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When a pulse of light traverses a material, it incurs a time delay referred to as the group delay. Should the group delay experienced by photons be attributed to the time they spend as atomic excitations? However reasonable this connection may seem, it appears problematic when the frequency of the light is close to the atomic resonance, as the group delay becomes negative in this regime. To address this question, we use the cross-Kerr effect to probe the degree of atomic excitation caused by a resonant transmitted photon, by measuring the phase shift on a separate beam that is weak and off-resonant. Our results, over a range of pulse durations and optical depths, are consistent with the recent theoretical prediction that the mean atomic excitation time caused by a transmitted photon (as measured via the time integral of the observed phase shift) equals the group delay experienced by the light. Specifically, we measure mean atomic excitation times ranging from $(-0.82\pm 0.31) \tau_0$ for the most narrowband pulse to $(0.54\pm 0.28) \tau_0$ for the most broadband pulse, where $\tau_0$ is the non-post-selected excitation time, given by the scattering (absorption) probability multiplied by the atomic lifetime $\tau_{\rm sp}$. These results suggest that negative values taken by times such as the group delay have more physical significance than has generally been appreciated.

Nekrashevych associated to each self-similar group action an ample groupoid and a C*-algebra. We provide exact sequences to compute the homology of the groupoid and the K-theory of the C*-algebra in terms of the homology of the group and K-theory of the group C*-algebra via the transfer map and the virtual endomorphism. Complete computations are then performed for the Grigorchuk group, the Grigorchuk--Erschler group, Gupta--Sidki groups and many others. Results are proved more generally for self-similar groupoids. As a consequence of our results and recent results of Xin Li, we are able to show that R\"over's simple group containing the Grigorchuk group is rationally acyclic but has nontrivial Schur multiplier. We prove many more R\"over--Nekrashevych groups of self-similar groups are rationally acyclic.

High-velocity stellar collisions near supermassive black holes may result in a complete disruption of the stars. The initial disruption can have energies on par with supernovae and power a very fast transient. In this work we examine the primary flare that will follow the initial transient, which arises when streams of gas from the disrupted stars travel around the central black hole and collide with each other on the antipodal side with respect to the original collision. We present a simple analytic estimate for the properties of the flare, which depends on the distance of the collision from the central black hole and on the center of mass velocity of the colliding stars. We also present first of their kind radiation-hydrodynamics simulations of a few examples of stellar collisions and post-collision flow of the ejected gas, and calculate the expected bolometric light curves. We find that such post-collision flares are expected to be similar to flares which arise in tidal disruptions events of single stars., Comment: 8 pages, submitted to ApJL

The jet cross-section and jet-substructure observables in $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV were measured by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC). Jets are reconstructed from charged-particle tracks and electromagnetic-calorimeter clusters using the anti-$k_{t}$ algorithm with a jet radius $R=0.3$ for jets with transverse momentum within $8.0

Mental health has become a growing concern among university students. While medication is a common treatment, understanding how university students manage their medication for mental health symptoms in real-world practice has not been fully explored. In this study, we conducted semi-structured interviews with university students to understand the unique challenges in the mental health medication management process and their coping strategies, particularly examining the role of various technologies in this process. We discovered that due to struggles with self-acceptance and the interdependent relationship between medication, symptoms, schedules, and life changes, the medication management process for students was a highly dynamic journey involving frequent dosage changes. Thus, students adopted flexible strategies of using minimal technology to manage their medication in different situations while maintaining a high degree of autonomy. Based on our findings, we propose design implications for future technologies to seamlessly integrate into their daily lives and assist students in managing their mental health medications.

Several recent techniques for modifying topological codes with single-qubit Clifford operators have shown high resilience against pure Pauli noise. Paramount to these findings has been the demonstration that several variants exhibit error thresholds often attaining or exceeding the zero-rate hashing bound, a known benchmark for code-capacity noise channels, for biased noise. Additionally, direct comparison with the hashing bound has shown that several topological codes outperform the hashing bound at points of finite Pauli noise biases. Motivated by these observations, we study zero-rate holographic quantum error correction codes, discovering very high threshold values under diverse and finitely-biased noise channels using a tensor-network decoding approach. Our results establish that all codes tested achieve or surpass the hashing bound at various points, ranging from pure 2-Pauli noise ($\eta = 0$) to pure 1-Pauli noise ($\eta = +\infty$), thereby demonstrating that holographic codes exhibit excellent error tolerance in the code-capacity picture. Such findings imply the existence of a structured and systematic method for constructing high-threshold codes suitable for realistically motivated noise channels. To our knowledge, this work is also the first instance of such remarkable threshold behavior in stabilizer quantum codes for the pure 2-Pauli noise regime, as well as for finitely-biased noise channels., Comment: 8 pages, 5 figures, 2 tables

Active soft matter frequently shows motility-induced phase separation (MIPS), where self-propelled particles condensate into clusters with an inner liquid-like structure. Such activity may also result in motility-induced crystallization (MIC) into clusters with an inner crystalline structure. We present a higher-order active Phase-Field-Crystal (PFC) model and employ it to study the interplay of passive (i.e., thermodynamic) and active (i.e., motility-induced) condensation and crystallization. Morphological phase diagrams indicate the various occurring phase coexistences and transitions, e.g., the destruction of passive clusters by density-independent activity and the creation of such clusters by a density-dependent activity. Finally, rotating crystallites are analyzed in some detail.

We implement a variant of the quantum pigeonhole paradox thought experiment to study whether classical counting principles survive in the quantum domain. We observe strong measurements significantly violate the pigeonhole principle (that among three pigeons in two holes, at least one pair must be in the same hole) and the sum rule (that the number of pigeon pairs in the same hole is the sum of the number of pairs across each of the holes) in an ensemble that is pre and postselected into particular separable states. To investigate whether measurement disturbance is a viable explanation for these counter-intuitive phenomena, we employ the first ever variable-strength measurement of a non-local observable. As we decrease the measurement strength, we find the violation of the sum rule decreases, yet the pigeonhole principle remains violated. In the weak limit, the sum rule is restored due to the cancellation between two weak values with equal and opposite imaginary parts. We observe the same kind of cancellation at higher measurement strengths, thus raising the question: do strong measurements have imaginary parts?, Comment: 8 pages, 4 figures

We introduce a new class of qubit codes that we call Evenbly codes, building on a previous proposal of hyperinvariant tensor networks. Its tensor network description consists of local, non-perfect tensors describing CSS codes interspersed with Hadamard gates, placed on a hyperbolic $\{p,q\}$ geometry with even $q\geq 4$, yielding an infinitely large class of subsystem codes. We construct an example for a $\{5,4\}$ manifold and describe strategies of logical gauge fixing that lead to different rates $k/n$ and distances $d$, which we calculate analytically, finding distances which range from $d=2$ to $d \sim n^{2/3}$ in the ungauged case. Investigating threshold performance under erasure, depolarizing, and pure Pauli noise channels, we find that the code exhibits a depolarizing noise threshold of about $19.1\%$ in the code-capacity model and $50\%$ for pure Pauli and erasure channels under suitable gauges. We also test a constant-rate version with $k/n = 0.125$, finding excellent error resilience (about $40\%$) under the erasure channel. Recovery rates for these and other settings are studied both under an optimal decoder as well as a more efficient but non-optimal greedy decoder. We also consider generalizations beyond the CSS tensor construction, compute error rates and thresholds for other hyperbolic geometries, and discuss the relationship to holographic bulk/boundary dualities. Our work indicates that Evenbly codes may show promise for practical quantum computing applications., Comment: 22 pages, 13 figures

Given a presentation of a monoid $M$, combined work of Pride and of Guba and Sapir provides an exact sequence connecting the relation bimodule of the presentation (in the sense of Ivanov) with the first homology of the Squier complex of the presentation, which is naturally a $\mathbb ZM$-bimodule. This exact sequence was used by Kobayashi and Otto to prove the equivalence of Pride's finite homological type (FHT) property with the homological finiteness condition bi-$\mathrm{FP}_3$. Guba and Sapir used this exact sequence to describe the abelianization of a diagram group. We prove here a generalization of this exact sequence of bimodules for presentations of associative algebras. Our proof is more elementary than the original proof for the special case of monoids.

We report the existence of localized states in dipolar Bose-Einstein condensates confined to a tubular geometry. We first perform a bifurcation analysis to track their emergence in a one-dimensional domain for numerical feasibility and find that localized states can become the ground state in suitable parameter regions. Their existence for parameters featuring a supercritical primary bifurcation shows that the latter is not sufficient to conclude that the phase transition is of second order, hence density modulations can jump rather than emerging gradually. Finally, we show that localized states also exist in a three-dimensional domain.

In the standard circuit model of quantum computation, the number and quality of the quantum gates composing the circuit influence the runtime and fidelity of the computation. The fidelity of the decomposition of quantum algorithms, represented as unitary matrices, to bounded depth quantum circuits depends strongly on the set of gates available for the decomposition routine. To investigate this dependence, we explore the design space of discrete quantum gate sets and present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The evaluation is conditioned on a set of unitary transformations representing target use cases on the quantum processors. The cost function considers three key factors: (i) the statistical distribution of the decomposed circuits' depth, (ii) the statistical distribution of process fidelities for the approximate decomposition, and (iii) the relative novelty of a gate set compared to other gate sets in terms of the aforementioned properties. The developed software, YAQQ (Yet Another Quantum Quantizer), enables the discovery of an optimized set of quantum gates through this tunable joint cost function. To identify these gate sets, we use the novelty search algorithm, circuit decomposition techniques, and stochastic optimization to implement YAQQ within the Qiskit quantum simulator environment. YAQQ exploits reachability tradeoffs conceptually derived from quantum algorithmic information theory. Our results demonstrate the pragmatic application of identifying gate sets that are advantageous to popularly used quantum gate sets in representing quantum algorithms. Consequently, we demonstrate pragmatic use cases of YAQQ in comparing transversal logical gate sets in quantum error correction codes, designing optimal quantum instruction sets, and compiling to specific quantum processors.

Metallic transition metal dichalcogenides (TMDs), consisting of H-NbSe$_2$, H-NbS$_2$, H-TaSe$_2$ and H-TaS$_2$, remain superconducting down to a thickness of a single layer. In these materials, thickness affects a variety of properties, including Ising protection, two-band superconductivity, and the critical temperature $T_C$, which decreases for the Nb-based, and increases for the Ta-based materials. This contradicting trend is puzzling, and has precluded the development of a unified theory. We approach the question of thickness-evolution of $T_C$ and the superconducting gap $\Delta$ by measuring high-resolution tunneling spectra in TaS$_2$-based stacked devices. Our measurements allow for simultaneous evaluation of $\Delta$, $T_C$, and the upper critical field $H_{C2}$. The latter, we find, is strongly enhanced towards the single-layer limit, following a $H_{C2} \propto \Delta^2$ proportionality ratio. Our main finding is that the same ratio holds for the entire family of metallic TMDs: TaS$_2$ and NbSe$_2$ of all thicknesses, bulk TaSe$_2$ and bulk NbS$_2$, extending over 4 orders of magnitude in $H_{C2}$ and covering both clean and dirty limits. We propose that this tunability across the TMD family is controlled by the competing charge density wave (CDW) phase. Using Gor'kov's theory, we calculate how a CDW order affects the quasiparticle density of states and the resulting $T_C$ and $H_{C2}$. Our results suggest that CDW is the key determinant factor limiting $T_C$ in the TMD family. They also show that $H_{C2}$ is universally enhanced by a factor of two orders of magnitude above the expected value, an effect that remains an open question., Comment: 28 pages, 16 figures

I explicitly compute the Eilenberg-Mac Lane homology of a completely simple semigroup using topological means. I also complete Gray and Pride's investigation into the homological finiteness properties of completely simple semigroups, as well as studying their topological finiteness properties. I give a topological proof of Pride's unpublished homological lower bound for the deficiency of a monoid or semigroup.

Investigating children's embodied learning in mixed-reality environments, where they collaboratively simulate scientific processes, requires analyzing complex multimodal data to interpret their learning and coordination behaviors. Learning scientists have developed Interaction Analysis (IA) methodologies for analyzing such data, but this requires researchers to watch hours of videos to extract and interpret students' learning patterns. Our study aims to simplify researchers' tasks, using Machine Learning and Multimodal Learning Analytics to support the IA processes. Our study combines machine learning algorithms and multimodal analyses to support and streamline researcher efforts in developing a comprehensive understanding of students' scientific engagement through their movements, gaze, and affective responses in a simulated scenario. To facilitate an effective researcher-AI partnership, we present an initial case study to determine the feasibility of visually representing students' states, actions, gaze, affect, and movement on a timeline. Our case study focuses on a specific science scenario where students learn about photosynthesis. The timeline allows us to investigate the alignment of critical learning moments identified by multimodal and interaction analysis, and uncover insights into students' temporal learning progressions.

We prove the Effros-Hahn conjecture for groupoid algebras with coefficients in a sheaf, obtaining as a consequence a description of the ideals in skew inverse semigroup rings. We also use the description of the ideals to characterize when the groupoid algebras with coefficients in a sheaf are von Neumann regular, primitive, semiprimitive, or simple. We apply our results to the topological dynamics of actions of inverse semigroups, describing the existence of dense orbits and minimality in terms of primitivity and simplicity, respectively, of the associated algebra. Moreover, we apply our results to the usual complex groupoid algebra of continuous functions with compact support, used to build the C*-algebra associated with a groupoid, and describe criteria for its simplicity.

Recent research indicates that low-inertia viscoelastic channel flow experiences supercritical non-normal mode elastic instability from laminar to sustained chaotic flow due to finite-size perturbations. The challenge of this study is to elucidate a realization of such a pathway when the intensity of the elastic wave is too low to amplify velocity fluctuations above the instability onset. The study identifies two subregions in the transition flow regime at Weissenberg number $Wi>Wi_c$, the instability onset. In the lower subregion at $Wi_c\leq Wi\leq 300$, we discover periodic spikes in the streamwise velocity time series $u(t)$ that appear in the chaotic power spectrum as low-frequency, high-intensity peaks resembling stochastic resonance (SR). In contrast, the spanwise velocity power spectrum, $E_w$, remains flat with low-intensity, noisy, and broad elastic wave peaks. The spikes significantly distort the probability density function of $u$, initiating and amplifying random streaks and wall-normal vorticity fluctuations. The SR appearance is similar to dynamical systems where chaotic attractor and limit cycle interact with external white noise. This similarity is confirmed by presenting a phase portrait in two subregions of the transition regime. In the upper subregion at $Wi>400$ the periodic spikes disappear and $E_w$ becomes chaotic with a large intensity elastic wave sufficient to self-organize and synchronize the streaks into cycles and to amplify the wall normal vorticity according to a recently proposed mechanism., Comment: 13 pages, 13 figures

We present the first global tuning, using GENIE, of four transverse kinematic imbalance measurements of neutrino-hydrocarbon scattering, both with and without pion final states, from the T2K and MINERvA experiments. As a proof of concept, we have simultaneously tuned the initial state and final-state interaction models (SF-LFG and hA, respectively), producing a new effective theory that more accurately describes the data., Comment: 27 pages, 17 figures

The goal of this paper is to use topological methods to compute $\mathrm{Ext}$ between irreducible representations of von Neumann regular monoids in which Green's $\mathscr L$- and $\mathscr J$-relations coincide (e.g., left regular bands). Our results subsume those of S.~Margolis, F.~Saliola, and B.~Steinberg, \emph{Combinatorial topology and the global dimension of algebras arising in combinatorics}, J. Eur. Math. Soc. (JEMS), \textbf{17}, 3037--3080 (2015). Applications include computing $\mathrm{Ext}$ between arbitrary simple modules and computing a quiver presentation for the algebra of Hsiao's monoid of ordered $G$-partitions (connected to the Mantaci-Reutenauer descent algebra for the wreath product $G\wr S_n$). We show that this algebra is Koszul, compute its Koszul dual and compute minimal projective resolutions of all the simple modules using topology. More generally, these results work for CW left regular bands of abelian groups. These results generalize the results of S.~Margolis, F.~V. Saliola, and B.~Steinberg. \emph{Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry}, Mem. Amer. Math. Soc., \textbf{274}, 1--135, (2021)., Comment: This is the second part of arXiv:2306.16379, the original version (v1,v2) was too long and split in two

The traditional formalism of quantum measurement (hereafter ``TQM'') describes processes where some properties of quantum states are extracted and stored as classical information. While TQM is a natural and appropriate description of how humans interact with quantum systems, it is silent on the question of how a more general, quantum, agent would do so. How do we describe the observation of a system by an observer with the ability to store not only classical information but quantum states in its memory? In this paper, we extend the idea of measurement to a more general class of sensors for quantum agents which interact with a system in such a way that the agent's memory stores information (classical or quantum) about the system under study. For appropriate sensory interactions, the quantum agent may ``learn'' more about the system than would be possible under any set of classical measurements -- but as we show, this comes at the cost of additional measurement disturbance. We experimentally demonstrate such a system and characterize the tradeoffs, which can be done by considering the information required to erase the effects of a measurement.

As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters. To adapt this problem for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval., Comment: 54 pages, 9 figures. Accompanying code repository: https://github.com/ArneWulff/ssr-with-qc-and-tn . Accompanying data repository: https://doi.org/10.4121/ae276609-55b0-4af1-88c0-1102b1b58990 . Changes: Major revision, addition of state-vector simulations of VQAs

Layered franckeite is a natural superlattice composed of two alternating layers of different compositions, SnS$_2$- and PbS-like. This creates incommensurability between the two species along the planes of the layers, resulting in spontaneous symmetry-break periodic ripples in the \textit{a}-axis orientation. Nevertheless, natural franckeite heterostructure has shown potential for optoelectronic applications mostly because it is a semiconductor with 0.7 eV bandgap, air-stable, and can be easily exfoliated down to ultrathin thicknesses. Here, we demonstrate that few-layer franckeite shows a highly anisotropic nonlinear optical response due to its lattice structure, which allow for the identification of the ripple axis. Moreover, we find that the highly anisotropic third-harmonic emission strongly varies with material thickness. These features are further corroborated by a theoretical nonlinear susceptibility model and the nonlinear transfer matrix method. Overall, our findings help to understand this material and propose a characterization method that could be used in other layered materials and heterostructures to assign their characteristic axes., Comment: 27 pages, 5 figures. The following article has been accepted by the Journal of Applied Physics. After it is published, it will be found by DOI: 10.1063/5.0186615

Large energy acceptance arcs have been proposed for applications such as cancer therapy, muon accelerators, and recirculating linacs. The efficacy of charged particle therapy can be improved by reducing the energy layer switching time, however this is currently limited by the small momentum acceptance of the beam delivery system ($<\pm$1\%). A `closed-dispersion arc' with a large momentum acceptance has the potential to remove this bottleneck, however such a beamline has not yet been constructed. We have developed a design methodology for large momentum acceptance arcs with Fixed Field Accelerator optics, applying it to a demonstrator beam delivery system for protons at 0.5--3.0MeV $\pm$42\% momentum acceptance) as part of the TURBO project at the University of Melbourne. Using realistic magnetic fields, a beamline has been designed with zero dispersion at either end. An algorithm has been devised for the construction of permanent magnet Halbach arrays for this beamline with multipole error below one part in $10^4$, using commercially available magnets. The sensitivity to errors has been investigated, finding that the delivered beam is robust in realistic conditions. This study demonstrates that a closed-dispersion arc with fixed fields can achieve a large momentum acceptance, and we outline future work required to develop these ideas into a complete proof-of-principle beam delivery system that can be scaled up for a medical facility., Comment: 20 pages including references, 16 figures. For submission to PRAB

Efficiently mapping quantum circuits onto hardware is an integral part of the quantum compilation process, wherein a quantum circuit is modified in accordance with the stringent architectural demands of a quantum processor. Many techniques exist for solving the quantum circuit mapping problem, many of which relate quantum circuit mapping to classical computer science. This work considers a novel perspective on quantum circuit mapping, in which the routing process of a simplified circuit is viewed as a composition of quantum operations acting on density matrices representing the quantum circuit and processor. Drawing on insight from recent advances in quantum information theory and information geometry, we show that a minimal SWAP gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states using the quantum Jensen-Shannon divergence. Additionally, we develop a novel initial placement algorithm based on a graph similarity search that selects the partition nearest to a graph isomorphism between interaction and coupling graphs. From these two ingredients, we then construct a polynomial-time algorithm for calculating the SWAP gate lower bound, which is directly compared alongside the IBM Qiskit compiler for over 600 realistic benchmark experiments, as well as against a brute-force method for smaller benchmarks. In our simulations, we unambiguously find that neither the brute-force method nor the Qiskit compiler surpass our bound, implying utility as a precise estimation of minimal overhead when realizing quantum algorithms on constrained quantum hardware. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing. We anticipate that this method may have diverse applicability outside of the scope of quantum information science, and we discuss several of these possibilities.

The capacity of a memoryless state-dependent channel is derived for a setting in which the encoder is provided with rate-limited assistance from a cribbing helper that observes the state sequence causally and the past channel inputs strictly-causally. Said cribbing may increase capacity but not to the level achievable by a message-cognizant helper., Comment: 8 pages

We study the question of when the algebra of an ample groupoid over a field is von Neumann regular and, more generally, when the algebra of a graded ample groupoid is graded von Neumann regular. For fields of characteristic $0$ we are able to provide a complete characterization. Over fields of positive characteristic, we merely have some sufficient and some necessary conditions for regularity. As applications we recover known results on regularity and graded regularity of Leavitt path algebras and inverse semigroups. We also prove a number of new results, in particular concerning graded regularity of algebras of Deaconu-Renault groupoids and Nekrashevych-Exel-Pardo algebras of self-similar groups., Comment: Minor correction to the description of the inverse semigroup for self-similar graphs

Concentrated Solar Thermal (CST) offers a promising solution for large-scale solar energy utilization as Thermal Energy Storage (TES) enables electricity generation independently of daily solar fluctuations, shifting to high-priced electricity intervals. The development of dispatch planning tools is mandatory to account for uncertainties associated with solar irradiation and electricity price forecasts as well as limited storage capacity. This study proposes the Stochastic Mixed Integer Linear Program (SMILP) to maximize expected profit within a specified scenario space. The SMILP scenario space is generated by different Empirical Cumulative Distribution Function percentiles of the potential solar energy to accumulate in storage and the expected profit is estimated using the Sample Average Approximation (SAA) method. SMILP exhibits robust performance, however, its computational time poses a challenge. Thus, three heuristic solutions are developed which run a set of deterministic optimizations on different historical weather profiles to generate candidate dispatching plans (DPs). The candidate DP with the best average performance on all profiles is then selected. The new methods were applied to a case study for a 115 MW CST plant in South Australia. When the historical database has a limited set of historical weather profiles, the SMILP achieves 6% to 9% higher profit than the closest benchmark when the DP is applied to novel weather conditions. With a large historical weather data, the performance of SMILP and Heuristic-2 becomes nearly identical because the SMILP can only utilize a limited number of trajectories for optimization without becoming computationally infeasible. In this case, Heuristic-2 emerges a practical alternative, since it provides similar average profit in a reasonable time (saving about 7 hours in computing time)., Comment: This paper is going to be submitted to "Energy Conversion and Management" for publication in Elsevier journal

This brief shares learnings from the community of Learn and Earn to Achieve Potential (LEAP) organizations and partners as they continue to deepen their practices to enhance the positive impact and durability of programming while also scaling to reach greater numbers of young people in similar situations. After a brief description of the national and local partnering organizations, the first section of the brief explores enhancements that the partners have made to the national models and the consequent development of a set of six core elements of LEAP opportunity pathways that help define what is being scaled.