arXiv subjects

Jianjun Zhang

Publications and source records attributed to Jianjun Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Deep learning based infrared small object segmentation: Challenges and future directions

Infrared sensing is a core method for supporting unmanned systems, such as autonomous vehicles and drones. Recently, infrared sensors have been widely deployed on mobile and stationary platforms for detection and classification of objects from long distances and in wide field of views. Given its success in the vision image analysis domain, deep learning has also been applied for object recognition in infrared images. However, techniques that have proven successful in visible light perception face new challenges in the infrared domain. These challenges include extremely low signal-to-noise ratios in infrared images, very small and blurred objects of interest, and limited availability of labeled/unlabeled training data due to the specialized nature of infrared sensors. Numerous methods have been proposed in the literature for the detection and classification of small objects in infrared images achieving varied levels of success. There is a need for a survey paper that critically analyzes existing techniques in this domain, identifies unsolved challenges and provides future research directions. This paper fills the gap and offers a concise and insightful review of deep learning-based methods. It also identifies the challenges faced by existing infrared object segmentation methods and provides a structured review of existing infrared perception methods from the perspective of these challenges and highlights the motivations behind the various approaches. Finally, this review suggests promising future directions based on recent advancements within this domain.

cs.CV↗

arXiv2025

A Mathematics Framework of Artificial Shifted Population Risk and Its Further Understanding Related to Consistency Regularization

Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency regularization term, there is a lack of research on the relationship between them. To address this gap, this paper introduces a more comprehensive mathematical framework for data augmentation. Through this framework, we establish that the expected risk of the shifted population is the sum of the original population risk and a gap term, which can be interpreted as a consistency regularization term. The paper also provides a theoretical understanding of this gap, highlighting its negative effects on the early stages of training. We also propose a method to mitigate these effects. To validate our approach, we conducted experiments using same data augmentation techniques and computing resources under several scenarios, including standard training, out-of-distribution, and imbalanced classification. The results demonstrate that our methods surpass compared methods under all scenarios in terms of generalization ability and convergence stability. We provide our code implementation at the following link: https://github.com/ydlsfhll/ASPR.

cs.LG↗

arXiv2025

Broadband bright biphotons from periodically poled triple-resonance metasurface

Biphotons from spontaneous parametric down conversion with broad bandwidth are highly wanted in many quantum technologies. However, achieving broad bandwidth in both frequency and momentum while keeping a high rate remains a challenge for both conventional nonlinear crystals and recently emerging nonlinear metasurfaces. Here, we address this challenge by introducing a periodically poled triple-resonance metasurface (PPTM) incorporating a nano-grating atop a periodically poled LiNbO$_3$ thin film. PPTM supports high-Q guided mode resonances at pump, signal, and idler wavelengths meanwhile enabling quasi-phase matching between three guided modes in a broad frequency/momentum range. The predicted biphoton rate is over 100 MHz/mW with a frequency bandwidth of 165 nm around 1550 nm and a momentum bandwidth of $13^\circ \times 6^\circ$, improving the state-of-the-art by over three orders of magnitude in rate and one order of magnitude in bandwidths. This ultrathin broadband bright biphoton source could stimulate system-level miniaturization of various free-space quantum photonic technologies.

physics.optics↗

arXiv2025

On nodal solutions with a prescribed number of nodes for a Kirchhoff-type problem

We are concerned with the existence and asymptotic behavior of multiple radial sign-changing solutions with the nodal characterization for a Kirchhoff-type problem involving the nonlinearity $|u|^{p-2}u(2<p<4)$ in $\mathbb{R}^3$. By developing some useful analysis techniques and introducing a novel definition of the Nehari manifold for the auxiliary system of the equations, we show that, for any positive integer $k$, the problem has a sign-changing solution $u_k^b$ changing signs exactly $k$ times. Furthermore, the energy of $u_k^b$ is strictly increasing in $k$, as well as some asymptotic behaviors of $u_k^b$ are obtained. Our result is a complement of [Deng Y, Peng S, Shuai W, {\it J. Funct. Anal.}, {\bf269}(2015), 3500-3527], where the case $2<p<4$ is left open.

math.AP↗

arXiv2025

Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer

Hot carriers, inheriting excess kinetic energy from high-energy photons, underpin numerous optoelectronic applications involving non-equilibrium transport processes. Current research on hot carriers has predominantly focused on inorganic materials, with little attention paid to organic-based systems due to their ultrafast energy relaxation and inefficient charge transport. Here, we overturn this paradigm by demonstrating highly mobile hot carriers in solution-processable, highly crystalline two-dimensional conjugated coordination polymer (2D c-CP) Cu3BHT (BHT = benzenehexathiol) films. Leveraging a suite of ultrafast spectroscopic and imaging techniques, we unravel the microscopic charge transport landscape in Cu3BHT films following non-equilibrium photoexcitation across temporal, spatial, and frequency domains, revealing two distinct high-mobility transport regimes. In the non-equilibrium transport regime, hot carriers achieve ultrahigh mobility of ~2,000 cm2 V-1 s-1, traversing grain boundaries up to 300 nm within a picosecond. In the quasi-equilibrium transport regime, free carriers exhibit Drude-type band-like transport with a remarkable mobility of ~400 cm2 V-1 s-1 and an intrinsic diffusion length exceeding 1 micrometer. These findings establish 2D c-CPs as versatile platforms for exploring high-mobility non-equilibrium transport, unlocking new opportunities for organic-based hot carrier applications.

cond-mat.mtrl-sci↗

arXiv2024

On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities

We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(εx)u=λu+\left(I_α*|u|^q\right)|u|^{q-2} u+\left(I_α*|u|^p\right)|u|^{p-2} u, \quad x \in \mathbb{R}^N, $$ subject to the constraint $$ \int_{\mathbb{R}^N}|u|^2 \mathrm{d}x=a>0, $$ where $N>2 s, s \in(0,1), α\in(0, N), \frac{N+α}{N} 0$ is a parameter, and $λ\in \mathbb{R}$ serves as an unknown parameter acting as a Lagrange multiplier. By employing the Lusternik-Schnirelmann category theory, we estimate the number of normalized solutions to this problem by virtue of the category of the set of minimum points of the potential function $V$.

math.AP↗

arXiv2024

Normalized solutions to Kirchhoff type equations with a critical growth nonlinearity

In this paper, we are concerned with normalized solutions of the Kirchhoff type equation \begin{equation*} -M\left(\int_{\R^N}|\nabla u|^2\mathrm{d} x\right)Δu = λu +f(u) \ \ \mathrm{in} \ \ \mathbb{R}^N \end{equation*} with $u \in S_c:=\left\{u \in H^1(\R^N): \int_{\R^N}u^2 \mathrm{d}x=c^2\right\}$. When $N=2$ and $f$ has exponential critical growth at infinity, normalized mountain pass type solutions are obtained via the variational methods. When $N \ge 4$, $M(t)=a+bt$ with $a$, $b>0$ and $f$ has Sobolev critical growth at infinity, we investigate the existence of normalized ground state solutions and normalized mountain pass type solutions. Moreover, the non-existence of normalized solutions is also considered.

math.AP↗

arXiv2024

A practical generalization metric for deep networks benchmarking

There is an ongoing and dedicated effort to estimate bounds on the generalization error of deep learning models, coupled with an increasing interest with practical metrics that can be used to experimentally evaluate a model's ability to generalize. This interest is not only driven by practical considerations but is also vital for theoretical research, as theoretical estimations require practical validation. However, there is currently a lack of research on benchmarking the generalization capacity of various deep networks and verifying these theoretical estimations. This paper aims to introduce a practical generalization metric for benchmarking different deep networks and proposes a novel testbed for the verification of theoretical estimations. Our findings indicate that a deep network's generalization capacity in classification tasks is contingent upon both classification accuracy and the diversity of unseen data. The proposed metric system is capable of quantifying the accuracy of deep learning models and the diversity of data, providing an intuitive and quantitative evaluation method, a trade-off point. Furthermore, we compare our practical metric with existing generalization theoretical estimations using our benchmarking testbed. It is discouraging to note that most of the available generalization estimations do not correlate with the practical measurements obtained using our proposed practical metric. On the other hand, this finding is significant as it exposes the shortcomings of theoretical estimations and inspires new exploration.

cs.LG↗

arXiv2024

Existence and nonexistence of least energy positive solutions to critical Schrödinger systems with Hardy potential

We are concerned with the following coupled Schrödinger system with Hardy potential in the critical case \begin{equation*} \begin{cases} -Δu_{i}-\frac{λ_{i}}{|x|^2}u_{i}=|u_i|^{2^*-2}u_i+\sum_{j\neq i}^{3}β_{ij}|u_{j}|^{\frac{2^*}{2}}|u_i|^{\frac{2^*}{2}-2}u_i, ~x\in \mathbb{R}^N, u_i\in D^{1,2}(\mathbb{R}^N),\,\, N\geq 3,\,\, i=1,2,3, \end{cases} \end{equation*} where $2^*=\frac{2N}{N-2}$, $λ_i\in (0,Λ_N), Λ_N:= \frac{(N-2)^2}{4}$, $β_{ij}=β_{ji}$ for $i \neq j$. By virtue of variational methods, we establish the existence and nonexistence of least energy solutions for the purely cooperative case ($β_{ij}> 0$ for any $i\neq j$) and the simultaneous cooperation and competition case ($β_{i_{1}j_{1}}>0$ and $β_{i_{2}j_{2}}<0$ for some $(i_{1}, j_{1})$ and $(i_{2}, j_{2})$). Moreover, it is shown that fully nontrivial ground state solutions exist when $β_{ij}\ge0$ and $N\ge5$, but {\bf NOT} in the weakly pure cooperative case ($β_{ij}>0$ and small, $i\neq j$) when $N=3,4$. We emphasize that this reveals that the existence of ground state solutions differs dramatically between $N=3, 4$ and higher dimensions $N\geq 5$. In particular, the cases of $N=3$ and $N\geq 5$ are more complicated than the case of $N=4$ and the proofs heavily depend on the dimension. Some novel tricks are introduced for $N=3$ and $N\ge5$.

math.AP↗

arXiv2024

Existence of normalized solutions of a Hartree-Fock system with mass subcritical growth

In this paper, we are concerned with normalized solutions in $H_{r}^{1}(\mathbb{R}^{3}) \times H_{r}^{1}(\mathbb{R}^{3})$ for Hartree-Fock type systems with the form \be\lab{ Hartree-Fock} \left\{ \begin{array}{ll} -Δu +αϕ_{u,v} u=λ_{1} u+\left | u \right | ^{2q-2} u+β\left | v \right | ^{q} \left | u \right | ^{q-2} u , \\ -Δv +αϕ_{u,v} v=λ_{2} v+\left | v\right | ^{2q-2} v+β\left | u \right | ^{q} \left | v \right | ^{q-2} v , \\ \int_{\mathbb{R}^{3}}\left | u \right | ^{2} {\rm d}x=a_{1} , \quad \int_{\mathbb{R}^{3}}\left | v \right | ^{2} {\rm d}x=a_{2} , \nonumber\\ \end{array} where $$ ϕ_{u, v}\left(x\right):=\int_{\mathbb{R}^{3}} \frac{u^{2}(y)+v^{2}(y)}{|x-y|} {\rm d}y \in D^{1,2}\left(\mathbb{R}^{3}\right). $$ Here $α,β>0, a_1,a_2>0$ and $1 0$ when $1 0$ small when $\frac{4}{3}\le q < \frac{3}{2}$. The nonexistence of normalized solutions is also considered for $\frac{3}{2}\le q < \frac{5}{3}$. Also, the orbital stability of standing waves is obtained under local well-posedness assumptions of the evolution problem.

math.AP↗

arXiv2024

Single-peak and multi-peak solutions for Hamiltonian elliptic systems in dimension two

This paper is concerned with the Hamiltonian elliptic system in dimension two\begin{equation*}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathbb{R}^2,\\ -ε^2Δv+V(x)v=f(u)\ & \text{in}\quad \mathbb{R}^2, \end{array}\right.\endaligned \end{equation*} where $V\in C(\mathbb{R}^2)$ has local minimum points, and $f,g\in C^1(\mathbb{R})$ are assumed to be of exponential growth in the sense of Trudinger-Moser inequality. When $V$ admits one or several local strict minimum points, we show the existence and concentration of single-peak and multi-peak semiclassical states respectively, as well as strong convergence and exponential decay. In addition, positivity of solutions and uniqueness of local maximum points of solutions are also studied. Our theorems extend the results of Ramos and Tavares [Calc. Var. 31 (2008) 1-25], where $f$ and $g$ have polynomial growth. It seems that it is the first attempt to obtain multi-peak semiclassical states for Hamiltonian elliptic system with exponential growth.

math.AP↗

arXiv2024

Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity

We are concerned with solutions of the following quasilinear Schrödinger equations \begin{eqnarray*} -{\mathrm{div}}\left(φ^{2}(u) \nabla u\right)+φ(u) φ^{\prime}(u)|\nabla u|^{2}+λu=f(u), \quad x \in \mathbb{R}^{N} \end{eqnarray*} with prescribed mass $$ \int_{\mathbb{R}^{N}} u^{2} \mathrm{d}x=c, $$ where $N\ge 3, c>0$, $λ\in \mathbb{R}$ appears as the Lagrange multiplier and $φ\in C ^{1}(\mathbb{R} ,\mathbb{R}^{+})$. The nonlinearity $f \in C\left ( \mathbb{R}, \, \mathbb{R} \right )$ is allowed to be mass-subcritical, mass-critical and mass-supercritical at origin and infinity. Via a dual approach, the fixed point index and a global branch approach, we establish the existence of normalized solutions to the problem above. The results extend previous results by L. Jeanjean, J. J. Zhang and X.X. Zhong to the quasilinear case.

math.AP↗

arXiv2024

Multiplicity of normalized solutions for the fractional Schrödinger equation with potentials

We get multiplicity of normalized solutions for the fractional Schrödinger equation $$ (-Δ)^su+V(\varepsilon x)u=λu+h(\varepsilon x)f(u)\quad \mbox{in $\mathbb{R}^N$}, \qquad\int_{\mathbb{R}^N}|u|^2dx=a, $$ where $(-Δ)^s$ is the fractional Laplacian, $s\in(0,1)$, $a,\varepsilon>0$, $λ\in\mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $V,h:\mathbb{R}^N\rightarrow[0,+\infty)$ are bounded and continuous, and $f$ is continuous function with $L^2$-subcritical growth. We prove that the numbers of normalized solutions are at least the numbers of global maximum points of $h$ when $\varepsilon$ is small enough.

math.AP↗

arXiv2023

On the Kirchhoff equation with prescribed mass and general nonlinearities

In the present paper, we apply a global branch approach to study the existence, non-existence and multiplicity of positive normalized solutions $(λ_c, u_c)\in \mathbb{R}\times H^1(\mathbb{R}^N)$ to the following Kirchhoff problem $$ -\left(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx\right)Δu+λu=g(u)~\hbox{in}~\mathbb{R}^N,\;N\geq 1 $$ satisfying the normalization constraint $ \displaystyle\int_{\mathbb{R}^N}u^2=c, $ which appears in free vibrations of elastic strings. The parameters $a,b>0$ are prescribed as well as the mass $c>0$. Due to the presence of the non-local term $b\int_{\mathbb{R}^N}|\nabla u|^2dx Δu$, such problems lack the mountain pass geometry in the higher dimension case $N\geq 5$. Our result seems to be the first attempt in this aspect.

math.AP↗

arXiv2023

Normalized ground states for a coupled Schrödinger system: Mass super-critical case

We consider the existence of solutions $(λ_1,λ_2, u, v)\in \mathbb{R}^2\times (H^1(\mathbb{R}^N))^2$ to systems of coupled Schrödinger equations $$ \begin{cases} -Δu+λ_1 u=μ_1 u^{p-1}+βr_1 u^{r_1-1}v^{r_2}\quad &\hbox{in}~\mathbb{R}^N,\\ -Δv+λ_2 v=μ_2 v^{q-1}+βr_2 u^{r_1}v^{r_2-1}\quad &\hbox{in}~\mathbb{R}^N,\\ 0 0$ and the prescribed masses $a,b>0$. We focus on the coupled purely mass super-critical case, i.e., $$2+\frac{4}{N} 0$ and $β>0$.

math.AP↗

arXiv2023

A global branch approach to normalized solutions for the Schrödinger equation

We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form \begin{equation*} -Δu+λu=g(u), \quad u \in H^1(\mathbb{R}^N), \, N \geq 1. \end{equation*} Our approach permits to handle in a unified way nonlinearities $g(s)$ which are either mass subcritical, mass critical or mass supercritical. Among its main ingredients is the study of the asymptotic behaviors of the positive solutions as $λ\rightarrow 0^+$ or $λ\rightarrow +\infty$ and the existence of an unbounded continuum of solutions in $(0, + \infty) \times H^1(\mathbb{R}^N)$.

math.AP↗

arXiv2023

Normalized solutions for critical Choquard systems

In this paper, we consider the critical Choquard system with prescribed mass \begin{equation*} \begin{aligned} \left\{ \begin{array}{lll} -Δu+λ_1u=(I_μ\ast |u|^{2^*_μ})|u|^{2^*_μ-2}u+νp(I_μ\ast |v|^q)|u|^{p-2}u\ & \text{in}\quad \mathbb{R}^N,\\ -Δv+λ_2v=(I_μ\ast |v|^{2^*_μ})|v|^{2^*_μ-2}v+νq(I_μ\ast |u|^p)|v|^{q-2}v\ & \text{in}\quad \mathbb{R}^N,\\ \int_{\mathbb{R}^N}u^2=a^2,\quad\int_{\mathbb{R}^N}v^2=b^2, \end{array}\right.\end{aligned} \end{equation*} where $N\geq3$, $0<μ 0$, we study the existence, non-existence and asymptotic behavior of normalized solutions by distinguishing three cases: $L^2$-subcritical case: $p+q<4+\frac{4-2μ}{N}$; $L^2$-critical case: $p+q=4+\frac{4-2μ}{N}$; $L^2$-supercritical case: $p+q>4+\frac{4-2μ}{N}$. In particular, in $L^2$-subcritical case, and either $N\in\{3,4\}$ or $N\geq5$ with $(\frac N2-1)p+\frac {N}{2}q\leq 2N-μ$ and $(\frac N2-1)q+\frac {N}{2}p\leq 2N-μ$, we prove that there exists $ν_0>0$ such that the system has a positive radial normalized ground state for $0<ν<ν_0$. In $L^2$-critical case and $N\in\{3,4\}$, we show there is $ν'_0>0$ such that the system has a positive radial normalized ground state for $0<ν<ν'_0$. In $L^2$-supercritical case and $N\in\{3,4\}$, there are two thresholds $ν_2\geqν_1\geq0$ such that a positive radial normalized solution exists if $ν>ν_2$, and no normalized ground state exists for $ν<ν_1$.

math.AP↗

arXiv2023

A Cu3BHT-Graphene van der Waals Heterostructure with Strong Interlayer Coupling

Two dimensional van der Waals heterostructures (2D are of significant interest due to their intriguing physical properties that are critically defined by the constituent monolayers and their interlayer coupling . However, typical inorganic 2 D vdWhs fall into the weakly coupled region, limiting efficient interfacial charge flow crucial for developing high performance quantum opto electronics. Here, we demonstrate strong interlayer coupling in Cu3 BHT (BHT = benzenehexathiol) graphene vdWhs an organic inorganic bilayer characterized by prominent interlayer charge transfer Monolayer Cu3 BHT with a Kagome lattice is synthesized on the water surface and then coupled with graphene to produce a cm2 scale 2D vdWh. Spectroscopic and electrical studies, along with theoretical calculation s show significant hole transfer from monolayer Cu3 BHT to graphene upon contact , being characteristic fingerprints for strong interlayer coupling This study unveils the great potential of integrating highly pi-conjugated 2D coordination polymers (2DCPs) into 2D vdWhs to explor e intriguing physical phenomena.

physics.app-ph↗