Miracle-dz/UniFAR-FTUs huggingface dataset:
Effective Condition Number Bounds for Convex Regularization

We derive bounds relating Renegar’s condition number to quantities that govern the statistical performance of convex regularization in settings that include the $\ell _{1}$ -analysis setting. Using results from conic integral geometry, we show that the bounds can be made to depend only on a random projection, or restriction, of the analysis operator to a lower dimensional space, and can still be effective if these operators are ill-conditioned. As an application, we get new bounds for the undersampling phase transition of composite convex regularizers. Key tools in the analysis are Slepian’s inequality and the kinematic formula from integral geometry.
Free boundaries subject to topological constraints

We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by striking results of T. Colding and W. Minicozzi concerning finitely connected, embedded, minimal surfaces. We review our earlier work on the simplest case, one-phase free boundaries in the plane in which the positive phase is simply connected. We also prove a new, purely topological, effective removable singularities theorem for free boundaries. At the same time, we formulate some open problems concerning the multiply connected case and make connections with the theory of minimal surfaces and semilinear variational problems.
Dispersive blow-up and persistence properties for the Schrödinger–Korteweg–de Vries system

We study the dispersive blow-up phenomena for the Schrödinger–Korteweg–de Vries (S-KdV) system. Roughly, dispersive blow-up has being called to the development of point singularities due to the focussing of short or long waves. In mathematical terms, we show that the existence of this kind of singularities is provided by the linear dispersive solution by proving that the Duhamel term is smoother. It seems that this result is the first regarding systems of nonlinear dispersive equations. To obtain our results we use, in addition to smoothing properties, persistence properties for solutions of the IVP in fractional weighted Sobolev spaces which we establish here.
Climate Equivalence and International Trade

Abstract This article examines a significant question in navigating trade and climate tension: how to recognize another country as having equivalent climate regulations. Such equivalence forms a core component of many proposed models of so-called climate clubs. Establishing equivalence between distinct national climate regulation regimes poses a unique challenge that draws upon both trade and environmental international cooperation. Drawing on existing proposals, I examine prospects for country-based cooperation through three models: ETS-linking, benchmarking of shared methods and minimum standards, and benchmarking of outcome duties. The analysis concludes that all models necessitate some trade-offs between the goals of rigorous oversight of climate objectives, inclusivity, and WTO compliance. Benchmarking of shared methods and minimum standards seems most feasible, and would provide a deeper level of integration between trade and climate cooperation, but necessitates a shift in how countries, particularly the EU, oversee regulatory compliance.
A Hybrid Visual–Haptic Framework for Motion Synchronization in Human–Robot Cotransporting: A Human Motion Prediction Method

In this article, we propose a hybrid visual–haptic framework enabling a robot to achieve motion synchronization in human–robot cotransporting. Visual sensing is employed in capturing human motion in real time. To deal with the inherent delays between the human’s initiative motion and the robot’s responsive motion in cotransporting, a human motion prediction method is developed to make the robot follow human motion proactively. Motion synchronization is achieved when the robot accurately tracks the filtered and predicted human motion. Force sensing is utilized to regulate interaction forces to ensure compliance when motion error between the human and robot is generated. A neural network (NN)-based control is proposed to achieve precise trajectory tracking. Comparative experimental results show that our proposed framework is effective in such cotransporting tasks.
The image of a tropical linear space

Given a tropical linear space $L \subseteq \mathbb{T}^n$ and a matrix $A \in \mathbb{T}^{m \times n}$, the image $AL$ of $L$ under $A$ is typically not a tropical linear space. We introduce a tropical linear space $\mathrm{tropim}_A(L)$, the tropical image, containing $AL$. We show under mild hypotheses that $\mathrm{tropim}_A(L)$ is realizable if $L$ is and apply the tropical image to construct the stable sum of two tropical linear spaces without a disjoint pair of bases.
Schur's Lemma for Coupled Reducibility and Coupled Normality

Let $\mathcal A = \{A_{ij} \}_{i, j \in \mathcal I}$, where $\mathcal I$ is an index set, be a doubly indexed family of matrices, where $A_{ij}$ is $n_i \times n_j$. For each $i \in \mathcal I$, let $\mathcal V_i$ be an $n_i$-dimensional vector space. We say $\mathcal A$ is reducible in the coupled sense if there exist subspaces, $\mathcal U_i \subseteq \mathcal V_i$, with $\mathcal U_i \neq \{0\}$ for at least one $i \in \mathcal I$, and $\mathcal U_i \neq \mathcal V_i$ for at least one $i$, such that $A_{ij} (\mathcal U_j) \subseteq \mathcal U_i$ for all $i, j$. Let $\mathcal B = \{B_{ij} \}_{i, j \in \mathcal I}$ also be a doubly indexed family of matrices, where $B_{ij}$ is $m_i \times m_j$. For each $i \in \mathcal I$, let $X_i$ be a matrix of size $n_i \times m_i$. Suppose $A_{ij} X_j = X_i B_{ij}$ for all~$i, j$. We prove versions of Schur's Lemma for $\mathcal A, \mathcal B$ satisfying coupled irreducibility conditions. We also consider a refinement of Schur's Lemma for sets of normal matrices and prove corresponding versions for $\mathcal A, \mathcal B$ satisfying coupled normality and coupled irreducibility conditions.
ST-TrackNet: A Multiple-Object Tracking Network Using Spatio-Temporal Information

Multiple-object tracking (MOT) is a crucial component in autonomous driving systems. However, inaccurate object detection is always the bottleneck for MOT. Most detectors are not designed to take the temporal information across consecutive frames into consideration. To take advantage of such information, we design a novel data representation, the spatio-temporal (ST) map, which collects a batch of detection results spatio-temporally, and we train a novel network, ST-TrackNet, to assign predicted track IDs to each positive detection across a sequence. With our ST map detection fed into the tracker, the correlation of objects between adjacent frames becomes prominent, which improves the performance of the tracker in the data association step. Moreover, the long-term trajectory in a sequence also helps to refine the detection results. We train and evaluate our network on the KITTI dataset, a CARLA simulation dataset, and a dataset recorded in a factory environment. Our approach generally achieves superior performance over the state-of-the-art. Note to Practitioners—We investigate the MOT problem in this paper. A spatio-temporal pipeline is proposed to provide a solution to this problem. Object detection results produced by off-the-shelf object detectors are used to form the proposed ST maps. In low signal-to-noise ratio (SNR) situations, our proposed framework can achieve more accurate and robust tracking results with more false-positives. Due to the simplicity and modular design of our framework, it can be applied directly after the detection stage to achieve the online tracking task. The proposed method is evaluated on several datasets, and the experimental results demonstrate its effectiveness. Our method can also be used for other autonomous driving applications, such as path planning and trajectory prediction.
Evaluating the effect of ocular aberrations on the simulated performance of a new refractive IOL design using adaptive optics.

Adaptive optics (AO) visual simulators are excellent platforms for non-invasive simulation visual performance with new intraocular lens (IOL) designs, in combination with a subject own ocular aberrations and brain. We measured the through focus visual acuity in subjects through a new refractive IOL physically inserted in a cuvette and projected onto the eye's pupil, while aberrations were manipulated (corrected, or positive/negative spherical aberration added) using a deformable mirror (DM) in a custom-developed AO simulator. The IOL increased depth-of-focus (DOF) to 1.53 ± 0.21D, while maintaining high Visual Acuity (VA, -0.07 ± 0.05), averaged across subjects and conditions. Modifying the aberrations did not alter IOL performance on average.
Legendre Drinfeld modules and universal supersingular polynomials

We introduce a certain family of Drinfeld modules that we propose as analogues of the Legendre normal form elliptic curves. We exhibit explicit formulas for a certain period of such Drinfeld modules as well as formulas for the supersingular locus in that family, establishing a connection between these two kinds of formulas. Lastly, we also provide a closed formula for the supersingular polynomial in the $\jmath$-invariant for generic Drinfeld modules.
The endogenous role of location evaluation for academic performance in university

The purpose of this paper is to contribute to the limited research on universities’ decision to innovate, using the network and knowledge-based perspectives as our theoretical underpinning. The first conclusion is that universities are more likely to locate their scientific productivity on a standalone campus than in a multi-campus system when the knowledge effect is more favorable. To make a contribution to industry and collaboration, universities are more likely to locate their scientific productivity in a multi-campus system. The second conclusion is that after controlling for endogeneity bias, the mean of academic performance for scientific productivity on a standalone campus is higher than it is on a multi-campus system. The third conclusion is that locating innovation activities in either a standalone or multi-campus system under theoretically appropriate conditions increases academic performance. These findings pose interesting challenges for knowledge management in innovation through a university’s location decision.
Existence and Regularity of solutions to 1-D Fractional Order Diffusion Equations

In this article we investigate the existence and regularity of 1-d steady state fractional order diffusion equations. Two models are investigated:the Riemann-Liouville fractional diffusion equation, and the Riemann-Liouville-Caputo fractional diffusion equation. For these models we explicitly show how the regularity of the solution depends upon the right hand side (rhs) function. We also establish for which Dirichlet and Neumann boundary conditions the models are well posed.
Variational Lagrangian formulation of the Euler equations for incompressible flow: A simple derivation

In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and the subsequent work on this topic rely heavily on the properties of Lie groups and Lie algebras which remain unfamiliar to most fluid dynamicists. In this note, we provide a simple derivation of Arnold's result which only uses the classical methods of calculus of variations. In particular, we show that the Lagrangian flow maps generated by the solutions of the incompressible Euler equations coincide with the stationary curves of an appropriate energy functional when the extremization is carried out over the set of volume-preserving diffeomorphisms.
Improved Two States Characteristics in MIS Tunnel Diodes by Oxide Local Thinning Enhanced Transient Current Behavior

The effect of oxide local thinning (OLT) on the increase in current two states in metal–insulator–semiconductor (MIS) tunnel diodes for dynamic memory usage has been demonstrated. Two orders of magnitude improvement in the read current window could be observed. The MIS sample after performing the deep depletion stress (DDS) would soft breakdown (SBD) and could be effectively considered that the oxide was locally thinned. Pulsed voltage program was used to write on fresh MIS (before SBD) and OLT MIS (after SBD). A larger magnitude of transient read current could be observed for OLT MIS, and subsequently the improved current two states characteristics. The read currents of OLT MIS were stable under the endurance test. The transient behavior of a fresh MIS could be understood by the charging and discharging of a capacitor. On the contrary, the tunneling current would be dominated in an OLT MIS. At the same time, since the electron tunneling only concentrated locally, OLT MIS would take longer to recover to the steady-state. The improvement of read current after OLT forming was reproducible, and various write programs were performed for further examination. TCAD simulations demonstrated that the electrons would leak out and the electron density would decrease under larger gate voltage for OLT MIS. This work has shown the potential of OLT MIS for the dynamic memory usage, and the idea of local thinning on the gate oxide might be beneficial for the design of the future dynamic memory.
Non-local initial problem for second order time-fractional and space-singular equation

In this work, we consider an initial problem for second order partial differential equations with Caputo fractional derivatives in the time-variable and Bessel operator in the space-variable. For non-local boundary conditions, we present a solution of this problem in an explicit form representing it by the Fourier-Bessel series. The obtained solution is written in terms of multinomial Mittag-Leffler functions and first kind Bessel functions.
A category-theoretic characterization of almost measurable cardinals

Through careful analysis of an argument of Brooke-Taylor and Rosicky, we show that the powerful image of any accessible functor is closed under colimits of $\kappa$-chains, $\kappa$ a sufficiently large almost measurable cardinal. This condition on powerful images, by methods resembling those of Lieberman and Rosicky, implies $\kappa$-locality of Galois types. As this, in turn, implies sufficient measurability of $\kappa$, via a paper of Boney and Unger, we obtain an equivalence: a purely category-theoretic characterization of almost measurable cardinals.
The star-shaped Λ-coalescent and Fleming–Viot process

ABSTRACT The star-shaped Λ-coalescent and corresponding Λ-Fleming–Viot process, where the Λ measure has a single atom at unity, are studied in this article. The transition functions and stationary distribution of the Λ-Fleming–Viot process are derived in a two-type model with mutation. The distribution of the number of non-mutant lines back in time in the star-shaped Λ-coalescent is found. Extensions are made to a model with d types, either with parent-independent mutation or general Markov mutation, and an infinitely-many-types model, when d → ∞. An eigenfunction expansion for the transition functions is found, which has polynomial right eigenfunctions and left eigenfunctions described by hyperfunctions. A further star-shaped model with general frequency-dependent change is considered and the stationary distribution in the Fleming–Viot process derived. This model includes a star-shaped Λ-Fleming–Viot process with mutation and selection. In a general Λ-coalescent explicit formulae for the transition functions and stationary distribution, when there is mutation, are unknown. However, in this article, explicit formulae are derived in the star-shaped coalescent.
Platinum Nanostructured Needle-Shaped Sensors for Ion Detection in Biomedical Applications

Ion-selective electrodes (ISEs) represent one of the main technologies for developing sensors to measure ions concentration in human tissues. All-solid-state ISEs are of key importance for sensor miniaturization, especially toward point-of-care applications. In this article, we propose an innovative needle-shaped sensor in sub-mm sizes with nanostructured platinum (Pt) for the aim of ion detection. It can be employed in biomedical applications, with particular regard to surgical procedures. The developed sensor has been tested for potassium (K+) detection, which is very important in cells functions assessment. For the first time in the literature, we investigate the effects on the morphology of electrodeposition voltage and time. In the past, similar nanofabrications have been successfully tried on usual planar geometries. Here, instead, Pt nanostructure (Pt-NS) growth is successfully shown on a thin Pt wire with a diameter of 0.1 mm only. Both granular and petal-like nanostructures are obtained depending on the applied deposition voltage. The minimum time needed to nanostructure the whole electrode surface is found for each deposition voltage, suggesting that higher absolute voltage values need higher deposition time. The electrochemical measurements performed on the Pt nanostructured K+ ISEs show enhanced stability over time with respect to non-nanostructured ISEs and a Nernstian response with the best sensitivity of 59.2 ± 2.4 mV/decade in the linear range from $10^{-{4}}$ to $10^{-{1}}$ M. These good results encourage to further extend this study toward sensing of other ions by means of these microfabricated needle-shaped sensors, which can be easily integrated into surgical instruments to be then used for diagnosis during surgical operations.
The congruent numbers have positive natural density

We prove that the rational elliptic curve y^2 = x^3 - n^2x satisfies the full Birch and Swinnerton-Dyer conjecture for at least 41.9% of positive squarefree integers n equal to 1, 2, or 3 mod 8, and that it satisfies the regular BSD conjecture for at least 55.9% of positive squarefree integers n equal to 5, 6, or 7 mod 8. In particular, at least 55.9% of positive squarefree integers equal to 5, 6, or 7 mod 8 are congruent numbers. These proofs complete an argument started by Tian, Yuan, and Zhang.
Anti-Inflammatory Effects of Compounds from Echinoderms

Chronic inflammation can extensively burden a healthcare system. Several synthetic anti-inflammatory drugs are currently available in clinical practice, but each has its own side effect profile. The planet is gifted with vast and diverse oceans, which provide a treasure of bioactive compounds, the chemical structures of which may provide valuable pharmaceutical agents. Marine organisms contain a variety of bioactive compounds, some of which have anti-inflammatory activity and have received considerable attention from the scientific community for the development of anti-inflammatory drugs. This review describes such bioactive compounds, as well as crude extracts (published during 2010–2022) from echinoderms: namely, sea cucumbers, sea urchins, and starfish. Moreover, we also include their chemical structures, evaluation models, and anti-inflammatory activities, including the molecular mechanism(s) of these compounds. This paper also highlights the potential applications of those marine-derived compounds in the pharmaceutical industry to develop leads for the clinical pipeline. In conclusion, this review can serve as a well-documented reference for the research progress on the development of potential anti-inflammatory drugs from echinoderms against various chronic inflammatory conditions.
Norm-dependent random matrix ensembles in external field and supersymmetry

The class of norm-dependent random matrix ensembles is studied in the presence of an external field. The probability density of the ensemble depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact mapping to superspace is performed. A transformation formula is derived which gives the probability density in superspace as a single integral over the probability density in ordinary space. This is done for orthogonal, unitary and symplectic symmetries. In the case of unitary symmetry, some explicit results for the correlation functions are derived.
Exotic expansions and pathological properties of $\zeta$-functions on conic manifolds

We give a complete classification and present new exotic phenomena of the meromorphic structure of $\zeta$-functions associated to general self-adjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic extensions of these $\zeta$-functions have, in general, countably many logarithmic branch cuts on the nonpositive real axis and unusual locations of poles with arbitrarily large multiplicity. The corresponding heat kernel and resolvent trace expansions also exhibit exotic behaviors with logarithmic terms of arbitrary positive and negative multiplicity. We also give a precise algebraic-combinatorial formula to compute the coefficients of the leading order terms of the singularities.
Almost Torus Manifolds of Non-negative Curvature

An almost torus manifold $M$ is the odd-dimensional analog of a torus manifold. Namely, it is a $(2n+1)$-dimensional orientable manifold with an effective, isometric, almost isotropy-maximal $T^n$-action. In this paper, we show that closed, simply-connected, non-negatively curved almost torus manifolds are equivariantly diffeomorphic to a quotient by a free linear torus action on a product of spheres, thus generalizing Wiemeler's classification of simply-connected, non-negatively curved torus manifolds.
Toward More Actionable Flood‐Risk Information

The increasingly urgent need to develop knowledge and practices to manage flood risks drives innovative information design. However, experts often disagree about design practices. As a result, flood‐risk estimates can diverge, leading to different conclusions for decision‐making. Using examples of household‐scale fluvial (riverine) flood‐risk information in the United States, we assess design features and risk communication approaches that may lead to more actionable information for decision‐making. We argue that increased attention to uncertainty characterization and model diagnostics is a critical intermediate step for developing simpler approaches for designing flood‐risk information. Simpler frameworks are desirable because flood risks change over time, and simpler frameworks are less costly to update. Developing frameworks for large spatial domains require collaboration grounded in principles of open science. Finally, systematically evaluating how decision‐makers access and use information can provide new insights to guide risk communication and information design.