The long term consequences of unwanted pregnancies carried to term on mothers have not been much explored. We use data from the Wisconsin Longitudinal Study (WLS) and propose a novel approach, namely two team cross-screening, to study the possible effects of unwanted pregnancies carried to term on various aspects of mothers' later-life mental health, physical health, economic well-being and life satisfaction. Our method, unlike existing approaches to observational studies, enables the investigators to perform exploratory data analysis, confirmatory data analysis and replication in the same study. This is a valuable property when there is only a single data set available with unique strengths to perform exploratory, confirmatory and replication analysis. In two team cross-screening, the investigators split themselves into two teams and the data is split as well according to a meaningful covariate. Each team then performs exploratory data analysis on its part of the data to design an analysis plan for the other part of the data. The complete freedom of the teams in designing the analysis has the potential to generate new unanticipated hypotheses in addition to a prefixed set of hypotheses. Moreover, only the hypotheses that looked promising in the data each team explored are forwarded for analysis (thus alleviating the multiple testing problem). These advantages are demonstrated in our study of the effects of unwanted pregnancies on mothers' later life outcomes.

A sender communicates private information about a hidden state to a receiver who seeks to match his action to that state. The sender strives to appear informed at the receiver's expense. I characterize informative equilibria under a broad class of signal structures and show that, when they exist, they are essentially unique. I show that informative equilibria can be noninfluential, in which case the receiver does not benefit from communication and relies only on prior information. My main results identify a complementarity that sufficiently precise prior information helps restore influential communication and characterize how the receiver's welfare depends on the quality of prior information. I also characterize how the sender's initial reputation for being informed shapes these results.

Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us inequalities to obtain lower bounds on the number of axioms. In this paper, we extend this result to higher-order equational theories. More precisely, we consider simply typed lambda calculus with product and unit types and study sets of equations between lambda terms. Then, we define homology groups of the given equational theory and show that a lower bound on the number of equations can be computed from the homology groups.

We study the impact of quantum gravitational memory burden - a backreaction effect that suppresses black hole evaporation - on neutrino signals from primordial black holes (PBHs). This suppression, modeled via a parameter k, reduces the high-energy muon neutrino fluence, particularly during the late stages of evaporation. We also consider beyond the Standard Model scenarios in which heavy neutral leptons (HNLs) are emitted by PBHs and subsequently decay, injecting secondary neutrinos that partially mitigate the suppression in the MeV-GeV range. We compute the full time-integrated neutrino spectrum and evaluate the expected IceCube event rates across the (k, mN) parameter space. We analyze both single source burst scenarios and the cumulative Galactic contribution assuming PBHs trace a realistic dark matter halo distribution. Even under optimistic proximity assumptions, the predicted event rates remain far below IceCube sensitivity, and population-level stacking within current observational bounds on the PBH abundance does not yield an observable signal in the considered mass range for PBH abundances consistent with existing observational constraints. These results demonstrate that entropy-suppressed evaporation substantially weakens neutrino detectability of light PBHs and must be consistently incorporated in future multi-messenger searches.

The group $\mathrm{SU}(3)$ has applications in several branches of physics. Many of these applications depend on availability of $\mathrm{SU}(3)$ coupling and recoupling coefficients. We have developed a modern Fortran library for calculation of the coupling coefficients, for both the $\mathrm{SU}(3)\supset\mathrm{U}(1)\times\mathrm{SU}(2)$ and $\mathrm{SU}(3)\supset\mathrm{SO}(3)$ group chains, and the recoupling coefficients. The library implements the algorithms of Draayer, Akiyama, and Millener, which are laid out in the paper. Performance of the library has been tested and compared to the Akiyama-Draayer (AD) library implementing the same algorithms as well as to a more recent implementation. Our library works for a larger range of $\mathrm{SU}(3)$ quantum numbers and provides more accurate coupling coefficients with large quantum numbers than the AD library.

Information diffusion on social media platforms is often assumed to occur primarily through explicit social connections, such as follower or friend ties. However, information frequently propagates beyond these observable ties -- through external websites, search engines, or algorithmic recommendations -- creating implicit links. How the presence of implicit links affects the diffusion process remains unclear. In this study, we investigate the characteristics of implicit links on Twitter using four large-scale datasets. Our analysis reveals that users who are farther from the original source in the social network are more likely to engage in diffusion via implicit links. Although implicit links contribute less to the overall diffusion volume than explicit links, they play a distinct role in disseminating content across diverse and topologically distant communities. We further examine the user attributes associated with the formation of implicit links and show that these features are unevenly distributed across the network and exhibit moderate levels of homophily and monophily. Together, these findings demonstrate that implicit links exert a meaningful influence on information diffusion and highlight the importance of incorporating them into models of diffusion and social influence.

Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping devices. Owing to the level of complexity in the clock structure and its energy consumption, such devices show trade-offs whose characterization remains an open challenge. Indeed, even conceptual designs for thermodynamically efficient quantum clocks are not yet well understood. In condensed matter theory, time-crystals were found as an exciting new phase of matter, featuring oscillations in (pseudo)-equilibrium with first experimental observations appearing recently. This naturally prompts the question: can time crystals be used as quantum clocks and what is their performance from a thermodynamic perspective? We answer this question and find that quantum time crystals are indeed genuine quantum clocks with a performance enhanced by the spontaneous breaking of time-translation symmetry.

Continuous-time control of multiple quadrotors in constrained environments under signal temporal logic (STL) specifications is critical due to their nonlinear dynamics, safety constraints, and the requirement to ensure continuous-time satisfaction of the specifications. To ensure such control, a two-stage framework is proposed to address this challenge. First, based on geometric control, a Lyapunov-based analysis of the rotational tracking dynamics is performed to facilitate multidimensional gain design. In addition, tracking-error bounds for subsequent STL robustness analysis are derived. Second, using the tracking-error bounds, a mixed-integer convex programming (MICP)-based planning framework with a backward-recursive scheme is developed. The framework is used to generate reference trajectories that satisfy multi-agent STL tasks while meeting the trajectory requirements imposed by geometric control. Numerical simulations demonstrate that, compared with uniform gains, the optimized multidimensional gains yield less conservative time-varying bounds, mitigate oscillations, and improve transient performance, while the proposed framework ensures the satisfaction of multi-agent STL tasks in constrained environments with provable tracking guarantees.

We characterize the strictly increasing symbols $φ:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_φ$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space $\mathcal{L}_0(\mathbb{N}_0)$. With this result we continue the recent research about this kind of spaces and operators, but our approach relies on establishing a natural isomorphism between the Lipschitz-type spaces over rooted trees and the classical spaces $\ell^{\infty}$ and $c_0$. Such isomorphism provides an alternative framework that simplifies and allows to improve many previous results about these spaces and the operators defined there.

Criminal activity data are typically available via a three-way tensor encoding the reported frequencies of different crime categories across time and space. The challenges that arise in the design of interpretable, yet realistic, model-based representations of the complex dependencies within and across these three dimensions have led to an increasing adoption of black-box predictive strategies. While this perspective has proved successful in producing accurate forecasts guiding targeted interventions, the lack of interpretable model-based characterizations of the dependence structures underlying criminal activity tensors prevents from inferring the cascading effects of these interventions across the different dimensions. We address this gap through the design of a low-rank bilinear autoregressive model which achieves comparable predictive performance to black-box strategies, while allowing interpretable inference on the dependence structures of reported criminal activities across crime categories, time and space. This representation incorporates the time dimension via an autoregressive construction that accounts for spatial effects and dependencies among crime categories through a separable low-rank bilinear formulation. When applied to Chicago police reports, the proposed model showcases remarkable predictive performance and also reveals interpretable dependence structures unveiling fundamental crime dynamics. These results facilitate the design of more refined intervention policies informed by the cascading effects of the policy itself.

We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions $c$, including Bregman and entropic transport divergences. We establish several properties of the resulting flows, including stability and energy identities. Using novel notions of convexity related to costs $c$, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.

It is generally assumed that the detection of a single photon as part of an interference pattern erases all possible which-path information. However, recent insights suggest that weak interactions can provide non-trivial experimental evidence for the physical delocalization of a single particle passing through an interferometer. Here, we present an experimental setup that can quantify the delocalization of individual photons using the rate of polarization flips induced by small rotations of polarization. The results show that photons detected in equal superpositions of the two paths are delocalized when detected in a high probability output port, and "super-localized" when detected in a low probability output port. We can thus confirm that delocalization depends on the detection of photons in the output of the interferometer, providing direct experimental evidence for the dependence of physical reality on the context established by a future measurement.

We investigate emergent superconductivity and non-reciprocal transport (magnetochiral anisotropy, superconducting diode effect) at the heterointerface of two non-superconducting van der Waals (vdW) materials, the Dirac semimetal ZrTe$_2$ and the antiferromagnetic iron chalcogenide FeTe, grown using molecular beam epitaxy. We show from electrical transport measurements that two-dimensional (2D) superconductivity arises at the heterointerface below a critical temperature $T_c \sim 10$K. In the superconducting transition region, non-reciprocal transport, characterized by the magneto-chiral anisotropy, exhibits a magnitude comparable to that observed in topological insulators, and is enhanced by a factor of three when the heterostructure is capped with a 2D vdW ferromagnet (CrTe$_2$). Below $T_c$, the superconducting diode effect exhibits an efficiency of 29%. With strong spin-orbit coupling in ZrTe$_2$, these epitaxial heterostructures provide an attractive epitaxial vdW platform for exploring unconventional superconductivity in Dirac semimetals and for developing non-reciprocal devices for superconducting electronics.

We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new formulas for the Poincaré polynomial of the moduli space $\overline{\mathcal{M}}_{0,n+1}$ of pointed stable rational curves, and recover several previous results by Keel, Getzler, Manin, and Aluffi--Marcolli--Nascimento. We also use our methods to produce examples of matroids and building sets for which the corresponding Chow ring has Hilbert series with non-log-concave coefficients. This contrasts with the real-rootedness and log-concavity conjectures of Ferroni--Schröter for matroids with maximal building sets, and of Aluffi--Chen--Marcolli for braid matroids with minimal building sets.

We present some new Poisson bivectors that are invariants by the Clebsch system flow. Symplectic integrators on their symplectic leaves exactly preserve the corresponding Casimir functions, which have different physical meanings. The Kahan discretization of the Clebsch system is discussed briefly.

Mistrustful quantum cryptographic protocols encode information in incompatible observables, so that any attempt by a dishonest party to access multiple pieces of information necessarily involves a tradeoff. A natural class of such strategies proceeds via consecutive measurements, where each measurement disturbs the state and influences subsequent information extraction. We introduce consecutive measurement theorems (CMTs) as a unified framework to quantify this tradeoff and argue that they capture the fundamental limitations underlying security in mistrustful quantum cryptography. Our main result is a tight characterization of the achievable region of success probabilities for single and consecutive measurements, strictly improving all previously known bounds. We further establish robust variants expressed in terms of fidelity and trace distance that remain valid under perturbations. These results yield strengthened and unified security guarantees for a range of primitives, including relativistic bit commitment, quantum oblivious transfer and quantum private query, and clarify the role of measurement disturbance as the key limitation on adversarial information extraction.

Analyzing synthesis pathways for target molecules in a chemical reaction network annotated with information on the kinetics of individual reactions is an area of active study. This work presents a computational methodology for searching for pathways in reaction networks which is based on integer linear programming and the modeling of reaction networks by directed hypergraphs. Often multiple pathways fit the given search criteria. To rank them, we develop an objective function based on physical arguments maximizing the probability of the pathway. We furthermore develop an automated pipeline to estimate the energy barriers of individual reactions in reaction networks. Combined, the methodology facilitates flexible and kinetically informed pathway investigations on large reaction networks by computational means, even for networks coming without kinetic annotation, such as those created via generative approaches for expanding molecular spaces. To demonstrate the methodology, we apply it on a chemical reaction network generated from 2-hydroxyethanenitrile, water, and ammonia, where we search for pathways to glycine and 2-hydroxyethanoic acid using the input molecules as precursors.

For a compact negatively curved space, we develop a thermodynamic formalism framework to study the space of quasimorphisms of its fundamental group modulo bounded functions. We prove that this space is Banach isomorphic to the space of Bowen functions on the associated Gromov geodesic flow, modulo a weak form of Livšic cohomology. We also show that each unbounded quasimorphism is associated with a unique invariant measure for the flow, which uniquely determines the cohomology class. As a consequence, we establish the Central Limit Theorem and the invariance principle for any unbounded quasimorphism with respect to Markov measures, and we prove that the associated equilibrium state has the Bernoulli property.

Totally equimodular matrices generalize totally unimodular matrices and arise in the context of box-total dual integral polyhedra. This work further explores the parallels between these two classes and introduces foundational building blocks for constructing totally equimodular matrices. Consequently, we present a decomposition theorem for totally equimodular matrices of full row rank. Building on this decomposition theorem, we prove that simplicial cones whose generators form the rows of a totally equimodular matrix sa\-tisfy strong integrality decomposition properties. More precisely, we provide the Hilbert basis for these cones and construct regular unimodular Hilbert triangulations in most cases. We conjecture that cases not covered here do not exist.

We prove that the total Cartier index of a bounded family of projective varieties of klt type is bounded.

Recent advances in leveraging LLMs for APR have demonstrated impressive capabilities in fixing software defects. However, current LLM-based approaches predominantly focus on mainstream programming languages like Java and Python, neglecting less prevalent but emerging languages such as Rust due to expensive training resources, limited datasets, and insufficient community support. This narrow focus creates a significant gap in repair capabilities across the programming language spectrum, where the full potential of LLMs for comprehensive multilingual program repair remains largely unexplored. To address this limitation, we introduce a novel cross-language program repair approach LANTERN that leverages LLMs' differential proficiency across languages through a multi-agent iterative repair paradigm. Our technique strategically translates defective code from languages where LLMs exhibit weaker repair capabilities to languages where they demonstrate stronger performance, without requiring additional training. A key innovation of our approach is an LLM-based decision-making system that dynamically selects optimal target languages based on bug characteristics and continuously incorporates feedback from previous repair attempts. We evaluate our method on xCodeEval, a comprehensive multilingual benchmark comprising 5,068 bugs across 11 programming languages. Results demonstrate significant enhancement in repair effectiveness, particularly for underrepresented languages, with Rust showing a 22.09% improvement in Pass@10 metrics. Our research provides the first empirical evidence that cross-language translation significantly expands the repair capabilities of LLMs and effectively bridges the performance gap between programming languages with different levels of popularity, opening new avenues for truly language-agnostic automated program repair.

Korten and Pitassi (FOCS, 2024) defined a new complexity class $L_2^P$ as the polynomial-time Turing closure of the Linear Ordering Principle. They put it between $MA$ (Merlin--Arthur protocols) and $S_2^P$ (the second symmetric level of the polynomial hierarchy). In this paper we sandwich $L_2^P$ between $P^{prMA}$ and $P^{prSBP}$. (The oracles here are promise problems, and $SBP$ is the only known class between $MA$ and $AM$.) The containment in $P^{prSBP}$ is proved via an iterative process that uses a $prSBP$ oracle to estimate the average order rank of a subset and find the minimum of a linear order. Another containment result of this paper is $P^{prO_2^P} \subseteq O_2^P$ (where $O_2^P$ is the input-oblivious version of $S_2^P$). These containment results altogether have several byproducts: We give an affirmative answer to an open question posed by of Chakaravarthy and Roy (Computational Complexity, 2011) whether $P^{prMA} \subseteq S_2^P$, thereby settling the relative standing of the existing (non-oblivious) Karp-Lipton-style collapse results of Chakaravarthy and Roy (2011) and Cai (2007), We give an affirmative answer to an open question of Korten and Pitassi whether a Karp-Lipton-style collapse can be proven for $L_2^P$, We show that the Karp-Lipton-style collapse to $P^{prOMA}$ is actually better than both known collapses to $P^{prMA}$ due to Chakaravarthy and Roy (Computational Complexity, 2011) and to $O_2^P$ also due to Chakaravarthy and Roy (STACS, 2006). Thus we resolve the controversy between previously incomparable Karp-Lipton collapses stemming from these two lines of research.

Optical frequency comb devices have unlocked new capabilities in telecommunications, sensing, and metrology. Yet, precise in situ control of the comb spectral envelope remains extremely challenging. By introducing mode coupling with non-trivial phases, we demonstrate a spectral shaping technique that enables continuous tuning of a dominant spectral lobe across the full bandwidth of a semiconductor laser frequency comb. We achieve this jointly leveraging the engineered geometry of the synthetic lattice formed by the cavity modes of the laser and the coherent dynamics enabled by its fast-gain recovery. We use dual-tone modulation of the cavity at its repetition rate and twice this frequency with a controlled relative phase to couple the comb modes into a triangular lattice. The relative phase between the two tones defines a lattice phase that breaks time-reversal symmetry and steers the lattice dynamics through the fast gain. With this approach, we experimentally control the spectral envelope of the comb such that a targeted region contains more than twice the intensity expected from a uniform distribution, demonstrating tunable spectral selectivity. This capability, achieved directly at the light generation stage in a fast-gain device, opens routes for efficient programmable waveform engineering with potential applications in ranging, data transmission, and sensing.

Selecting a subset of the $k$ "best" items from a dataset of $n$ items, based on a scoring function, is a key task in decision-making. Given the rise of automated decision-making software, it is important that the outcome of this process, called top-$k$ selection, is fair. Here we consider the problem of identifying a fair linear scoring function for top-$k$ selection. The function computes a score for each item as a weighted sum of its (numerical) attribute values, and must ensure that the selected subset includes adequate representation of a minority or historically disadvantaged group. Existing algorithms do not scale efficiently, particularly in higher dimensions. Our hardness analysis shows that in more than two dimensions, no algorithm is likely to achieve good scalability with respect to dataset size, and the computational complexity is likely to increase rapidly with dimensionality. However, the hardness results also provide key insights guiding algorithm design, leading to our two-pronged solution: (1) For small values of $k$, our hardness analysis reveals a gap in the hardness barrier. By addressing various engineering challenges, including achieving efficient parallelism, we turn this potential of efficiency into an optimized algorithm delivering substantial practical performance gains. (2) For large values of $k$, where the hardness is robust, we employ a practically efficient algorithm which, despite being theoretically worse, achieves superior real-world performance. Experimental evaluations on real-world datasets then explore scenarios where worst-case behavior does not manifest, identifying areas critical to practical performance. Our solution achieves speed-ups of up to several orders of magnitude compared to SOTA, an efficiency made possible through a tight integration of hardness analysis, algorithm design, practical engineering, and empirical evaluation.

Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial semantics that model languages with variable binding and their substitution structure, and that provide substitution-safe recursion principles. There are different approaches to implementing languages with variable binding depending on the choice of representation for contexts and free variables, such as unscoped syntax, or well-scoped syntax with finite or infinite contexts. Abstractly, each approach corresponds to choosing a different monoidal category to model contexts and binding, each choice yielding a different notion of "model" for the same abstract specification (or "signature"). In this work, we provide tools to compare and relate the models obtained from a signature for different choices of monoidal category. We do so by showing that initial semantics naturally has a 2-categorical structure when parametrized by the monoidal category modeling contexts. We thus can relate models obtained from different choices of monoidal categories provided the monoidal categories themselves are related. In particular, we use our results to relate the models of the different implementation -- de Bruijn vs locally nameless, finite vs infinite contexts -- , and to provide a generalized recursion principle for simply-typed syntax.

We show that the Starobinsky inflation model based on $R^2$ gravity has a special feature that it provides a unique scalaron-two-graviton vertex with a coupling proportional to $1/M_P$. In this model stochastic gravitational waves are produced when the scalaron - which is the massive scalar mode of the metric - decays into gravitons during reheating. This decay is accompanied by decay of scalaron into matter as well through a similar coupling, providing an efficient reheating. The stochastic gravitational waves thus produced have characteristic strain $h_c\sim 10^{-35}-10^{-34}$ in the frequency range $10^{6}-10^{12}\, {\rm Hz}$ which makes them accessible to resonant cavity searches for graviton to photon conversions. The detection of these high frequency gravitational waves would be a significant step in experimentally testing the Starobinsky inflation model.

In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The latter can manifest as coherent noise that is especially detrimental. Here, we study the impact of coherent errors and their mitigation under standard error-reduction techniques, both theoretically and experimentally on a trapped-ion quantum computer. As a representative case study, we implement a range of Grover's algorithm circuits containing up to 10 qubits and 26 two-qubit gates. We demonstrate the effectiveness of randomized compiling (RC) and algorithm error detection (ED), where the latter is realized via post-selection on ancillary qubits that ideally return to the ground state at the end of each circuit. Our results highlight a synergetic effect: combining RC and ED yields the largest reductions in errors, indicating that these methods can work together to extend the capabilities of near-term quantum devices for moderately deep circuits.

This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in Euclidean spaces. Such a model captures the desired features of both fuzzy fractional differential inclusions with integral boundary conditions and fractional differential variational inequalities within the same framework. The existence of solutions for such a novel system is obtained under different conditions. Moreover, a numerical example is provided to illustrate our abstract results.

Building upon the recent findings regarding inverse phase transitions in the early universe, we present the first natural realisation of this phenomenon within a supersymmetry-breaking sector. We demonstrate that inverse hydrodynamics, which is characterized by the fluid being aspirated by the bubble wall rather than being pushed or dragged, is actually not limited to a phase of (re)heating but can also occur within the standard cooling cosmology. Through a numerical analysis of the phase transition, we establish a simple and generic criterion to determine its hydrodynamics based on the generalised pseudo-trace. Our results provide a proof of principle highlighting the need to account for these new fluid solutions when considering cosmological phase transitions and their phenomenological implications.

We investigate the influence of the nuclear symmetry energy and its density slope parameter on the neutron dripline and neutron star properties using a semi-classical liquid drop model (LDM) and energy density functionals constrained by chiral effective field theory. To analyze finite nuclei and mass tables, the nuclear symmetry energy at saturation density is fixed, and the surface tension is determined to minimize the root-mean-square deviation of the total binding energy for 2208 nuclei. Correlations between symmetry energy parameters and neutron driplines, crust-core transition densities, and the radii of $1.4\,\msun$ neutron stars are explored using the LDM framework. Additionally, we examine the relationship between macroscopic properties, such as neutron star radii ($R_{1.4}$), and microscopic properties, including the number of isotopes and the last bound nucleus for $Z=28$, within the LDM context.