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Active polymers possess numerous unique properties that are quite different from those observed in the system of small active molecule due to the intricate interplay between their activity and topological constraints. This study focuses on the conformational changes induced by activity, impacting effective stiffness and crucially influencing entanglement and dynamics. When the two terminals of a linear chain undergo active modification through coupling to a high-temperature thermal bath, there is a substantial increase in chain size, indicating a notable enhancement in effective stiffness. Unlike in passive semiflexible chains where stiffness predominantly affects local bond angles, activity-induced stiffness manifests at the scale of tens of monomers. While activity raises the ambient temperature, it significantly decreases diffusion by over an order of magnitude. The slowdown of dynamics observed can be attributed to increased entanglement due to chain elongation., Comment: 10 pages, 5 figures

Polymer chains immersed in different solvent molecules exhibit diverse properties due to multiple spatiotemporal scales and complex interactions. Using molecular dynamics simulations, we study the conformational and static properties of tagged chains in different solvent molecules. Two types of solvent molecules were examined: one type consisted of chain molecules connected by bonds, while the other type consisted of individual bead molecules without any bonds. The only difference between the two solvent molecules lay in the chain connectivity. Our results show a compression of the tagged chains with the addition of bead or chain molecules. Chain molecule confinement induces a stronger compression compared to bead molecule confinement. In chain solvent molecules, the tagged chain's radius of gyration reached a minimum at a monomer volume fraction of $\sim0.3$. Notably, the probability distributions of chain size remain unchanged at different solvent densities, irrespective of whether the solvent consists of beads or polymers. Furthermore, as solvent density increases, a crossover from a unimodal to a bimodal distribution of bond angles is observed, indicating the presence of both compressed and expanded regions within the chain. The effective monomer-solvent interaction is obtained by calculating the partial radial distribution function and the potential of the mean force. In chain solvent, the correlation hole effect results in a reduced number of nearest neighbors around tagged monomers compared to bead solvents. The calculation of pore size distribution reveals that the solvent nonhomogeneity induced by chain connectivity leads to a broader distribution of pore sizes and larger pore dimensions at low volume fractions. These findings provide a deeper understanding of the conformational behavior of polymer chains in different solvent environments., Comment: 10 pages, 8 figures

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.

M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and $\ell_p$-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.

The identification of deuteron with momentum in range of $0.52$-$0.72$ GeV/$c$ has been studied with the specific ionization energy loss information, using the data sample collected by the BESIII detector at center-of-mass energies between $4.009$ and $4.946$ GeV. Clean deuteron samples are selected using time of flight information. For all data samples, the deuteron identification efficiencies are higher than $95\%$, with a maximum difference of $(4.93\pm0.95)\%$ between data and MC simulation. These verify the effectiveness of the deuteron identification method based on the specific ionization energy loss, and provide valuable information for the future studies of the processes involving deuteron in the final state at BESIII.

Let $\mu_{M,D}$ be the planar self-affine measure generated by an expansive integer matrix $M\in M_2(\mathbb{Z})$ and a non-collinear integer digit set $D=\left\{\begin{pmatrix} 0\\0\end{pmatrix},\begin{pmatrix} \alpha_{1}\\ \alpha_{2} \end{pmatrix}, \begin{pmatrix} \beta_{1}\\ \beta_{2} \end{pmatrix}, \begin{pmatrix} -\alpha_{1}-\beta_{1}\\ -\alpha_{2}-\beta_{2} \end{pmatrix}\right\}$. In this paper, we show that $\mu_{M,D}$ is a spectral measure if and only if there exists a matrix $Q\in M_2(\mathbb{R})$ such that $(\tilde{M},\tilde{D})$ is admissible, where $\tilde{M}=QMQ^{-1}$ and $\tilde{D}=QD$. In particular, when $\alpha_1\beta_2-\alpha_2\beta_1\notin 2\Bbb Z$, $\mu_{M,D}$ is a spectral measure if and only if $M\in M_2(2\mathbb{Z})$.

For an expanding integer matrix $M\in M_2(\mathbb{Z})$ and an integer digit set $D=\{(0,0)^t,(\alpha_1,\alpha_2)^t,(\beta_1,\beta_2)^t\}$ with $\alpha_1\beta_2-\alpha_2\beta_1\neq0$, let $\mu_{M,D}$ be the Sierpinski-type self-affine measure defined by $\mu_{M,D}(\cdot)=\frac{1}{3}\sum_{d\in D}\mu_{M,D}(M(\cdot)-d)$. In [5.36], the authors separately investigated the spectral property of the measure $\mu_{M,D}$ in the case of $\det(M)\notin 3\mathbb{Z}$ or $\alpha_1\beta_2-\alpha_2\beta_1\notin 3\mathbb{Z}$. In this paper, we consider the remaining case where $\det(M)\in 3\mathbb{Z}$ and $\alpha_1\beta_2-\alpha_2\beta_1\in 3\mathbb{Z}$, and give the necessary and sufficient conditions for $\mu_{M,D}$ to be a spectral measure. This completely settles the spectrality of the Sierpinski-type self-affine measure $\mu_{M,D}$.

Let $\mu_{M,D}$ be the self-affine measure generated by an expanding integer matrix $M\in M_n(\mathbb{Z})$ and a finite digit set $D\subset\mathbb{Z}^n$. It is well known that the two measures $\mu_{M,D}$ and $\mu_{\tilde{M},\tilde{D}}$ have the same spectrality if $\tilde{M}=B^{-1}MB$ and $\tilde{D}=B^{-1}D$, where $B\in M_n(\mathbb{R})$ is a nonsingular matrix. This fact is usually used to simplify the digit set $D$ or the expanding matrix $M$. However, it often transforms integer digit set $D$ or expanding matrix $M$ into real, which brings many difficulties to study the spectrality of $\mu_{\tilde{M},\tilde{D}}$. In this paper, we introduce a similarity transformation of general linear group $GL_n(p)$ for some self-affine measures, and discuss their spectrality. This kind of similarity transformation can keep the integer properties of $D$ and $M$ simultaneously, which leads to many advantages in discussing the spectrality of self-affine measures. As an application, we extend some well-known spectral self-affine measures to more general forms.

All the previous studies on photonic tunneling are just based on a simple and directly analogy with a one-dimensional quantum-mechanical tunneling, without taking into account the horizontal structure of electromagnetic waves along the waveguide, such that they are oversimplified and incomplete. Here we present a more serious deliberation on photonic tunneling through cut-off waveguides, and obtain a strictly theoretical model with some new results., Comment: 22 pages, no figure

We investigate the valence transition in three-dimensional topological Kondo insulator through slave-boson analysis of periodic Anderson model. By including the effect of intra-atomic Coulomb correlation $U_{fc}$ between conduction and local electrons, we find a first-order valence transition from Kondo region to mixed valence upon ascending of local level above a critical $U_{fc}$, and this valence transition usually occurs very close to or simultaneously with a topological transition. Near the parameter region of zero-temperature valence transition, rise of temperature can generate a thermal valence transition from mixed valence to Kondo region, accompanied by a first-order topological transition. Remarkably, above a critical $U_{fc}$ which is considerable smaller than that generating paramagnetic valence transition, the original continuous antiferromagnetic transition is shifted to first order one, at which a discontinuous valence shift takes place. Upon increased $U_{fc}$, the paramagnetic valence transition approaches then converges with the first-order antiferromagnetic transition, leaving an significant valence shift on the magnetic boundary. The continuous antiferromagnetic transition, first-order antiferromagnetic transition, paramagnetic valence transition and topological transitions are all summarized in a global phase diagram. Our proposed exotic transition processes can help to understand the thermal valence variation as well as the valence shift around the pressure-induced magnetic transition in topological Kondo insulator candidates and in other heavy-fermion systems., Comment: 9 pages, 7 figures

By using an extended slave-boson method, we draw a global phase diagram summarizing both magnetic phases and paramagnetic (PM) topological insulating phases (TI$_s$) in three-dimensional topological Kondo insulator (TKI). By including electron hopping (EH) up to third neighbor, we identify four strong topological insulating (STI) phases and two weak topological insulating (WTI) phases, then the PM phase diagrams characterizing topological transitions between these TI$_s$ are depicted as functions of EH, $f$-electron energy level and hybridization constant. We also find an insulator-metal transition from a STI phase which has surface Fermi rings and spin textures in qualitative agreement to TKI candidate SmB$_6$. In weak hybridization regime, antiferromagnetic (AF) order naturally arises in the phase diagrams, and depending on how the magnetic boundary crosses the PM topological transition lines, AF phases are classified into AF topological insulator (AFTI) and non-topological AF insulator (nAFI), according to their $\mathcal{Z}_2$ indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTI, showing distinguishable surface dispersions around their Dirac points., Comment: 4 pages, 5 figures

The (1, 0)+(0, 1) representation of the group SL(2, C) provides a six-component spinor equivalent to the electromagnetic field tensor. By means of the (1, 0)+(0, 1) description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin-orbit coupling of photons. Once the gravitational spin-orbit coupling is taken into account, the traditional radius of the circular photon orbit in the Schwarzschild geometry should be replaced with two different radiuses corresponding to the photons with the helicities of +1 and -1, respectively. Owing to the splitting of energy levels induced by the spin-orbit coupling, photons (from Hawking radiations, say) escaping from a Schwarzschild black hole are partially polarized, provided that their initial velocities possess nonzero tangential components., Comment: 23 pages, no figure. arXiv admin note: substantial text overlap with arXiv:1508.02321

Guided waves and surface waves can be taken as two typical examples of structured optical fields with the transverse spin. Analytical derivations are developed to demonstrate that (i) guided waves also carry the transverse spin that depends on the mean direction of propagation, which may have important applications in spin-dependent unidirectional optical interfaces; (ii) the quantization form of the transverse spin is for the first time revealed, which is not obvious and related to an ellipticity; (iii) from a unified point of view, the transverse spin can be attributed to the presence of an effective rest mass of structured optical fields; (iv) the transverse spin can also be described by the spin matrix of the photon field; (v) unlike a free optical field whose spin projection on the propagation direction is the only observable, owing to the effective rest mass, the spin projection of structured optical fields on other directions is also an observable, such that one can develop an optical analogy of spintronics. A preliminary idea about the potential applications of the transverse spin is presented, but an in-depth and complete study will be presented in our next work., Comment: 30 pages, 7 figure

Because spatio-temporal tensors are associated with the Lorentz group, whereas spinors are associated with its covering group SL(2, C), one can associate with every tensor a spinor (but not vice versa). In particular, the (1,0)+(0,1) representation of SL(2, C) can provide a six-component spinor equivalent to the electromagnetic field tensor. The chief aim of this work is to develop the (1,0)+(0,1) description for the electromagnetic field in the absence of sources, rigorously and systematically, which should be useful if we are to deal with those issues involving with single-photon states and the angular momentum of light, etc. Based on our formalism, the quantum theory and some symmetries of the photon field can be discussed in a new manner, and the spin-orbit interaction of photons can be described in a form that is closely analogous to that of the Dirac electron. Moreover, in terms of the (1,0)+(0,1) description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin-orbit coupling of photons., Comment: 60 pages, no figure. It will provide a comprehensive reference for some of our future works

In this paper, we present a new experimental progress in brief on the recent observation of the charged charmonium-like state Z_c(4020)^{+/-} states and its iso-spin partner Z_c(4020)^{0} in pi pi hc process at the BESIII experiment. The charged Z_{c}(4020) is its decay into \pi^{+/-} hc final state, and carries electric charge, thus it contains at least four quarks. The observation of both charge and neutral state makes Z_{c}(4020) the first iso-spin triplet Z_{c} state observed in experiment., Comment: 5 pages, 7 figures

In Schwarzschild spacetime, the gravitational spin-orbit couplings of the massless Dirac field and the photon field can be studied in a unified way. In contrary to the previous investigations presented mainly at the quantum-mechanical level, our work is presented at the level of quantum field theory without resorting to the Foldy-Wouthuysen transformation. If massless Dirac particles and photons have the same momentums, their energy-level splittings due to the gravitational spin-orbit couplings are the same. Massless Dirac particles and photons coming from the Hawking radiations are partially polarized as long as their original momentums are not parallel to the radial direction of a Schwarzschild black hole., Comment: 13 pages, no figure