What happens when employers value worker welfare in frictional labor markets? We show this "responsibility" creates an endogenous wedge in the marginal labor cost -- akin to a hiring subsidy -- altering wage and vacancy incentives rather than only changing the surplus split. The wedge is strongest when outside options are weak and separations rare, implying larger wage premia in slack, low-mobility markets. In a wage-posting model with on-the-job search, responsible firms may occupy the high-wage segment even when less productive. In a DMP model, responsible firms commit to higher worker bargaining power, raising the value of unemployment and thereby wages at regular firms.

Photo-control of correlated phases is central to advancing and manipulating novel functional properties of quantum materials. Here, we explore microwave enhancement of superconductivity in flat bands through generation of nonequilibrium quasiparticles at subgap frequencies. In conventional superconductors, it is known to occur via radiation absorption determined by fermi velocity, which however is small in flat bands resulting in quenched quasiparticle excitations. Strikingly, in contrast to the conventional paradigm we show a non-vanishing microwave absorption in flat band systems enabled by Bloch quantum geometry leading to superconducting gap enhancement, underscoring the band-geometric origin of nonequilibrium flat band superconductivity. Specifically, we demonstrate this in twisted bilayer graphene, a promising candidate material, and find significant gap enhancement near critical temperature. This work highlights that the nonequilibrium dynamics of materials with non-trivial flat bands as a promising area for future experimental and theoretical investigation.

A reduced-dimensional asymptotic modelling approach is presented for the analysis of two-phase flow in a thin cylinder with aperture of order $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small positive parameter. We consider a nonlinear Muskat-Leverett two-phase flow model expressed in terms of a fractional flow formulation and Darcy's law with a saturation and the reduced pressure as unknown. We assume that the capillary pressure is non-singular and neglect the acceleration of gravity in Darcy's law. Given flows seep through the lateral surface of the cylinder. This exchange process leads to a non-homogeneous Neumann boundary condition with an intensity factor $\varepsilon^α$ $(α\ge 1)$ which controls the mass transport.Furthermore, the absolute permeability tensor comprises an intensity coefficient $\varepsilon^β,$ $β\in \Bbb R,$ in the transversal directions. The asymptotic behaviour of the solution is studied as $\varepsilon \to 0,$ i.e. when the thin cylinder shrinks into an interval. Two qualitatively distinct cases are discovered in the asymptotic behavior of the solution: $α=1 \ \text{and} \ β<2,$ and $α> β-1 \ \text{and} \ α>1.$ In each of these cases, the asymptotic approximations are constructed for the pressures, saturations and velocities of these flows, and the corresponding asymptotic estimates are proved in various norms, including energy and uniform pointwise norms. Depending on the values of the parameters $α$ and $β,$ the first terms of the asymptotics are solutions to the corresponding nonlinear elliptic-parabolic system of two differential equations, which is a one-dimensional model of the Muskat-Leverett two-phase flow.

We prove that order zero operators in the pseudodifferential calculus associated to a filtration defined by Androulidakis, Mohsen and Yuncken are bounded on $L_p$ spaces for $1<p<\infty.$

Optical imaging plays a crucial role in advancing science and technology, enabling applications in fields ranging from biomedicine to astronomy. However, imaging through scattering media such as biological tissues, fog, or turbulent atmosphere remains a major challenge. Light scattering and absorption in such media make imaging challenging; in the case of time varying scatterers and low-light regime imaging has not been demonstrated so far. We present the first demonstration of non-invasive imaging of dim objects hidden behind dynamic scattering layers, obtaining robust reconstruction even at extremely low photon counts per frame. We achieve this by developing a new data-processing approach. In our experiment, we utilize a photon number resolving camera to capture a sequence of frames, containing on average, less than one photon per pixel. We validate our approach in microscopy, where we reconstruct images of biological samples stained with standard fluorescent dyes. Beyond microscopy, our approach can be applied in LIDAR systems for imaging through fog, and endoscopy using multimode and multicore fibers.

E-commerce operations are essentially online, with customer orders arriving dynamically. However, very little is known about the performance of online policies for warehousing with respect to optimality, particularly for order picking and batching operations, which constitute a substantial portion of the total operating costs in warehouses. We aim to close this gap for one of the most prominent dynamic algorithms, namely reoptimization (Reopt), which reoptimizes the current solution each time when a new order arrives. We examine Reopt in the Online Order Batching, Sequencing, and Routing Problem (OOBSRP), in both cases when the picker uses either a manual pushcart or a robotic cart. Moreover, we examine the noninterventionist Reopt in the case of a manual pushcart, wherein picking instructions are provided exclusively at the depot. We establish analytical performance bounds employing worst-case and probabilistic analysis. We demonstrate that, under generic stochastic assumptions, Reopt is almost surely asymptotically optimal and, notably, we validate its near-optimal performance in computational experiments across a broad range of warehouse settings. These results underscore Reopt's relevance as a method for online warehousing applications.

Conformal inference is a versatile tool for building prediction sets in regression or classification. We study the false coverage proportion (FCP) in a simultaneous inference setting with a calibration sample of $n$ points and a test sample of $m$ points. We identify the exact, distribution-free, asymptotic distribution of the FCP when both $n$ and $m$ tend to infinity. This shows in particular that FCP control can be achieved by using the well-known Kolmogorov distribution, and puts forward that the asymptotic variance is decreasing in the ratio $n/m$. We then provide a number of extensions by considering the problems of novelty detection, weighted conformal inference or distribution shift between the calibration sample and the test sample. In particular, our asymptotic results allow to accurately quantify the asymptotic behavior of the errors (a miscovering interval or declaring a false novelty) when weighted conformal inference is used.

Harnessing the nonlinear response of a medium is essential for applications including frequency conversion and light amplification, as well as for the generation of quantum many-body correlations of light or matter. However, achieving these effects typically requires high drive intensities and thick samples, which induce undesired heating effects that typically suppress quantum correlations. In this work, we demonstrate that atom-thin arrays of quantum emitters exhibit a robust nonlinear response even at arbitrarily weak drive intensities. This discovery challenges the long-held assumption that weakly driven ensembles behave classically; instead, we reveal that subradiant states provide a dominant nonlinear contribution that persists in the low-intensity limit. Using a Dynamical Mean-Field Theory (DMFT) approach, we predict that these nonlinearities generate a quantum-correlated steady state composed of interacting pairs of subradiant excitations, characterized by long-range correlations and multi-mode squeezing. Our findings establish a new frontier for nonlinear quantum optics at minimal power, and provide a scalable protocol for preparing multimode squeezing, offering potential for applications in quantum metrology.

This paper proves the Giroux Correspondence in dimension three using Heegaard splittings of contact manifolds. In two of the authors earlier paper they proved the Giroux Correspondence for tight contact 3-manifolds via convex Heegaard surfaces, and simultaneously, Honda, Breen and Huang gave an alldimensions proof of the Giroux Correspondence by generalising convex surface theory to higher dimensions. This paper extends the Heegaard splitting approach to arbitrary (not necessarily tight) contact 3-manifolds in order to provide a proof accessible to a low-dimensional audience. The proof assumes classification moves relating bypass decompositions for isotopic contact structures on cobordisms that are topological products; in the Appendix, we prove this result in the 3- dimensional setting.

We provide a rigorous justification of various kinetic regimes exhibited by the nonlinear Schrödinger equation with an additive stochastic forcing and a viscous dissipation. The importance of such damped-driven models stems from their wide empirical use in studying turbulence for nonlinear wave systems. The force injects energy into the system at large scales, which is then transferred across scales, thanks to the nonlinear wave interactions, until it is eventually dissipated at smaller scales. The presence of such scale-separated forcing and dissipation allows for the constant flux of energy in the intermediate scales, known as the inertial range, which is the focus of the vast amount of numerical and physical literature on wave turbulence. Roughly speaking, our results provide a rigorous kinetic framework for this turbulent behavior by proving that the stochastic dynamics can be effectively described by a deterministic damped-driven kinetic equation, which carries the full picture of the turbulent energy dynamic across scales (like cascade spectra or other flux solutions). The analysis extends previous works in the unperturbed setting arXiv:1912.09518-arXiv:2301.07063 to the above empirically motivated damped driven setting. Here, in addition to the size $L$ of the system, and the strength $λ$ of the nonlinearity, an extra thermodynamic parameter has to be included in the kinetic limit ($L\to \infty, λ\to 0$), namely the strength $ν$ of the forcing and dissipation. Various regimes emerge depending on the relative sizes of $L$, $λ$ and $ν$, which give rise to different kinetic equations. Two major novelties of this work is the extension of the Feynman diagram analysis to additive stochastic objects, and the sharp asymptotic development of the leading terms in that expansion.

This research compares PDF parsing and Optical Character Recognition (OCR) methods for extracting Nepali content from PDFs. PDF parsing offers fast and accurate extraction but faces challenges with non-Unicode Nepali fonts. OCR, specifically PyTesseract, overcomes these challenges, providing versatility for both digital and scanned PDFs. The study reveals that while PDF parsers are faster, their accuracy fluctuates based on PDF types. In contrast, OCRs, with a focus on PyTesseract, demonstrate consistent accuracy at the expense of slightly longer extraction times. Considering the project's emphasis on Nepali PDFs, PyTesseract emerges as the most suitable library, balancing extraction speed and accuracy.

We show that the sign of the Euler characteristic of an $S$-arithmetic subgroup of a simple algebraic group depends on the $S$-congruence completion only, except possibly in type ${}^6 D_4$. Consequently, the sign is a profinite invariant for such $S$-arithmetic groups with the congruence subgroup property. This generalizes previous work of the first author with Kionke--Raimbault--Sauer.

The concept of randomness in quantum computing has been central to construct benchmarking tools, cryptographic protocols, as well as a proof of beyond classical computation. Discerning whether quantum states (or unitaries) are randomly distributed is a computational task that requires an enormous amount of quantum computational resources. This work addresses such a challenge, a hierarchical discrimination algorithm to efficiently test the if a set of states $S$ generated from a black-box quantum device with an unknown distribution is (in)compatible with a random distribution. To this end, we reduce the complexity of the problem by selecting an observable with known spectrum to study the statistical properties of its expectation values with respect to the quantum states from an unknown (black-box) quantum device. Concurrently, we use our first technical result, a connection between Haar-randomness and the Dirichlet distribution, to analytically compute Haar-random moments of the observable. Our Haar-random discriminator test is then simply to compare those statistical moments such that if $S$ fails the test it is enough to state that the quantum devices does not output randomly distributed states. Else, we can not (yet) confirm that the states follow a Haar-random distribution. We further provide extension to this algorithm by permutation- and unitary-equivalent randomization of observable at increasing computational resources, which allows us to more accurately state whether $S$ is compatible with Haar-randomness. We envision the use of the discriminator test as quantum device benchmark by discriminating if the states generated are Haar-random incompatible.

We say that an edge-coloring of a graph $G$ is proper if every pair of incident edges receive distinct colors, and is rainbow if no two edges of $G$ receive the same color. Furthermore, given a fixed graph $F$, we say that $G$ is rainbow $F$-saturated if $G$ admits a proper edge-coloring which does not contain any rainbow subgraph isomorphic to $F$, but the addition of any edge to $G$ makes such an edge-coloring impossible. The maximum number of edges in a rainbow $F$-saturated graph is the rainbow Turán number, whose study was initiated in 2007 by Keevash, Mubayi, Sudakov, and Verstraëte. Recently, Bushaw, Johnston, and Rombach introduced study of a corresponding saturation problem, asking for the minimum number of edges in a rainbow $F$-saturated graph. We term this minimum the proper rainbow saturation number of $F$, denoted $\mathrm{sat}^*(n,F)$. We asymptotically determine $\mathrm{sat}^*(n,C_4)$, answering a question of Bushaw, Johnston, and Rombach. We also exhibit constructions which establish upper bounds for $\mathrm{sat}^*(n,C_5)$ and $\mathrm{sat}^*(n,C_6)$.

We consider the balayage of a measure $μ$ defined on a domain $Ω$ onto its boundary $\partial Ω$. Assuming that $Ω$ has a corner of opening $πα$ at a point $z_0 \in \partial Ω$ for some $0 < α\leq 2$ and that $dμ(z) \asymp |z-z_{0}|^{2b-2}d^{2}z$ as $z\to z_0$ for some $b > 0$, we obtain the precise rate of vanishing of the balayage of $μ$ near $z_{0}$. The rate of vanishing is universal in the sense that it only depends on $α$ and $b$. We also treat the case when the domain has multiple corners at the same point. Moreover, when $2b\leq \frac{1}α$, we provide explicit constants for the upper and lower bounds.

A measurement of a primordial non-Gaussianity (PNG) signal through late- or early-Universe probes has the potential to transform our understanding of the physics of the primordial Universe. $N$-body simulations, such as the public \textsc{AbacusPNG} set presented in this study, consisting of 9 boxes, each of size $L_{\rm box} = 2~{\rm Gpc}/h$ and particle mass of $1.01 \times 10^{10} \ M_\odot/h$, provide a viable path forward. As validation, we find good agreement between the simulations and our expectations from one-loop perturbation theory and the `separate universe' method for the matter bispectrum, matter power spectrum and the halo bias parameter associated with PNG, $b_ϕ$. As a science application, we investigate the link between halo assembly bias and $b_ϕ$ for halo properties known to play a vital role in accurately predicting galaxy clustering: concentration, shear (environment), and accretion rate. We find a strong response for all three parameters, suggesting that the connection between $b_ϕ$ and the assembly history of halos needs to be taken into account by future PNG analyses. We further perform the first study of the $b_ϕ$ parameter from fits to early DESI data of the luminous red galaxy (LRG) and quasi-stellar object (QSO) samples and comment on the effect on $f_{\rm NL}$ constraints for the allowed galaxy-halo models (note that $σ[f_{\rm NL}] \propto \frac{σ[b_ϕ]}{b_ϕ}$). We find that the error on $f_{\rm NL}$ is 21, 6, 22 for the LRGs at $z = 0.5$ and $z = 0.8$ and QSOs at $z = 1.4$, respectively, suggesting that a thorough understanding of galaxy assembly bias is warranted so as to perform robust high-precision analysis of local-type PNG with future surveys. Simulations publicly available at https://app.globus.org/file-manager?origin_id=ffc65d7a-0bf9-11ec-90b4-41052087bc27

We present an analytical calculation of the complete $α^6$ correction to energies of $nP$-levels of two-body systems consisting of the spin-$0$ or $1/2$ extended-size particles with arbitrary masses and magnetic moments. The obtained results apply to a wide class of two-body systems such as hydrogen, positronium, muonium, and pionic or aniprotonic helium ion. We found an additional $α^6$ correction for $nP$-levels of positronium, which was previously overlooked. Our results are also relevant for light muonic atoms, whose accurate theoretical predictions are required for extracting the nuclear charge radii.

In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions may influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more realistic model, uncertainty can be quantified, e.g., using the robust optimization approach: We assume that the leader does not know the follower's objective precisely, but only up to some uncertainty set, and her aim is to optimize the worst case of the corresponding scenarios. Now the question arises how the complexity of bilevel optimization changes under the additional complications of this uncertainty. We make a further step towards answering this question by examining an easy bilevel problem. In the Bilevel Selection Problem (BSP), the leader and the follower each select some items from their own item set, while a common number of items to select in total is given, and each player minimizes the total costs of the selected items, according to different sets of item costs. We show that the BSP can be solved in polynomial time and then investigate its robust version. If the two players' item sets are disjoint, it can still be solved in polynomial time for several types of uncertainty sets. Otherwise, we show that the Robust BSP is NP-hard and present a 2-approximation algorithm and exact exponential-time approaches. Furthermore, we investigate variants of the BSP where one or both of the two players take a continuous decision. One variant leads to an example of a bilevel optimization problem whose optimal value may not be attained. For the Robust Continuous BSP, where all variables are continuous, we also develop a new approach for the setting of discrete uncorrelated uncertainty, which gives a polynomial-time algorithm for the Robust Continuous BSP and a pseudopolynomial-time algorithm for the Robust Bilevel Continuous Knapsack Problem.

This paper studies irreducible characters of the $q$-rook monoid algebra $R_n(q)$ using the vertex algebraic method. Based on the Frobenius formula for $R_n(q)$, a new iterative character formula is derived with the help of the vertex operator realization of the Schur symmetric function. The same idea also leads to a simple proof of the Murnaghan-Nakayama rule for $R_n(q)$. We also introduce the bitrace for the $q$-rook monoid and derive its combinatorial formula as a generalization of the bitrace formula for the Iwahori-Hecke algebra. The character table of $R_n(q)$ with $|μ|=5$ is listed in the appendix.

We propose logit-based IV and augmented logit-based IV estimators that serve as alternatives to the traditionally used 2SLS estimator in the model where both the endogenous treatment variable and the corresponding instrument are binary. Our novel estimators are as easy to compute as the 2SLS estimator but have an advantage over the 2SLS estimator in terms of causal interpretability. In particular, in certain cases where the probability limits of both our estimators and the 2SLS estimator take the form of weighted-average treatment effects, our estimators are guaranteed to yield non-negative weights whereas the 2SLS estimator is not.

We introduce a way to compare actions in decision problems. One action is safer than another if the set of beliefs at which the decision-maker prefers the safer action expands as the decision-maker becomes more risk averse. We provide a full characterization of this relation, show that it is equivalent to robust conceptions of single-crossing and second-order stochastic dominance, and reveal that in monotone decision problems it totally orders the decision-maker's set of actions. We discuss applications to games, insurance, investment hedging, and security design.

Using the introduction of comprehensive sex education in Sweden as a natural experiment, we explore how educational curricula can shape social norms and impact personal well-being. Inspired by liberal values, the curriculum taught more than just biology. It instilled lessons on abstinence, rational family planning, and the importance of taking social responsibility for personal decisions. We find that the reform successfully addressed its intended outcomes, reducing unwanted pregnancies, leading to fertility postponements and increasing female labor force participation. The findings suggest that social norms, internalized through school-based sex education, persistently affect peoples outcomes in significant ways.

The article is devoted to a comparison of the Čech cohomology with the coefficients in a presheaf of Abelian groups and the topos cohomology of the sheaf generated by this presheaf for a poset with the Aleksandrov topology. The article consists of three parts. The first part provides information from the theory of cohomology of small categories and cohomology of simplicial sets with systems of coefficients. The second part is devoted to Laudal's Theorem stating that covering cohomology for an arbitrary topological space with coefficients in the presheaf of Abelian groups is isomorphic to the derived limit functors. The third part presents the main results. The criterion for the invariance of cohomology groups of small categories when passing to the inverse image leads to necessary and sufficient isomorphism conditions for the Čech cohomology of an arbitrary presheaf and the topos cohomology of the sheaf generated by this presheaf. In particular, for a finite poset, these conditions reduce to the acyclicity of the upper secrions of Dedekind-MacNeille cuts having a non-empty lower section, and the verification of these conditions is algorithmically computable.

We propose an efficient framework using Dynnikov coordinates for homotopy-aware multi-agent path planning in planar domains that may contain obstacles. We developed a method for generating multiple homotopically distinct solutions for the multi-agent path planning problem in planar domains by combining our framework with revised prioritized planning and proved its completeness under specific assumptions. Experimentally, we demonstrated that our method is significantly faster than a method without Dynnikov coordinates. We also confirmed experimentally that homotopy-aware planning contributes to avoiding locally optimal solutions when searching for low-cost trajectories for a swarm of agents in a continuous environment.

We consider the spatially inhomogeneous Landau equation in the case of very soft and Coulomb potentials, $γ\in [-3,-2]$. We show that solutions can be continued as long as the following three quantities remain finite, uniformly in $t$ and $x$: (1) the mass density, (2) the velocity moment of order $s$ for any small $s>0$, and (3) the $L^p_v$ norm for any $p>3/(5+γ)$. In particular, we do not require a bound on the energy density.

The non-thermal nature of the cosmological gravitational wave background (CGWB) makes it difficult to define the initial condition for the graviton distribution, which determines the initial contribution to the CGWB anisotropies. Specifically, unlike Cosmic Microwave Background (CMB) photons, primordial gravitational waves (GWs) are not necessarily subject to adiabatic initial conditions. For the CGWB generated by quantum fluctuations of the metric during inflation the initial conditions are not adiabatic. The violation of adiabaticity arises from the presence of independent tensor perturbations during inflation, which behave as two extra fields that affect the standard single-clock argument. The non-adiabatic initial contribution enhances the total CGWB angular power spectrum compared to the standard adiabatic case. Given the high degree of correlation between the CGWB and Cosmic Microwave Background (CMB) anisotropies, we present the constrained realization maps of the CGWB built using the high-resolution CMB Planck maps for different initial conditions.

A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. This generalizes the previous work [P. Bella and R.V. Kohn. Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate.

The reliability of analysis is becoming increasingly important as point-of-care diagnostics are transitioning from single analyte detection towards multiplexed multianalyte detection. Multianalyte detection benefits greatly from complementary metal-oxide semiconductor (CMOS) integrated sensing solutions, offering miniaturized multiplexed sensing arrays with integrated readout electronics and extremely large sensor counts. The development of CMOS back end of line integration compatible graphene field-effect transistor (GFET) based biosensing has been rapid during the last few years, both in terms of the fabrication scale-up and functionalization towards biorecognition from real sample matrices. The next steps in industrialization relate to improving reliability and require increased statistics. Regarding functionalization towards truly quantitative sensors and on-chip bioassays with improved statistics require sensor arrays with reduced variability in functionalization. Such multiplexed bioassays, whether based on graphene or on other sensitive nanomaterials, are among the most promising technologies for label-free electrical biosensing. As an important step towards that, we report wafer-scale fabrication of CMOS integrated GFET arrays with high yield and uniformity, designed especially for biosensing applications. We demonstrate the operation of the sensing platform array with 512 GFETs in simultaneous detection for sodium chloride concentration series. This platform offers a truly statistical approach on GFET based biosensing and further to quantitative and multi-analyte sensing. The reported techniques can also be applied to other fields relying on functionalized GFETs, such as gas or chemical sensing or infrared imaging.

The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.

Bounded model checking (BMC) is an efficient formal verification technique which allows for desired properties of a software system to be checked on bounded runs of an abstract model of the system. The properties are frequently described in some temporal logic and the system is modeled as a state transition system. In this paper we propose a novel counting logic, $\mathcal{L}_{C}$, to describe the temporal properties of client-server systems with an unbounded number of clients. We also propose two dimensional bounded model checking ($2D$-BMC) strategy that uses two distinguishable parameters, one for execution steps and another for the number of tokens in the net representing a client-server system, and these two evolve separately, which is different from the standard BMC techniques in the Petri Nets formalism. This $2D$-BMC strategy is implemented in a tool called DCModelChecker which leverages the $2D$-BMC technique with a state-of-the-art satisfiability modulo theories (SMT) solver Z3. The system is given as a Petri Net and properties specified using $\mathcal{L}_{C}$ are encoded into formulas that are checked by the solver. Our tool can also work on industrial benchmarks from the Model Checking Contest (MCC). We report on these experiments to illustrate the applicability of the $2D$-BMC strategy.