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Published work

53 published item(s)

preprint2026arXiv

Sat3R: Satellite DSM Reconstruction via RPC-Aware Depth Fine-tuning

Accurate Digital Surface Model (DSM) reconstruction from satellite imagery is critical for applications such as disaster response, urban planning, and large-scale geographic mapping. Existing approaches face a fundamental trade-off: optimization-based methods achieve strong accuracy but require hours of per-scene computation, while generalizable geometry foundation models offer near-instant inference but fail to generalize to satellite imagery due to the domain gap introduced by the Rational Polynomial Camera (RPC) model and mismatched depth scale distributions. We present Sat3R, a feed-forward framework that bridges this gap via RPC-aware metric depth fine-tuning of Depth Anything V2 using the Scale-Invariant Logarithmic (SiLog) loss. By constructing physically consistent pseudo depth supervision from RPC geometry, Sat3R adapts a monocular depth foundation model to the satellite domain without per-scene optimization. Experiments on the DFC2019 benchmark demonstrate that Sat3R reduces MAE by 38% over zero-shot feed-forward baselines and achieves competitive accuracy against optimization-based methods, while delivering over 300x speedup. Sat3R demonstrates that feed-forward models, when properly adapted to the satellite domain, can match optimization-based accuracy at a fraction of the computational cost, paving the way for practical large-scale satellite DSM reconstruction.

preprint2022arXiv

Final bound-state formation effect on dark matter annihilation

If the annihilation products of dark matter (DM) are non-relativistic and couples directly to a light force mediator, the non-perturbation effect like final state bound state (FBS) formation and final state Sommerfeld (FSS) effect must be considered. Non-relativistic region of final particles will appear when there is small mass split between DM and products, so we study those effects in the degenerate region of mass (including kinematics forbidden case) using two specific models. We demonstrate that FBS effect will significantly modify the DM relic abundance comparing to the standard perturbation calculation in some mass split region. We emphasize that FBS effect is comparable to the FSS effect in those mass split. The conservation angular momentum are subtle considering FBS formation, in some cases there may be not $s$-wave, so we use two models exhibit the different partial wave FBS effect contribution. We also show that the FBS formation with vector boson emission process also contributes in DM relic abundance, and first calculate the $p$-wave FSS effect in the specific model.

preprint2021arXiv

A systematic mapping study on security countermeasures of in-vehicle communication systems

The innovations of vehicle connectivity have been increasing dramatically to enhance the safety and user experience of driving, while the rising numbers of interfaces to the external world also bring security threats to vehicles. Many security countermeasures have been proposed and discussed to protect the systems and services against attacks. To provide an overview of the current states in this research field, we conducted a systematic mapping study on the topic area "security countermeasures of in-vehicle communication systems". 279 papers are identified based on the defined study identification strategy and criteria. We discussed four research questions related to the security countermeasures, validation methods, publication patterns, and research trends and gaps based on the extracted and classified data. Finally, we evaluated the validity threats, the study identification results, and the whole mapping process. We found that the studies in this topic area are increasing rapidly in recent years. However, there are still gaps in various subtopics like automotive Ethernet security, anomaly reaction, and so on. This study reviews the target field not only related to research findings but also research activities, which can help identify research gaps at a high level and inspire new ideas for future work.

preprint2021arXiv

Binary fraction of O and B-type stars from LAMOST data

Binary stars plays important role in the evolution of stellar populations . The intrinsic binary fraction ($f_{bin}$) of O and B-type (OB) stars in LAMOST DR5 was investigated in this work. We employed a cross-correlation approach to estimate relative radial velocities for each of the stellar spectra. The algorithm described by \cite{2013A&A...550A.107S} was implemented and several simulations were made to assess the performance of the approach. Binary fraction of the OB stars are estimated through comparing the uni-distribution between observations and simulations with the Kolmogorov-Smirnov tests. Simulations show that it is reliable for stars most of whom have $6,7$ and $8$ repeated observations. The uncertainty of orbital parameters of binarity become larger when observational frequencies decrease. By adopting the fixed power exponents of $π=-0.45$ and $κ=-1$ for period and mass ratio distributions, respectively, we obtain that $f_{bin}=0.4_{-0.06}^{+0.05}$ for the samples with more than 3 observations. When we consider the full samples with at least 2 observations, the binary fraction turns out to be $0.37_{-0.03}^{+0.03}$. These two results are consistent with each other in $1σ$.

preprint2021arXiv

The Binarity of Early-type Stars from LAMOST Medium-resolution Spectroscopic Survey

Massive binaries play significant roles in many fields. Identification of massive stars, particularly massive binaries, is of great importance. In this paper, by adopting the technique of measuring the equivalent widths of several spectral lines, we identified 9,382 early-type stars from LAMOST medium-resolution survey and divided the sample into four groups, T1 ($\sim$O-B4), T2 ($\sim$B5), T3 ($\sim$B7), and T4 ($\sim$B8-A). The relative radial velocities $RV_{\rm rel}$ were calculated using the Maximum Likelihood Estimation. The stars with significant changes of $RV_{\rm rel}$ and at least larger than 15.57km s$^{-1}$ were identified as spectroscopic binaries. We found that the observed spectroscopic binary fractions for the four groups are $24.6\%\pm0.5\%$, $20.8\%\pm0.6\%$, $13.7\%\pm0.3\%$, and $7.4\%\pm0.3\%$, respectively. Assuming that orbital period ($P$) and mass ratio ($q$) have intrinsic distributions as $f(P) \propto P^π$ (1\textless$P$\textless1000 days) and $f(q) \propto q^κ$ (0.1\textless$q$\textless1), respectively, we conducted a series of Monte-Carlo simulations to correct observational biases for estimating the intrinsic multiplicity properties. The results show that the intrinsic binary fractions for the four groups are 68$\%\pm8\%$, 52$\%\pm3\%$, 44$\%\pm6\%$, and 44$\%\pm6\%$, respectively. The best estimated values for $π$ are -1$\pm0.1$, -1.1$\pm0.05$, -1.1$\pm0.1$, and -0.6$\pm0.05$, respectively. The $κ$ cannot be constrained for groups T1 and T2 and is -2.4$\pm0.3$ for group T3 and -1.6$\pm0.3$ for group T4. We confirmed the relationship of a decreasing trend in binary fractions towards late-type stars. No correlation between the spectral type and the orbital period distribution has been found yet, possibly due to the limitation of observational cadence.

preprint2021arXiv

The Spectroscopic Binaries from LAMOST Medium-Resolution Survey (MRS). I. Searching for Double-lined Spectroscopic Binaries (SB2s) with Convolutional Neural Network

We developed a convolutional neural network (CNN) model to distinguish the double-lined spectroscopic binaries (SB2s) from others based on single exposure medium-resolution spectra ($R\sim 7,500$). The training set consists of a large set of mock spectra of single stars and binaries synthesized based on the MIST stellar evolutionary model and ATLAS9 atmospheric model. Our model reaches a novel theoretic false positive rate by adding a proper penalty on the negative sample (e.g., 0.12\% and 0.16\% for the blue/red arm when the penalty parameter $Λ=16$). Tests show that the performance is as expected and favors FGK-type Main-sequence binaries with high mass ratio ($q \geq 0.7$) and large radial velocity separation ($Δv \geq 50\,\mathrm{km\,s^{-1}}$). Although the real false positive rate can not be estimated reliably, validating on eclipsing binaries identified from Kepler light curves indicates that our model predicts low binary probabilities at eclipsing phases (0, 0.5, and 1.0) as expected. The color-magnitude diagram also helps illustrate its feasibility and capability of identifying FGK MS binaries from spectra. We conclude that this model is reasonably reliable and can provide an automatic approach to identify SB2s with period $\lesssim 10$ days. This work yields a catalog of binary probabilities for over 5 million spectra of 1 million sources from the LAMOST medium-resolution survey (MRS), and a catalog of 2198 SB2 candidates whose physical properties will be analyzed in our following-up paper. Data products are made publicly available at the journal as well as our Github website.

preprint2020arXiv

Data-Flow-Based Extension of the System-Theoretic Process Analysis for Security (STPA-Sec)

Security analysis is an essential activity in security engineering to identify potential system vulnerabilities and achieve security requirements in the early design phases. Due to the increasing complexity of modern systems, traditional approaches, which only consider component failures and simple cause-and-effect linkages, lack the power to identify insecure incidents caused by complex interactions among physical systems, human and social entities. By contrast, a top-down System-Theoretic Process Analysis for Security (STPA-Sec) approach views losses as resulting from interactions, focuses on controlling system vulnerabilities instead of external threats and is applicable for complex socio-technical systems. In this paper, we proposed an extension of STPA-Sec based on data flow structures to overcome STPA-Sec's limitations and achieve security constraints of information-critical systems systematically. We analyzed a Bluetooth digital key system of a vehicle by using both the proposed and the original approach to investigate the relationship and differences between both approaches as well as their applicability and highlights. To conclude, the proposed approach can identify more information-related problems with technical details and be used with other STPA-based approaches to co-design systems in multi-disciplines under the unified STPA process framework.

preprint2020arXiv

Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence

The paper proves a result on the convergence of discrete conformal maps to the Riemann mappings for Jordan domains. It is a counterpart of Rodin-Sullivan's theorem on convergence of circle packing mappings to the Riemann mapping in the new setting of discrete conformality. The proof follows the same strategy that Rodin-Sullivan used by establishing a rigidity result for regular hexagonal triangulations of the plane and estimating the quasiconformal constants associated to the discrete conformal maps.

preprint2020arXiv

Final state Sommerfeld effect on dark matter relic abundance

If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. We study this effect on DM relic abundance in the thermal freeze-out scenario. As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles are non-relativistic. The size of the final state Sommerfeld (FSS) effect depends on the strength of the potential, as well as on the mass ratio of the final and initial state particles. We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy. Another feature of the FSS effect is that it could be suppressed when its time scale is longer than the lifetime of the final state particles. As a corollary, we also study in the DM coannihilation scenario where the initial state Sommerfeld effect between two coannihilators could be reduced due to their instability, which may need to be taken into account for an accurate calculation of the DM relic abundance.

preprint2020arXiv

How Heavy can Neutralino Dark Matter be?

What is the upper limit of the mass of the neutralino dark matter whose thermal relic is consistent with the observation? If the neutralino dark matter and colored sparticles are extremely degenerated in mass, with a mass difference less than the QCD scale, the dark matter annihilation is significantly increased and enjoys the "second freeze-out" after the QCD phase transition. In this case, the neutralino dark matter with a mass much greater than 100 TeV can realize the correct dark matter abundance. We study the dark matter abundance and its detection in the case of such highly degenerated mass spectrum of the neutralino dark matter and colored supersymmetric particles.

preprint2020arXiv

Second-order Neural Network Training Using Complex-step Directional Derivative

While the superior performance of second-order optimization methods such as Newton's method is well known, they are hardly used in practice for deep learning because neither assembling the Hessian matrix nor calculating its inverse is feasible for large-scale problems. Existing second-order methods resort to various diagonal or low-rank approximations of the Hessian, which often fail to capture necessary curvature information to generate a substantial improvement. On the other hand, when training becomes batch-based (i.e., stochastic), noisy second-order information easily contaminates the training procedure unless expensive safeguard is employed. In this paper, we adopt a numerical algorithm for second-order neural network training. We tackle the practical obstacle of Hessian calculation by using the complex-step finite difference (CSFD) -- a numerical procedure adding an imaginary perturbation to the function for derivative computation. CSFD is highly robust, efficient, and accurate (as accurate as the analytic result). This method allows us to literally apply any known second-order optimization methods for deep learning training. Based on it, we design an effective Newton Krylov procedure. The key mechanism is to terminate the stochastic Krylov iteration as soon as a disturbing direction is found so that unnecessary computation can be avoided. During the optimization, we monitor the approximation error in the Taylor expansion to adjust the step size. This strategy combines advantages of line search and trust region methods making our method preserves good local and global convergency at the same time. We have tested our methods in various deep learning tasks. The experiments show that our method outperforms exiting methods, and it often converges one-order faster. We believe our method will inspire a wide-range of new algorithms for deep learning and numerical optimization.

preprint2020arXiv

SilkViser:A Visual Explorer of Blockchain-based Cryptocurrency Transaction Data

Many blockchain-based cryptocurrencies provide users with online blockchain explorers for viewing online transaction data. However, traditional blockchain explorers mostly present transaction information in textual and tabular forms. Such forms make understanding cryptocurrency transaction mechanisms difficult for novice users (NUsers). They are also insufficiently informative for experienced users (EUsers) to recognize advanced transaction information. This study introduces a new online cryptocurrency transaction data viewing tool called SilkViser. Guided by detailed scenario and requirement analyses, we create a series of appreciating visualization designs, such as paper ledger-inspired block and blockchain visualizations and ancient copper coin-inspired transaction visualizations, to help users understand cryptocurrency transaction mechanisms and recognize advanced transaction information. We also provide a set of lightweight interactions to facilitate easy and free data exploration. Moreover, a controlled user study is conducted to quantitatively evaluate the usability and effectiveness of SilkViser. Results indicate that SilkViser can satisfy the requirements of NUsers and EUsers. Our visualization designs can compensate for the inexperience of NUsers in data viewing and attract potential users to participate in cryptocurrency transactions.

preprint2019arXiv

Quadrilateral Mesh Generation II : Meromorphic Quartic Differentials and Abel-Jacobi Condition

This work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic. Each quad-mesh induces a conformal structure of the surface, and a meromorphic differential, where the configuration of singular vertices correspond to the configurations the poles and zeros (divisor) of the meroromorphic differential. Due to Riemann surface theory, the configuration of singularities of a quad-mesh satisfies the Abel-Jacobi condition. Inversely, if a satisfies the Abel-Jacobi condition, then there exists a meromorphic quartic differential whose equals to the given one. Furthermore, if the meromorphic quadric differential is with finite, then it also induces a a quad-mesh, the poles and zeros of the meromorphic differential to the singular vertices of the quad-mesh. Besides the theoretic proofs, the computational algorithm for verification of Abel-Jacobi condition is explained in details. Furthermore, constructive algorithm of meromorphic quartic differential on zero surfaces is proposed, which is based on the global algebraic representation of meromorphic. Our experimental results demonstrate the efficiency and efficacy of the algorithm. This opens up a direction for quad-mesh generation using algebraic geometric approach.

preprint2016arXiv

DynIMS: A Dynamic Memory Controller for In-memory Storage on HPC Systems

In order to boost the performance of data-intensive computing on HPC systems, in-memory computing frameworks, such as Apache Spark and Flink, use local DRAM for data storage. Optimizing the memory allocation to data storage is critical to delivering performance to traditional HPC compute jobs and throughput to data-intensive applications sharing the HPC resources. Current practices that statically configure in-memory storage may leave inadequate space for compute jobs or lose the opportunity to utilize more available space for data-intensive applications. In this paper, we explore techniques to dynamically adjust in-memory storage and make the right amount of space for compute jobs. We have developed a dynamic memory controller, DynIMS, which infers memory demands of compute tasks online and employs a feedback-based control model to adapt the capacity of in-memory storage. We test DynIMS using mixed HPCC and Spark workloads on a HPC cluster. Experimental results show that DynIMS can achieve up to 5X performance improvement compared to systems with static memory allocations.

preprint2016arXiv

Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds

We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescribed cone angles at all edges is (if non-empty) a smooth complex manifold of dimension the sum of the genera of the vertex links. Moreover, we show that the complex lengths of a collection of peripheral elements give a local holomorphic parameterisation of this manifold.

preprint2015arXiv

A new combinatorial class of 3-manifold triangulations

We define a new combinatorial class of triangulations of closed 3-manifolds, satisfying a weak version of 0-efficiency combined with a weak version of minimality, and study them using twisted squares. As an application, we obtain strong restrictions on the topology of a 3-manifold from the existence of non-smooth maxima of the volume function on the space of circle-valued angle structures.

preprint2015arXiv

Beyond the CMSSM without an Accelerator: Proton Decay and Direct Dark Matter Detection

We consider two potential non-accelerator signatures of generalizations of the well-studied constrained minimal supersymmetric standard model (CMSSM). In one generalization, the universality constraints on soft supersymmetry-breaking parameters are applied at some input scale $M_{in}$ below the grand unification (GUT) scale $M_{GUT}$, a scenario referred to as `sub-GUT'. The other generalization we consider is to retain GUT-scale universality for the squark and slepton masses, but to relax universality for the soft supersymmetry-breaking contributions to the masses of the Higgs doublets. As with other CMSSM-like models, the measured Higgs mass requires supersymmetric particle masses near or beyond the TeV scale. Because of these rather heavy sparticle masses, the embedding of these CMSSM-like models in a minimal SU(5) model of grand unification can yield a proton lifetime consistent with current experimental limits, and may be accessible in existing and future proton decay experiments. Another possible signature of these CMSSM-like models is direct detection of supersymmetric dark matter. The direct dark matter scattering rate is typically below the reach of the LUX-ZEPLIN (LZ) experiment if $M_{in}$ is close to $M_{GUT}$, but may lie within its reach if $M_{in} \lesssim 10^{11}$ GeV. Likewise, generalizing the CMSSM to allow non-universal supersymmetry-breaking contributions to the Higgs offers extensive possibilities for models within reach of the LZ experiment that have long proton lifetimes.

preprint2015arXiv

Big Data Analytics on Traditional HPC Infrastructure Using Two-Level Storage

Data-intensive computing has become one of the major workloads on traditional high-performance computing (HPC) clusters. Currently, deploying data-intensive computing software framework on HPC clusters still faces performance and scalability issues. In this paper, we develop a new two-level storage system by integrating Tachyon, an in-memory file system with OrangeFS, a parallel file system. We model the I/O throughputs of four storage structures: HDFS, OrangeFS, Tachyon and two-level storage. We conduct computational experiments to characterize I/O throughput behavior of two-level storage and compare its performance to that of HDFS and OrangeFS, using TeraSort benchmark. Theoretical models and experimental tests both show that the two-level storage system can increase the aggregate I/O throughputs. This work lays a solid foundation for future work in designing and building HPC systems that can provide a better support on I/O intensive workloads with preserving existing computing resources.

preprint2015arXiv

Gluino Coannihilation Revisited

Some variants of the MSSM feature a strip in parameter space where the lightest neutralino is identified as the lightest supersymmetric particle (LSP), the gluino is the next-to-lightest supersymmetric particle (NLSP) and is nearly degenerate with the LSP, and the relic cold dark matter density is brought into the range allowed by astrophysics and cosmology by coannihilation with the gluino NLSP. We calculate the relic density along this gluino coannihilation strip in the MSSM, including the effects of gluino-gluino bound states and initial-state Sommerfeld enhancement, and taking into account the decoupling of the gluino and LSP densities that occurs for large values of the squark mass. We find that bound-state effects can increase the maximum LSP mass for which the relic cold dark matter density lies within the range favoured by astrophysics and cosmology by as much as ~ 50% if the squark to gluino mass ratio is 1.1, and that the LSP may weigh up to ~ 8 TeV for a wide range of the squark to gluino mass ratio \lesssim 100.

preprint2015arXiv

Scenarios for Gluino Coannihilation

We study supersymmetric scenarios in which the gluino is the next-to-lightest supersymmetric particle (NLSP), with a mass sufficiently close to that of the lightest supersymmetric particle (LSP) that gluino coannihilation becomes important. One of these scenarios is the MSSM with soft supersymmetry-breaking squark and slepton masses that are universal at an input GUT renormalization scale, but with non-universal gaugino masses. The other scenario is an extension of the MSSM to include vector-like supermultiplets. In both scenarios, we identify the regions of parameter space where gluino coannihilation is important, and discuss their relations to other regions of parameter space where other mechanisms bring the dark matter density into the range allowed by cosmology. In the case of the non-universal MSSM scenario, we find that the allowed range of parameter space is constrained by the requirement of electroweak symmetry breaking, the avoidance of a charged LSP and the measured mass of the Higgs boson, in particular, as well as the appearance of other dark matter (co)annihilation processes. Nevertheless, LSP masses $m_χ\lesssim 8$~TeV with the correct dark matter density are quite possible. In the case of pure gravity mediation with additional vector-like supermultiplets, changes to the anomaly-mediated gluino mass and the threshold effects associated with these states can make the gluino almost degenerate with the LSP, and we find a similar upper bound.

preprint2014arXiv

A discrete uniformization theorem for polyhedral surfaces II

A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying Gauss-Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.

preprint2014arXiv

Closing in on the Tip of the CMSSM Stau Coannihilation Strip

Near the tip of the stau coannihilation strip in the CMSSM with a neutralino LSP, the astrophysical cold dark matter density constraint forces the stau-neutralino mass difference to be small. If this mass difference is smaller than the tau mass, the stau may decay either in the outer part of an LHC detector - the `disappearing track' signature - or be sufficiently long-lived to leave the detector before decaying - the long-lived massive charged-particle signature. We combine searches for these signatures with conventional missing transverse energy searches during LHC Run 1, identifying the small remaining parts of the CMSSM stau coannihilation strip region that have not yet been excluded, and discussing how they may be explored during Run 2 of the LHC.

preprint2014arXiv

Discrete Conformal Deformation: Algorithm and Experiments

In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing curvature, that is to deform the metric discrete conformally so that the curvature of the resulting metric coincides with the prescribed curvature. We explicitly construct a discrete conformal map between the input triangulated surface and the deformed triangulated surface. Our algorithm can handle the surface with any topology with or without boundary, and can find a deformed metric for any prescribed curvature satisfying the Gauss-Bonnet formula. In addition, we present the numerical examples to show the convergence of our discrete conformality and to demonstrate the efficiency and the robustness of our algorithm.

preprint2014arXiv

The Unified Surface Ricci Flow

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternative methods so far. This work introduces the unified theoretic framework for discrete Surface Ricci Flow, including all common schemes: Thurston's Circle Packing, Tangential Circle Packing, Inversive Distance Circle Packing and Discrete Yamabe. Furthermore, this work also introduces a novel scheme, virtual radius circle packing, under the unified framework. This work gives explicit geometric interpretation to the discrete Ricci energy for all the schemes, and Hessian of the discrete Ricci energy for schemes with Euclidean back ground geometry. The unified frame work deepen our understanding to the the discrete surface Ricci flow theory, and inspired us to discover the new schemes, improved the flexibility and robustness of the algorithms, greatly simplified the implementation and improved the debugging efficiency. Experimental results shows the unified surface Ricci flow algorithms can handle general surfaces with different topologies, and is robust to meshes with different qualities, and effective for solving real problems.

preprint2014arXiv

Volume and rigidity of hyperbolic polyhedral $3$-manifolds

We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature. The main tool used in the proof is the Fenchel dual of the volume function.

preprint2013arXiv

A Variational Principle for Improving 2D Triangle Meshes based on Hyperbolic Volume

In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle structures whose maximizer is unique and consists only of equilateral triangles. This energy functional is related to hyperbolic volume of ideal 3-simplex. Even with extra constraints on the angles for embedding the mesh into the plane and preserving the boundary, the energy functional remains well-behaved. We devise an efficient algorithm for maximizing the energy functional over these extra constraints. We apply our algorithm to various datasets and compare its performance with that of CVT. The experimental results show that our algorithm produces the meshes with both the angles and the aspect ratios of triangles lying in tighter intervals.

preprint2013arXiv

Enhancement of Majorana Dark Matter Annihilation Through Higgs Bremsstrahlung

For Majorana dark matter, gauge boson bremsstrahlung plays an important role in enhancing an otherwise helicity-suppressed s-wave annihilation cross-section. This is well known for processes involving a radiated photon or gluon together with a Standard Model fermion-antifermion pair, and the case of massive electroweak gauge bosons has also recently been studied. Here we show that internal Higgs bremsstrahlung also lifts helicity suppression and could be the dominant contribution to the annihilation rate in the late Universe for dark matter masses below ~1 TeV. Using a toy model of leptophilic dark matter, we calculate the annihilation cross-section into a lepton-antilepton pair with a Higgs boson and investigate the energy spectra of the final stable particles at the annihilation point.

preprint2013arXiv

Gravitino Decays and the Cosmological Lithium Problem in Light of the LHC Higgs and Supersymmetry Searches

We studied previously the impact on light-element abundances of gravitinos decaying during or after Big-Bang nucleosynthesis (BBN). We found regions of the gravitino mass m_{3/2} and abundance zeta_{3/2} plane where its decays could reconcile the calculated abundance of Li7 with observation without perturbing the other light-element abundances unacceptably. Here we revisit this issue in light of LHC measurements of the Higgs mass and constraints on supersymmetric model parameters, as well as updates in the astrophysical measurements of light-element abundances. In addition to the constrained minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses at the GUT scale (the CMSSM) studied previously, we also study models with universality imposed below the GUT scale and models with non-universal Higgs masses (NUHM1). We calculate the total likelihood function for the light-element abundances, taking into account the observational uncertainties. We find that gravitino decays provide a robust solution to the cosmological Li7 problem along strips in the (m_{3/2}, zeta_{3/2}) plane along which the abundances of deuterium, He4 and Li7 may be fit with chi^2_min < 3, compared with chi^2 ~ 34 if the effects of gravitino decays are unimportant. The minimum of the likelihood function is reduced to chi^2 < 2 when the uncertainty on D/H is relaxed and < 1 when the lithium abundance is taken from globular cluster data.

preprint2013arXiv

Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations

In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computational geometry is established.

preprint2012arXiv

A TQFT of Turaev-Viro type on shaped triangulations

A shaped triangulation is a finite triangulation of an oriented pseudo three manifold where each tetrahedron carries dihedral angles of an ideal hyberbolic tetrahedron. To each shaped triangulation, we associate a quantum partition function in the form of an absolutely convergent state integral which is invariant under shaped 3-2 Pachner moves and invariant with respect to shape gauge transformations generated by total dihedral angles around internal edges through the Neumann-Zagier Poisson bracket. Similarly to Turaev-Viro theory, the state variables live on edges of the triangulation but take their values on the whole real axis. The tetrahedral weight functions are composed of three hyperbolic gamma functions in a way that they enjoy a manifest tetrahedral symmetry. We conjecture that for shaped triangulations of closed 3-manifolds, our partition function is twice the absolute value squared of the partition function of Techmüller TQFT defined by Andersen and Kashaev. This is similar to the known relationship between the Turaev-Viro and the Witten-Reshetikhin-Turaev invarints of three manifolds. We also discuss interpretations of our construction in terms of three-dimensional supersymmetric field theories related to triangulated three-dimensional manifolds.

preprint2012arXiv

Metastable Charged Sparticles and the Cosmological Li7 Problem

We consider the effects of metastable charged sparticles on Big-Bang Nucleosynthesis (BBN), including bound-state reaction rates and chemical effects. We make a new analysis of the bound states of negatively-charged massive particles with the light nuclei most prominent in BBN, and present a new code to track their abundances, paying particular attention to that of Li7. Assuming, as an example, that the gravitino is the lightest supersymmetric particle (LSP), and that the lighter stau slepton, stau_1, is the metastable next-to-lightest sparticle within the constrained minimal supersymmetric extension of the Standard Model (CMSSM), we analyze the possible effects on the standard BBN abundances of stau_1 bound states and decays for representative values of the gravitino mass. Taking into account the constraint on the CMSSM parameter space imposed by the discovery of the Higgs boson at the LHC, we delineate regions in which the fit to the measured light-element abundances is as good as in standard BBN. We also identify regions of the CMSSM parameter space in which the bound state properties, chemistry and decays of metastable charged sparticles can solve the cosmological Li7 problem.

preprint2012arXiv

The Higgs Mass beyond the CMSSM

The apparent discovery of a Higgs boson with mass ~125 GeV has had a significant impact on the constrained minimal supersymmetric extension of the Standard Model in which the scalar masses, gaugino masses and tri-linear A-terms are assumed to be universal at the GUT scale (the CMSSM). Much of the low-mass parameter space in the CMSSM has been excluded by supersymmetric particle searches at the LHC as well as by the Higgs mass measurement and the emergent signal for B_s to mu^+ mu^-. Here, we consider the impact of these recent LHC results on several variants of the CMSSM with a primary focus on obtaining a Higgs mass of ~125 GeV. In particular, we consider the one- and two-parameter extensions of the CMSSM with one or both of the Higgs masses set independently of the common sfermion mass, m_0 (the NUHM1,2). We also consider the one-parameter extension of the CMSSM in which the input universality scale M_in is below the GUT scale (the sub-GUT CMSSM). We find that when M_in < M_GUT large regions of parameter space open up where the relic density of neutralinos can successfully account for dark matter with a Higgs boson mass ~125 GeV. In some of these regions essential roles are played by coannihilation processes that are usually less important in the CMSSM with M_in = M_GUT. Finally, we reconsider mSUGRA models with sub-GUT universality, which have the same number of parameters as the CMSSM. Here too, we find phenomenologically viable regions of parameter space, which are essentially non-existent in GUT-scale mSUGRA models. Interestingly, we find that the preferred range of the A-term straddles that predicted by the simplest Polonyi model.

preprint2011arXiv

An Enhanced Cosmological Li6 Abundance as a Potential Signature of Residual Dark Matter Annihilations

Residual late-time dark matter particle annihilations during and after Big Bang Nucleosynthesis (BBN) may alter the predicted cosmological abundances of the light elements. Within the constrained minimal supersymmetric extension of the Standard Model (the CMSSM) with a neutralino LSP, we find negligible effects on the abundances of Deuterium, He3, He4 and Li7 predicted by homogeneous BBN, but potentially a large enhancement in the predicted abundance of Li6. This enhancement may be as much as two orders of magnitude in the focus-point WMAP strip and in the coannihilation and funnel regions for large tan beta for small m_{1/2}, and the effect is still significant at large m_{1/2}. However, the potential Li6 enhancement is negligible in the part of the coannihilation strip for tan beta = 10 that survives the latest LHC constraints. A similar enhancement of the \li6 abundance may also be found in a model with common, non-universal Higgs masses (the NUHM1).

preprint2011arXiv

Gyromagnetic Factors and Atomic Clock Constraints on the Variation of Fundamental Constants

We consider the effect of the coupled variations of fundamental constants on the nucleon magnetic moment. The nucleon g-factor enters into the interpretation of the measurements of variations in the fine-structure constant, alpha, in both the laboratory (through atomic clock measurements) and in astrophysical systems (e.g. through measurements of the 21 cm transitions). A null result can be translated into a limit on the variation of a set of fundamental constants, that is usually reduced to alpha. However, in specific models, particularly unification models, changes in alpha are always accompanied by corresponding changes in other fundamental quantities such as the QCD scale, Lambda_QCD. This work tracks the changes in the nucleon g-factors induced from changes in Lambda_QCD and the light quark masses. In principle, these coupled variations can improve the bounds on the variation of alpha by an order of magnitude from existing atomic clock and astrophysical measurements. Unfortunately, the calculation of the dependence of g-factors on fundamental parameters is notoriously model-dependent.

preprint2011arXiv

Harmonic Functions for Data Reconstruction on 3D Manifolds

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches) and each node on the mesh will have an initial value. While the mesh is refined the algorithm will provide a smooth function on the redefined manifolds. However, when data points are not dense and the original mesh is not allowed to be changed, how is the "continuous and/or smooth" reconstruction possible? This paper will present a new method using harmonic functions to solve the problem. Our method contains the following steps: (1) Partition the boundary surfaces of the 3D manifold based on sample points so that each sample point is on the edge of the partition. (2) Use gradually varied interpolation on the edges so that each point on edge will be assigned a value. In addition, all values on the edge are gradually varied. (3) Use discrete harmonic function to fit the unknown points, i.e. the points inside each partition patch. The fitted function will be a harmonic or a local harmonic function in each partitioned area. The function on edge will be "near" continuous (or "near" gradually varied). If we need a smoothed surface on the manifold, we can apply subdivision algorithms. This paper has also a philosophical advantage over triangulation meshes. People usually use triangulation for data reconstruction. This paper employs harmonic functions, a generalization of triangulation because linearity is a form of harmonic. Therefore, local harmonic initialization is more sophisticated then triangulation. This paper is a conceptual and methodological paper. This paper does not focus on detailed mathematical analysis nor fine algorithm design.

preprint2011arXiv

Understanding and predicting synthetic lethal genetic interactions in Saccharomyces cerevisiae using domain genetic interactions

Genetic interactions have been widely used to define functional relationships between proteins and pathways. In this study, we demonstrated that yeast synthetic lethal genetic interactions can be explained by the genetic interactions between domains of those proteins. The domain genetic interactions rarely overlap with the domain physical interactions from iPfam database and provide a complementary view about domain relationships. Moreover, we found that domains in multidomain yeast proteins contribute to their genetic interactions differently. The domain genetic interactions help more precisely define the function related to the synthetic lethal genetic interactions, and then help understand how domains contribute to different functionalities of multidomain proteins. Using the probabilities of domain genetic interactions, we were able to predict novel yeast synthetic lethal genetic interactions. Furthermore, we had also identified novel compensatory pathways from the predicted synthetic lethal genetic interactions. Our study significantly improved the understanding of yeast mulitdomain proteins, the synthetic lethal genetic interactions and the functional relationships between proteins and pathways.

preprint2010arXiv

Cell decompositions of Teichmüller spaces of surfaces with boundary

A family of coordinates $ψ_h$ for the Teichmüller space of a compact surface with boundary was introduced in \cite{l2}. In the work \cite{m1}, Mondello showed that the coordinate $ψ_0$ can be used to produce a natural cell decomposition of the Teichmüller space invariant under the action of the mapping class group. In this paper, we show that the similar result also works for all other coordinate $ψ_h$ for any $h \geq 0$.

preprint2010arXiv

Discrete Laplace-Beltrami Operator Determines Discrete Riemannian Metric

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from its eigenvalues and eigenfunctions determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete Laplace-Beltrami operator and the discrete Riemannian metric (unique up to a scaling) are mutually determined by each other. Given an Euclidean polyhedral surface, its Riemannian metric is represented as edge lengths, satisfying triangle inequalities on all faces. The Laplace-Beltrami operator is formulated using the cotangent formula, where the edge weight is defined as the sum of the cotangent of angles against the edge. We prove that the edge lengths can be determined by the edge weights unique up to a scaling using the variational approach. First, we show that the space of all possible metrics of a polyhedral surface is convex. Then, we construct a special energy defined on the metric space, such that the gradient of the energy equals to the edge weights. Third, we show the Hessian matrix of the energy is positive definite, restricted on the tangent space of the metric space, therefore the energy is convex. Finally, by the fact that the parameter on a convex domain and the gradient of a convex function defined on the domain have one-to-one correspondence, we show the edge weights determines the polyhedral metric unique up to a scaling. The constructive proof leads to a computational algorithm that finds the unique metric on a topological triangle mesh from a discrete Laplace-Beltrami operator matrix.

preprint2010arXiv

Effectively integrating information content and structural relationship to improve the GO-based similarity measure between proteins

The Gene Ontology (GO) provides a knowledge base to effectively describe proteins. However, measuring similarity between proteins based on GO remains a challenge. In this paper, we propose a new similarity measure, information coefficient similarity measure (SimIC), to effectively integrate both the information content (IC) of GO terms and the structural information of GO hierarchy to determine the similarity between proteins. Testing on yeast proteins, our results show that SimIC efficiently addresses the shallow annotation issue in GO, thus improves the correlations between GO similarities of yeast proteins and their expression similarities as well as between GO similarities of yeast proteins and their sequence similarities. Furthermore, we demonstrate that the proposed SimIC is superior in predicting yeast protein interactions. We predict 20484 yeast protein-protein interactions (PPIs) between 2462 proteins based on the high SimIC values of biological process (BP) and cellular component (CC). Examining the 214 MIPS complexes in our predicted PPIs shows that all members of 159 MIPS complexes can be found in our PPI predictions, which is more than those (120/214) found in PPIs predicted by relative specificity similarity (RSS). Integrating IC and structural information of GO hierarchy can improve the effectiveness of the semantic similarity measure of GO terms. The new SimIC can effectively correct the effect of shallow annotation, and then provide an effective way to measure similarity between proteins based on Gene Ontology.

preprint2010arXiv

Nuclear Reaction Uncertainties, Massive Gravitino Decays and the Cosmological Lithium Problem

We consider the effects of uncertainties in nuclear reaction rates on the cosmological constraints on the decays of unstable particles during or after Big-Bang nucleosynthesis (BBN). We identify the nuclear reactions due to non-thermal hadrons that are the most important in perturbing standard BBN, then quantify the uncertainties in these reactions and in the resulting light-element abundances. These results also indicate the key nuclear processes for which improved cross section data would allow different light-element abundances to be determined more accurately, thereby making possible more precise probes of BBN and evaluations of the cosmological constraints on unstable particles. Applying this analysis to models with unstable gravitinos decaying into neutralinos, we calculate the likelihood function for the light-element abundances measured currently, taking into account the current experimental errors in the determinations of the relevant nuclear reaction rates. We find a region of the gravitino mass and abundance in which the abundances of deuterium, He4 and Li7 may be fit with chi^2 = 5.5, compared with chi^2 = 31.7 if the effects of gravitino decays are unimportant. The best-fit solution is improved to chi^2 ~ 2.0 when the lithium abundance is taken from globular cluster data. Some such re-evaluation of the observed light-element abundances and/or nuclear reaction rates would be needed if this region of gravitino parameters is to provide a complete solution to the cosmological Li7 problem.

preprint2010arXiv

Rigidity of Polyhedral Surfaces, III

This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfaces introduced by P. Bowers and K. Stephenson as a generalization of Andreev-Thurston's circle packing. They conjectured that inversive distance circle packings are rigid. Using a recent work of R. Guo on variational principle associated to the inversive distance circle packing, we prove rigidity conjecture of Bowers-Stephenson in this paper. We also show that each polyhedral metric on a triangulated surface is determined by various discrete curvatures introduced in our previous work, verifying a conjecture in \cite{Lu1}. As a consequence, we show that the discrete Laplacian operator determines a Euclidean polyhedral metric up to scaling.

preprint2010arXiv

The gravitino coupling to broken gauge theories applied to the MSSM

We consider gravitino couplings in theories with broken gauge symmetries. In particular, we compute the single gravitino production cross section in W+ W- fusion processes. Despite recent claims to the contrary, we show that this process is always subdominant to gluon fusion processes in the high energy limit. The full calculation is performed numerically; however, we give analytic expressions for the cross section in the supersymmetric and electroweak limits. We also confirm these results with the use of the effective theory of goldstino interactions.

preprint2010arXiv

Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston's spinning construction and a volume rigidity result attributed by Dunfield to Thurston, Gromov and Goldman. As an application, we show that this gives a new algorithm to detect hyperbolic structures on closed 3-manifolds.

preprint2010arXiv

Triangulated 3-Manifolds: from Haken's normal surfaces to Thurston's algebraic equation

We give a brief summary of some of our work and our joint work with Stephan Tillmann on solving Thurston's equation and Haken equation on triangulated 3-manifolds in this paper. Several conjectures on the existence of solutions to Thurston's equation and Haken equation are made. Resolutions of these conjecture will lead to a new proof of the Poincaré conjecture without using the Ricci flow. We approach these conjectures by a finite dimensional variational principle so that its critical points are related to solutions to Thurston's gluing equation and Haken's normal surface equation. The action functional is the volume. This is a generalization of an earlier program by Casson and Rivin for compact 3-manifolds with torus boundary.

preprint2010arXiv

Volume Optimization, Normal Surfaces and Thurston's Equation on Triangulated 3-Manifolds

We propose a finite dimensional variational principle on triangulated 3-manifolds so that its critical points are related to solutions to Thurston's gluing equation and Haken's normal surface equation. The action functional is the volume. This is a generalization of an earlier program by Casson and Rivin for compact 3-manifolds with torus boundary. Combining the result in this paper and the work of Futer-Guéritaud, Segerman-Tillmann and Luo-Tillmann, we obtain a new finite dimensional variational formulation of the Poncare-conjecture. This provides a step toward a new proof the Poincaré conjecture without using the Ricci flow.

preprint2009arXiv

Nucleosynthesis Constraints on a Massive Gravitino in Neutralino Dark Matter Scenarios

The decays of massive gravitinos into neutralino dark matter particles and Standard Model secondaries during or after Big-Bang nucleosynthesis (BBN) may alter the primordial light-element abundances. We present here details of a new suite of codes for evaluating such effects, including a new treatment based on PYTHIA of the evolution of showers induced by hadronic decays of massive, unstable particles such as a gravitino. We also develop an analytical treatment of non-thermal hadron propagation in the early universe, and use this to derive analytical estimates for light-element production and in turn on decaying particle lifetimes and abundances. We then consider specifically the case of an unstable massive gravitino within the constrained minimal supersymmetric extension of the Standard Model (CMSSM). We present upper limits on its possible primordial abundance before decay for different possible gravitino masses, with CMSSM parameters along strips where the lightest neutralino provides all the astrophysical cold dark matter density. We do not find any CMSSM solution to the cosmological Li7 problem for small m_{3/2}. Discounting this, for m_{1/2} ~ 500 GeV and tan beta = 10 the other light-element abundances impose an upper limit m_{3/2} n_{3/2}/n_γ< 3 \times 10^{-12} GeV to < 2 \times 10^{-13} GeV for m_{3/2} = 250 GeV to 1 TeV, which is similar in both the coannihilation and focus-point strips and somewhat weaker for tan beta = 50, particularly for larger m_{1/2}. The constraints also weaken in general for larger m_{3/2}, and for m_{3/2} > 3 TeV we find a narrow range of m_{3/2} n_{3/2}/n_γ, at values which increase with m_{3/2}, where the Li7 abundance is marginally compatible with the other light-element abundances.

preprint2007arXiv

Rigidity of polyhedral surfaces, II

We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover a uniform approach on several variational principles on polyhedral surfaces with or without boundary. As a consequence, the work of Penner, Bobenko-Springborn and Thurston on rigidity of polyhedral surfaces and circle patterns are extended to a very general context.

preprint2006arXiv

A characterization of spherical polyhedron surfaces

A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedron surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obtained. A characterization of spherical polyhedron surfaces in terms of the triangulation and the angle assignment is established.

preprint2005arXiv

Volume and angle structures on 3-manifolds

We propose an approach to find constant curvature metrics on triangulated closed 3-manifolds using a finite dimensional variational method whose energy function is the volume. The concept of an angle structure on a tetrahedron and on a triangulated closed 3-manifold is introduced following the work of Casson, Murakami and Rivin. It is proved by A. Kitaev and the author that any closed 3-manifold has a triangulation supporting an angle structure. The moduli space of all angle structures on a triangulated 3-manifold is a bounded open convex polytope in a Euclidean space. The volume of an angle structure is defined. Both the angle structure and the volume are natural generalizations of tetrahedra in the constant sectional curvature spaces and their volume. It is shown that the volume functional can be extended continuously to the compact closure of the moduli space. In particular, the maximum point of the volume functional always exists in the compactification. The main result shows that for a 1-vertex triangulation of a closed 3-manifold if the volume function on the moduli space has a local maximum point, then either the manifold admits a constant curvature Riemannian metric or the manifold contains a non-separating 2-sphere or real projective plane.