MSS is an algorithm to determine the radii and positions of spheres that fill a given volume. In the context of granular materials, MSS is a particle generator for DEM simulations of complex-shaped particles. Here, each particle of a given shape is represented by a set of spheres that collectively approximate the particle. This technique of particle shape representation is often referred to as the multi-sphere approach. We show that, for a given number of spheres, MSS provides a closer approximation to the target shape at lower computational costs than other DEM multi-sphere particle generators reported in the literature.

We prove that for any dominant cocharacter $μ$ and any parahoric level $K$, the augmented admissible set $\widehat{\Adm(μ)^K}$ in the Iwahori-Weyl group is dual EL-shellable. This resolves a conjecture of Görtz and provides a new proof of the Cohen-Macaulay property for the special fibres of local models with parahoric level structure. In particular, the result settles the previously open cases of residue characteristic $2$ and non-reduced root systems. This approach is characteristic-free and intrinsic to the structure of admissible sets. Moreover, our construction yields an explicit shelling, which translates into an inductive, component-by-component building procedure for the special fibre that preserves Cohen-Macaulayness at each step. As a consequence, we obtain the Cohen-Macaulayness of many local models of Shimura varieties considered in the literature, most notably those satisfying the He-Pappas-Rapoport description, as well as the local models characterized by Scholze-Weinstein and constructed by Anschütz-Gleason-Lourenço-Richarz. Via the usual local model diagram, these results imply the Cohen-Macaulay property for the corresponding integral models of Shimura varieties whenever available. This gives a new proof that the integral models constructed by Kisin-Pappas-Zhou are Cohen-Macaulay.

We characterize 16 challenges faced by those investigating and developing remote and synchronous collaborative experiences around visualization. Our work reflects the perspectives and prior research efforts of an international group of 29 experts from across human-computer interaction and visualization sub-communities. The challenges are anchored around five collaborative activities that exhibit a centrality of visualization and multimodal communication. These activities include exploratory data analysis, creative ideation, visualization-rich presentations, joint decision making grounded in data, and real-time data monitoring. The challenges also reflect the changing dynamics of these activities in the face of recent advances in extended reality (XR) and artificial intelligence (AI). As an organizing scheme for future research at the intersection of visualization and computer-supported cooperative work, we align the challenges with a sequence of four sets of research and development activities: technological choices, social factors, AI assistance, and evaluation.

Transition metal dichalcogenides (TMDCs) constitute a promising platform for symmetry-engineered responses to circularly polarized light. The high crystal symmetry of centrosymmetric 2H-phase TMDCs inherently forbids the circular photogalvanic effect, thereby necessitating external stimuli such as electric fields or strain to lower the symmetry for its activation. While Schottky junctions provide a ubiquitous built-in field for potentially inducing circular photocurrents, the mechanism for the generation and control of circular photocurrents in TMDCs is not understood. In this study, we fabricated a localized gold-MoTe2 heterostructure and demonstrate a pronounced circular photocurrent at the interface under normal incidence. The photocurrent is attributed to circular photogalvanic effect governed by the strength and direction of the built-in electric field, enabling continuous modulation via an external bias. First-principles calculations show that the gold interface induces a spin splitting in the valence bands of MoTe2, establishing a valley-dependent spin ordering. The observed circular photocurrent from multilayer 2H-MoTe2 under normal incidence indicates the breaking of C3 rotational symmetry by the local in-plane field. These results establish an effective strategy for developing voltage-tunable circularly polarized photodetectors and valleytronic devices.

Videoconference conversations about data often entail screen sharing visualization artifacts, in which nonverbal communication goes largely ignored. Beyond presentation use cases, conversations supported by visualization also arise in collaborative decision making, technical interviews, and tutoring: use cases that benefit from participants being able to see one another as they exchange questions about the data. In this paper, we employ a reciprocal compositing of visualization and interface widgets over the mirrored video of one's conversation partner, suggestive of a pane of glass, in which both parties can simultaneously manipulate composited elements via bimanual gestures. We demonstrate our approach with implementations of several visualization interfaces spanning the aforementioned use cases, and we evaluate our approach in a study (N = 16) comparing it to videoconferencing while using a mouse to interact with a collaborative web application. Our findings suggest that our approach promotes feelings of presence and mutual awareness of analytical intent.

Leveraged ETFs (L-ETFs) are exchange-traded funds that achieve price movements several times greater than an index by holding index-linked futures such as Nikkei Stock Average Index futures. It is known that when the price of an L-ETF falls, the L-ETF uses the liquidity of futures to limit the decline through arbitrage trading. Conversely, when the price of a futures contract falls, the futures contract uses the liquidity of the L-ETF to limit its decline. However, the impact of arbitrage trading on the liquidity of these markets has been little studied. Therefore, the present study used artificial market simulations to investigate how the liquidity (Volume, SellDepth, BuyDepth, Tightness) of both markets changes when prices plummet in either (i.e., the L-ETF or futures market), depending on the presence or absence of arbitrage trading. As a result, it was found that when erroneous orders occur in the L-ETF market, the existence of arbitrage trading causes liquidity to be supplied from the futures market to the L-ETF market in terms of SellDepth and Tightness. When erroneous orders occur in the futures market, the existence of arbitrage trading causes liquidity to be supplied from the L-ETF market to the futures market in terms of SellDepth and Tightness, and liquidity to be supplied from the futures market to the L-ETF market in terms of Volume. We also analyzed the internal market mechanisms that led to these results.

We propose ISS-RegAuth, a lightweight indoor space authentication framework that authenticates a user by comparing LiDAR captures of personal rooms. Prior work processes every point in the cloud, where planar surfaces such as walls and floors dominate similarity calculations, causing latency and potential privacy exposure. In contrast, ISS-RegAuth retains only 1-2\% of Intrinsic Shape Signatures (ISS) keypoints, computes their Fast Point Feature Histograms, and performs RANSAC and ICP on this sparse set. On 100 ARKitScenes pairs, this approach reduces the equal-error rate from 0.02 to 0.00, cuts processing time by 20\%, and lowers transmitted data to 2.2\% of the original. These results show that keypoint-based sparse representation can make privacy-preserving, edge-deployable indoor space authentication practical. As an early step, this work opens a path toward device-independent authentication and account-recovery mechanisms that rely on users' physical environments.

We improve our previously proposed two Higgs doublet model of six-dimensional $SU(4)$ gauge theory compactified on an orbifold $T^2/Z_2$ by introducing the brane localized gauge kinetic terms. Since two Higgs doublets are identified with massless zero modes in extra spatial components of the six-dimensional gauge field, the Higgs sector in our model is constrained by the six-dimensional gauge symmetry. As a result, our Higgs potential at tree-level is automatically CP conserving and $Z_2$ symmetric, which are assumed by hand in the ordinary two Higgs doublet models. The scalar masses breaking the $Z_2$ symmetry softly are generated at one-loop. We show that the Standard Model Higgs mass can be obtained by tuning the size of the brane localized gauge kinetic terms as well as the electroweak symmetry breaking is realized. Other physical Higgs masses are predicted.

Stacking and twisting two dimensional materials has garnered enormous attention across the condensed matter and the nanophotonic communities. The surge of interest stems from the emergence of novel photophysical phenomena that arise due to the interlayer coupling of the individual layers. Here, we demonstrate that the twist degree of freedom can modulate a single quantum emitter at room temperature. We employ a van der Waals homobilayer of hexagonal boron nitride (hBN) and model the emission properties of quantum emitters as a function of the twist angle. Density functional theory results show that the embedded emitters are strongly influenced by the twist angle and the stacking of the top hBN layer. We consequently engineer these systems experimentally, and demonstrate in-situ tuning of embedded quantum emitters by mechanically twisting the top hBN layer, achieving tunability of over 30 nm (~ 100 meV). Our work demonstrates that mechanical twisting can be harnessed to modulate the embedded quantum emitters in a vdW material, marking a crucial step towards a programmable on-chip quantum circuitry.

Magnetic flux ropes are ubiquitous magnetic structures found in plasmas ranging from astrophysical to laboratory. We employ a newly-developed parallel-kinetic-perpendicular-moment (PKPM) model to simulate the 3D interaction and evolution of two line-tied flux ropes at realistic laboratory plasma parameters, while retaining essential parallel kinetic physics in the system. We find that ropes undergo a current-dependent transition from a diamagnetic to paramagnetic regime, which we quantify with a simple analytic model. Although the macroscopic structural evolution qualitatively differs significantly between these regimes, analyzing the reconnection in proper field-aligned coordinates reveals that the underlying kinetic dynamics remain similar. Using the squashing factor and quasi-potential as diagnostics of 3D magnetic reconnection, we identify the formation of a quasi-separatrix layer and show that these quantities provide consistent metrics for reconnection rate and structure.

We present a first systematic study of $I=1/2$ proton-$Λ$ ($p$-$Λ$) scattering from lattice QCD, using seven sets of $(2+1)$-flavor lattice ensembles with pion masses spanning 135-317 MeV and three lattice spacings with $a=(0.052,0.077, 0.105)$ fm. Using Lüscher's finite-volume method, effective range expansion and chiral/continuum extrapolations, we obtain the inverse of scattering length and effective range for the $^1S_0$ channel as 0.177(83) GeV and 2.9(1.4) fm, and for the $^3S_1$ channel as 0.016(76) GeV and 1.8(1.1) fm. From the derived S-wave phase shifts, we provide an estimate of the $p-Λ$ scattering cross section. Our results for scattering length, effective range and cross sections are in good agreement with available experimental measurements. We also find that the $p-Λ$ system sustains attractive interactions. These results provide critical input for the unification of nuclear force theories and the construction of neutron star equations of state.

We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+α.$ Our main focus is on the long-time asymptotic behavior of the system. The proofs of our results combine techniques developed for short-range interactions, properties of $α$-stable laws, and a Tauberian theorem. This model is more intricate and realistic for some applications, such as neural networks, where long-range connections are present.

The emergence of breathing solitons in mode-locked lasers presents a fundamental challenge for the theoretical modelling of mode locking, with the mechanisms underlying below- and above-threshold breathing solitons, and the origins of their distinct nonlinear dynamics, remaining poorly understood. Here, we develop a model that incorporates both spatial and temporal gain dynamics, enabling us to elucidate the origins of these two classes of pulsating states. We show that below-threshold breathing solitons arise from the interplay between Q-switching and soliton shaping, whereas Kerr nonlinearity and dispersion dominate the formation of above-threshold breathers. The model further captures the markedly different dynamical properties of these regimes. Experimental observations corroborate the simulations, validating the predictive power of the framework. Beyond providing a refined theoretical basis for ultrafast laser design, this work advances the broader understanding of non-equilibrium dynamics in mode-locked lasers and offers new perspectives on breathing soliton phenomena across diverse physical systems.

Although organizations increasingly position AI adoption as a pathway to competitiveness and innovation, organizations' perspectives on productivity and efficiency often clash with workers' perspectives on AI's economic and social value. Through design workshops with 15 UX designers, we examine how AI adoption unfolds across individual, team, and organizational scales. At the individual level, designers weighed efficiency, skill development, and professional worth. At the team level, they negotiated collaboration, responsibility, and rigor. At the organizational level, adoption was shaped by compliance requirements and organizational norms. Across these scales, discourses of efficiency carried social and ethical dimensions of responsibility, trust, and autonomy. We view adoption as a site where roles, relationships, and power are reconfigured. We argue that AI adoption should be understood as a process of negotiating values, and call for future work examining how AI systems redistribute responsibility among team members, while understanding how such shifts could strengthen worker agency.

Isomorphic factorizations of complete graphs originate from the seminal work of Frank Harary and collaborators, who initiated the systematic study of decompositions of complete graphs into pairwise isomorphic spanning subgraphs. In this paper, we investigate isomorphic factorizations of complete graphs into Cayley graphs on CI-groups. Let $Γ=Cay(G,S)$ denote the Cayley graph of finite group $G$. We obtain a necessary and sufficient condition on CI-group $G$ so that the complete graph on $|G|$ vertices can be edge-partitioned into $k$-copies of Cayley graph of the same CI-group $G$ each isomorphic to $Cay(G,S)$ for some inverse-closed subset $S\subset G\setminus\{1\}$. Further we give a construction of isomorphic factorizations of the complete graph into Cayley graphs on CI-group.

Within the framework of quantum field theory and the Standard Model (SM), we investigate the prospects of studying entanglement measures and Bell-type spin-correlation observables in the electroweak process $e^- e^+\to τ^-τ^+$ at the center-of-mass (COM) energies of $\sqrt{s}=3.670,4.630$, and $7.000$ GeV at the proposed Super Tau-Charm Facility (STCF) in China. Focusing on the hadronic decay channel $τ^\pm\to π^\pm ν$, we determine the spin-correlation coefficients of the $τ^-τ^+$ system within the SM framework using measurable production kinematics, namely the $τ$ velocities and scattering angles in the COM frame. From these correlation coefficients, we construct concurrence and a Bell-type correlation combination as defined in the literature. Assuming an integrated luminosity of 1 ab$^{-1}$ for each considered COM energy, and incorporating realistic detector efficiencies as well as statistical and systematic uncertainties, we estimate the expected sensitivity to these observables at STCF. Our results indicate that, under the SM hypothesis, the corresponding Bell-type correlation combinations could be resolved with high statistical significance at STCF.

We investigate the spectral and dynamical properties of the fractional nonlinear Schrödinger (fNLS) equation with harmonic confinement. In this setting, the classical Laplacian is replaced by its fractional power $(-\partial_x^2)^{α/2}$ with $α\in(1,2]$, introducing nonlocal, Lévy-type dispersion. This modification fundamentally alters the balance between nonlinearity, dispersion, and trapping, reshaping both the structure and stability of stationary states. Using a Fourier pseudo-spectral discretization, we compute stationary branches as functions of the temporal frequency $Ω$ in focusing ($σ=+1$) and defocusing ($σ=-1$) regimes, and assess spectral stability via the linearized eigenvalue problem. Direct simulations, performed with split-step and exponential time-differencing integrators, confirm these predictions and reveal $α$-dependent transitions between coherent oscillations, bounded breathing dynamics, and decoherence or fragmentation. Our results show that decreasing $α$ systematically shifts bifurcation curves, fragments stability windows for excited states, and amplifies instability in the focusing regime, while supporting robust coherence in the defocusing case. Beyond clarifying how harmonic confinement mediates the interplay between nonlinearity and fractional dispersion, the study also provides benchmarks for numerical treatments of fractional operators and points toward potential applications in nonlinear optics, Bose--Einstein condensates, and anomalous transport phenomena.

The interplay of dynamics and transport leads to intriguing spatiotemporal behaviors of nonequilibrium macroscopic quantum systems. By means of time-resolved spectroscopy, we here provide microscopic insights into the interplay of ballistic transport and many-particle interactions for an exciton-polariton condensate. We observed anomalous condensation of a coherent polariton flow propagating away from the hot reservoir, accompanied by ultrafast oscillations of its population in the time domain with a period of a few picoseconds. On the basis of time- and spatially-resolved photo luminescence imaging characterization, we reveal that the inter-mode coherent energy transfer, controllable via an incoherent excitonic reservoir, gives rise to the observed ultrafast oscillations. Theoretically, modeling was conducted using an open-dissipative Gross-Pitaevskii equation, with the simulation results fully reproducing our experimental observations. These results advance the fundamental understanding of light-matter interactions in nonequilibrium systems associated with the interplay of dynamics and transport.

We prove a sharp inequality between the Alexander-Taylor capacity and the functional capacity in a complex Sobolev space on a compact Kähler manifold. The latter space and capacity were introduced by Dinh, Sibony and Vigny.

Hybrid quantum networks offer a promising architecture for scalable quantum information processing and a future quantum internet, as they can combine the complementary strengths of disparate physical platforms. While single-atom systems provide deterministic quantum logic gates, atomic ensembles enable large-capacity quantum storage. However, generating entanglement between such heterogeneous systems has remained an open challenge, primarily due to fundamental spectral mismatches and system complexity. Here, we demonstrate a hybrid quantum network that entangles a single trapped $\mathrm{^{171}Yb^{+}}$ ion and a quantum memory based on $\rm ^{153}Eu^{3+}\colon\!Y_2SiO_5$ crystal over a 75-m separation. Using polarization-maintaining quantum frequency conversion, we map spin-photon entanglement onto a hybrid entanglement between a single spin qubit and a collective excitation of the quantum memory. The resulting entangled state achieves a fidelity of $(89.21 \pm 2.23)\%$ and violates the CHSH-Bell inequality by 6 standard deviations ($S = 2.328 \pm 0.055$), confirming nonlocality between two heterogeneous nodes. This work establishes entanglement between a quantum processing module with a multiplexed quantum memory node, representing a key step toward a scalable, multifunctional quantum internet.

As the LIGO-VIRGO-KAGRA Network of gravitational-wave detectors improves in sensitivity, accumulating hundreds of gravitational-wave detections per year, it becomes imperative to improve tests of general relativity in concert. The test of Hawking's law of area increase has gained prominence since GW250114, where black holes in General Relativity were tested with unprecedented precision, using the linear ringdown and pre-merger portions of the signal. A closely related test is the Inspiral-Merger-Ringdown Consistency Test, which assesses the consistency of the high- and low-frequency parts of the signals. In this letter, I present a multi-parameter Multi-Segment Consistency Test (MSCT) that generalizes and improves upon existing tests by ensuring that the extrinsic properties of the signal are consistent across its independent segments and by adopting an accelerated time-domain approach. The improved area law test is then presented as a projection of this MSCT test. These crucial improvements, which bring physical consistency to the area law test, lead to more stringent constraints on the increase in estimated area from observed binary black hole mergers, while also capturing covariances among the parameters. Applying the two-segment version of this test to the inspiral and ringdown parts of GW250114, and keeping some of the extrinsic parameters common between the segments, I test the signal to unprecedented accuracy, obtaining $4.61 ^{+0.24} _{-0.11}σ$ significant result for the area increase, even as more than 4 pre-merger cycles of the signal are excluded from the analysis. Also, I infer that the final state lies within the 15\% highest posterior density confidence interval.

While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit simplicity, suffer from a fundamental limitation: inefficient sampling in vast infeasible regions. This often results in suboptimal solutions that violate constraints and impede convergence to high-quality results. In contrast, ansatz-based approaches enforce solution feasibility by design but require complex, problem-specific circuits that are challenging to implement on current noisy intermediate-scale quantum devices. To overcome these limitations, we introduce an alternative VQA whose core innovation lies in a strategically designed loss function. This function offers a dual advantage. First, it is provably guaranteed that its global minimum corresponds uniquely to the optimal feasible solution, as this is achieved by ensuring universally higher loss values for all infeasible solutions. Second, it furnishes distinct computational pathways for feasible versus infeasible regions, thus creating clear and non competing guidance for the optimizer. As a result of these combined features, the algorithm's overall performance is significantly enhanced. Regarding hardware overhead, our design requires adding only an efficient validation oracle module to the penalty-based circuit, resulting in a circuit complexity significantly lower than that of ansatz-based approaches with their custom mixers. To validate the practical efficiency of our method, we empirically demonstrate its effectiveness by solving minimum vertex cover and maximum independent set problems on random graphs of varying small-scale sizes.

Mobile agentic AI is extending autonomous capabilities to resource-constrained platforms such as edge robots and unmanned aerial vehicles (UAVs), where strict size, weight, power, and cost (SWAP-C) constraints and intermittent wireless connectivity limit both on-device computation and cloud access. Existing approaches mostly optimize per-round communication efficiency, yet mobile agents must sustain competence across a stream of tasks. We propose a knowledge-driven reasoning framework that extracts reusable decision structures from past execution, synchronizes them over bandwidth-limited links, and injects them into on-device reasoning to reduce latency, energy, and error accumulation. A DIKW-inspired taxonomy distinguishes raw observations, episode-scoped traces, and persistent cross-task knowledge, and categorizes knowledge into retrieval, structured, procedural, and parametric representations, each with a distinct tradeoff between reasoning speedup and failure risk. A key finding is that knowledge exposure is non-monotonic: too little forces costly trial-and-error replanning, while too much introduces conflicting cues and errors. A UAV case study validates the framework, where a compact knowledge pack synchronized over intermittent backhaul enables a 3B-parameter onboard model to achieve perfect mission reliability with lower reasoning cost than both knowledge-free on-device reasoning and cloud-centric replanning.

In July 2025, the University of Adelaide hosted the Astronomical Society of Australia's Annual Scientific Meeting on its North Terrace campus. We ran the conference in a hybrid mode, with options for in-person and online attendance. This report details the procedures that we used to enable the online mode of the conference at minimal cost and minimal inconvenience to the in-person attendees. We discuss our choices of hardware and software and how we integrated these systems together. We summarise our experience of organising a local AV team and the procedures that we set for running the AV in each session. We present statistics of the online attendance numbers and post-conference survey feedback, and discuss the lessons we feel other organisers may particularly be able to learn from.

Using the in-out formalism, we derive the exact one-loop QED effective actions for spinor field in a uniform electric field in two-dimensional global (anti-)de Sitter (A)dS$_2$ spacetime. The one-loop effective action probed by a scalar or spinor field is determined by the scattering matrix relating the out-vacuum to the in-vacuum, which is in turn fixed by the Bogoliubov coefficients of the corresponding Klein-Gordon or Dirac equation in the presence of both a gauge field and curved spacetime. Remarkably, the vacuum persistence amplitude -- twice the imaginary part of the one-loop effective action -- is related, via the Bogoliubov relations, to the mean number of particle-antiparticle pairs spontaneously produced by the background fields. The Bogoliubov coefficients or mean number of pair-production for charged scalar and spinor fields in global (A)dS$_2$ lead to QED effective actions expressed in terms of both proper-time integrals and Hurwitz zeta functions. These effective actions reveal a strong interplay between the electric field and spacetime curvature and correctly reproduce the limiting cases of pure (A)dS$_2$ spacetime and a uniform electric field in Minkowski space. We further discuss the physical implications of the resulting QED effective actions in (A)dS$_2$.

Compact, electrically driven sources of coherent terahertz (THz) radiation remain a challenge due to the lack of efficient gain media and scalable device platforms. Here, we propose and theoretically investigate a cavity-based THz gain mechanism enabled by Berry curvature dipole (BCD) in a DC-biased, low-symmetry two-dimensional (2D) material. Placing the biased 2D layer at the center of a Fabry-Perot cavity enhances light-matter interactions, enabling direct conversion of DC electrical power into coherent THz radiation. We analyze the conditions for amplification and lasing, and identify the parameter regimes that support self-oscillatory coherent emission. Rather than introducing a specific device implementation, our work establishes the physical principles and operating conditions for BCD-enabled THz gain and lasing and provides the theoretical foundation for future realizations. The chiral nature of BCD-induced response enables bias-tunable chiral optical gain, selective polarization eigenstate amplification, and electrically controlled handedness of the emitted radiation. Importantly, substantial amplification and lasing are achieved using only a single 2D material, significantly simplifying device design while preserving scalability across the THz band via cavity-length tuning. This platform is broadly applicable to low-symmetry 2D materials with finite BCD, offering a general route toward compact, frequency-tunable, and polarization-selective THz sources.

We compute Donaldson-Thomas(DT) invariants and their descendant invariants for the local Calabi-Yau 4-fold over the Mukai-Umemura variety via several localization formulas. Assuming that the genus-one Gopakumar-Vafa(GV) type invariants vanish, our computations verify the predictions of Cao, Maulik, and Toda.

We propose to use counterdiabatic driving (CD) shortcut and the Floquet engineering to realize the robust and fast state transfer in the dissipation cavity magnon-polaritons non-Hermitian (NH) system. For the two-level NH cavity magnon-polaritons Hamiltonian, an accurate and fast population transfer is achieved from the microwave photon to the magnon by two coherent control techniques; counterdiabatic driving shortcut and non-Hermitian shortcuts (NHSs). Additionally, by using the CD technique, the population evolution speed of non-Hermitian systems is faster than that via the NHS technique in the broken-symmetric regime. Furthermore, we compare their performances in the presence of the coupling strength and systematic errors, the CD technique features a broad range of high efficiencies of the transition probability above 99.9%, showing that the CD technique is more robustness against these errors than the NHS technique. It is worth noting that this advantage becomes more significant as the gain rate of system parameters increases. The work provides a basis for achieving the robust coherent control in NH cavity electromagnonics.

We present a localized data assimilation (DA) scheme based on the sequential Markov Chain Monte Carlo (SMCMC) technique [Ruzayqat et al., 2024], a provably convergent method for filtering high-dimensional, nonlinear, and potentially non-Gaussian state-space models. Unlike particle filters, which are exact methods for nonlinear non-Gaussian models, SMCMC does not assign weights to samples and therefore avoids weight degeneracy in small-ensemble regimes. We design two localization approaches within the SMCMC framework that exploit spatial sparsity of observations to reduce the effective degrees of freedom and improve efficiency. The first variant collects observed blocks into a single reduced domain and runs parallel MCMC chains over this combined region. The second variant further reduces the per-chain state dimension by decomposing the observed region into independent blocks, each augmented with a compact halo, and applying Gaspari--Cohn observation-noise tapering to smoothly down-weight distant observations. When the observation model is linear and Gaussian, we show that our approximate filtering density reduces to a Gaussian mixture from which independent samples can be drawn exactly. For nonlinear or non-Gaussian observation models, we employ an MCMC kernel. We test on high-dimensional ($d \sim 10^4 - 10^5$) state-space models, including a linear Gaussian model and a nonlinear multilayer shallow water equation with both linear and nonlinear observation operators. We consider Gaussian and non-Gaussian (Student-$t$) observation noise, showing that LSMCMC naturally handles heavy-tailed errors that cause ensemble Kalman methods to diverge. Observations include synthetic and real data from the Surface Water and Ocean Topography (SWOT) mission (NASA) and ocean drifter data (NOAA). We compare the two variants against each other and the local ensemble transform Kalman filter (LETKF).

In this article, we propose an algorithm for the nonlinear conjugate gradient method to find a Pareto critical point of unconstrained multiobjective interval optimization problems. In this algorithm, we use the Wolfe line search procedure to find the step length. After defining the standard Wolfe conditions and the strong Wolfe conditions, we prove that there exists an interval of the step length that satisfies the standard Wolfe conditions and the strong Wolfe conditions. Further, to study the convergence analysis of our proposed algorithm, we derive the result related to the Zoutendijk condition. In the convergence analysis, first, we prove the global convergence property of our proposed algorithm for a general conjugate gradient algorithmic parameter. Further, we consider four variants of the conjugate gradient algorithmic parameter, such as Fletcher-Reeves, conjugate descent, Dai-Yuan, and modified Dai-Yuan. For each variant of the algorithmic parameter, we prove the global convergence results of our proposed algorithm. Finally, we test our algorithm on some test problems and make a performance profile.