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Gang Yang

Publications and source records attributed to Gang Yang.

At least 145 records · Page 8Linked to original sources
arXiv2017

Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz

In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories. To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. We hope that the derivation presented in this paper elucidates further this completely new point of view on the origin, as well as on the structure, of TBA equations in integrable models.

hep-th↗
arXiv2017

Magnetic MIMO Signal Processing and Optimization for Wireless Power Transfer

In magnetic resonant coupling (MRC) enabled multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems, multiple transmitters (TXs) each with one single coil are used to enhance the efficiency of simultaneous power transfer to multiple single-coil receivers (RXs) by constructively combining their induced magnetic fields at the RXs, a technique termed "magnetic beamforming". In this paper, we study the optimal magnetic beamforming design in a multi-user MIMO MRC-WPT system. We introduce the multi-user power region that constitutes all the achievable power tuples for all RXs, subject to the given total power constraint over all TXs as well as their individual peak voltage and current constraints. We characterize each boundary point of the power region by maximizing the sum-power deliverable to all RXs subject to their minimum harvested power constraints. For the special case without the TX peak voltage and current constraints, we derive the optimal TX current allocation for the single-RX setup in closed-form as well as that for the multi-RX setup. In general, the problem is a non-convex quadratically constrained quadratic programming (QCQP), which is difficult to solve. For the case of one single RX, we show that the semidefinite relaxation (SDR) of the problem is tight. For the general case with multiple RXs, based on SDR we obtain two approximate solutions by applying time-sharing and randomization, respectively. Moreover, for practical implementation of magnetic beamforming, we propose a novel signal processing method to estimate the magnetic MIMO channel due to the mutual inductances between TXs and RXs. Numerical results show that our proposed magnetic channel estimation and adaptive beamforming schemes are practically effective, and can significantly improve the power transfer efficiency and multi-user performance trade-off in MIMO MRC-WPT systems.

cs.IT↗
arXiv2017

Two-Loop SL(2) Form Factors and Maximal Transcendentality

Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand's numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.

hep-th↗
arXiv2016

Compensatory interactions to stabilize multiple steady states or mitigate the effects of multiple deregulations in biological networks

Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those corresponding to disease. Previous work designed compensatory interactions to stabilize an attractor of a Boolean network after single node damage. We generalize this method to a multinode damage scenario and to the simultaneous stabilization of multiple steady state attractors. We classify the emergent situations, with a special focus on combinatorial effects, and characterize each class through simulation. We explore how the structural and functional properties of the network affect its resilience and its possible repair scenarios. We demonstrate the method's applicability to two intracellular network models relevant to cancer. This work has implications in designing prevention strategies for complex disease.

physics.bio-ph↗
arXiv2016

Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory

Using color-kinematics duality, we construct for the first time the full integrand of the five-loop Sudakov form factor in N=4 super-Yang-Mills theory, including non-planar contributions. This result also provides a first manifestation of the color-kinematics duality at five loops. The integrand is explicitly ultraviolet finite when D<26/5, coincident with the known finiteness bound for amplitudes. If the double-copy method could be applied to the form factor, this would indicate an interesting ultraviolet finiteness bound for N=8 supergravity at five loops. The result is also expected to provide an essential input for computing the five-loop non-planar cusp anomalous dimension.

hep-th↗
arXiv2016

On a four-loop form factor in N=4

We report on progress toward computing a four-loop supersymmetric form factor in maximally supersymmetric Yang-Mills theory. A representative example particle content from the involved supermultiplets is a stress-tensor operator with two on-shell gluons. In previous work, the integrand for this form factor was obtained using color-kinematic duality in a particularly simple form. Here the result of applying integration-by-parts identities is discussed and cross-checks of the result is performed. Rational IBP relations and their reduction are introduced as a potentially useful aide.

hep-th↗
arXiv2016

Heavy Dirac fermions in a graphene/topological insulator hetero-junction

The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {\it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can reduce the Fermi velocity of Dirac fermions. Due to the negligible linear term, interaction effects will be greatly enhanced and can drive "heavy" Dirac fermion states into the half quantum Hall state with non-zero Hall conductance.

cond-mat.mes-hall↗
arXiv2016

Towards a four-loop form factor

The four-loop, two-point form factor contains the first non-planar correction to the lightlike cusp anomalous dimension. This anomalous dimension is a universal function which appears in many applications. Its planar part in N = 4 SYM is known, in principle, exactly from AdS/CFT and integrability while its non-planar part has been conjectured to vanish. The integrand of the form factor of the stress-tensor multiplet in N = 4 SYM including the non-planar part was obtained in previous work. We parametrise the difficulty of integrating this integrand. We have obtained a basis of master integrals for all integrals in the four-loop, two-point class in two ways. First, we computed an IBP reduction of the integrand of the N = 4 form factor using massive computer algebra (Reduze). Second, we computed a list of master integrals based on methods of the Mint package, suitably extended using Macaulay2 / Singular. The master integrals obtained in both ways are consistent with some minor exceptions. The second method indicates that the master integrals apply beyond N = 4 SYM, in particular to QCD. The numerical integration of several of the master integrals will be reported and remaining obstacles will be outlined

hep-th↗
arXiv2015

Master integrals for the four-loop Sudakov form factor

The light-like cusp anomalous dimension is a universal function in the analysis of infrared divergences. In maximally ($\mathcal{N}=4$) supersymmetric Yang-Mills theory (SYM) in the planar limit, it is known, in principle, to all loop orders. The non-planar corrections are not known in any theory, with the first appearing at the four-loop order. The simplest quantity which contains this correction is the four-loop two-point form factor of the stress tensor multiplet. This form factor was largely obtained in integrand form in a previous work for $\mathcal{N}=4$ SYM, up to a free parameter. In this work, a reduction of the appearing integrals obtained by solving integration-by-parts (IBP) identities using a modified version of Reduze is reported. The form factor is shown to be independent of the remaining parameter at integrand level due to an intricate pattern of cancellations after IBP reduction. Moreover, two of the integral topologies vanish after reduction. The appearing master integrals are cross-checked using independent algebraic-geometry techniques explored in the Mint package. The latter results provide the basis of master integrals applicable to generic form factors, including those in Quantum Chromodynamics. Discrepancies between explicitly solving the IBP relations and the MINT approach are highlighted. Remaining bottlenecks to completing the computation of the four-loop non-planar cusp anomalous dimension in $\mathcal{N}=4$ SYM and beyond are identified.

hep-th↗
arXiv2015

The structure of pentaquarks $P_c^+$ in the chiral quark model

The recent experimental results of LHCb collaboration suggested the existence of pentaquark states with charmonium. To understand the structure of the states, a dynamical calculation of 5-quark systems with quantum numbers $IJ^P=\frac{1}{2}(\frac{1}{2})^\pm$, $\frac{1}{2}(\frac{3}{2})^\pm$ and $\frac{1}{2}(\frac{5}{2})^\pm$ is performed in the framework of chiral quark model with the help of gaussian expansion method. The results show that the negative parity states can be bound states while all of the positive parity states are the scattering states. The $P_c(4380)$ state is suggested to be the bound state of $Σ^*_cD$. Although the energy of $Σ_cD^*$ is very close to the mass of $P_c(4450)$, the inconsistent parity prevents the assignment. The calculated distances between quarks confirm the molecular nature of the states. Other five-quark bound states of the combination of $Σ_cD$ and $Σ^*_cD^*$ are also found in the region about 4.3GeV and 4.5GeV.

hep-ph↗
arXiv2015

A Coherent Integration Method Based on Radon Non-uniform FRFT for Random Pulse Repetition Interval (RPRI) Radar

To solve the range cell migration (RCM) and spectrum spread during the integration time induced by the motion of a target, this paper proposes a new coherent integration method based on Radon non-uniform FRFT (NUFRFT) for random pulse repetition interval (RPRI) radar. In this method, RCM is eliminated via searching in the motion parameters space and the spectrum spread is resolved by using NUFRFT. Comparisons with other popular methods, moving target detection (MTD), Radon-Fourier transform (RFT), and Radon-Fractional Fourier Transform (RFRFT) are performed. The simulation results demonstrate that the proposed method can detect the moving target even in low SNR scenario and is superior to the other two methods.

stat.ME↗
arXiv2015

On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders

We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV divergence of this result, we obtain the two-loop dilatation operator in this sector. Furthermore, we calculate the corresponding finite remainder functions. Since the operators break the supersymmetry, the remainder functions do not have the property of uniform transcendentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expressions. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.

hep-th↗
arXiv2015

Magnetic Beamforming for Wireless Power Transfer

Magnetic resonant coupling (MRC) is an efficient method for realizing the near-field wireless power transfer (WPT). The use of multiple transmitters (TXs) each with one coil can be applied to enhance the WPT performance by focusing the magnetic fields from all TX coils in a beam toward the receiver (RX) coil, termed as "magnetic beamforming". In this paper, we study the optimal magnetic beamforming for an MRC-WPT system with multiple TXs and a single RX. We formulate an optimization problem to jointly design the currents flowing through different TXs so as to minimize the total power drawn from their voltage sources, subject to the minimum power required by the RX load as well as the TXs' constraints on the peak voltage and current. For the special case of identical TX resistances and neglecting all TXs' constraints on the peak voltage and current, we show that the optimal current magnitude of each TX is proportional to the mutual inductance between its TX coil and the RX coil. In general, the problem is a non-convex quadratically constrained quadratic programming (QCQP) problem, which is reformulated as a semidefinite programming (SDP) problem. We show that its semidefinite relaxation (SDR) is tight. Numerical results show that magnetic beamforming significantly enhances the deliverable power as well as the WPT efficiency over the uncoordinated benchmark scheme of equal current allocation.

cs.IT↗
arXiv2015

Crystal growth and detector performance of large size high-purity Ge crystals

High-purity germanium crystals approximately 12 cm in diameter were grown in a hydrogen atmosphere using the Czochralski method. The dislocation density of the crystals was determined to be in the range of 2000 - 4200 cm-2, which meets a requirement for use as a radiation detector. The axial and radial distributions of impurities in the crystals were measured and are discussed. A planar detector was also fabricated from one of the crystals and then evaluated for electrical and spectral performance. Measurements of gamma-ray spectra from Cs-137 and Am-241 sources demonstrate that the detector has excellent energy resolution.

physics.ins-det↗
arXiv2015

Multi-Antenna Wireless Energy Transfer for Backscatter Communication Systems

We study RF-enabled wireless energy transfer (WET) via energy beamforming, from a multi-antenna energy transmitter (ET) to multiple energy receivers (ERs) in a backscatter communication system, such as RFID, where each ER (or RFID tag) reflects back a portion of the incident signal to the ET (or RFID reader). For such a system, the acquisition of the forward-channel (i.e., ET-to-ER) state information (F-CSI) at the ET is challenging, since the ERs are typically too energy-and-hardware-constrained to estimate or feed back the F-CSI. The ET leverages its observed backscatter signals to estimate the backscatter-channel (i.e., ET-to-ER-to-ET) state information (BS-CSI) directly. We first analyze the harvested energy obtained by using the estimated BS-CSI. Furthermore, we optimize the channel-training energy and the energy allocation weights for different energy beams, for weighted-sum-energy (WSE) maximization and proportional-fair-energy (PFE) maximization. For WET to single ER, we obtain the optimal channel-training energy in a semi-closed form. For WET to multiple ERs, the optimal WET scheme for WSE maximization is shown to use only one energy beam. For PFE maximization, we show it is a biconvex problem, and propose a block-coordinate-descent based algorithm to find the close-to-optimal solution. Numerical results show that with the optimized solutions, the harvested energy suffers slight reduction of less than 10%, compared to that obtained by using the perfect F-CSI. Hence, energy beamforming by using the estimated BS-CSI is promising, as the complexity and energy requirement is shifted from the ERs to the ET.

cs.IT↗
arXiv2015

Throughput Optimization for Massive MIMO Systems Powered by Wireless Energy Transfer

This paper studies a wireless-energy-transfer (WET) enabled massive multiple-input-multiple-output (MIMO) system (MM) consisting of a hybrid data-and-energy access point (H-AP) and multiple single-antenna users. In the WET-MM system, the H-AP is equipped with a large number $M$ of antennas and functions like a conventional AP in receiving data from users, but additionally supplies wireless power to the users. We consider frame-based transmissions. Each frame is divided into three phases: the uplink channel estimation (CE) phase, the downlink WET phase, as well as the uplink wireless information transmission (WIT) phase. Firstly, users use a fraction of the previously harvested energy to send pilots, while the H-AP estimates the uplink channels and obtains the downlink channels by exploiting channel reciprocity. Next, the H-AP utilizes the channel estimates just obtained to transfer wireless energy to all users in the downlink via energy beamforming. Finally, the users use a portion of the harvested energy to send data to the H-AP simultaneously in the uplink (reserving some harvested energy for sending pilots in the next frame). To optimize the throughput and ensure rate fairness, we consider the problem of maximizing the minimum rate among all users. In the large-$M$ regime, we obtain the asymptotically optimal solutions and some interesting insights for the optimal design of WET-MM system. We define a metric, namely, the massive MIMO degree-of-rate-gain (MM-DoRG), as the asymptotic UL rate normalized by $\log(M)$. We show that the proposed WET-MM system is optimal in terms of MM-DoRG, i.e., it achieves the same MM-DoRG as the case with ideal CE.

cs.IT↗
arXiv2014

On Cotorsion pairs of chain complexes

In the paper we first construct a new cotorsion pair, in the category of chain complexes, from two given cotorsion pairs in the category of modules, and then we consider completeness of such pairs under certain conditions.

math.RA↗