brane, which leads to the four-dimensional Newton's law; while the massive modes are nonlocalized and only contribute a small correction to the Newton's law at a large distance.

preprint2016arXiv

Resource Allocation and Rate Gains in Practical Full-Duplex Systems

Full-duplex communication has the potential to substantially increase the throughput in wireless networks. However, the benefits of full-duplex are still not well understood. In this paper, we characterize the full-duplex rate gains in both single-channel and multi-channel use cases. For the single-channel case, we quantify the rate gain as a function of the remaining self-interference and SNR values. We also provide a sufficient condition under which the sum of uplink and downlink rates on a full-duplex channel is concave in the transmission power levels. Building on these results, we consider the multi-channel case. For that case, we introduce a new realistic model of a small form-factor (e.g., smartphone) full-duplex receiver and demonstrate its accuracy via measurements. We study the problem of jointly allocating power levels to different channels and selecting the frequency of maximum self-interference suppression, where the objective is maximizing the sum of the rates over uplink and downlink OFDM channels. We develop a polynomial time algorithm which is nearly optimal in practice under very mild restrictions. To reduce the running time, we develop an efficient nearly-optimal algorithm under the high SINR approximation. Finally, we demonstrate via numerical evaluations the capacity gains in the different use cases and obtain insights into the impact of the remaining self-interference and wireless channel states on the performance.

preprint2016arXiv

Robust Scheduling for Flexible Processing Networks

Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e., policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper, we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under non-restrictive assumptions.

preprint2015arXiv

Matching the linear spectra of twinlike defects

Twinlike defects refer to topological defect solutions of some apparently different field models that share the same defect configuration and the same energy density. Usually, one can distinguish twinlike defects in terms of their linear spectra, but in some special cases twinlike defects even share the same linear spectrum. In this paper, we derive the algebraic conditions for two twinlike defects to share identical linear spectrum from the viewpoint of the normal modes of the linear fluctuations. We also extend our discussion to braneworld models, where gravity plays an important role.

preprint2015arXiv

The structure of $f(R)$-brane model

Recently, a family of interesting analytical brane solutions were found in $f(R)$ gravity with $f(R)=R+αR^2$ in Ref. [Phys. Lett. B 729, 127 (2014)]. In these solutions, inner brane structure can be turned on by tuning the value of the parameter $α$. In this paper, we investigate how the parameter $α$ affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of $α$, despite the brane has an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton KK modes has a singular structure, and there exists a series of graviton resonant modes. The contribution of the massive graviton KK modes to the Newton's law of gravity is discussed shortly.

preprint2014arXiv

$K$-field kinks: stability, exact solutions and new features

We study a class of noncanonical real scalar field models in $(1+1)$-dimensional flat space-time. We first derive the general criterion for the classical linear stability of an arbitrary static soliton solution of these models. Then we construct first-order formalisms for some typical models and derive the corresponding kink solutions. The linear structures of these solutions are also qualitatively analyzed and compared with the canonical kink solutions.

preprint2014arXiv

$U(1)$ Gauge Field Localization on Bloch Brane with Chumbes-Holf da Silva-Hott Mechanism

We follow the Chumbes-Holf da Silva-Hott (CHH) mechanism to study the (qusi-)localization of $U(1)$ gauge field on the Bloch brane. The localization of $U(1)$ gauge field is discussed for four kinds of Bloch brane solutions: the original Bloch brane solution, the generalized Bloch brane solution, and the degenerate Bloch brane solutions I and II. With the CHH mechanism, we find that the mass spectrum of the gauge field Kaluza-Klein modes is continuous and only the zero mode of the gauge field is localized on the brane. For the massive modes, there exist resonant modes only on the degenerate Bloch branes.

preprint2014arXiv

Asymptotic optimality of a greedy randomized algorithm in a large-scale service system with general packing constraints

We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple types of arriving customers, where a customer's mean service time depends on its type. There is an infinite number of servers. Multiple customers can be placed for service into one server, subject to general "packing" constraints. Service times of different customers are independent, even if served simultaneously by the same server. Each new arriving customer is placed for service immediately, either into a server already serving other customers (as long as packing constraints are not violated) or into an idle server. After a service completion, each customer leaves its server and the system. We propose an extremely simple and easily implementable customer placement algorithm, called Greedy-Random (GRAND). It places each arriving customer uniformly at random into either one of the already occupied servers (subject to packing constraints) or one of the so-called zero-servers, which are empty servers designated to be available to new arrivals. One instance of GRAND, called GRAND($aZ$), where $a\ge 0$ is a parameter, is such that the number of zero-servers at any given time $t$ is $aZ(t)$, where $Z(t)$ is the current total number of customers in the system. We prove that GRAND($aZ$) with $a>0$ is asymptotically optimal, as the customer arrival rates grow to infinity and $a\to 0$, in the sense of minimizing the total number of occupied servers in steady state. In addition, we study by simulations various versions of GRAND and observe the dependence of convergence speed and steady-state performance on the number of zero-servers.

preprint2014arXiv

Brane structure and metastable graviton in five-dimensional model with (non)canonical scalar field

The appearance of inner brane structure is an interesting issue in domain wall {brane model}. Because such structure usually leads to quasilocalized modes of various kinds of bulk fields. In this paper, we construct a domain wall brane model by using a scalar field $ϕ$, which couples to its kinetic term. The inner brane structure emerges as the scalar-kinetic coupling increases. With such brane structure, we show that it is possible to obtain gravity resonant modes in both tensor and scalar sectors. The number of the resonant modes depends on the vacuum expectation value of $ϕ$ and the form of scalar-kinetic coupling. The correspondence between our model and the canonical one is also discussed. The noncanonical and canonical background scalar fields are connected by an integral equation, while the warp factor remains the same. Via this correspondence, the canonical and noncanonical models share the same linear perturbation spectrum. So the gravity resonances {obtained} in the noncanonical frame can also be obtained in the standard model. However, due to the inequivalence between the corresponding background scalar solutions, the localization condition for the left-chiral fermion zero mode can be largely different in different frames. Our estimate shows that the magnitude of the Yukawa coupling in the noncanonical frame might be hundreds times larger than the one in the canonical frame, if one demands the localization of the left-chiral fermion zero mode as well as the appearance of a few gravity resonance modes.

preprint2014arXiv

On Queue-Size Scaling for Input-Queued Switches

We study the optimal scaling of the expected total queue size in an $n\times n$ input-queued switch, as a function of the number of ports $n$ and the load factor $ρ$, which has been conjectured to be $Θ(n/(1-ρ))$. In a recent work, the validity of this conjecture has been established for the regime where $1-ρ= O(1/n^2)$. In this paper, we make further progress in the direction of this conjecture. We provide a new class of scheduling policies under which the expected total queue size scales as $O(n^{1.5}(1-ρ)^{-1}\log(1/(1-ρ)))$ when $1-ρ= O(1/n)$. This is an improvement over the state of the art; for example, for $ρ= 1 - 1/n$ the best known bound was $O(n^3)$, while ours is $O(n^{2.5}\log n)$.

preprint2014arXiv

Pure Geometric Branes and Mass Hierarchy

We consider a toy model with flat thin branes embedded in a 5-dimensional Weyl integrable manifold, where the geometric Weyl scalar provides the material that constitute the brane configurations. The brane configuration is similar to the Randall-Sundrum model. However, it is found that the massless graviton is localized on the brane with negative tension. So in order to solve the gauge hierarchy problem our world should be confined on the positive tension brane, and this is crucial to reproduce a correct Friedmann-like equation on the brane. The spacings of graviton mass spectrum are very tiny, but these massive gravitons are hidden in low energy experiments because they are weakly coupled with matter on the brane.

preprint2013arXiv

Brane worlds in critical gravity

Recently, Lu and Pope proposed critical gravities in [Phys. Rev. Lett. 106, 181302 (2011)]. In this paper we construct analytic brane solutions in critical gravity with matter. The Gibbons-Hawking surface term and junction condition are investigated, and the thin and thick brane solutions are obtained. All these branes are embedded in five-dimensional anti-de Sitter spacetimes. Our solutions are stable against scalar perturbations, and the zero modes of scalar perturbations cannot be localized on the branes.

preprint2013arXiv

Linearization of thick K-branes

We study the linearization of a class of thick K-branes, namely, four-dimensional domain walls generated by a scalar field with particular nonstandard kinetic terms. The master equations for linear perturbations are derived from the point of view of both dynamical equations and quadratic action. The spectra of the canonical normal modes are studied using supersymmetric quantum mechanics. Our results indicate that the scalar perturbation is nonlocalizable in general. Conditions for stable $K$-branes are also found.

preprint2013arXiv

Non-perturbative procedure for stable $K$-brane

We propose a novel first-order formalism for a type of $K$-brane systems. An example solution is presented and studied. We illustrate how the noncanonical kinetic term can affect the properties of the model, such as the stability of the solutions, the localization of fermion and graviton. We argue that our solution is stable against linear perturbations. The tensor zero mode of graviton can be localized while the scalar zero mode cannot. The localization condition for fermion is also discussed.

preprint2012arXiv

A large-scale service system with packing constraints: Minimizing the number of occupied servers

We consider a large-scale service system model motivated by the problem of efficient placement of virtual machines to physical host machines in a network cloud, so that the total number of occupied hosts is minimized. Customers of different types arrive to a system with an infinite number of servers. A server packing configuration is the vector $k = (k_i)$, where $k_i$ is the number of type-$i$ customers that the server "contains". Packing constraints are described by a fixed finite set of allowed configurations. Upon arrival, each customer is placed into a server immediately, subject to the packing constraints; the server can be idle or already serving other customers. After service completion, each customer leaves its server and the system. It was shown recently that a simple real-time algorithm, called Greedy, is asymptotically optimal in the sense of minimizing $\sum_k X_k^{1+α}$ in the stationary regime, as the customer arrival rates grow to infinity. (Here α>0, and $X_k$ denotes the number of servers with configuration $k$.) In particular, when parameter αis small, Greedy approximately solves the problem of minimizing $\sum_k X_k$, the number of occupied hosts. In this paper we introduce the algorithm called Greedy with sublinear Safety Stocks (GSS), and show that it asymptotically solves the exact problem of minimizing $\sum_k X_k$. An important feature of the algorithm is that sublinear safety stocks of $X_k$ are created automatically - when and where necessary - without having to determine a priori where they are required. Moreover, we also provide a tight characterization of the rate of convergence to optimality under GSS. The GSS algorithm is as simple as Greedy, and uses no more system state information than Greedy does.

preprint2012arXiv

Domain Wall Brane in Eddington Inspired Born-Infeld Gravity

Recently, inspired by Eddington's theory, an alternative gravity called Eddington-inspired Born-Infeld gravity was proposed by Ba$\tilde{\text{n}}$ados and Ferreira. It is equivalent to Einstein's general relativity in vacuum, but deviates from it when matter is included. Interestingly, it seems that the cosmological singularities are prevented in this theory. Based on the new theory, we investigate a thick brane model with a scalar field presenting in the five-dimensional background. A domain wall solution is obtained, and further, we find that at low energy the four-dimensional Einstein gravity is recovered on the brane. Moreover, the stability of gravitational perturbations is ensured in this model.

preprint2012arXiv

Gravity localization and mass hierarchy in scalar-tensor branes

We consider a braneworld model in the scalar-tensor gravity. In order to solve the gauge hierarchy problem in this model, our world should be confined on the positive tension brane rather than on the negative one. This is crucial to reproduce a correct Friedmann-like equation on the brane. Interestingly, it is found that the spacing of mass spectrum in this scenario is very tiny, but the light gravitons cannot be observed individually in colliders because of their sufficiently weak interaction with matter fields on the visible brane.

preprint2012arXiv

Thick Brane Split Caused by Spacetime Torsion

In this paper we apply the five-dimensional $f(T)$ gravity with $f(T)=T+k T^n$ to brane scenario to explore the solutions under a given warp factor, and we find that the analytic domain wall solution will be a double-kink solution when the geometric effect of spacetime torsion is strongly enhanced. We also investigate the localization of fermion fields on the split branes corresponding to the double-kink solution.

preprint2011arXiv

Domain wall brane in squared curvature gravity

We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schrödinger equation with a volcano potential, and the other a Pöschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states.

preprint2011arXiv

Tensor perturbations of $f(R)$-branes

We analyze the tensor perturbations of flat thick domain wall branes in $f(R)$ gravity. Our results indicate that under the transverse and traceless gauge, the metric perturbations decouple from the perturbation of the scalar field. Besides, the perturbed equation reduces to the familiar Klein-Gordon equation for massless spin-2 particles only when the bulk curvature is a constant or when $f(R)=R$. As an application of our results, we consider the possibility of localizing gravity on some flat thick branes. The stability of these brane solutions is also shortly discussed.

preprint2010arXiv

de Sitter Thick Brane Solution in Weyl Geometry

In this paper, we consider a de Sitter thick brane model in a pure geometric Weyl integrable five-dimensional space-time, which is a generalization of Riemann geometry and is invariant under a so-called Weyl rescaling. We find a solution of this model via performing a conformal transformation to map the Weylian structure into a familiar Riemannian one with a conformal metric. The metric perturbations of the model are discussed. For gravitational perturbation, we get the effective modified P$\ddot{\text{o}}$schl-Teller potential in corresponding Schr$\ddot{\text{o}}$dinger equation for Kaluza-Klein (KK) modes of the graviton. There is only one bound state, which is a normalizable massless zero mode and represents a stable 4-dimensional graviton. Furthermore, there exists a mass gap between the massless mode and continuous KK modes. We also find that the model is stable under the scalar perturbation in the metric. The correction to the Newtonian potential on the brane is proportional to $e^{-3 r β/2}/r^2$, where $β$ is the de Sitter parameter of the brane. This is very different from the correction caused by a volcano-like effective potential.

preprint2010arXiv

Entropy/Area spectra of the charged black hole from quasinormal modes

With the new physical interpretation of quasinormal modes proposed by Maggiore, the quantum area spectra of black holes have been investigated recently. Adopting the modified Hod's treatment, results show that the area spectra for black holes are equally spaced and the spacings are in a unified form, $\triangle A=8π\hbar$, in Einstein gravity. On the other hand, following Kunstatter's method, the studies show that the area spectrum for a nonrotating black hole with no charge is equidistant. And for a rotating (or charged) black hole, it is also equidistant and independent of the angular momentum $J$ (or charge $q$) when the black hole is far from the extremal case. In this paper, we mainly deal with the area spectrum of the stringy charged Garfinkle-Horowitz-Strominger black hole, originating from effective action that emerges in the low-energy string theory. We find that both methods give the same results-that the area spectrum is equally spaced and does not depend on the charge $q$. Our study may provide new insights into understanding the area spectrum and entropy spectrum for stringy black holes.

preprint2010arXiv

Qualitative Properties of alpha-Weighted Scheduling Policies

We consider a switched network, a fairly general constrained queueing network model that has been used successfully to model the detailed packet-level dynamics in communication networks, such as input-queued switches and wireless networks. The main operational issue in this model is that of deciding which queues to serve, subject to certain constraints. In this paper, we study qualitative performance properties of the well known $α$-weighted scheduling policies. The stability, in the sense of positive recurrence, of these policies has been well understood. We establish exponential upper bounds on the tail of the steady-state distribution of the backlog. Along the way, we prove finiteness of the expected steady-state backlog when $α<1$, a property that was known only for $α\geq 1$. Finally, we analyze the excursions of the maximum backlog over a finite time horizon for $α\geq 1$. As a consequence, for $α\geq 1$, we establish the full state space collapse property.

preprint2010arXiv

Scalar-Kinetic Branes

This work tries to find out thick brane solutions in braneworld scenarios described by a real scalar field in the presence of a scalar-kinetic term $F(X,ϕ)=Xϕ^m$ with a single extra dimension, where $X=\frac12\nabla_Mϕ\nabla^Mϕ$ stands for the standard kinetic term and $m=0,1,2\cdots$. We mainly consider bent branes, namely de Sitter and Anti-de Sitter four-dimensional slices. The solutions of a flat brane are obtained when taking the four-dimensional cosmological constant $Λ_4\rightarrow 0$. When the parameter $m=0$, these solutions turn to those of the standard scenario. The localization and spectrum of graviton on these branes are also analyzed.