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Published work

79 published item(s)

preprint2026arXiv

An Embarrassingly Simple Graph Heuristic Reveals Shortcut-Solvable Benchmarks for Sequential Recommendation

Sequential recommendation has increasingly shifted toward generative recommenders that combine sequential patterns with semantic item information. Yet these methods are often evaluated on a small set of widely used benchmarks, raising a key question: do these benchmarks actually require the advanced modeling capabilities that modern generative recommenders claim to provide? We conduct a benchmark audit with an intentionally simple graph heuristic. Starting from only the last one or two interacted items, it retrieves candidates from a few-hop item-transition graph and ranks them by item-feature similarity. Despite using no sequence encoder, generative objective, or training, this heuristic matches or outperforms many modern baselines, with relative NDCG@10 improvements of 38.10% and 44.18% over the best competing baseline on Amazon Review Sports and CDs. We show that this behavior reflects shortcut solvability rather than an artifact of one heuristic. We identify three shortcut structures that can make next-item prediction easier than expected: low-branching local transitions, feature-smooth transitions, and limited dependence on long user histories. These shortcuts need not appear together; even one or two strong signals can make simple local retrieval highly competitive, while weakening them makes the benefits of more sophisticated models clearer. Across 14 datasets, model rankings vary substantially with dataset properties, yet the heuristic remains competitive on 10 of them. Our findings suggest that strong performance on standard benchmarks does not always demonstrate advanced sequential, semantic, or generative modeling ability. We call for more careful dataset selection and dataset-level diagnostic analysis when using benchmarks to support claims about new recommendation models.

preprint2026arXiv

FlexiVoice: Enabling Flexible Style Control in Zero-Shot TTS with Natural Language Instructions

This study proposes FlexiVoice, a text-to-speech (TTS) synthesis system capable of flexible style control with zero-shot voice cloning. The speaking style is controlled by a natural-language instruction and the voice timbre is provided by a speech reference in zero-shot manner. FlexiVoice is built with an LLM core, which takes text as input, and also takes an optional natural language instruction and an optional speech reference to control style and timbre, respectively. FlexiVoice is equipped with a novel Progressive Post-Training (PPT) scheme that progressively unlocks accurate and flexible controllability. In particular, it first employs Direct Preference Optimization (DPO) to enable FlexiVoice to accurately follow both natural language instruction and speech reference simultaneously. It then uses a multi-objective Group Relative Policy Optimization (GRPO) to disentangle style instruction, reference timbre, and textual content. Finally, it adapts instruction GRPO for more advanced instruction following. Experimental results show that FlexiVoice surpasses competing baselines and demonstrates strong capability in decoupling control factors. Human evaluations further confirm its naturalness, controllability, and robustness. Audio samples are available at https://flexi-voice.github.io.

preprint2026arXiv

Interference-governed electromagnetic-thermal coupling and heat transport in pulse EUV-irradiated multilayer nanofilms

Mo-Si multilayer mirrors are central to extreme ultraviolet lithography, where nanoscale optical interference and heat accumulation together constrain reflectivity and operational stability. Here we develop an analytical electromagnetic-thermal coupling model that directly links transfer-matrix-based interference-controlled energy deposition with transient heat conduction in EUV-irradiated multilayers. The model reveals a fundamental trade-off whereby increasing the multilayer period number enhances reflectivity but simultaneously elevates temperature by impeding heat dissipation. Interference-driven volumetric absorption further gives rise to pronounced axial temperature gradients and a post-pulse downward migration of the heat-flux maximum, a delayed-heating effect inaccessible to conventional surface-flux-based models. Systematic analysis establishes scaling laws connecting interfacial thermal resistance, beam size, and incident energy density to thermal confinement and temperature rise. By incorporating interfacial compaction kinetics, the model enables a quantitative assessment of mirror lifetime. This work offers a theoretical tool for thermal-optical co-design of multilayer nanostructures including EUV mirrors under pulsed irradiation across a wide spectral range.

preprint2026arXiv

PEAR: Planner-Executor Agent Robustness Benchmark

Large Language Model (LLM)-based Multi-Agent Systems (MAS) have emerged as a powerful paradigm for tackling complex, multi-step tasks across diverse domains. However, despite their impressive capabilities, MAS remain susceptible to adversarial manipulation. Existing studies typically examine isolated attack surfaces or specific scenarios, leaving a lack of holistic understanding of MAS vulnerabilities. To bridge this gap, we introduce PEAR, a benchmark for systematically evaluating both the utility and vulnerability of planner-executor MAS. While compatible with various MAS architectures, our benchmark focuses on the planner-executor structure, which is a practical and widely adopted design. Through extensive experiments, we find that (1) a weak planner degrades overall clean task performance more severely than a weak executor; (2) while a memory module is essential for the planner, having a memory module for the executor does not impact the clean task performance; (3) there exists a trade-off between task performance and robustness; and (4) attacks targeting the planner are particularly effective at misleading the system. These findings offer actionable insights for enhancing the robustness of MAS and lay the groundwork for principled defenses in multi-agent settings.

preprint2024arXiv

Formation of collisional ring galaxies in Milgromian dynamics

Ring galaxies are rare in the Universe. A head-on or off-centre collision between an intruder galaxy and a disc galaxy leads to a collisional ring galaxy (CRG) when the intruder-to-target mass ratio (ITMR) is over 0.1 in Newtonian dynamics. Within the framework of Milgromian dynamics, the strong equivalence principle is violated due to the presence of an external field. When two galaxies collide towards each other, the dynamical mass of the phantom dark halo in a galaxy is suppressed by the external field induced by the other galaxy. As a consequence of such suppression, the gravitational perturbation for the target galaxy introduced by a collision is weakened. In this case, a minor collision may not be capable of generating a CRG. In this work, we address this issue and perform a series of numerical simulations of collisions by tuning the values of ITMR. We find that the critical ITMR is 0.5 in MOND, which is much larger than that in Newtonian dynamics. The observed massive ring galaxies, such as Arp 147, can be effectively interpreted by CRGs in MOND. This interpretation does not necessitate the presence of dark matter halos for either the target or intruder galaxies. Moreover, for a larger inclination angle or a larger impact parameter, the off-centred ring structure is fainter. The larger critical ITMR indicates that it is harder to form a CRG in Milgrom's Modified Newtonian Dynamics (MOND). To account for the observed ring structures of the NGC 922-like galaxies in MOND, it is necessary to invoke other scenarios than a dry minor collision.

preprint2022arXiv

Deblur-NeRF: Neural Radiance Fields from Blurry Images

Neural Radiance Field (NeRF) has gained considerable attention recently for 3D scene reconstruction and novel view synthesis due to its remarkable synthesis quality. However, image blurriness caused by defocus or motion, which often occurs when capturing scenes in the wild, significantly degrades its reconstruction quality. To address this problem, We propose Deblur-NeRF, the first method that can recover a sharp NeRF from blurry input. We adopt an analysis-by-synthesis approach that reconstructs blurry views by simulating the blurring process, thus making NeRF robust to blurry inputs. The core of this simulation is a novel Deformable Sparse Kernel (DSK) module that models spatially-varying blur kernels by deforming a canonical sparse kernel at each spatial location. The ray origin of each kernel point is jointly optimized, inspired by the physical blurring process. This module is parameterized as an MLP that has the ability to be generalized to various blur types. Jointly optimizing the NeRF and the DSK module allows us to restore a sharp NeRF. We demonstrate that our method can be used on both camera motion blur and defocus blur: the two most common types of blur in real scenes. Evaluation results on both synthetic and real-world data show that our method outperforms several baselines. The synthetic and real datasets along with the source code is publicly available at https://limacv.github.io/deblurnerf/

preprint2022arXiv

High-throughput decoder of quasi-cyclic LDPC codes with limited precision for continuous-variable quantum key distribution systems

More than Mbps secret key rate was demonstrated for continuous-variable quantum key distribution (CV-QKD) systems, but real-time postprocessing is not allowed, which is restricted by the throughput of the error correction decoding in postprocessing. In this paper, a high-throughput FPGA-based quasi-cyclic LDPC decoder is proposed and implemented to support Mbps real-time secret key rate generation for CV-QKD for the first time. A residual bit error correction algorithm is used to solve the problem of high frame errors rate (FER) caused by the limited precision of the decoder. Specifically, real-time high-speed decoding for CV-QKD systems with typical code rates 0.2 and 0.1 is implemented on a commercial FPGA, and two throughputs of 360.92Mbps and 194.65Mbps are achieved, respectively, which can support 17.97 Mbps and 2.48 Mbps real-time generation of secret key rates under typical transmission distances of 25km and 50km, correspondingly. The proposed method paves the way for high-rate real-time CV-QKD deployment in secure metropolitan area network.

preprint2022arXiv

Microbiome subcommunity learning with logistic-tree normal latent Dirichlet allocation

Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. These subcommunities are informative for understanding the biological interplay of microbes and for predicting health outcomes. However, microbiome compositions typically display substantial cross-sample heterogeneities in subcommunity compositions -- that is, the variability in the proportions of microbes in shared subcommunities across samples -- which is not accounted for in prior analyses. As a result, LDA can produce inference which is highly sensitive to the specification of the number of subcommunities and often divides a single subcommunity into multiple artificial ones. To address this limitation, we incorporate the logistic-tree normal (LTN) model into LDA to form a new MM model. This model allows cross-sample variation in the composition of each subcommunity around some "centroid" composition that defines the subcommunity. Incorporation of auxiliary Pólya-Gamma variables enables a computationally efficient collapsed blocked Gibbs sampler to carry out Bayesian inference under this model. By accounting for such heterogeneity, our new model restores the robustness of the inference in the specification of the number of subcommunities and allows meaningful subcommunities to be identified.

preprint2022arXiv

Secure two-way fiber-optic time transfer against sub-ns asymmetric delay attack

Two-way fiber-optic time transfer is a promising precise time synchronization technique with sub-nanosecond accuracy. However, asymmetric delay attack is a serious threat which cannot be prevent by any encryption method. In this paper, a dynamic model based scheme is proposed to defense the sub-nanosecond asymmetric delay attack. A threshold is set according to the estimated time difference by a two-state clock model where the fixed frequency difference is excluded from the time difference to detect the asymmetric delay attack which is smaller than the time difference induced by the fixed frequency difference. Theoretical simulation and experimental demonstration are implemented to prove the feasibility of the scheme. A two-way fiber-optic time transfer system with time stability with 24.5ps, 3.98ps, and 2.95ps at 1s, 10s, and 100s averaging time is shown under sub-ns asymmetric time delay attack experimentally. The proposed method provides a promising secure sub-ns precise time synchronization technique against asymmetric delay attack.

preprint2022arXiv

TVConv: Efficient Translation Variant Convolution for Layout-aware Visual Processing

As convolution has empowered many smart applications, dynamic convolution further equips it with the ability to adapt to diverse inputs. However, the static and dynamic convolutions are either layout-agnostic or computation-heavy, making it inappropriate for layout-specific applications, e.g., face recognition and medical image segmentation. We observe that these applications naturally exhibit the characteristics of large intra-image (spatial) variance and small cross-image variance. This observation motivates our efficient translation variant convolution (TVConv) for layout-aware visual processing. Technically, TVConv is composed of affinity maps and a weight-generating block. While affinity maps depict pixel-paired relationships gracefully, the weight-generating block can be explicitly overparameterized for better training while maintaining efficient inference. Although conceptually simple, TVConv significantly improves the efficiency of the convolution and can be readily plugged into various network architectures. Extensive experiments on face recognition show that TVConv reduces the computational cost by up to 3.1x and improves the corresponding throughput by 2.3x while maintaining a high accuracy compared to the depthwise convolution. Moreover, for the same computation cost, we boost the mean accuracy by up to 4.21%. We also conduct experiments on the optic disc/cup segmentation task and obtain better generalization performance, which helps mitigate the critical data scarcity issue. Code is available at https://github.com/JierunChen/TVConv.

preprint2021arXiv

Distillation based Multi-task Learning: A Candidate Generation Model for Improving Reading Duration

In feeds recommendation, the first step is candidate generation. Most of the candidate generation models are based on CTR estimation, which do not consider user's satisfaction with the clicked item. Items with low quality but attractive title (i.e., click baits) may be recommended to the user, which worsens the user experience. One solution to this problem is to model the click and the reading duration simultaneously under the multi-task learning (MTL) framework. There are two challenges in the modeling. The first one is how to deal with the zero duration of the negative samples, which does not necessarily indicate dislikes. The second one is how to perform multi-task learning in the candidate generation model with double tower structure that can only model one single task. In this paper, we propose an distillation based multi-task learning (DMTL) approach to tackle these two challenges. We model duration by considering its dependency of click in the MTL, and then transfer the knowledge learned from the MTL teacher model to the student candidate generation model by distillation. Experiments conducted on dataset gathered from traffic logs of Tencent Kandian's recommender system show that the proposed approach outperforms the competitors significantly in modeling duration, which demonstrates the effectiveness of the proposed candidate generation model.

preprint2021arXiv

Global Yamabe flow on asymptotically flat manifolds

In this paper, we study the existence of global Yamabe flow on asymptotically flat (in short, AF or ALE) manifolds. Note that the ADM mass is preserved in dimensions 3,4 and 5. We present a new general local existence of Yamabe flow on a complete Riemannian manifold with the initial metric quasi-isometric to a background metric of bounded scalar curvature. Asymptotic behaviour of the Yamabe flow on ALE manifolds is also addressed provided the initial scalar curvature is non-negative and there is a bounded subsolution to the corresponding Poisson equation. We also present a maximum principle for a very general parabolic equations on the complete Riemannian manifolds.

preprint2021arXiv

New Yamabe-type flow in a compact Riemannian manifold

In this paper, we set up a new Yamabe type flow on a compact Riemannian manifold $(M,g)$ of dimension $n\geq 3$. Let $ψ(x)$ be any smooth function on $M$. Let $p=\frac{n+2}{n-2}$ and $c_n=\frac{4(n-1)}{n-2}$. We study the Yamabe-type flow $u=u(t)$ satisfying {u_t}=u^{1-p}(c_nΔu-ψ(x)u)+r(t)u, \ \ in \ M\times (0,T),\ T>0 with r(t)=\int_M(c_n|\nabla u|^2+ψ(x)u^2)dv/ \int_Mu^{p+1}, which preserves the $L^{p+1}(M)$-norm and we can show that for any initial metric $u_0>0$, the flow exists globally. We also show that in some cases, the global solution converges to a smooth solution to the equation c_nΔu-ψ(x)u+r(\infty)u^{p}=0, \ \ on \ M and our result may be considered as a generalization of the result of T.Aubin, Proposition in p.131 in \cite{A82}.

preprint2020arXiv

Coarsened mixtures of hierarchical skew normal kernels for flow cytometry analyses

Flow cytometry (FCM) is the standard multi-parameter assay for measuring single cell phenotype and functionality. It is commonly used for quantifying the relative frequencies of cell subsets in blood and disaggregated tissues. A typical analysis of FCM data involves cell classification---that is, the identification of cell subgroups in the sample---and comparisons of the cell subgroups across samples or conditions. While modern experiments often necessitate the collection and processing of samples in multiple batches, analysis of FCM data across batches is challenging because differences across samples may occur due to either true biological variation or technical reasons such as antibody lot effects or instrument optics across batches. Thus a critical step in comparative analyses of multi-sample FCM data---yet missing in existing automated methods for analyzing such data---is cross-sample calibration, whose goal is to align corresponding cell subsets across multiple samples in the presence of technical variations, so that biological variations can be meaningfully compared. We introduce a Bayesian nonparametric hierarchical modeling approach for accomplishing both calibration and cell classification simultaneously in a unified probabilistic manner. Three important features of our method make it particularly effective for analyzing multi-sample FCM data: a nonparametric mixture avoids prespecifying the number of cell clusters; a hierarchical skew normal kernel that allows flexibility in the shapes of the cell subsets and cross-sample variation in their locations; and finally the "coarsening" strategy makes inference robust to departures from the model such as heavy-tailness not captured by the skew normal kernels. We demonstrate the merits of our approach in simulated examples and carry out a case study in the analysis of two multi-sample FCM data sets.

preprint2020arXiv

Constants and heat flow on graphs

In this article, we first introduce the concepts of vector fields and their divergence, and we recall the concepts of the gradient, Laplacian operator, Cheeger constants, eigenvalues, and heat kernels on a locally finite graph $V$. We give a projective characteristic of the eigenvalues. We also give an extension of Barta Theorem. Then we introduce the mini-max value of a function on a locally finite and locally connected graph. We show that for a coercive function on on a locally finite and locally connected graph, there is a mini-max value of the function provided it has two strict local minima values. We consider the discrete Morse flow for the heat flow on a finite graph in the locally finite graph $V$. We show that under suitable assumptions on the graph one has a weak discrete Morse flow for the heat flow on $S$ on any time interval. We also study the heat flow with time-variable potential and its discrete Morse flow. We propose the concepts of harmonic maps from a graph to a Riemannian manifold and pose some open questions.

preprint2020arXiv

High-throughput GPU layered decoder of multi-edge type low density parity check codes in continuous-variable quantum key distribution systems

The decoding throughput in the postprocessing is one of the bottlenecks for a continuous-variable quantum key distribution (CV-QKD) system. In this paper, we propose a layered decoder to decode quasi-cyclic multi-edge type LDPC (QC-METLDPC) codes based on graphic processing unit (GPU) in continuous-variable quantum key distribution (CV-QKD) systems. We optimize the storage method of the parity check matrix, merge the sub-matrices which are unrelated, and decode multiple codewords in parallel on GPU. Simulation results demonstrate that the average decoding speed of LDPC codes with three typical code rates, i.e., 0.1, 0.05 and 0.02, is up to 64.11Mbits/s, 48.65Mbits/s and 39.51Mbits/s, respectively, when decoding 128 codewords of length 106 simultaneously without early termination.

preprint2020arXiv

Passivation mechanisms and pre-oxidation effects on model surfaces of FeCrNi austenitic stainless steel

Passivation mechanisms were investigated on (100)-oriented Fe-18Cr-13Ni surfaces with direct transfer between surface preparation and analysis by X-ray photoelectron spectroscopy and scanning tunneling microscopy and electrochemical characterization. Starting from oxide-free surfaces, pre-oxidation at saturation under ultra-low pressure (ULP) oxygen markedly promotes the oxide film Cr(III) enrichment and hinders/delays subsequent iron oxidation in water-containing environment. Exposure to sulfuric acid at open circuit potential causes preferential dissolution of oxidized iron species. Anodic passivation forces oxide film re-growth, Cr(III) dehydroxylation and further enrichment. ULP pre-oxidation promotes Cr(III) hydroxide formation at open circuit potential, compactness of the nanogranular oxide film and corrosion protection.

preprint2020arXiv

Privacy-preserving collaborative machine learning on genomic data using TensorFlow

Machine learning (ML) methods have been widely used in genomic studies. However, genomic data are often held by different stakeholders (e.g. hospitals, universities, and healthcare companies) who consider the data as sensitive information, even though they desire to collaborate. To address this issue, recent works have proposed solutions using Secure Multi-party Computation (MPC), which train on the decentralized data in a way that the participants could learn nothing from each other beyond the final trained model. We design and implement several MPC-friendly ML primitives, including class weight adjustment and parallelizable approximation of activation function. In addition, we develop the solution as an extension to TF Encrypted~\citep{dahl2018private}, enabling us to quickly experiment with enhancements of both machine learning techniques and cryptographic protocols while leveraging the advantages of TensorFlow's optimizations. Our implementation compares favorably with state-of-the-art methods, winning first place in Track IV of the iDASH2019 secure genome analysis competition.

preprint2020arXiv

The gamma-ray and Optical Variability Analysis of the BL Lac Object 3FGL J0449.4-4350

We have assembled the historical light curves of the BL Lac Object 3FGL J0449.4-4350 at optical and gamma-ray bands, the time spanning about 10 years, analyzed the periodic variability of the light curves by using four different methods (Lomb-Scargle periodogram, REDFIT38, Jurkevich and DACF). We detected a marginally possible quasi-periodic oscillation (QPO) of ~450 days. Assuming it originates from the helical motion jet in a supermassive binary black hole (SMBBH) system undergoing major merger, we estimate the primary black hole mass M~7.7*10^{9} M_sun. To explore the origin of the gamma-ray, we investigated the optical-gamma-ray correlations using discrete correlation function (DCF) method, and found that the correlation between the two bands is very significant. This strong correlation tends to imply lepton self-synchro-Compton (LSSC) model to produce the gamma-ray.

preprint2020arXiv

Tritonlike molecules of three identical baryons

In nuclear physics, triton and helium-3 nucleus can be understood as three-body hadronic molecules. Analogous to the loosely bound structures for the triton and helium-3 nucleus, whether there is a bound state formed by three hadrons leaves us an open issue. Based on the one-boson exchange model as well as the adoption of the variational approach, we make a comprehensive investigation on the tritonlike systems of three identical baryons $NNN$, $ΛΛΛ$, $ΞΞΞ$ and $ΣΣΣ$. We predict that the three-body molecular states for the systems of three identical hadrons of baryon octet are probably existent as long as their two-body subsystems have bound states. The numerical results of this work may be helpful for the theoretical and experimental researches on the tri-hadron molecules in future.

preprint2016arXiv

$p$-adic Gross-Zagier Formula for Heegner Points on Shimura Curves over Totally Real Fields

The main result of this text is a generalization of Perrin-Riou's p-adic Gross-Zagier formula to the case of Shimura curves over totally real fields. Let $F$ be a totally real field. Let $f$ be a Hilbert modular form over $F$ of parallel weight $2$, which is a new form and is ordinary at $p$. Let $E$ be a totally imaginary quadratic extension of $F$ of discriminant prime to $p$ and to the conductor of $f$. We may construct a $p$-adic $L$ function that interpolates special values of the complex $L$ functions associated to $f$, $E$ and finite order Hecke characters of $E$. The $p$-adic Gross-Zagier formula relates the central derivative of this $p$-adic $L$ function to the $p$-adic height of a Heegner divisor on a certain Shimura curve. The strategy of the proof is close to that of the original work of Perrin-Riou. In the analytic part, we construct the analytic kernel via adelic computations; in the geometric part, we decompose the geometric kernel into two parts: places outside $p$ and places dividing $p$. For places outside $p$, the $p$-adic heights are essentially intersection numbers and are computed in works of S. Zhang, and it turns out that this part is closely related to the analytic kernel. For places dividing $p$, we use the method in the work of J. Nekovář to show that the contribution of this part is zero.

preprint2016arXiv

Analysis of distributional variation through multi-scale Beta-Binomial modeling

Many statistical analyses involve the comparison of multiple data sets collected under different conditions in order to identify the difference in the underlying distributions. A common challenge in multi-sample comparison is the presence of various confounders, or extraneous causes other than the conditions of interest that also contribute to the difference across the distributions. They result in false findings, i.e., identified differences that are not replicable in follow-up investigations. We consider an ANOVA approach to addressing this issue in multi-sample comparison---by collecting replicate data sets under each condition, thereby allowing the identification of the interesting distributional variation from the extraneous ones. We introduce a multi-scale Bayesian hierarchical model for the analysis of distributional variation (ANDOVA) under this design, based on a collection of Beta-Binomial tests targeting variations of different scales at different locations across the sample space. Instead treating the tests independently, the model employs a graphical structure to introduce dependency among the individual tests thereby allowing borrowing of strength among them. We derive efficient inference recipe through a combination of numerical integration and message passing, and evaluate the ability of our method to effectively address ANDOVA through extensive simulation. We utilize our method to analyze a DNase-seq data set for identifying differences in transcriptional factor binding.

preprint2016arXiv

Bernstein theorem for translating solitons of hypersurfaces

In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $\re^{n+1}$, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in $R^{n+k}$, namely, if the $L^n$ norm of the second fundamental form of the soliton is small enough, then it is a hyperplane.

preprint2016arXiv

Convexity and the Dirichlet problem of translating mean curvature flows

In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.

preprint2016arXiv

Efficient functional ANOVA through wavelet-domain Markov groves

We introduce a wavelet-domain functional analysis of variance (fANOVA) method based on a Bayesian hierarchical model. The factor effects are modeled through a spike-and-slab mixture at each location-scale combination along with a normal-inverse-Gamma (NIG) conjugate setup for the coefficients and errors. A graphical model called the Markov grove (MG) is designed to jointly model the spike-and-slab statuses at all location-scale combinations, which incorporates the clustering of each factor effect in the wavelet-domain thereby allowing borrowing of strength across location and scale. The posterior of this NIG-MG model is analytically available through a pyramid algorithm of the same computational complexity as Mallat's pyramid algorithm for discrete wavelet transform, i.e., linear in both the number of observations and the number of locations. Posterior probabilities of factor contributions can also be computed through pyramid recursion, and exact samples from the posterior can be drawn without MCMC. We investigate the performance of our method through extensive simulation and show that it outperforms existing wavelet-domain fANOVA methods in a variety of common settings. We apply the method to analyzing the orthosis data.

preprint2016arXiv

Hamilton type estimates for heat equations on manifolds

In this paper, we study the gradient estimates of Li-Yau-Hamilton type for positive solutions to both drifting heat equation and the simple nonlinear heat equation problem $$ u_t-Δu=au\log u, \ \ u>0 $$ on the compact Riemannian manifold $(M,g)$ of dimension $n$ and with non-negative (Bakry-Emery)-Ricci curvature. Here $a\leq 0$ is a constant. The latter heat equation is a basic evolution equation which is the negative gradient heat flow to the functional of Log-Sobolev inequality on the Riemannian manifold. We derive various versions of gradient estimates which generalize Hamilton's gradient estimate. An question concerning the Hamilton type gradient estimate for the simple nonlinear heat equation is addressed.

preprint2016arXiv

Magnetic moments of the hidden-charm pentaquark states

The magnetic moment of a baryon state is an equally important dynamical observable as its mass, which encodes crucial information of its underlying structure. According to the different color-flavor structure, we have calculated the magnetic moments of the hidden-charm pentaquark states with $J^P={\frac{1}{2}}^{\pm}$, ${\frac{3}{2}}^{\pm}$, ${\frac{5}{2}}^{\pm}$ and ${\frac{7}{2}}^{+}$ in the molecular model, the diquark-triquark model and the diquark-diquark-antiquark model respectively. Although a good description for the pentaquark mass spectrum and decay patterns has been obtained in all the three models, different color-flavor structures lead to different magnetic moments, which can be used to pin down their inner structures and distinguish various models.

preprint2016arXiv

Strong decay patterns of the hidden-charm pentaquark states $P_c(4380)$ and $P_c(4450)$

With the heavy quark symmetry and spin rearrangement scheme, we study the strong decay behavior of the hidden-charm pentaquark states with $J^P={\frac{3}{2}}^{\pm}, {\frac{5}{2}}^{\pm}$ assuming they are molecular candidates composed of ${\bar D}^{(\ast)}$ and $Σ_c^{(\ast)}$. We obtain several typical ratios of the partial decay widths of the hidden-charm pentaquarks. For the three S-wave $(\bar{D}Σ_c^*)$, $(\bar{D}^*Σ_c)$ and $(\bar{D}^*Σ_c^*)$ molecular pentaquarks with $J^P={{3}/{2}}^{-}$, we have obtained the ratio of their $J/ψN$ decay widths: $Γ\left[(\bar D{Σ^{\ast}_c})\right]:Γ\left[({\bar D}^{\ast}Σ_c)\right]:Γ\left[({\bar D}^{\ast}{Σ^{\ast}_c})\right]=2.7:1.0:5.4$, which may be useful to further test the possible molecular assignment of the $P_c$ states.

preprint2015arXiv

Finite time blowup of generalized Euler ODE in matrix geometry

In this paper, we study the finite time blowup of the generalized Euler ODE in the matrix geometry. We can extend Sullivan's result which is about the finite time blowup result of initial invertible linear operators to singular linear operators. we can give a complete answer to the question of Sullivan in the case when the initial matrix A is symmetric in the finite dimensional vector space W. Some open questions are proposed in the last part of the paper.

preprint2015arXiv

Gap Theorems for Locally Conformally Flat Manifolds

In this paper, we prove a gap result for a locally conformally flat complete non-compact Riemannian manifold with bounded non-negative Ricci curvature and a scalar curvature average condition. We show that if it has positive Green function, then it is flat. This result is proved by setting up new global Yamabe flow. Other extensions related to bounded positive solutions to a schrodinger equation are also discussed.

preprint2015arXiv

Global Kahler-Ricci Flow on Complete Non-Compact Manifolds

In this paper, we study the global Kähler-Ricci flow on a complete non-compact Kähler manifold. We prove the following result. Assume that $(M,g_0)$ is a complete non-compact Kähler manifold such that there is a potential function $f$ of the Ricci tensor, i.e., $$ R_{i\bar{j}}(g_0)=f_{i\bar{j}}. $$ Assume that the quantity $|f|_{C^0}+|\nabla_{g_0}f|_{C^0}$ is finite and the L2 Sobolev inequality holds true on $(M,g_0)$. Then the Kahler-Ricci flow with the initial metric $g_0$ either blows up at finite time or infinite time to Ricci flat metric or exists globally with Ricci-flat limit at infinite time. A related is also discussed.

preprint2015arXiv

Markov adaptive Pólya trees and multi-resolution adaptive shrinkage in nonparametric modeling

We introduce a hierarchical nonparametric model for probability measures based on a multi-resolution transformation of probability distributions. The model allows a varying amount of shrinkage to be applied to data features of different scales and/or at different locations in the sample space, and the varying shrinkage level is locally adaptive to the empirical behavior of the data. Moreover, the model's hierarchical design---through a latent Markov tree structure---allows borrowing of information across locations and scales in setting the adaptive shrinkage level. Inference under the model proceeds efficiently using general recipes for conjugate hierarchical models. We illustrate the work of the model in density estimation and evaluate its performance through simulation under several schematic scenarios carefully designed to be representative of a variety of applications. We compare its performance to those of several state-of-the-art nonparametric models---the Pólya tree, the optional Pólya tree, and the Dirichlet process mixture of normals. In addition, we establish several important theoretical properties for the model including absolute continuity, full nonparametricity, and posterior consistency.

preprint2015arXiv

Nature of magnetotransport in metal/insulating-ferromagnet heterostructures: Spin Hall magnetoresistance or magnetic proximity effect

We study the anomalous Hall-like effect (AHLE) and the effective anisotropic magnetoresistance (EAMR) in antiferromagnetic γ -IrMn3/Y3Fe5O12(YIG) and Pt/YIG heterostructures. For γ -IrMn3/YIG, the EAMR and the AHLE resistivity change sign with temperature due to the competition between the spin Hall magnetoresistance (SMR) and the magnetic proximity effect (MPE) induced by the interfacial antiferromagnetic uncompensated magnetic moment. In contrast, for Pt/YIG the AHLE resistivity changes sign with temperature whereas no sign change is observed in the EAMR. This is because the MPE and the SMR play a dominant role in the AHLE and the EAMR, respectively. As new types of galvanomagnetic property, the AHLE and the EAMR have proved vital in disentangling the MPE and the SMR in metal/insulating-ferromagnet heterostructures.

preprint2015arXiv

Stability of cigar soliton

In this paper, we shall use the Kähler geometry formulation to study the global behavior of the Ricci flow on $R^2$. The geometric feature of our Ricci flow is that it has finite width. Our aim is to determine the limiting metric (which corresponds an eternal Ricci flow) obtained by L.F.Wu. We can use the classification result of Daskalopoulos-Sesum to give a sufficient condition such that the limiting metric of L.F.Wu is the metric of cigar soliton.

preprint2015arXiv

Strong decay patterns of the hidden-charm tetraquarks

With the spin rearrangement, we have performed a comprehensive investigation of the decay patterns of the S-wave tetraquarks and P-wave tetraquarks where the P-wave excitation exists either between the diquark and anti-diquark pair or inside the diquark. Especially, we compare the decay patterns of $Y(4260)$ with different inner structures such as the conventional charmonium, the molecule, the P-wave tetraquark and the hybrid charmonium. We notice the $J/ψππ$ mode is suppressed in the heavy quark symmetry limit if $Y(4260)$ is a molecular state. Moreover the hybrid charmonium and hidden-charm tetraquark have very similar decay patterns. Both of them decay into the $J/ψππ$ and open charm modes easily. We also discuss the decay patterns of $X(3872)$, $Y(4360)$, and several charged states such as $Z_c(4020)$. The $h_cπ^{\pm}$ decay mode disfavors the tetraquark assumption of $Z_c(4020)$.

preprint2015arXiv

The recoil correction and spin-orbit force for the possible $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ states

In the framework of the one-boson exchange model, we have calculated the effective potentials between two heavy mesons $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ from the t- and u-channel $π$-, $η$-, $ρ$-, $ω$- and $σ$-meson exchanges. We keep the recoil corrections to the $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ systems up to $O(\frac{1}{M^2})$, which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are favorable to the formation of the molecular states in the $I^G=1^+$, $J^{PC}=1^{+-}$ in the $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ systems.

preprint2014arXiv

Exotic Four Quark Matter: $Z_1(4475)$

Motivated by the LHCb's recent confirmation of $Z_1(4475)$ as the $J^P=1^+$ resonance, we investigate various exotic interpretations of $Z_1(4475)$, which may be an axial vector tetraquark state, the P-wave excitation of the S-wave $D_1 {\bar D}^\ast$ or $D_2 {\bar D}^\ast$ molecule, the S-wave molecule composed of a $D$ or $D^*$ meson and a D-wave vector $D$ meson, or the cousin molecular state of $Z_c(3900)$ and $Z_c(4020)$ composed of a $D$ or $D^*$ meson and their radial excitations. With the help of the heavy quark symmetry, we predict the typical radiative and hidden-charm and open-charm strong decay patterns of $Z_1(4475)$, which are crucial to further identify the molecular state assignment of $Z_1(4475)$.

preprint2014arXiv

Multi-resolution two-sample comparison through the divide-merge Markov tree

We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample space. Multi-scale two-sample comparison is achieved through inferring the underlying state of the process along the partition tree. The Markov design allows the process to incorporate spatial clustering of differential structures, which is commonly observed in two-sample problems but ignored by existing methods. Inference is carried out under the Bayesian paradigm through recursive propagation algorithms. We demonstrate the work of our method through simulated data and a real flow cytometry data set, and show that it substantially outperforms other state-of-the-art two-sample tests in several settings.

preprint2014arXiv

Probing the $XYZ$ states through radiative decays

In this work, we have adopted the spin rearrangement scheme in the heavy quark limit and extensively investigated three classes of the radiative decays: $\mathfrak{M}\to (b\bar{b})+γ$, $(b\bar{b})\to \mathfrak{M}+γ$, $ \mathfrak{M} \to \mathfrak{M}^\prime+γ$, corresponding to the electromagnetic transitions between one molecular state and bottomonium, one bottomonium and molecular state, and two molecular states respectively. We also extend the same formalism to study the radiative decays of the molecular states with hidden charm. We have derived some model independent ratios when the initial or final states belong to the same spin flavor multiplet. Future experimental measurement of these ratios will test the molecular picture and explore the underlying structures of the $XYZ$ states.

preprint2014arXiv

Resolving the puzzling decay patterns of charged $Z_c$ and $Z_b$ states

We investigate the ratio of the branching fractions of the molecular candidates decaying into the ground and radially excited states within the quark interchange model. Our numerical results suggest that these molecular candidates are more likely to decay into the radially excited states than into ground states. Especially, the ratio $Γ[Z_c(4430)\to πψ(2S)]$/$Γ[Z_c(4430)\to πJ/ψ]\sim 9.8$ is close to the experimental measurement, which supports the interpretation of $Z_c(4430)$ as the $\bar{D}D^*(2S)$ molecular state. The ratios of the branching fractions of $Z_b(10610)$ and $Z_b(10650)$ to $πΥ(2S, 3S)$ and $πΥ(1S)$ agrees very well with Belle's measurement. We also predict the similar ratios for $Z_c(3900)$, $Z_c(4020)$, $R_{Z_c(3900)}$$\approx$1.3 and $R_{Z_c(4020)}$$\approx$$4.7$. Hopefully the $πψ(2S)$ mode, and ratios $R_{Z_c(3900)}$ and $R_{Z_c(4020)}$ will be measured by the BESIII and Belle collaborations in the near future, which shall be very helpful to understand the underlying dynamics of these exotic states.

preprint2014arXiv

Scalable Bayesian model averaging through local information propagation

We show that a probabilistic version of the classical forward-stepwise variable inclusion procedure can serve as a general data-augmentation scheme for model space distributions in (generalized) linear models. This latent variable representation takes the form of a Markov process, thereby allowing information propagation algorithms to be applied for sampling from model space posteriors. In particular, we propose a sequential Monte Carlo method for achieving effective unbiased Bayesian model averaging in high-dimensional problems, utilizing proposal distributions constructed using local information propagation. We illustrate our method---called LIPS for local information propagation based sampling---through real and simulated examples with dimensionality ranging from 15 to 1,000, and compare its performance in estimating posterior inclusion probabilities and in out-of-sample prediction to those of several other methods---namely, MCMC, BAS, iBMA, and LASSO. In addition, we show that the latent variable representation can also serve as a modeling tool for specifying model space priors that account for knowledge regarding model complexity and conditional inclusion relationships.

preprint2014arXiv

Stochastic Calculus for Markov Processes Associated with Semi-Dirichlet Forms

Let $(\mathcal{E},D(\mathcal{E}))$ be a quasi-regular semi-Dirichlet form and $(X_t)_{t\geq0}$ be the associated Markov process. For $u\in D(\mathcal{E})_{loc}$, denote $A_t^{[u]}:=\tilde{u}(X_{t})-\tilde{u}(X_{0})$ and $F^{[u]}_t:=\sum_{0<s\leq t}(\tilde u(X_{s})-\tilde u(X_{s-}))1_{\{|\tilde u(X_{s})-\tilde u(X_{s-})|>1\}}$, where $\tilde{u}$ is a quasi-continuous version of $u$. We show that there exist a unique locally square integrable martingale additive functional $Y^{[u]}$ and a unique continuous local additive functional $Z^{[u]}$ of zero quadratic variation such that $$A_t^{[u]}=Y_t^{[u]}+Z_t^{[u]}+F_t^{[u]}.$$ Further, we define the stochastic integral $\int_0^t\tilde v(X_{s-})dA_s^{[u]}$ for $v\in D(\mathcal{E})_{loc}$ and derive the related Itô's formula.

preprint2014arXiv

Strong decays of the $XYZ$ states

Through the spin rearrangement scheme in the heavy quark limit, we have performed a comprehensive investigation of the decay pattern and production mechanism of the hidden beauty di-meson states, which are either composed of a P-wave bottom meson and an S-wave bottom meson or two S-wave bottom mesons. We further extend the corresponding formula to discuss the decay behavior of some charmonium-like states by combining the experimental information with our numerical results. The typical ratios presented in this work can be measured by future experiments like BESIII, Belle, LHCb and the forthcoming BelleII, which shall provide important clues to the inner structures of the exotic states.

preprint2014arXiv

The Spin-orbit force, recoil corrections and possible $B \bar{B}^{*}$ and $D \bar{D}^{*}$ molecular states

In the framework of the one boson exchange model, we have calculated the effective potentials between two heavy mesons $B \bar{B}^{*}$ and $D \bar{D}^{*}$ from the t- and u-channel $π$, $η$, $ρ$, $ω$ and $σ$ meson exchange with four kinds of quantum number: $I=0$, $J^{PC}=1^{++}$; $I=0$, $J^{PC}=1^{+-}$; $I=1$, $J^{PC}=1^{++}$; $I=1$, $J^{PC}=1^{+-}$. We keep the recoil corrections to the $B \bar{B}^{*}$ and $D \bar{D}^{*}$ system up to $O(\frac{1}{M^2})$. The spin orbit force appears at $O(\frac{1}{M})$, which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are unfavorable to the formation of the molecular states in the $I=0$, $J^{PC}=1^{++}$ and $I=1$, $J^{PC}=1^{+-}$ channels in the $D \bar{D}^{*}$ systems.

preprint2013arXiv

Bochner formula and Bernstein type estimates on locally finite graphs

In this paper, we consider three typical problems on a locally finite connected graph. The first one is to study the Bochner formula for the Laplacian operator on a locally finite connected graph. We use the Bochner formula to derive the Bernstein type estimate of the heat equation. The second is to derive the Reilly type formula of the Laplacian operator. The last one is to obtain global positive solution to porous-media equation via the use of Aronson-Benilan argument. There is not much work in the direction of the study of nonlinear heat equations on locally finite connected graphs.

preprint2013arXiv

Neutral genomic regions refine models of recent rapid human population growth

Human populations have experienced dramatic growth since the Neolithic revolution. Recent studies that sequenced a very large number of individuals observed an extreme excess of rare variants, and provided clear evidence of recent rapid growth in effective population size, though estimates have varied greatly among studies. All these studies were based on protein-coding genes, in which variants are also impacted by natural selection. In this study, we introduce targeted sequencing data for studying recent human history with minimal confounding by natural selection. We sequenced loci very far from genes that meet a wide array of additional criteria such that mutations in these loci are putatively neutral. As population structure also skews allele frequencies, we sequenced a sample of relatively homogeneous ancestry by first analyzing the population structure of 9,716 European Americans. We employed very high coverage sequencing to reliably call rare variants, and fit an extensive array of models of recent European demographic history to the site frequency spectrum. The best-fit model estimates ~3.4% growth per generation during the last ~140 generations, resulting in a population size increase of two orders of magnitude. This model fits the data very well, largely due to our observation that assumptions of more ancient demography can impact estimates of recent growth. This observation and results also shed light on the discrepancy in demographic estimates among recent studies.

preprint2012arXiv

Discrete Morse flow for Ricci flow and Porous Media equation

In this paper, we study the discrete Morse flow for the Ricci flow on football, which is the 2-sphere with removed north and south poles and with the metric $g_0$ of constant scalar curvature, and and for Porous media equation on a bounded regular domain in the plane. We show that with a suitable assumption about $g(0)$ we have a weak approximated discrete Morse flow for the approximated Ricci flow and Porous media equation on any time intervals.

preprint2011arXiv

A complete proof of Hamilton's conjecture

In this paper, we give the full proof of a conjecture of R.Hamilton that for $(M^3, g)$ being a complete Riemannian 3-manifold with bounded curvature and with the Ricci pinching condition $Rc\geq \ep R g$, where $R>0$ is the positive scalar curvature and $\ep>0$ is a uniform constant, $M^3$ is compact. One of the key ingredients to exclude the local collapse in singularities of the Ricci flow is the use of pinching-decaying estimate. The other important part of our argument is to role out the Type III singularity complete noncompact Ricci flow with positive Ricci pinching condition. We get this goal by obtaining an Ricci expander based on the monotonicity formula of weighted reduced volume.

preprint2011arXiv

Coupling optional Pólya trees and the two sample problem

Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well as the dimensionality increases and provides no easy way to characterize the difference should it exist. In this work, we propose a theoretical framework for inference that addresses these challenges in the form of a prior for Bayesian nonparametric analysis. The new prior is constructed based on a random-partition-and-assignment procedure similar to the one that defines the standard optional Pólya tree distribution, but has the ability to generate multiple random distributions jointly. These random probability distributions are allowed to "couple", that is to have the same conditional distribution, on subsets of the sample space. We show that this "coupling optional Pólya tree" prior provides a convenient and effective way for both the testing of two sample difference and the learning of the underlying structure of the difference. In addition, we discuss some practical issues in the computational implementation of this prior and provide several numerical examples to demonstrate its work.

preprint2011arXiv

Remarks on scalar curvature of Yamabe solitons

In this paper, we consider the scalar curvature of Yamabe solitons. In particular we show that, with natural conditions and non positive Ricci curvature, any complete Yamabe soliton has constant scalar curvature, namely, it is a Yamabe metric. We also show that the quadratic decay at infinity of the Ricci curvature of a complete non-compact Yamabe soliton has non-negative scalar curvature. A new proof of Kazdan-Warner condition is also presented.

preprint2011arXiv

Shubnikov-de Haas oscillations of a single layer graphene under dc current bias

Shubnikov-de Haas (SdH) oscillations under a dc current bias are experimentally studied on a Hall bar sample of single layer graphene. In dc resistance, the bias current shows the common damping effect on the SdH oscillations and the effect can be well accounted for by an elevated electron temperature that is found to be linearly dependent on the current bias. In differential resistance, a novel phase inversion of the SdH oscillations has been observed with increasing dc bias, namely we observe the oscillation maxima develop into minima and vice versa. Moreover, it is found that the onset biasing current, at which a SdH extremum is about to invert, is linearly dependent on the magnetic field of the SdH extrema. These observations are quantitatively explained with the help of a general SdH formula.

preprint2010arXiv

Boundary value problem for a classical semilinear parabolic equation

In this paper, we study the boundary value problem of the classical semilinear parabolic equations $$ u_t-Δu=|u|^{p-1}u, \ \ in \ \ Ω\times (0,T) $$ and $u=0$ on the boundary $\partialΩ\times [0,T)$ and $u=ϕ$ at $t=0$, where $Ω\subset R^n$ is a compact $C^1$ domain, $1<p\leq p_S$ is a fixed constant, and $ϕ\in C^2_0(Ω)$ is a given smooth function. Introducing new idea, we show that there are two sets $\tilde{W}$ and $\tilde{Z}$ such that for $ϕ\in W$, there is a global positive solution $u(t)\in \tilde{W}$ with $h^1$ omega limit $\{0\}$ and for $ϕ\in \tilde{Z}$, the solution blows up at finite time.

preprint2010arXiv

Gradient estimates for a simple nonlinear heat equation on manifolds

In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem $$ u_t-Δu=au\log u+Vu, \ \ u>0 $$ on the compact Riemannian manifold $(M,g)$ of dimension $n$ and with non-negative Ricci curvature. Here $a\leq 0$ is a constant, $V$ is a smooth function on $M$ with $-ΔV\leq A$ for some positive constant $A$. This heat equation is a basic evolution equation and it can be considered as the negative gradient heat flow to $W$-functional (introduced by G.Perelman), which is the Log-Sobolev inequalities on the Riemannian manifold and $V$ corresponds to the scalar curvature.

preprint2010arXiv

Heat flow method to Lichnerowicz type equation on closed manifolds

In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -Δu=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-Δu=A(x)u^{-p}-B(x)u^{q},\quad in\quad M\times\mathbb{R}^{+}, u(x,0)=u_0,\quad in\quad M with the positive smooth initial data $u_0$.

preprint2010arXiv

On the generalized Feynman-Kac transformation for nearly symmetric Markov processes

Suppose $X$ is a right process which is associated with a non-symmetric Dirichlet form $(\mathcal{E},D(\mathcal{E}))$ on $L^{2}(E;m)$. For $u\in D(\mathcal{E})$, we have Fukushima's decomposition: $\tilde{u}(X_{t})-\tilde{u}(X_{0})=M^{u}_{t}+N^{u}_{t}$. In this paper, we investigate the strong continuity of the generalized Feynman-Kac semigroup defined by $P^{u}_{t}f(x)=E_{x}[e^{N^{u}_{t}}f(X_{t})]$. Let $Q^{u}(f,g)=\mathcal{E}(f,g)+\mathcal{E}(u,fg)$ for $f,g\in D(\mathcal{E})_{b}$. Denote by $J_1$ the dissymmetric part of the jumping measure $J$ of $(\mathcal{E},D(\mathcal{E}))$. Under the assumption that $J_1$ is finite, we show that $(Q^{u},D(\mathcal{E})_{b})$ is lower semi-bounded if and only if there exists a constant $α_0\ge 0$ such that $\|P^{u}_{t}\|_2\leq e^{α_0 t}$ for every $t>0$. If one of these conditions holds, then $(P^{u}_{t})_{t\geq0}$ is strongly continuous on $L^{2}(E;m)$. If $X$ is equipped with a differential structure, then this result also holds without assuming that $J_1$ is finite.

preprint2010arXiv

Optional Pólya tree and Bayesian inference

We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting "optional Pólya tree" distribution has large support in total variation topology and yields posterior distributions that are also optional Pólya trees with computable parameter values.