arXiv subjects

Bo Feng

Publications and source records attributed to Bo Feng.

At least 55 records · Page 3Linked to original sources

arXiv2023

A block Lanczos method for large-scale quadratic minimization problems with orthogonality constraints

Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale QMPO. Krylov subspace methods are popular for large-scale optimization problems. In this work, we propose a block Lanczos method for solving the large-scale QMPO. In the proposed method, the original problem is projected into a small-sized one, and the Riemannian Trust-Region method is employed to solve the reduced QMPO. Convergence results on the optimal solution, the optimal objective function value, the multiplier and the KKT error are established. Moreover, we give the convergence speed of optimal solution, and show that if the block Lanczos process terminates, then an exact KKT solution is derived. Numerical experiments illustrate the numerical behavior of the proposed algorithm, and demonstrate that it is more powerful than many state-of-the-art algorithms for large-scale quadratic minimization problems with orthogonality constraints.

math.NA↗

arXiv2022

One-loop diagrams with quadratic propagators from the worldsheet

It is well known that forward limits of tree-level amplitudes (and those trivalent diagrams they consist of) produce one-loop amplitudes and trivalent diagrams with propagators linear in the loop momentum. They naturally arise from one-loop worldsheet formulae, and an important open problem is how to recombine them into usual one-loop diagrams with quadratic propagators. In this paper, we study a new collection of worldsheet functions: generalized one-loop Parke-Taylor factors with tensor numerators, which are conjectured to serve as a basis for one-loop worldsheet functions with this nice property. We present all-multiplicity, closed-form expressions for combinations of one-loop trivalent diagrams with quadratic propagators and tensor numerators to arbitrary rank (including possible tadpole contributions), produced by any pair of Parke-Taylor factors. We also briefly comment on reducing worldsheet functions onto such a basis, and applications to one-loop amplitudes in physical theories.

hep-th↗

arXiv2022

PV-Reduction of Sunset Topology with Auxiliary Vector

Passarino-Veltman (PV) reduction method has been proved to be very useful for the computation of general one-loop integrals. However, not much progress has been made when applying to higher loops. Recently, we have improved the PV-reduction method by introducing an auxiliary vector. In this paper, we apply our new method to the simplest two-loop integrals, i.e., the sunset topology. We show how to use differential operators to establish algebraic recursion relations for reduction coefficients. Our algorithm can be easily applied to the reduction of integrals with arbitrary high-rank tensor structures. We demonstrate the efficiency of our algorithm by computing the reduction with the total tensor rank up to four.

hep-ph↗

arXiv2022

Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals

In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants.

hep-ph↗

arXiv2022

Reduction with Degenerate Gram matrix for One-loop Integrals

An improved PV-reduction method for one-loop integrals with auxiliary vector $R$ has been proposed in \cite{Feng:2021enk,Hu:2021nia}. It has also been shown that the new method is a self-completed method in \cite{Feng:2022uqp}. Analytic reduction coefficients can be easily produced by recursion relations in this method, where the Gram determinant appears in denominators. The singularity caused by Gram determinant is a well-known fact and it is important to address these divergences in a given frame. In this paper, we propose a systematical algorithm to deal with this problem in our method. The key idea is that now the master integral of the highest topology will be decomposed into combinations of master integrals of lower topologies. By demanding the cancellation of divergence for obtained general reduction coefficients, we solve decomposition coefficients as a Taylor series of the Gram determinant. Moreover, the same idea can be applied to other kinds of divergences.

hep-ph↗

arXiv2022

One-loop CHY-Integrand of Bi-adjoint Scalar Theory

In this paper, the one-loop CHY-integrands of bi-adjoint scalar theory has been reinvestigated. Differing from previous constructions, we have explicitly removed contributions from tadpole and massless bubbles when taking the forward limit of corresponding tree-level amplitudes. The way to remove those singular contributions is to exploit the idea of 'picking poles', which is to multiply a special cross ratio factor with the role of isolating terms having a particular pole structure.

hep-th↗

arXiv2022

Universal Treatment of Reduction for One-Loop Integrals in Projective Space

Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with the reduction problem of one-loop integrals with general tensor structures as well as propagators with arbitrary higher powers. In this paper, we show that how to combine Feynman parametrization and embedding formalism to give a universal treatment of reductions for general one-loop integrals, even including the degenerated cases, such as the vanishing Gram determinant. Results from this method can be written in a compact and symmetric form.

hep-ph↗

arXiv2022

Reduction of General One-loop Integrals Using Auxiliary Vector

As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the Passarino-Veltman (PV) reduction method is also widely used for one-loop integrals. Recently, we have proposed an improved PV reduction method, i.e., the PV reduction method with auxiliary vector $R$, which can easily give analytical reduction results for any tensor rank. However, our results are only for integrals with propagators with power one. In this paper, we generalize our method to one-loop integrals with general tensor structures and propagators with general powers. Our ideas are simple. We solve the generalised reduction problem by combining differentiation over masses and proper limit of reduction with power-one propagators. Finally, we demonstrate our method with several examples. With the result in this paper, we have shown that our improved PV-reduction method with auxiliary vector is a self-completed reduction method for one-loop integrals.

hep-th↗

arXiv2022

GTrans: Spatiotemporal Autoregressive Transformer with Graph Embeddings for Nowcasting Extreme Events

Spatiotemporal time series nowcasting should preserve temporal and spatial dynamics in the sense that generated new sequences from models respect the covariance relationship from history. Conventional feature extractors are built with deep convolutional neural networks (CNN). However, CNN models have limits to image-like applications where data can be formed with high-dimensional arrays. In contrast, applications in social networks, road traffic, physics, and chemical property prediction where data features can be organized with nodes and edges of graphs. Transformer architecture is an emerging method for predictive models, bringing high accuracy and efficiency due to attention mechanism design. This paper proposes a spatiotemporal model, namely GTrans, that transforms data features into graph embeddings and predicts temporal dynamics with a transformer model. According to our experiments, we demonstrate that GTrans can model spatial and temporal dynamics and nowcasts extreme events for datasets. Furthermore, in all the experiments, GTrans can achieve the highest F1 and F2 scores in binary-class prediction tests than the baseline models.

cs.LG↗

arXiv2022

Joint Planning of Distributed Generations and Energy Storage in Active Distribution Networks: A Bi-Level Programming Approach

In order to improve the penetration of renewable energy resources for distribution networks, a joint planning model of distributed generations (DGs) and energy storage is proposed for an active distribution network by using a bi-level programming approach in this paper. In this model, the upper-level aims to seek the optimal location and capacity of DGs and energy storage, while the lower-level optimizes the operation of energy storage devices. To solve this model, an improved binary particle swarm optimization (IBPSO) algorithm based on chaos optimization is developed, and the optimal joint planning is achieved through alternating iterations between the two levels. The simulation results on the PG & E 69-bus distribution system demonstrate that the presented approach manages to reduce the planning deviation caused by the uncertainties of DG outputs and remarkably improve the voltage profile and operational economy of distribution systems.

eess.SY↗

arXiv2021

Earthquake Nowcasting with Deep Learning

We review previous approaches to nowcasting earthquakes and introduce new approaches based on deep learning using three distinct models based on recurrent neural networks and transformers. We discuss different choices for observables and measures presenting promising initial results for a region of Southern California from 1950-2020. Earthquake activity is predicted as a function of 0.1-degree spatial bins for time periods varying from two weeks to four years. The overall quality is measured by the Nash Sutcliffe Efficiency comparing the deviation of nowcast and observation with the variance over time in each spatial region. The software is available as open-source together with the preprocessed data from the USGS.

physics.geo-ph↗

arXiv2021

Solving the Families In the Wild Kinship Verification Challenge by Program Synthesis

Kinship verification is the task of determining whether a parent-child, sibling, or grandparent-grandchild relationship exists between two people and is important in social media applications, forensic investigations, finding missing children, and reuniting families. We demonstrate high quality kinship verification by participating in the 2021 Recognizing Families in the Wild challenge which provides the largest publicly available dataset in the field. Our approach is among the top 3 winning entries in the competition. We ensemble models written by both human experts and a foundation model, OpenAI Codex, trained on text and code. We use Codex to generate model variants, and also demonstrate its ability to generate entire running programs for kinship verification tasks of specific relationships.

cs.CV↗

arXiv2021

Note on solutions of scattering equations

In the CHY-frame for the amplitudes, there are two kinds of singularities we need to deal with. The first one is the pole singularities when the kinematics is not general, such that some of $S_A\to 0$. The second one is the collapse of locations of points after solving scattering equations (i.e., the singular solutions). These two types of singularities are tightly related to each other, but the exact mapping is not well understood. In this paper, we have initiated the systematic study of the mapping. We have demonstrated the different mapping patterns using three typical situations, i.e., the factorization limit, the soft limit and the forward limit.

hep-th↗

arXiv2021

Inverse Kinematics and Dexterous Workspace Formulation for 2-Segment Continuum Robots with Inextensible Segments

The inverse kinematics (IK) problem of continuum robots has been investigated in depth in the past decades. Under the constant-curvature bending assumption, closed-form IK solution has been obtained for continuum robots with variable segment lengths. Attempting to close the gap towards a complete solution, this paper presents an efficient solution for the IK problem of 2-segment continuum robots with one or two inextensible segments (a.k.a, constant segment lengths). Via representing the robot's shape as piecewise line segments, the configuration variables are separated from the IK formulation such that solving a one-variable nonlinear equation leads to the solution of the entire IK problem. Furthermore, an in-depth investigation of the boundaries of the dexterous workspace of the end effector caused by the configuration variables limits as well as the angular velocity singularities of the continuum robots was established. This dexterous workspace formulation, which is derived for the first time to the best of the authors' knowledge, is particularly useful to find the closest orientation to a target pose when the target orientation is out of the dexterous workspace. In the comparative simulation studies between the proposed method and the Jacobian-based IK method involving 500,000 cases, the proposed variable separation method solved 100% of the IK problems with much higher computational efficiency.

cs.RO↗

arXiv2021

Analytic Tadpole Coefficients of One-loop Integrals

One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators over an auxiliary vector $R$. Using differential operators, we establish the corresponding differential equations for tadpole coefficients at the first step. Then using the tensor structure of tadpole coefficients, we transform the differential equations to the recurrence relations for undetermined tensor coefficients. These recurrence relations can be solved easily by iteration, and we can obtain analytic expressions of tadpole coefficients for arbitrary one-loop integrals.

hep-th↗

arXiv2021

Spatiotemporal Pattern Mining for Nowcasting Extreme Earthquakes in Southern California

Geoscience and seismology have utilized the most advanced technologies and equipment to monitor seismic events globally from the past few decades. With the enormous amount of data, modern GPU-powered deep learning presents a promising approach to analyze data and discover patterns. In recent years, there are plenty of successful deep learning models for picking seismic waves. However, forecasting extreme earthquakes, which can cause disasters, is still an underdeveloped topic in history. Relevant research in spatiotemporal dynamics mining and forecasting has revealed some successful predictions, a crucial topic in many scientific research fields. Most studies of them have many successful applications of using deep neural networks. In Geology and Earth science studies, earthquake prediction is one of the world's most challenging problems, about which cutting-edge deep learning technologies may help discover some valuable patterns. In this project, we propose a deep learning modeling approach, namely \tseqpre, to mine spatiotemporal patterns from data to nowcast extreme earthquakes by discovering visual dynamics in regional coarse-grained spatial grids over time. In this modeling approach, we use synthetic deep learning neural networks with domain knowledge in geoscience and seismology to exploit earthquake patterns for prediction using convolutional long short-term memory neural networks. Our experiments show a strong correlation between location prediction and magnitude prediction for earthquakes in Southern California. Ablation studies and visualization validate the effectiveness of the proposed modeling method.

physics.geo-ph↗

arXiv2021

CryptoGRU: Low Latency Privacy-Preserving Text Analysis With GRU

Billions of text analysis requests containing private emails, personal text messages, and sensitive online reviews, are processed by recurrent neural networks (RNNs) deployed on public clouds every day. Although prior secure networks combine homomorphic encryption (HE) and garbled circuit (GC) to preserve users' privacy, naively adopting the HE and GC hybrid technique to implement RNNs suffers from long inference latency due to slow activation functions. In this paper, we present a HE and GC hybrid gated recurrent unit (GRU) network, CryptoGRU, for low-latency secure inferences. CryptoGRU replaces computationally expensive GC-based $tanh$ with fast GC-based $ReLU$, and then quantizes $sigmoid$ and $ReLU$ with a smaller bit length to accelerate activations in a GRU. We evaluate CryptoGRU with multiple GRU models trained on 4 public datasets. Experimental results show CryptoGRU achieves top-notch accuracy and improves the secure inference latency by up to $138\times$ over one of state-of-the-art secure networks on the Penn Treebank dataset.

cs.CR↗

arXiv2021

Reduction of one-loop integrals with higher poles by unitarity cut method

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators.

hep-th↗