arXiv subjects

Cong Chen

Publications and source records attributed to Cong Chen.

121 records · Page 7Linked to original sources

arXiv2018

Matrix Product Operator Restricted Boltzmann Machines

A restricted Boltzmann machine (RBM) learns a probability distribution over its input samples and has numerous uses like dimensionality reduction, classification and generative modeling. Conventional RBMs accept vectorized data that dismisses potentially important structural information in the original tensor (multi-way) input. Matrix-variate and tensor-variate RBMs, named MvRBM and TvRBM, have been proposed but are all restrictive by model construction, which leads to a weak model expression power. This work presents the matrix product operator RBM (MPORBM) that utilizes a tensor network generalization of Mv/TvRBM, preserves input formats in both the visible and hidden layers, and results in higher expressive power. A novel training algorithm integrating contrastive divergence and an alternating optimization procedure is also developed. Numerical experiments compare the MPORBM with the traditional RBM and MvRBM for data classification and image completion and denoising tasks. The expressive power of the MPORBM as a function of the MPO-rank is also investigated.

cs.CV↗

arXiv2018

Deep Compression of Sum-Product Networks on Tensor Networks

Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor networks, thus leading to a highly efficient representation that we call tensor SPNs (tSPNs). For the first time, through mapping an SPN onto a tSPN and employing novel optimization techniques, we demonstrate remarkable parameter compression with negligible loss in accuracy.

cs.LG↗

arXiv2018

Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies

By correlating time- and angle-resolved photoemission and time-resolved transverse- magneto- optical Kerr effect measurements, both at extreme ultraviolet wavelengths, we uncover the universal nature of the ultrafast photoinduced magnetic phase transition in Ni. This allows us to explain the ultrafast magnetic response of Ni at all laser fluences - from a small reduction of the magnetization at low laser fluences, to complete quenching at high laser fluences. Both probe methods exhibit the same demagnetization and recovery timescales. We further show that the ultrafast demagnetization in Ni is indeed a magnetic phase transition that is launched within 20 fs, followed by demagnetization of the material within ~200 fs, and subsequent recovery of the magnetization on timescales ranging from 500 fs to >70 ps. We also provide evidence of two competing channels with two distinct timescales in the recovery process, that suggest the presence of coexisting phases in the material.

cond-mat.mtrl-sci↗

arXiv2018

Quantification of the underlying mechanisms and relationship among cancer, metastasis and differentiation/development

Recurrence and metastasis have been regarded as two of the greatest obstacles for curing cancer. Cancer stem cell (CSC) have been found. They contribute to cancer development with the distinct feature of recurrence and resistance to the popular treatments such as drugs and chemotherapy. In addition, recent discoveries suggest that the epithelial mesenchymal transition (EMT) is an essential process in normal embryogenesis and tissue repair, which is a required step in cancer metastasis. Although there are many indications showing the connections between metastasis and stem cell, researches often studied them separately or at most bi-laterally, not in an integrated way. In this study, we aim at exploring the global mechanisms and interrelationship among cancer, development and metastasis which are currently poorly understood. To start, we constructed a core gene regulatory network motif which contain specific genes and microRNAs of CSC, EMT and cancer. We uncovered seven distinct states emerged from the underlying landscape. They are identified as Normal, Premalignant, Cancer, stem cell (SC), cancer stem cell (CSC), Lesion and Hyperlasia state. Given the biological definition of each state, we also discussed the metastasis ability of each state. We show how and which types of cells can be transformed to a cancer state and the connections among cancer, CSC and EMT. The barrier height and flux of the kinetic paths are explored to quantify how and which cells switch stochastically between the states. Our landscape model provides a quantitative way which reveals the global mechanisms of cancer, development and metastasis.

q-bio.CB↗

arXiv2018

A Support Tensor Train Machine

There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilizes a rank-one tensor to capture the data structure, thereby alleviating the overfitting and curse of dimensionality problems in the conventional support vector machine (SVM). However, the expressive power of a rank-one tensor is restrictive for many real-world data. To overcome this limitation, we introduce a support tensor train machine (STTM) by replacing the rank-one tensor in an STM with a tensor train. Experiments validate and confirm the superiority of an STTM over the SVM and STM.

cs.LG↗

arXiv2017

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossing points with linear dispersion, around which the quasiparticles resemble the relativistic Dirac Fermions. It can be described by a 4 * 4 massless Dirac Hamiltonian which can be decomposed into a pair of Weyl points or gaped into an insulator. Thus, crystal symmetry is critical to guarantee the stable existence. On the contrary, by breaking crystal symmetry, a DSM may transform into a Weyl semimetal (WSM) or a topological insulator (TI). Here, by taking hexagonal LiAuSe as an example, we find that it is a starfruit shaped multiple nodal chain semimetal in the absence of spin-orbit coupling(SOC). In the presence of SOC, it is an ideal DSM naturally with the Dirac points locating at Fermi level exactly, and it would transform into WSM phase by introducing external Zeeman field or by magnetic doping with rare-earth atom Sm. It could also transform into TI state by breaking rotational symmetry. Our studies show that DSM is a critical point for topological phase transition, and the conclusion can apply to most of the DSM materials, not limited to the hexagonal material LiAuSe.

cond-mat.mtrl-sci↗

arXiv2017

Selfish Jobs with Favorite Machines: Price of Anarchy vs Strong Price of Anarchy

We consider the well-studied game-theoretic version of machine scheduling in which jobs correspond to self-interested users and machines correspond to resources. Here each user chooses a machine trying to minimize her own cost, and such selfish behavior typically results in some equilibrium which is not globally optimal: An equilibrium is an allocation where no user can reduce her own cost by moving to another machine, which in general need not minimize the makespan, i.e., the maximum load over the machines. We provide tight bounds on two well-studied notions in algorithmic game theory, namely, the price of anarchy and the strong price of anarchy on machine scheduling setting which lies in between the related and the unrelated machine case. Both notions study the social cost (makespan) of the worst equilibrium compared to the optimum, with the strong price of anarchy restricting to a stronger form of equilibria. Our results extend a prior study comparing the price of anarchy to the strong price of anarchy for two related machines (Epstein, Acta Informatica 2010), thus providing further insights on the relation between these concepts. Our exact bounds give a qualitative and quantitative comparison between the two models. The bounds also show that the setting is indeed easier than the two unrelated machines: In the latter, the strong price of anarchy is $2$, while in ours it is strictly smaller.

cs.GT↗

arXiv2017

Graphdiyne Nanoribbons with Open Hexagonal Rings: Existence of Topological Unprotected Edge States

Using first principles calculations, we studied a new class of graphdiyne nanoribbons (GDYNR) with open hexagonal rings on the edges.To avoid the effects from dangling bond, hydrogen or oxygen atoms were absorbed on the edges. There are two kinds of GDYNR depending on the edge structures, armchair and zigzag. The electronic structures show that all of them are semiconductors. The band gap can be tuned by the width of GDYNR. As the width of nanoribbons increases, the energy gap decreases firstly and then increases, and reaches a minimum gap for both kinds. To understand the intriguing phenomenon, we constructed a tight-binding model for GDYNR and found that the existence of the minimum of the energy gap is due to the competition between the interaction within the two edges and the coupling in between. Furthermore, topological unprotected edge states are found in the band structure of a semi-infinite system by calculating surface Green's function. If GDYNR could be synthesized in experiments, it would be useful for the nanodevices in the future.

cond-mat.mtrl-sci↗

arXiv2017

The nilpotent variety of $W(1;n)_{p}$ is irreducible

In the late 1980s, Premet conjectured that the nilpotent variety of any finite dimensional restricted Lie algebra over an algebraically closed field of characteristic $p>0$ is irreducible. This conjecture remains open, but it is known to hold for a large class of simple restricted Lie algebras, e.g. for Lie algebras of connected reductive algebraic groups, and for Cartan series $W, S$ and $H$. In this paper, with the assumption that $p>3$, we confirm this conjecture for the minimal $p$-envelope $W(1;n)_p$ of the Zassenhaus algebra $W(1;n)$ for all $n\geq 2$.

math.RA↗

arXiv2017

Hybrid Dirac Semimetal in CaAgBi Materials Family

Based on their formation mechanisms, Dirac points in three-dimensional systems can be classified as accidental or essential. The former can be further distinguished into type-I and type-II, depending on whether the Dirac cone spectrum is completely tipped over along certain direction. Here, we predict the coexistence of all three kinds of Dirac points in the low-energy band structure of CaAgBi-family materials with a stuffed Wurtzite structure. Two pairs of accidental Dirac points reside on the rotational axis, with one pair being type-I and the other pair type-II; while another essential Dirac point is pinned at the high symmetry point on the Brillouin zone boundary. Due to broken inversion symmetry, the band degeneracy around accidental Dirac points is completely lifted except along the rotational axis, which may enable the splitting of chiral carriers at a ballistic p-n junction with a double negative refraction effect. We clarify their symmetry protections, and find both the Dirac-cone and Fermi arc topological surface states.

cond-mat.mtrl-sci↗

arXiv2016

Criticality-Enhanced Magnetocaloric Effect in Quantum Spin Chain Material Copper Nitrate

Low-dimensional quantum magnets, due to the existence of abundant exotic quantum phases therein and experimental feasibilities in laboratories, continues intriguing people in condensed matter physics. In this work, a comprehensive study of Cu(NO$_3$)$_2$ $\cdot$ 2.5H$_2$O (copper nitrate hemipentahydrate, CN), a spin chain material, is performed with multi-technique approach including thermal tensor network (TTN) simulations, first-principles calculations, as well as magnetization measurements in experiments. Employing a cutting-edge TTN method developed in the present work, we determine the couplings $J=5.13$ K, $α=0.23(1)$ and Landé factors $g_{\parallel}=2.31$, $g_{\perp}=2.14$ in an alternating Heisenberg antiferromagnetic chain model, with which one can fit strikingly well the magnetothermodynamic properties. Part of the fitted experimental data are measured on the single-crystal CN specimens synthesized by us. Based on first-principles calculations, we reveal explicitly the spin chain scenario in CN by displaying the calculated electron density distributions, from which the distinct superexchange paths are visualized. On top of that, we investigated the magnetocaloric effect (MCE) in CN by calculating its isentropes and magnetic Grüeisen parameter (GP). Prominent quantum-criticality-enhanced MCE was uncovered, the TTN simulations are in good agreements with measured isentropic lines in the sub-Kelvin region. We propose that CN is potentially a very promising quantum critical coolant, due to the remarkably enhanced MCE near both critical fields of moderate strengths as 2.87 and 4.08 T, respectively.

cond-mat.str-el↗

arXiv2014

Controlling the electronic structure of graphene using surface-adsorbate interactions

We show that strong coupling between graphene and the substrate is mitigated when 0.8 monolayer of Na is adsorbed and consolidated on top graphene-on-Ni(111). Specifically, the π state is partially restored near the K-point and the energy gap between the π and π* states reduced to 1.3 eV after adsorption, as measured by angle-resolved photoemission spectroscopy. We show that this change is not caused by intercalation of Na to underneath graphene but it is caused by an electronic coupling between Na on top and graphene. We show further that graphene can be decoupled to a much higher extent when Na is intercalated to underneath graphene. After intercalation, the energy gap between the π and π* states is reduced to 0 eV and these states are identical as in freestanding and n-doped graphene. We conclude thus that two mechanisms of decoupling exist: a strong decoupling through intercalation, which is the same as one found using noble metals, and a weak decoupling caused by electronic interaction with the adsorbate on top.

cond-mat.mtrl-sci↗

arXiv2012

Model theoretic connected components of finitely generated nilpotent groups

We prove that for a finitely generated infinite nilpotent group G with a first order structure (G,*,...), the connected component G*0 of a sufficiently saturated extension G* of G exists and equals $\bigcap_{n\in\N} {g^n : g\in G^*}$. We construct a first order expansion of Z by a predicate (Z,+,P) such that the type-connected component Z*00_{\emptyset} is strictly smaller than Z*0. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for the van der Waerden theorem.

math.LO↗