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Published work

41 published item(s)

preprint2026arXiv

Catching the Infection Before It Spreads: Foresight-Guided Defense in Multi-Agent Systems

Large multimodal model-based Multi-Agent Systems (MASs) enable collaborative complex problem solving through specialized agents. However, MASs are vulnerable to infectious jailbreak, where compromising a single agent can spread to others, leading to widespread compromise. Existing defenses counter this by training a more contagious cure factor, biasing agents to retrieve it over virus adversarial examples (VirAEs). However, this homogenizes agent responses, providing only superficial suppression rather than true recovery. We revisit these defenses, which operate globally via a shared cure factor, while infectious jailbreak arise from localized interaction behaviors. This mismatch limits their effectiveness. To address this, we propose a training-free Foresight-Guided Local Purification (FLP) framework, where each agent reasons over future interactions to track behavioral evolution and eliminate infections. Specifically, each agent simulates future behavioral trajectories over subsequent chat rounds. To reflect diversity in MASs, we introduce a multi-persona simulation strategy for robust prediction across interaction contexts. We then use response diversity as a diagnostic signal to detect infection by analyzing inconsistencies across persona-based predictions at both retrieval-result and semantic levels. For infected agents, we apply localized purification: recent infections are mitigated via immediate album rollback, while long-term infections are handled using Recursive Binary Diagnosis (RBD), which recursively partitions the image album and applies the same diagnosis strategy to localize and eliminate VirAEs. Experiments show that FLP reduces the maximum cumulative infection rate from over 95% to below 5.47%. Moreover, retrieval and semantic metrics closely match benign baselines, indicating effective preservation of interaction diversity.

preprint2025arXiv

MiMo-Audio: Audio Language Models are Few-Shot Learners

Existing audio language models typically rely on task-specific fine-tuning to accomplish particular audio tasks. In contrast, humans are able to generalize to new audio tasks with only a few examples or simple instructions. GPT-3 has shown that scaling next-token prediction pretraining enables strong generalization capabilities in text, and we believe this paradigm is equally applicable to the audio domain. By scaling MiMo-Audio's pretraining data to over one hundred million of hours, we observe the emergence of few-shot learning capabilities across a diverse set of audio tasks. We develop a systematic evaluation of these capabilities and find that MiMo-Audio-7B-Base achieves SOTA performance on both speech intelligence and audio understanding benchmarks among open-source models. Beyond standard metrics, MiMo-Audio-7B-Base generalizes to tasks absent from its training data, such as voice conversion, style transfer, and speech editing. MiMo-Audio-7B-Base also demonstrates powerful speech continuation capabilities, capable of generating highly realistic talk shows, recitations, livestreaming and debates. At the post-training stage, we curate a diverse instruction-tuning corpus and introduce thinking mechanisms into both audio understanding and generation. MiMo-Audio-7B-Instruct achieves open-source SOTA on audio understanding benchmarks (MMSU, MMAU, MMAR, MMAU-Pro), spoken dialogue benchmarks (Big Bench Audio, MultiChallenge Audio) and instruct-TTS evaluations, approaching or surpassing closed-source models. Model checkpoints and full evaluation suite are available at https://github.com/XiaomiMiMo/MiMo-Audio.

preprint2024arXiv

Follow Your Pose: Pose-Guided Text-to-Video Generation using Pose-Free Videos

Generating text-editable and pose-controllable character videos have an imperious demand in creating various digital human. Nevertheless, this task has been restricted by the absence of a comprehensive dataset featuring paired video-pose captions and the generative prior models for videos. In this work, we design a novel two-stage training scheme that can utilize easily obtained datasets (i.e.,image pose pair and pose-free video) and the pre-trained text-to-image (T2I) model to obtain the pose-controllable character videos. Specifically, in the first stage, only the keypoint-image pairs are used only for a controllable text-to-image generation. We learn a zero-initialized convolutional encoder to encode the pose information. In the second stage, we finetune the motion of the above network via a pose-free video dataset by adding the learnable temporal self-attention and reformed cross-frame self-attention blocks. Powered by our new designs, our method successfully generates continuously pose-controllable character videos while keeps the editing and concept composition ability of the pre-trained T2I model. The code and models will be made publicly available.

preprint2022arXiv

A Meta Path Based Evaluation Method for Enterprise Credit Risk

Nowadays small and medium-sized enterprises have become an essential part of the national economy. With the increasing number of such enterprises, how to evaluate their credit risk becomes a hot issue. Unlike big enterprises with massive data to analyze, it is hard to find enough information of small enterprises to assess their financial status. Limited by the lack of primary data, how to inference small enterprises' credit risk from secondary data, like information of their upstream, downstream, parent, and subsidiary enterprises attracts big attention from industry and academy. Targeting on accurately evaluating the credit risk of the small and medium-sized enterprise (SME), in this paper, we exploit the representative power of Information Network on various kinds of SME entities and SME relationships to solve the problem. A novel feature named meta path feature proposed to measure the credit risk, which makes us able to evaluate the financial status of SMEs from various perspectives. Experiments show that our method is effective to identify SMEs with credit risks.

preprint2022arXiv

Asymptotic behavior of 2D Wave-Klein-Gordon coupled system under null condition

We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{αβ}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small in some weighted Sobolev space, which do not necessarily have compact support, and we also show the optimal time decay of the solution. The major difficulties lie in the slow decay nature of the wave and the Klein-Gordon components in two space dimensions, in addition, extra difficulties arise due to the presence of the null form $Q_0$ which is not of divergence form and is not compatible with the Klein-Gordon equations. To overcome the difficulties, a new observation for the structure of the null form $Q_0$ is required.

preprint2022arXiv

Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations

In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field and a massless Dirac field. More precisely, our main result is twofold: 1) we show sharp time decay for the pointwise estimates of the solutions which imply the asymptotic stability of this system; 2) we show the linear scattering result of this system which is a fundamental problem when it is viewed as dispersive equations. Our result is valid for general small, high-regular initial data, in particular, there is no restriction on the support of the initial data.

preprint2022arXiv

Limits on inference of gravitational entanglement

Combining gravity with quantum mechanics remains one of the biggest challenges of physics. In the past years, experiments with opto-mechanical systems have been proposed that may give indirect clues about the quantum nature of gravity. In a recent variation of such tests [D. Carney et al., Phys.Rev.X Quantum 2, 030330 (2021)], the authors propose to gravitationally entangle an atom interferometer with a mesoscopic oscillator. The interaction results in periodic drops and revivals of the interferometeric visibility, which under specific assumptions indicate the gravitational generation of entanglement. Here we study semi-classical models of the atom interferometer that can reproduce the same effect. We show that the core signature -- periodic collapses and revivals of the visibility -- can appear if the atom is subject to a random unitary channel, including the case where the oscillator is fully classical and situations even without explicit modelling of the oscillator. We also show that the non-classicality of the oscillator vanishes unless the system is very close to its ground state, and even when the system is in the ground state, the non-classicality is limited by the coupling strength. Our results thus indicate that deducing entanglement from the proposed experiment is very challenging, since fulfilling and verifying the non-classicality assumptions is a significant challenge on its own right.

preprint2022arXiv

Nonlinear stability of the totally geodesic wave maps in non-isotropic manifolds

In this article we investigate a type of totally geodesic map which has its image being a geodesic in an anisotropic Riemannian manifold. We consider its nonlinear stability among the family of wave maps. We first establish the factorization property and then formulate the stability problem into a PDE system in a specially constructed chart of geodesic normal coordinates. With a generalization of the hyperboloidal foliation, we establish the global existence result associate to small initial data for this PDE system, which leads to the geometric stability.

preprint2022arXiv

Simulating Authenticated Broadcast in Networks of Bounded Degree

The authenticated broadcast is simulated in the bounded-degree networks to provide efficient broadcast primitives for building efficient higher-layer Byzantine protocols. A general abstraction of the relay-based broadcast system is introduced, in which the properties of the relay-based broadcast primitives are generalized. With this, fault-tolerant propagation is proposed as a building block of the broadcast primitives. Meanwhile, complementary systems are proposed in complementing fault-tolerant propagation and localized communication. Analysis shows that efficient fault-tolerant propagation can be built with sufficient initiation areas. Meanwhile, by integrating fault-tolerant propagation and localized communication, efficient broadcast primitives can be built in bounded-degree networks.

preprint2022arXiv

Toward Systematic Considerations of Missingness in Visual Analytics

Data-driven decision making has been a common task in today's big data era, from simple choices such as finding a fast way to drive home, to complex decisions on medical treatment. It is often supported by visual analytics. For various reasons (e.g., system failure, interrupted network, intentional information hiding, or bias), visual analytics for sensemaking of data involves missingness (e.g., data loss and incomplete analysis), which impacts human decisions. For example, missing data can cost a business millions of dollars, and failing to recognize key evidence can put an innocent person in jail. Being aware of missingness is critical to avoid such catastrophes. To fulfill this, as an initial step, we consider missingness in visual analytics from two aspects: data-centric and human-centric. The former emphasizes missingness in three data-related categories: data composition, data relationship, and data usage. The latter focuses on the human-perceived missingness at three levels: observed-level, inferred-level, and ignored-level. Based on them, we discuss possible roles of visualizations for handling missingness, and conclude our discussion with future research opportunities.

preprint2021arXiv

Minimizing the number of edges in $\mathcal{C}_{\ge r}$-saturated graphs

Given a family of graphs $\mathcal{F}$, a graph $G$ is said to be $\mathcal{F}$-saturated if $G$ does not contain a copy of $F$ as a subgraph for any $F\in\mathcal{F}$ but the addition of any edge $e\notin E(G)$ creates at least one copy of some $F\in\mathcal{F}$ within $G$. The minimum size of an $\mathcal{F}$-saturated graph on $n$ vertices are called the saturation number, denoted by $\sat(n, \mathcal{F})$. Let $\mathcal{C}_{\ge r}$ be the family of cycles of length at least $r$. Ferrara et al. (2012) gave lower and upper bounds of $\sat(n, C_{\ge r})$ and determined the exact values of $\sat(n, C_{\ge r})$ for $3\le r\le 5$. In this paper, we determine the exact value of $\sat(n,\mathcal{C}_{\ge r})$ for $r=6$ and $28\le \frac{n}2\le r\le n$ and give new upper and lower bounds for the other cases.

preprint2020arXiv

An End-to-End Dialogue State Tracking System with Machine Reading Comprehension and Wide & Deep Classification

This paper describes our approach in DSTC 8 Track 4: Schema-Guided Dialogue State Tracking. The goal of this task is to predict the intents and slots in each user turn to complete the dialogue state tracking (DST) based on the information provided by the task's schema. Different from traditional stage-wise DST, we propose an end-to-end DST system to avoid error accumulation between the dialogue turns. The DST system consists of a machine reading comprehension (MRC) model for non-categorical slots and a Wide & Deep model for categorical slots. As far as we know, this is the first time that MRC and Wide & Deep model are applied to DST problem in a fully end-to-end way. Experimental results show that our framework achieves an excellent performance on the test dataset including 50% zero-shot services with a joint goal accuracy of 0.8652 and a slot tagging F1-Score of 0.9835.

preprint2020arXiv

Exact minimum codegree thresholds for $K_4^-$-covering and $K_5^-$-covering

Given two $3$-graphs $F$ and $H$, an $F$-covering of $H$ is a collection of copies of $F$ in $H$ such that each vertex of $H$ is contained in at least one copy of them. Let {$c_2(n,F)$} be the maximum integer $t$ such that every 3-graph with minimum codegree greater than $t$ has an $F$-covering. In this note, we answer an open problem of Falgas-Ravry and Zhao (SIAM J. Discrete Math., 2016) by determining the exact value of {$c_2(n, K_4^-)$} and {$c_2(n, K_5^-)$}, where $K_t^-$ is the complete $3$-graph on $t$ vertices with one edge removed.

preprint2020arXiv

Maximizing the number of independent sets of fixed size in $K_n$-covered graphs

A graph $G$ is $H$-covered by some given graph $H$ if each vertex in $G$ is contained in a copy of $H$. In this note, we give the maximum number of independent sets of size $t\ge 3$ in $K_n$-covered graphs of size $N\ge n+t-1$ and determine its extremal graph. The result answers a question proposed by Chakraborit and Loh. The proof uses an edge-switching operation of hypergraphs which remains the number of independent sets nondecreasing.

preprint2020arXiv

Measurements of the growth and saturation of electron Weibel instability in optical-field ionized plasmas

The temporal evolution of the magnetic field associated with electron thermal Weibel instability in optical-field ionized plasmas is measured using ultrashort (1.8 ps), relativistic (45 MeV) electron bunches from a linear accelerator. The self-generated magnetic fields are found to self-organize into a quasi-static structure consistent with a helicoid topology within a few ps and such a structure lasts for tens of ps in underdense plasmas. The measured growth rate agrees well with that predicted by the kinetic theory of plasmas taking into account collisions. Magnetic trapping is identified as the dominant saturation mechanism.

preprint2020arXiv

Optical squeezing for an optomechanical system without quantising the mechanical motion

Witnessing quantumness in mesoscopic objects is an important milestone for both quantum technologies and foundational reasons. Cavity optomechanics offers the ideal system to achieve this by combing high precision optical measurements with mechanical oscillators. However, mechanical quantumness can only be established if the behaviour is incompatible with any classical description of an oscillator. After explicitly considering classical and hybrid quantum-classical descriptions of an optomechanical system, we rule out squeezing of the optical field as such a witness by showing it is also predicted without quantizing the mechanical oscillator.

preprint2020arXiv

Quantum persistent tennis racket dynamics of nanorotors

Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate momentof inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect,quickly averages to zero in classical ensembles since the flipping period varies significantly uponapproaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermalasymmetric nanorotors and show that classically forbidden tunnelling gives rise to persistent tennisracket dynamics, in stark contrast to the classical expectation. We characterise this effect, demon-strating that quantum coherent flipping dynamics can persist even in the regime where millions ofangular momentum states are occupied. This persistent flipping offers a promising route for observ-ing and exploiting quantum effects in rotational degrees of freedom for molecules and nanoparticles.

preprint2020arXiv

Region-of-interest micro-focus CT based on an all-optical inverse Compton scattering source

Micro-focus computed tomography (CT), enabling the reconstruction of hyperfine structure within objects, is a powerful nondestructive testing tool in many fields. Current X-ray sources for micro-focus CT are typically limited by their relatively low photon energy and low flux. An all-optical inverse Compton scattering source (AOCS) based on laser wakefield accelerator (LWFA) can generate intense quasi-monoenergetic X/gamma-ray pulses in the keV-MeV range with micron-level source size, and its potential application for micro-focus CT has become very attractive in recent years due to the fast pace progress made in LWFA. Here we report the first experimental demonstration of high-fidelity micro-focus CT using AOCS (~70 keV) by imaging and reconstructing a test object with complex inner structures. A region-of-interest (ROI) CT method is adopted to utilize the relatively small field-of-view (FOV) of AOCS to obtain high-resolution reconstruction. This demonstration of the ROI micro-focus CT based on AOCS is a key step for its application in the field of hyperfine nondestructive testing.

preprint2020arXiv

The Turán number for the edge blow-up of trees

The edge blow-up of a graph $F$ is the graph obtained from replacing each edge in $F$ by a clique of the same size where the new vertices of the cliques are all different. In this article, we concern about the Turán problem for the edge blow-up of trees. Erdős et al. (1995) and Chen et al. (2003) solved the problem for stars. The problem for paths was resolved by Glebov (2011). Liu (2013) extended the above results to cycles and a special family of trees with the minimum degree at most two in the smaller color class (paths and proper subdivisions of stars were included in the family). In this article, we extend Liu's result to all the trees with the minimum degree at least two in the smaller color class. Combining with Liu's result, except one particular case, the Turán problem for the edge blow-up of trees is completely resolved. Moreover, we determine the maximum number of edges in the family of $\{K_{1,k}, kK_2, 2K_{1,k-1}\}$-free graphs and the extremal graphs, which is an extension of a result given by Abbott et al. (1972).

preprint2020arXiv

Towards Privacy-aware Task Allocation in Social Sensing based Edge Computing Systems

With the advance in mobile computing, Internet of Things, and ubiquitous wireless connectivity, social sensing based edge computing (SSEC) has emerged as a new computation paradigm where people and their personally owned devices collect sensor measurements from the physical world and process them at the edge of the network. This paper focuses on a privacy-aware task allocation problem where the goal is to optimize the computation task allocation in SSEC systems while respecting the users' customized privacy settings. It introduces a novel Game-theoretic Privacy-aware Task Allocation (G-PATA) framework to achieve the goal. G-PATA includes (i) a bottom-up game-theoretic model to generate the maximum payoffs at end devices while satisfying the end user's privacy settings; (ii) a top-down incentive scheme to adjust the rewards for the tasks to ensure that the task allocation decisions made by end devices meet the Quality of Service (QoS) requirements of the applications. Furthermore, the framework incorporates an efficient load balancing and iteration reduction component to adapt to the dynamic changes in status and privacy configurations of end devices. The G-PATA framework was implemented on a real-world edge computing platform that consists of heterogeneous end devices (Jetson TX1 and TK1 boards, and Raspberry Pi3). We compare G-PATA with state-of-the-art task allocation schemes through two real-world social sensing applications. The results show that G-PATA significantly outperforms existing approaches under various privacy settings (our scheme achieved as much as 47% improvements in delay reduction for the application and 15% more payoffs for end devices compared to the baselines.).

preprint2016arXiv

Cooling a Mechanical Resonator to Quantum Regime by heating it

We consider a mechanical resonator made of diamond, which contains a nitrogen-vacancy center (NV center) locating at the end of the oscillator. A second order magnetic gradient is applied and inducing coupling between mechanical modes and the NV center. By applying proper external magnetic field, the energy difference between NV center electron spin levels can be tuned to match the energy difference between two mechanical modes $a$ and $b$. A laser is used for continuously initializing the NV center electron spin. The mode $a$ with lower frequency is driven by a thermal bath. We find that the temperature of the mode $b$ is significantly cooled when the heating bath temperature is increased. We discuss the conditions that quantum regime cooling requires, and confirm the results by numerical simulation. Finally we give the intuitive physical explanation on this unusual effect.

preprint2016arXiv

Design and Performance of a Lead Fluoride Detector as a Luminosity Monitor

Precise luminosity measurements for the OLYMPUS two-photon exchange experiment at DESY were performed by counting scattering events with alternating beams of electrons and positrons incident on atomic electrons in a gaseous hydrogen target. Final products of Møller, Bhabha, and pair annihilation interactions were observed using a pair of lead fluoride Cherenkov calorimeters with custom housings and electronics, adapted from a system used by the A4 parity violation experiment at MAMI. This paper describes the design, calibration, and operation of these detectors. An explanation of the Monte Carlo methods used to simulate the physical processes involved both at the scattering vertices and in the detector apparatus is also included.

preprint2016arXiv

Direct Imaging of Dynamic Glassy Behavior in a Strained Manganite Film

Complex many-body interaction in perovskite manganites gives rise to a strong competition between ferromagnetic metallic and charge ordered phases with nanoscale electronic inhomogeneity and glassy behaviors. Investigating this glassy state requires high resolution imaging techniques with sufficient sensitivity and stability. Here, we present the results of a near-field microwave microscope imaging on the strain driven glassy state in a manganite film. The high contrast between the two electrically distinct phases allows direct visualization of the phase separation. The low temperature microscopic configurations differ upon cooling with different thermal histories. At sufficiently high temperatures, we observe switching between the two phases in either direction. The dynamic switching, however, stops below the glass transition temperature. Compared with the magnetization data, the phase separation was microscopically frozen, while spin relaxation was found in a short period of time.

preprint2016arXiv

One-parameter class of uncertainty relations based on entropy power

We use the concept of entropy power to derive a new one-parameter class of information-theoretic uncertainty relations for pairs of conjugate observables in an infinite-dimensional Hilbert space. This class constitutes an infinite tower of higher-order statistics uncertainty relations, which allows one in principle to determine the shape of the underlying information-distribution function by measuring the relevant entropy powers. We illustrate the capability of the new class by discussing two examples: superpositions of vacuum and squeezed states and the Cauchy-type heavy-tailed wave function.

preprint2016arXiv

The global nonlinear stability of Minkowski space for the Einstein equations in presence of a massive field

We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations and Klein-Gordon equations are coupled. This method is based on a (3+1) foliation (of the interior of a future light cone in Minkowski spacetime) by spacelike and asymptotically hyperboloidal hypersurfaces. In the new formulation of the method, we succeed to cover wave-Klein-Gordon systems containing "strong interaction" terms at the level of the metric, and then generalize our method in order to establish a new existence theory for the Einstein equations of general relativity. Following pioneering work by Lindblad and Rodnianski on the Einstein equations in wave coordinates, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields.

preprint2016arXiv

Torsional optomechanics of a levitated nonspherical nanoparticle

An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tensor. The torsional vibration frequency can be one order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly-polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of $10^{-29} ~\mathrm{N}\cdot \mathrm{m}/\sqrt{\mathrm{ Hz}}$ under realistic conditions.

preprint2015arXiv

A Distance-based Paraconsistent Semantics for DL-Lite

DL-Lite is an important family of description logics. Recently, there is an increasing interest in handling inconsistency in DL-Lite as the constraint imposed by a TBox can be easily violated by assertions in ABox in DL-Lite. In this paper, we present a distance-based paraconsistent semantics based on the notion of feature in DL-Lite, which provides a novel way to rationally draw meaningful conclusions even from an inconsistent knowledge base. Finally, we investigate several important logical properties of this entailment relation based on the new semantics and show its promising advantages in non-monotonic reasoning for DL-Lite.

preprint2015arXiv

Search for the deeply bound $K^-pp$ state from the semi-inclusive forward-neutron spectrum in the in-flight $K^-$ reaction on helium-3

An experiment to search for the $K^-pp$ bound state was performed via the in-flight $^3$He($K^-,n)$ reaction using 5.3 $\times$ $10^9$ kaons at 1 GeV/$c$ at the J-PARC hadron experimental facility. In the semi-inclusive neutron missing-mass spectrum at $θ_{n}^{lab}=0^\circ$, no significant peak was observed in the region corresponding to $K^-pp$ binding energy larger than 80 MeV, where a bump structure has been reported in the $Λp$ final state in different reactions. Assuming the state to be isotropically decaying into $Λp$, mass-dependent upper limits on the production cross section were determined to be 30--180, 70--250, and 100--270 $μ$b/sr, for the natural widths of 20, 60, and 100 MeV, respectively, at 95\% confidence level.

preprint2015arXiv

Structure of $X_b$ from line shape analysis

We study the production line shape of $B^\ast\bar B$ near threshold, where the $B^\ast \bar B$ pair comes from the resonance $X_b$. Our study shows that the line shape depends sensitively on the binding energy and the probability of finding an elementary state in the physical bound state. Both of the two parameters are crucial to identify the structure of $X_b$. Therefore, the line shape measurement can shed light on the structure of $X_b$.

preprint2015arXiv

The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model

The Hyperboloidal Foliation Method (introduced by the authors in 2014) is extended here and applied to the Einstein equations of general relativity. Specifically, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields, while existing methods only apply to massless scalar fields. First of all, by analyzing the structure of the Einstein equations in wave coordinates, we exhibit a nonlinear wave-Klein-Gordon model defined on a curved background, which is the focus of the present paper. For this model, we prove here the existence of global-in-time solutions to the Cauchy problem, when the initial data have sufficiently small Sobolev norms. A major difficulty comes from the fact that the class of conformal Killing fields of Minkowski space is significantly reduced in presence of a massive scalar field, since the scaling vector field is not conformal Killing for the Klein-Gordon operator. Our method relies on the foliation (of the interior of the light cone) of Minkowski spacetime by hyperboloidal hypersurfaces and uses Lorentz-invariant energy norms. We introduce a frame of vector fields adapted to the hyperboloidal foliation and we establish several key properties: Sobolev and Hardy-type inequalities on hyperboloids, as well as sup-norm estimates which correspond to the sharp time decay for the wave and the Klein-Gordon equations. These estimates allow us to control interaction terms associated with the curved geometry and the massive field, by distinguishing between two levels of regularity and energy growth and by a successive use of our key estimates in order to close a bootstrap argument.

preprint2014arXiv

Mathematical Validity of the f(R) Theory of Modified Gravity

We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert functional, is replaced by a function f=f(R). The field equations involve up to fourth-order derivatives of the spacetime metric, and the challenge is to understand the structure of these high-order terms. We propose a formulation of the initial value problem in modified gravity when the initial data are prescribed on a hypersurface. In addition to the induced metric and second fundamental form of the initial slice and the initial matter content, an initial data set must also provide the spacetime scalar curvature and its time-derivative. We introduce an augmented conformal formulation, as we call it, in which the spacetime curvature is an independent variable. In the so-called wave gauge, the field equations of modified gravity reduce a coupled system of nonlinear wave-Klein-Gordon equations with defocusing potential, whose unknowns are the conformally-transformed metric and the scalar curvature, as well as the matter fields. We are able to establish the existence of maximal globally hyperbolic developments when the matter is represented by a scalar field. We analyze the so-called Jordan coupling and work with the Einstein metric, which is conformally equivalent to the physical metric --the conformal factor depending upon the scalar curvature. Our analysis leads us to a rigorous validation of the theory of modified gravity. We derive quantitative estimates, which are uniform in terms of the nonlinearity f(R), and we prove that asymptotically flat spacetimes of modified gravity are `close' to Einstein spacetimes, when the function f(R) in the action functional of modified gravity is `close' to the Einstein-Hilbert integrand R.

preprint2014arXiv

On the measure of conflicts: A MUS-Decomposition Based Framework

Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we emphasize one such property, named Decomposability, rarely discussed in the literature due to its modeling difficulties. To this end, we propose an independent decomposition which is more intuitive than existing proposals. To analyze inconsistency in a more fine-grained way, we introduce a graph representation of a knowledge base and various MUSdecompositions. One particular MUS-decomposition, named distributable MUS-decomposition leads to an interesting partition of inconsistencies in a knowledge base such that multiple experts can check inconsistencies in parallel, which is impossible under existing measures. Such particular MUSdecomposition results in an inconsistency measure that satisfies a number of desired properties. Moreover, we give an upper bound complexity of the measure that can be computed using 0/1 linear programming or Min Cost Satisfiability problems, and conduct preliminary experiments to show its feasibility.

preprint2014arXiv

The hyperboloidal foliation method

The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave equations posed on a curved spacetime and to derive uniform energy bounds and optimal rates of decay in time. We are also able to encompass the wave equation and the Klein-Gordon equation in a unified framework and to establish a well-posedness theory for nonlinear wave-Klein-Gordon systems and a large class of nonlinear interactions. The hyperboloidal foliation of Minkowski spacetime we rely upon in this book has the advantage of being geometric in nature and, especially, invariant under Lorentz transformations. As stated, our theory applies to many systems arising in mathematical physics and involving a massive scalar field, such as the Dirac-Klein-Gordon system. As it provides uniform energy bounds and optimal rates of decay in time, our method appears to be very robust and should extend to even more general systems.

preprint2012arXiv

A certificate for semidefinite relaxations in computing positive dimensional real varieties

For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal J generated by the kernel of a truncated moment matrix and nesting between I and its real radical ideal. We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic delta-regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations.

preprint2012arXiv

The K1.8BR spectrometer system at J-PARC

A new spectrometer system was designed and constructed at the secondary beam line K1.8BR in the hadron hall of J-PARC to investigate $\bar K N$ interactions and $\bar K$-nuclear bound systems. The spectrometer consists of a high precision beam line spectrometer, a liquid $^3$He/$^4$He/D$_2$ target system, a Cylindrical Detector System that surrounds the target to detect the decay particles from the target region, and a neutron time-of-flight counter array located $\sim$15 m downstream from the target position. Details of the design, construction, and performance of the detector components are described.

preprint2012arXiv

Unexpected Surface Implanted Layer in Static Random Access Memory Devices Observed by Microwave Impedance Microscope

Real-space mapping of doping concentration in semiconductor devices is of great importance for the microelectronic industry. In this work, a scanning microwave impedance microscope (MIM) is employed to resolve the local conductivity distribution of a static random access memory (SRAM) sample. The MIM electronics can also be adjusted to the scanning capacitance microscopy (SCM) mode, allowing both measurements on the same region. Interestingly, while the conventional SCM images match the nominal device structure, the MIM results display certain unexpected features, which originate from a thin layer of the dopant ions penetrating through the protective layers during the heavy implantation steps.

preprint2011arXiv

Global existence of small amplitude solution to nonlinear system of wave and Klein-Gordon equations in four space-time dimensions

In this article one will develop a so-called hyperboloidal foliation method, which is an energy method based on a foliation of space-time into hyperboloidal hypersurfaces. This method permits to treat the wave equations and the Klein-Gordon equations in the same framework so that one can apply it to the coupled systems of wave and Klein-Gordon equations. As an application, one will establish the global-in-time existence of small amplitude solution to the coupled wave and Klei-Gordon equations with quadratic nonlinearity in four space-time dimensions under certain conditions. Compared with those introduced by S. Katayama, the conditions imposed in this article permit to include some important nonlinear terms. All of these suggests that this method may be a more natural way of regarding the wave operator.

preprint2011arXiv

Global existence of small amplitude solutions to nonlinear coupled wave-Klein-Gordon systems in four space-time dimension with hyperboloidal foliation method

In this article one will develop a new type of energy method based on a foliation of spacetime into hyperboloidal hypersurfaces . As we will see, with this method, some classical results such as global existence and almost global existence of regular solutions to the quasi-linear wave equations and Klein-Gordon equations will be established in a much simpler and much more natural way. Most importantly, the global existence of regular solutions to a general type of coupled quasilinear wave-Klein-Gordon system will be established. All of this suggests that compared with the classical method, this hyperboloidal foliation of space-time may be a more natural way to regard the wave operator.

preprint2011arXiv

Global solutions of coupled Klein-Gordon equations with different velocities in four space-time dimensions

In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a classical boot-strap argument combined with a serious of techniques including conformal energy estimate, global sobolev's lemma and Hardy type inequalities.

preprint2011arXiv

The Minimum-Rank Gram Matrix Completion via Modified Fixed Point Continuation Method

The problem of computing a representation for a real polynomial as a sum of minimum number of squares of polynomials can be casted as finding a symmetric positive semidefinite real matrix (Gram matrix) of minimum rank subject to linear equality constraints. In this paper, we propose algorithms for solving the minimum-rank Gram matrix completion problem, and show the convergence of these algorithms. Our methods are based on the modified fixed point continuation (FPC) method. We also use the Barzilai-Borwein (BB) technique and a specific linear combination of two previous iterates to accelerate the convergence of modified FPC algorithms. We demonstrate the effectiveness of our algorithms for computing approximate and exact rational sum of squares (SOS) decompositions of polynomials with rational coefficients.

preprint2009arXiv

Self-Sustained Collective Oscillation Generated in an Array of Non-Oscillatory Cells

Oscillations represent a ubiquitous phenomenon in biological systems. The conventional models of biological periodic oscillations are usually proposed as interconnecting transcriptional feedback loops. Some specific proteins function as transcription factors, which in turn negatively regulate the expression of the genes that encode those "clock protein". These loops may lead to rhythmic changes in gene expression of a cell. In the case of multi-cellular tissue, the collective oscillation is often obtained from synchronization of these cells, which manifest themselves as autonomous oscillators. In contrast, here, we propose a different scenario for the occurrence of collective oscillation in a multi-cellular system independent of oscillation, neither intrinsically oscillatory cells nor periodic external stimulation. It is a coupling induced oscillation, with the consideration of wave propagation due to the intracellular communication.