We investigate the potential to detect low-frequency gravitational waves (GWs) through their imprints on the proper motions of distant quasars observed by the Gaia mission. Using astrometric data from Gaia DR3, we simulate the effect of GWs on the proper motions of quasars, incorporating their actual sky positions and measurement uncertainties. We investigate two data analysis techniques for the extraction and characterization of GW signals from quasar proper motions: Vector Spherical Harmonics (VSH) and angular correlation functions, commonly referred to as Hellings-Downs curves (HDC). Using realistic simulated data, we forecast their sensitivity and accuracy to GWs, and evaluate the impact of systematic errors. From these simulations, we derive an upper limit on the amplitude of a stochastic GW background, constrained by the observational timespan, astrometric precision, and the sky distribution of quasars. Compared to HDC, VSH appears more statistically robust, less prone to selection effects, and with a significantly smaller computational cost, scaling as N. The HDC method is more sensitive for detecting gravitational waves, but its complexity scales as N^2. We find that, with Gaia DR3 proper motion errors, the lower limit for a detectable GW strain is of 10^{-11}, with possible improvements to about 3 x 10^{-12} for the next Gaia Data Release 4 (for the same number of quasars). This limit holds for a stochastic GW spectrum integrated over all frequencies less than half the inverse of the 34-month observational timespan of Gaia DR3, corresponding to approximately 5.6 nHz. We also investigate how different data-restriction and weighting schemes influence the final estimate of the gravitational wave strain.

Agrivoltaic systems--photovoltaic (PV) panels installed above agricultural land--have emerged as a promising dual-use solution to address competing land demands for food and energy production. In this paper, we propose a model predictive control (MPC) approach to dual-axis agrivoltaic panel tracking control that dynamically adjusts panel positions in real time to maximize power production and crop yield given solar irradiance and ambient temperature measurements. We apply convex relaxations and shading factor approximations to reformulate the MPC optimization problem as a convex second-order cone program that determines the PV panel position adjustments away from the sun-tracking trajectory. Through case studies, we demonstrate our approach, exploring the Pareto front between i) an approach that maximizes power production without considering crop needs and ii) crop yield with no agrivoltaics. We also conduct a case study exploring the impact of forecast error on MPC performance. We find that dynamically adjusting agrivoltaic panel position helps us actively manage the trade-offs between power production and crop yield, and that active panel control enables the agrivoltaic system to achieve land equivalent ratio values of up to 1.897.

We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.

Two distinct knots are said to be friends if their complements, filled along the 0-slope, produce diffeomorphic 3-manifolds. In this article, we develop a practical algorithm, implemented using SnapPy and Regina, to search for a friend of a given knot. As an application, we construct a census of simple knots that admit friends and use these data to formulate conjectures about knot friends.

In most galaxies, the central black hole accounts for no more than a percent of the total mass in stars. Recently, however, extremely over-massive black holes with ratios of 10% have been reported in dwarf galaxies at z<1 and at cosmic dawn (z>5.5) by JWST. Both findings have been interpreted as signatures of the still mysterious origins of super-massive black holes, such that most of the black hole mass was built at birth rather than through black hole accretion. Here we show that among evolved galaxies over-massive black holes are also present, indicating that overmassive BHs are not a signature unique to black hole formation channels. The first large-area sky survey of the eROSITA X-ray telescope on board SpectrRG identified 200 quasars by their luminous hard X-ray radiation. These signpost rapidly growing black holes. Complementary optical spectroscopy from the Sloan Digital Sky Survey and archival UV to IR photometric data combined with galaxy-quasar decomposition techniques allow us unbiased estimates of cosmological distances, black hole masses and host galaxy stellar masses. We securely identify a sample of over-massive black holes with BH-to-host ratios of more than 5%, which may have undergone exponential accretion spurts lasting about a billion years. Our survey identified a high space density of at least 4/Gpc^3 of overmassive black holes near cosmic noon. This indicates an accretion channel disconnected from the stellar population that cause strong deviations from galaxy scaling relations. This channel is currently not part of galaxy evolution models. The identified channel, if applicable also for the first billion years of cosmic time, can explain JWST AGN without requiring them to signify imprints of black hole seeding mechanism.

We examine solutions of the hydrodynamic equations for dark matter (DM) modeled as a Bose-Einstein condensate (BEC) with axionlike interaction, forming a spherically symmetric halo in dwarf galaxies. Small perturbations and decoherence of the BEC DM arise from changes in the gravitational background induced by subgalactic baryonic processes. Focusing on the events in the central region of a galaxy, overlapping with the stable DM core, we consider three scenarios: (i) expansion of a gaseous shell mimicking stellar explosions, (ii) collapse of a shell modeling star formation, and (iii) contraction of a stellar cluster toward the galactic center, driven by dynamical friction within a gaseous shell. Numerical parameters are extracted from observational data for NGC 2366. Our results show central DM density increases of 0.01 percent and DM wind velocities of up to several meters per second. A greater increase in density is observed at lower wind speeds and vice versa. These results raise the question of whether minor DM variations significantly affect star formation. In analyzing the fate of the cumulative impact of baryonic processes, we turn to the quantum excitation model with a discrete spectrum in finite volume. In the inhomogeneous DM halo, including unstable phase, metastable excitations associated with false vacuum states decay over 32 million years. This induces the decay of the system's evolutionary operator. Meanwhile, the Beliaev damping, originating from the decay of stable quasiparticles, emerges in the next order of perturbation.

Marathons are now common ways of seeing cities, yet little is known about how representative their routes are. Using 311 marathon routes across five continents, we compare landmarks and amenities along the course with those elsewhere in the same city, finding that museums are 15.7 times denser near the route and that the median city has about 8.5 times more luxury brands near the route than elsewhere in the city. These patterns persist under perturbed routes with the same start and finish lines: monuments and landmarks, in particular, are more prevalent on the race course than on similar alternative routes, suggesting that marathons function as intentionally selective urban portraits.

Accurate and reliable safety metrics are paramount for functional safety verification of ASICs in automotive systems. Traditional FMEDA (Failure Modes, Effects, and Diagnostic Analysis) metrics, such as SPFM (Single Point Fault Metric) and LFM (Latent Fault Metric), depend on the precision of failure mode distribution (FMD) and diagnostic coverage (DC) estimations. This reliance can often leads to significant, unquantified uncertainties and a dependency on expert judgment, compromising the quality of the safety analysis. This paper proposes a novel approach that introduces error propagation theory into the calculation of FMEDA safety metrics. By quantifying the maximum deviation and providing confidence intervals for SPFM and LFM, our method offers a direct measure of analysis quality. Furthermore, we introduce an Error Importance Identifier (EII) to pinpoint the primary sources of uncertainty, guiding targeted improvements. This approach significantly enhances the transparency and trustworthiness of FMEDA, enabling more robust ASIC safety verification for ISO 26262 compliance, addressing a longstanding open question in the functional safety community.

Hate speech online targets individuals or groups based on identity attributes and spreads rapidly, posing serious social risks. Memes, which combine images and text, have emerged as a nuanced vehicle for disseminating hate speech, often relying on cultural knowledge for interpretation. However, existing multimodal hate speech datasets suffer from coarse-grained labeling and a lack of integration with surrounding discourse, leading to imprecise and incomplete assessments. To bridge this gap, we propose an agentic annotation framework that coordinates seven specialized agents to generate hierarchical labels and rationales. Based on this framework, we construct M^3 (Multi-platform, Multi-lingual, and Multimodal Meme), a dataset of 2,455 memes collected from X, 4chan, and Weibo, featuring fine-grained hate labels and human-verified rationales. Benchmarking state-of-the-art Multimodal Large Language Models reveals that these models struggle to effectively utilize surrounding post context, which often fails to improve or even degrades detection performance. Our finding highlights the challenges these models face in reasoning over memes embedded in real-world discourse and underscores the need for a context-aware multimodal architecture. Our dataset and code are available at https://github.com/mira-ai-lab/M3.

Demographers rely on a variety of tools and methods to work with mortality schedules - model life tables, fitting methods, summary-indicator prediction, and forecasting - largely developed independently and not providing structurally coherent sex-specific outputs. The multi-dimensional mortality model (MDMx) unifies all four within one Tucker tensor decomposition demonstrated using the Human Mortality Database (HMD). Period life tables from the HMD are organized as a four-way tensor of logit(1qx) indexed by sex, age, country, and year. Shared factor matrices for sex and age make every output schedule structurally coherent by construction. From this decomposition four capabilities emerge: model life tables via clustering and smooth within-regime trajectories; life table fitting via a three-stage algorithm with Bayes-factor disruption detection; summary-indicator prediction mapping child or adult mortality to complete schedules, reformulating SVD-Comp in tensor coordinates; and forecasting via a damped local linear trend Kalman filter on PCA-reduced core matrices with hierarchical drift.

Portfolio backtesting is the primary tool for evaluating investment strategies before deployment, yet practitioners implicitly assume that different engines produce identical results for the same strategy. we formalise implementation risk, the systematic divergence in backtested portfolio metrics arising solely from differences in how engines implement the same logical strategy, and propose four metrics grounded in metrology to quantify it: engine sensitivity, implementation uncertainty interval, divergence amplification factor, and conclusion stability index. we execute 15 benchmark strategies through five independent open-source engines on 30 non-overlapping stratified asset buckets comprising 180 s&p 500 stocks under four transaction-cost regimes. at zero cost, all five engines agree exactly (maximum divergence 0.000%), isolating transaction-cost implementation as the sole source of disagreement. under nonzero costs, divergence is structured and predictable (spearman rho = 0.93 with cost intensity), remaining below 0.75 percentage points for most strategies but reaching 3.71% for high-turnover rotation strategies. source-code forensics uncovered seven previously undocumented defects across three engines, abstracted into a five-category failure-mode taxonomy. all engines agree on the sign of every performance metric (conclusion stability index = 1), so implementation risk does not alter investment decisions for the strategies studied but introduces measurable ambiguity in performance attribution. code and benchmark data are publicly available.

Efficient multi-user multi-task video transmission is an important research topic within the realm of current wireless communication systems. To reduce the transmission burden and save communication resources, we propose a goal-oriented semantic communication framework for optical flow-based multi-user multi-task video transmission (OF-GSC). At the transmitter, we design a semantic encoder that consists of a motion extractor and a patch-level optical flow-based semantic representation extractor to effectively identify and select important semantic representations. At the receiver, we design a transformer-based semantic decoder for high-quality video reconstruction and video classification tasks. To minimize the communication time, we develop a deep deterministic policy gradient (DDPG)-based bandwidth allocation algorithm for multi-user transmission. For video reconstruction tasks, our OF-GSC framework achieves a significant improvement in the received video quality, as evidenced by a 13.47% increase in the structural similarity index measure (SSIM) score in comparison to DeepJSCC. For video classification tasks, OF-GSC achieves a Top-1 accuracy slightly surpassing the performance of VideoMAE with only 25% required data under the same mask ratio of 0.3. For bandwidth allocation optimization, our DDPG-based algorithm reduces the maximum transmission time by 25.97% compared with the baseline equal-bandwidth allocation scheme.

Scientists across all disciplines share a common challenge: the divide between their theoretical knowledge and the specialized skills and time needed to build interactive tools to communicate this expertise. While large language models (LLMs) offer unparalleled acceleration in code generation, they frequently prioritize functional syntax over scientific accuracy, risking visually convincing but scientifically invalid results. This work advocates the Scientist-AI-Loop (SAIL), a framework designed to harness this speed without compromising rigor. By separating domain logic from code syntax, SAIL enables researchers to maintain strict oversight of scientific concepts and constraints while delegating code implementation to AI. We illustrate this approach through two open-source, browser-based astrophysics tools: an interactive gravitational lensing visualization and a large-scale structure formation sandbox, both publicly available. Our methodology condensed development to mere days while maintaining scientific integrity. We specifically address failure modes where AI-generated code neglects phenomenological boundaries or scientific validity. While cautioning that research-grade code requires stringent protocols, we demonstrate through two examples that SAIL provides an effective code generation workflow for outreach, teaching, professional presentations, and early-stage research prototyping. This framework contributes to a foundation for the further development of AI-assisted scientific software.

Extreme mass-ratio inspirals (EMRIs), comprising a stellar-mass compact object (CO) orbiting a supermassive black hole (BH), are key targets for future space-based gravitational-wave (GW) observatories. Incorporating the spin of the secondary body into waveform models not only enhances measurement precision but also offers insight into the spin distribution of stellar-mass objects. In this work, we construct the flux and waveform for an EMRI with a spinning secondary in a Kerr background under the linear-spin approximation. Using the radiative prescription (half-retarded minus half-advanced field), we derive orbit-averaged evolution equations for the fundamental constants of motion, including the energy, angular momentum, Carter-like constant, and the parallel spin component. This framework provides a tractable route to generating waveforms that incorporate the secondary spin, with the potential for further simplification in future work.

Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families of states. This work introduces a method for preparing quantum states whose amplitudes are given by a degree$-d$ polynomial, using circuits with logarithmic depth in the number $n$ of qubits and only $\mathcal O(n)$ ancilla qubits, improving previous approaches that required linear-depth circuits. The construction first relies on a block-encoding of an affine diagonal operator based on its Pauli-basis decomposition, which involves only $n$ terms. A modified linear-combination-of-unitaries (LCU) technique is introduced to implement this decomposition in logarithmic depth, together with a novel circuit for the EXACT-one oracle that flags basis states in which exactly one qubit is in the state $|1\rangle$. It then uses a generalized quantum eigenvalue transformation (GQET) to promote this affine operator to an arbitrary degree polynomial. Theoretical analysis and numerical simulations are reported along with a proof-of-principle implementation on a trapped-ion quantum processor using $14$ qubits and more than $500$ primitive quantum gates. Because polynomial approximations are ubiquitous in scientific computing, this construction provides a scalable and resource-efficient approach to quantum state preparation, further improving the potential of quantum algorithms in fields such as chemistry, physics, engineering, and finance.

Let $K$ be a number field with algebraic closure $\overline{K}$ and let $S$ be a finite set of places of $K$ that contain all the archimedean places. For an integer $d \ge 2$, consider the unicritical polynomial family $f_{d,c}(z) = z^d + c$. Recently, Benedetto and Ih studied the distribution of post-critically finite parameters $c$ that are $S$-integral relative to a fixed point $α\in \overline{K}$ such that $f_{d, α}$ is not post-critically finite. In this paper, we study the quantitative aspects of their result. In particular, under some additional assumptions we establish quantitative bounds on the number of $S$-integral post-critically finite parameters in the generalized Mandelbrot set $\mathcal{M}_{d, v}$ relative to a non post-critically finite parameter $α$ as $α$ varies over number fields of bounded degree.

We expand our novel computational method for unit commitment (UC) to include long-horizon planning. We introduce a fast novel algorithm to commit hydro-generators, provably accurately. We solve problems with thousands of generators at 5 minute market intervals. We show that our method can solve interconnect size UC problems in approximately 1 minute on a commodity hardware and that an increased planning horizon leads to sizable operational cost savings (our objective). This scale is infeasible for current state-of-the-art tools. We attain this runtime improvement by introducing a heuristic tailored for UC problems. Our method can be implemented using existing continuous optimization solvers and adapted for different applications. Combined, the two algorithms would allow an operator operating large systems with hydro units to make horizon-aware economic decisions.

I provide multiple examples of conformal field theories (CFTs) on the worldsheet that describe string propagation in target space wormholes connecting two disjoint asymptotic manifolds. The worldsheet approach goes beyond the framework of supergravity by incorporating wormholes for which the size of the throat is comparable to the string scale. Typically, strongly coupled CFTs describe these stringy wormholes, which include Euclidean wormholes, double cones, and Einstein-Rosen bridges. Finally, I interpret a conformal manifold that contains $\text{SU}(2)_k$ and $\big(\text{SU}(2)_k \times \text{U}(1)_{k'}\big)/\text{U}(1)$ CFTs as mediating a transition between a closed Universe and a wormhole.

Let $ir(G)$ and $γ(G)$ be the irredundance number and the domination number of a graph $G$, respectively. A graph $G$ is called irredundance perfect if $ir(H)=γ(H)$ for every induced subgraph $H$ of $G$. The subclass of $P_6$-free irredundance perfect graphs has been studied extensively. In this paper, we present a characterization of this graph class in terms of eleven forbidden induced subgraphs.

The recent realization of millisecond-scale coherence with tantalum-on-silicon transmon qubits showed that depositing the Al/AlOx/Al Josephson junction in a high purity, ultrahigh vacuum environment was critical for achieving lifetime-limited coherence, motivating careful examination of the aluminum surface two-level system (TLS) bath. Here, we measure the microwave absorption arising from surface TLSs in superconducting aluminum resonators, following methodology developed for tantalum resonators. We vary film and surface properties and correlate microwave measurements with materials characterization. We find that the lifetimes of superconducting aluminum resonators are primarily limited by surface losses associated with TLSs in the 2.7 nm-thick native AlOx. Treatment with 49% HF removes surface AlOx completely; however, rapid oxide regrowth limits improvements in surface loss and long term device stability. Using these measurements we estimate that TLSs in aluminum interfaces contribute around 27% of the relaxation rate of state-of-the-art tantalum-on-silicon qubits that incorporate aluminum-based Josephson junctions.

Galaxy surveys demand fast large-scale structure forward models that preserve large-scale phases while providing realistic nonlinear morphology at fixed force resolution. Single-step Lagrangian Perturbation Theory (LPT) solvers are efficient, but they typically yield overly diffuse filaments and knots and underpredict small-scale clustering. We introduce Ridged Lagrangian Perturbation Theory (RLPT), a modular two-step scheme: a standard long-range LPT/ALPT transport is followed by a single post-processing Eulerian ridging update that reconstructs a short-range, curl-free displacement from the realised density field through a smooth scale separation and a Poisson inversion. This explicit completion layer is inexpensive, preserves the large-scale solution, and provides a small set of transparent parameters to tune the short-range response. We test RLPT against particle-mesh and $N$-body references and find that one additional ridging step systematically improves both nonlinear power and field-level agreement relative to 2LPT/ALPT baselines. Finally, we demonstrate that ridging can be repurposed as a deterministic subgrid relocation model: even when the underlying dark-matter field is only ``good enough'' on the mesh, ridging enables controlled tuning of tracer clustering beyond the nominal resolution, which is particularly relevant for mock-galaxy production and observational systematics sensitive to close pairs.

How much macroeconomic information is contained in a single input-output table? We feed FIGARO 64-sector symmetric tables into DEPLOYERS, a Darwinian agent-based simulator, producing genuine out-of-sample GDP forecasts. For each year, the model reads one FIGARO table for year N, self-organizes an artificial economy through evolutionary natural selection, then runs 12 months of autonomous free-market dynamics whose emergent growth rate predicts year N+1. The I-O table is the only input: no time series, no estimated parameters, no expectations formation, no external forecasts. We present five results. First, a 9-year Austrian panel (2010-2018) using 12-seed ensembles produces MAE of 1.22 pp overall; for five non-crisis years, MAE falls to 0.42 pp -- comparable to the best professional forecaster (WIFO: 0.48 pp). A Swedish 9-year panel independently confirms this accuracy (normal-years MAE 0.80 pp). Second, cross-country portability is demonstrated across 33 of 37 tested FIGARO countries with zero parameter changes. Third, a German 9-year panel reveals systematic +3.7 pp positive bias from export dependency -- an informative negative result pointing to multi-country network simulation as the natural extension. Fourth, a COVID-19 simulation demonstrates the I-O structure as a shock propagation mechanism: a 19-month timeline produces Year 1 GDP -4.62% vs empirical -6.6%. Fifth, emergent firm size distributions match European Commission data without micro-target calibration. These results establish the I-O table as serving a dual purpose: structural baseline engine and dynamic shock propagation mechanism. Since FIGARO covers 46 countries, the approach is immediately portable without retuning parameters.

Differential privacy (DP) enables safe data release, with synthetic data generation emerging as a common approach in recent years. Yet standard synthesizers preserve all dependencies in the data, including spurious correlations between sensitive attributes and outcomes. In fairness-critical settings, this reproduces unwanted bias. A principled remedy is to enforce conditional independence (CI) constraints, which encode domain knowledge or legal requirements that outcomes be independent of sensitive attributes once admissible factors are accounted for. DP synthesis typically proceeds in two phases: (i) a measure- ment step that privatizes selected marginals, often structured via maximum spanning trees (MSTs), and (ii) a reconstruction step that fits a probabilistic model consistent with the noisy marginals. We propose PrivCI, which enforces CI during the measurement step via a CI-aware greedy MST algorithm that integrates feasibility checks into Kruskal's construction under the exponential mechanism, improving accuracy over competing methods. Experiments on standard fairness benchmarks show that PrivCI achieves stronger fidelity and predictive accuracy than prior baselines while satisfying the specified CI constraints.

Brasília offers a rare test of how urban form shapes experienced segregation. Built almost at once around modernist neighbourhood units, then expanded through planned satellites and informal peripheries, it lets us ask whether urban form turns mobility into mixing or into a more efficient engine of separation. We combine data on human mobility with urban morphometrics, amenities, road networks, along with enclosures and tessellations that capture segregation at the scales where access is structured: districts, neighbourhoods, blocks, and street-and-building cells. We find that segregation intensifies as resolution sharpens, from 0.282 at the district scale to 0.545 at the block scale, indicating that Brasília looks most integrated at coarse units and most segregated where everyday encounters are actually organised. Mobility softens home segregation for most users, but not symmetrically: poorer groups travel farther, while affluent groups remain the most selectively exposed. civic cores and mid-rise, mixed-use areas are the least segregated morphotypes, yet they occupy only a sliver of the metropolis. Elsewhere, rich lakefront suburbs and dense poor settlements reach similarly high segregation through opposite spatial logics. Amenities predict lower segregation, while barriers and enclosed residential interiors predict higher segregation. Built form explains more of this pattern than visit volume alone in the segregation models: integration is less a property of residential design than of shared destinations and porous connections. Planned capitals can build order without building isolation if they distribute mixing space rather than sequestering it.

A family $\mathcal{G}$ of sets is a weak copy of a poset $P$ if there is a bijection $f:P\rightarrow \mathcal{G}$ such that $p\leqslant q$ implies $f(p)\subseteq f(q)$. If $f$ satisfies $p\leqslant q$ if and only if $f(p)\subseteq f(q)$, the $\mathcal{G}$ is a strong copy of $P$. We study the anti-Ramsey numbers $\mathrm{ar}(n,P), \mathrm{ar^*}(n,P)$, the maximum number of colors used in a coloring of $2^{[n]}$ that does not admit a rainbow weak or strong copy of $P$, respectively. We establish connections to the well-studied extremal numbers $\mathrm{La}(n,P)$ and $\mathrm{La^*}(n,P)$ and determine asymptotically $\mathrm{ar^*}(n,T)$ for all tree posets $T$ and $\mathrm{ar^*}(n,O_{2k})$ for all crown posets $O_{2k}$.

\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then we attempt to characterize the distribution. We establish the conditions under which the distribution exhibits unimodality. We provide non-analytical formulas for the mean resultant length and the Kullback-Leibler divergence, and analytical form for the cumulative probability function and the entropy of the GCPC distribution. We propose log-likelihood ratio tests for one, or two location parameters without assuming equality of the concentration parameters. We revisit maximum likelihood estimation with and without predictors. In the regression setting we briefly mention the addition of circular and simplicial predictors. Simulation studies illustrate a) the performance of the log-likelihood ratio test when one falsely assumes that the true distribution is the wrapped Cauchy distribution, and b) the empirical rate of convergence of the regression coefficients. Using a real data analysis example we show how to avoid the log-likelihood being trapped in a local maximum and we correct a mistake in the regression setting.

We study the Klein-Gordon equation in one spatial and one temporal dimension. Physically, this equation describes the wave function of a relativistic spinless boson with positive rest mass. Mathematically, this is the most elementary hyperbolic partial differential equation, after the wave equation itself. Relative to the origin, the spacetime splits according to the light cones, and we find four quarter-planes, two of which are timelike while the remaining two are spacelike. Not unexpectedly, the solutions behave quite differently in the two types of quarter-planes. It turns out that the spacelike quarter-planes exhibit a Liouville phenomenon, where insufficient growth forces the solutions to display a certain kind of symmetry, where the values on the two linear edges are in a one-to-one relation. This phenomenon shares features with the classical Liouville theorem as well as the Phragmen-Lindelof principle for harmonic functions.

We consider the problem of characterizing derived endomorphism algebras of simple objects in length categories up to quasi-isomorphism. We give such a characterization for module categories, abelian categories, exact categories, as well as, for certain differential graded analogues of them. It turns out that the property of being $d$-complicial ($d\geq 1$), in the sense of Lurie, of the involved simple-minded collections plays a central role. We also explain how this characterization can be interpreted as a coherent generation property for any minimal $A_{\infty}$-model of the derived endomorphism algebra. Along the way, we propose a notion of length exact differential graded categories and explain how they relate to length abelian $d$-truncated differential graded categories, generalizing results of Enomoto.

In this paper we construct stable $IT_{0}$ trosion free sheaves on compactified Jacobian of an integral nodal curve. Our construction is functorial in nature and it provides an uniform method which works for both smooth and nodal curve.

The exchange of quantum information among nodes in a quantum network is one of the main challenges in modern technologies. Superconducting waveguide QED networks hold great potential for realizing distributed quantum computation, where distinct nodes communicate via itinerant single photons. Yet, different frequencies among the nodes restrict their applicability and limit scalability. Here we derive the controls required to shape single photons arbitrarily detuned with respect to their natural frequency, allowing thus for an on-demand and deterministic exchange of quantum information among frequency detuned nodes. We provide a theoretical framework, analyzing the properties of the controls for typical photon shapes, identifying operation regimes amenable for experimental realization. We then show how these controls enable frequency-selective quantum state transfer among non-resonant and distant nodes of a realistic network. In addition, we also provide a simple extension for remote entanglement generation between these nodes. The suitability and high-fidelity of these protocols is supported by numerical simulations, highlighting the novel networking possibilities unlocked when shaping frequency-tunable single photons.