This paper considers the problem of scheduling uplinks and downlinks transmissions in an Internet of Things (IoT) network that uses a mode-based time structure and Rate Splitting Multiple Access (RSMA). Further, devices employ power splitting to harvest energy and receive data simultaneously from a Hybrid Access Point (HAP). To this end, this paper outlines a Mixed Integer Linear Program (MILP) that can be employed by a HAP to optimize the following quantities over a given time horizon: (i) mode (downlink or uplink) of time slots, (ii) transmit power of each packet, (iii) power splitting ratio of devices, and (iv) decoding order in uplink slots. The MILP yields the optimal number of packet transmissions over a given planning horizon given non-causal channel state information. We also present a learning based approach to determine the mode of each time slot using causal channel state information. The results show that the learning based approach achieves 90% of the optimal number of packet transmissions, and the HAP receives 25% more packets as compared to competing approaches.

Communication is essential for advancing science and technology. Quantum communication, in particular, benefits from the use of catalysts. During the communication process, these catalysts enhance performance while remaining unchanged. Although chemical catalysts that undergo deactivation typically perform worse than those that remain unaffected, quantum catalysts, referred to as embezzling catalysts, can surprisingly outperform their non-deactivating counterparts despite experiencing slight alterations. In this work, we employ embezzling quantum catalysts to enhance the transmission of both quantum and classical information. Our results reveal that using embezzling catalysts augments the efficiency of information transmission across noisy quantum channels, ensuring a non-zero catalytic channel capacity. Furthermore, we introduce catalytic superdense coding, demonstrating how embezzling catalysts can enhance the transmission of classical information. Finally, we explore methods to reduce the dimensionality of catalysts, a step toward making quantum catalysis a practical reality.

Quantum teleportation is the process of transferring quantum information using classical communication and pre-shared entanglement. This process can benefit from the use of catalysts, which are ancillary entangled states that can enhance teleportation without being consumed. While chemical catalysts undergoing deactivation invariably exhibit inferior performance compared to those unaffected by deactivation, quantum catalysts, termed embezzling catalysts, that are subject to deactivation, may surprisingly outperform their non-deactivating counterparts. In this work, we present teleportation protocols with embezzling catalyst that can achieve arbitrarily high fidelity, namely the teleported state can be made arbitrarily close to the original state, with finite-dimensional embezzling catalysts. We show that some embezzling catalysts are universal, meaning that they can improve the teleportation fidelity for any pre-shared entanglement. We also explore methods to reduce the dimension of catalysts without increasing catalyst consumption, an essential step towards realizing quantum catalysis in practice.

Let C_1 and C_2 be skew circuits in a binary matroid having circumference c. For any positive integer k there is a constant a_k such that if min { |A| ; C_1 \subset A \subset E-A} > a_k, then |C_1| + |C_2| < 2c -k.

We present an entanglement-based quantitative phase gradient microscopy technique that employs principles from quantum ghost imaging and ghost diffraction. In this method, a transparent sample is illuminated by both photons of an entangled pair - one detected in the near-field (position) and the other in the far-field (momentum). Due to the strong correlations offered by position-momentum entanglement, both conjugate observables can be inferred nonlocally, effectively enabling simultaneous access to the sample's transmission and phase gradient information. This dual-domain measurement allows for the quantitative recovery of the full amplitude and phase profile of the sample. Unlike conventional classical and quantum phase imaging methods, our approach requires no interferometry, spatial scanning, microlens arrays, or iterative phase-retrieval algorithms, thereby circumventing many of their associated limitations. Furthermore, intrinsic temporal correlations between entangled photons provide robustness against dynamic and structured background light. We demonstrate quantitative phase and amplitude imaging with a spatial resolution of 2.76 $μ$m and a phase sensitivity of $λ/100$ using femtowatts of illuminating power, representing the highest performance reported to date in quantum phase imaging. This technique opens new possibilities for non-invasive imaging of photosensitive samples, wavefront sensing in adaptive optics, and imaging under complex lighting environments.

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain examples of tensor categories, develop general principles and demonstrate how this question connects with the ongoing study of the structure theory of tensor categories. We also formalise a theory of polynomial functors as functors that act coherently on all tensor categories. We conclude that the classification of such functors is a different way of posing the above question of which representations of symmetric groups appear. Finally, we extend the classical notion of strict polynomial functors from the category of (super) vector spaces to arbitrary tensor categories, and show that this idea is also a different packaging of the same information.

Unifying quantum theory and general relativity is the holy grail of contemporary physics. Nonetheless, the lack of experimental evidence driving this process led to a plethora of mathematical models with a substantial impossibility of discriminating among them or even establishing if gravity really needs to be quantized or if, vice versa, quantum mechanics must be "gravitized" at some scale. Recently, it has been proposed that the observation of the generation of entanglement by gravitational interaction, could represent a breakthrough demonstrating the quantum nature of gravity. A few experimental proposals have been advanced in this sense, but the extreme technological requirements (e.g., the need for free-falling gravitationally-interacting masses in a quantum superposition state) make their implementation still far ahead. Here we present a feasibility study for a table-top nanodiamond-based interferometer eventually enabling easier and less resource-demanding quantum gravity tests. With respect to the aforementioned proposals, by relying on quantum superpositions of steady massive (mesoscopic) objects our interferometer may allow exploiting just small-range electromagnetic fields (much easier to implement and control) and, at the same time, the re-utilization of the massive quantum probes exploited, inevitably lost in free-falling interferometric schemes.

A family of random matrices $\boldsymbol{X}^N=(X_1^N,\ldots,X_d^N)$ is said to converge strongly to a family of bounded operators $\boldsymbol{x}=(x_1,\ldots,x_d)$ when $\|P(\boldsymbol{X}^N,\boldsymbol{X}^{N*})\|\to\|P(\boldsymbol{x}, \boldsymbol{x}^*)\|$ for every noncommutative polynomial $P$. This phenomenon plays a key role in several recent breakthroughs on random graphs, geometry, and operator algebras. However, proofs of strong convergence are notoriously delicate and have relied largely on problem-specific methods. In this paper, we develop a new approach to strong convergence that uses only soft arguments. Our method exploits the fact that for many natural models, the expected trace of $P(\boldsymbol{X}^N,\boldsymbol{X}^{N*})$ is a rational function of $\frac{1}{N}$ whose lowest order asymptotics are easily understood. We develop a general technique to deduce strong convergence directly from these inputs using the inequality of A. and V. Markov for univariate polynomials and elementary Fourier analysis. To illustrate the method, we develop the following applications. 1. We give a short proof of the result of Friedman that random regular graphs have a near-optimal spectral gap, and obtain a sharp understanding of the large deviations probabilities of the second eigenvalue. 2. We prove a strong quantitative form of the strong convergence property of random permutation matrices due to Bordenave and Collins. 3. We extend the above to any stable representation of the symmetric group, providing many new examples of the strong convergence phenomenon.

This paper is to investigate an elliptic fibration over $\mathbb{CP}^2$ arising from the Lagrange top from the viewpoint of complex algebraic geometry. The description of the discriminant locus of this elliptic fibration is given in detail. Moreover, the concrete description of the discriminant locus and the complete classification of singular fibres of the elliptic fibration are obtained according to Miranda's theory of elliptic threefolds after suitable modifications of the base and total spaces. Furthermore, the monodromy of the elliptic fibration is described.

We enumerate all isotopy classes of degree three Morse polynomials ${\mathbb R}^3 \to {\mathbb R}^1$ with nonsingular principal homogeneous parts, proving that there are exactly 37 of them. We also count all 2258 isotopy classes of {\em strictly} Morse polynomials ${\mathbb R}^3 \to {\mathbb R}^1$ of degree three with the maximal possible number (eight) of real critical points. A main tool in this classification is a combinatorial computer program that formalizes Morse surgeries, local monodromy and Picard-Lefschetz theory.

We study the monotonicity of information costs: more informative experiments must be more costly. As criteria for informativeness, we consider the standard information orders introduced by Blackwell (1951, 1953) and Lehmann (1988). We provide simple necessary and sufficient conditions for a cost function to be monotone with respect to each order, grounded in their garbling characterizations. Finally, we examine several well-known cost functions from the literature through the lens of these conditions.

For an abelian length category $\mathcal{A}$ with only finitely many isoclasses of simple objects, we have the wall-chamber structure and the TF equivalence on the dual real Grothendieck group $K_0(\mathcal{A})_\mathbb{R}^*=\operatorname{Hom}_\mathbb{R}(K_0(\mathcal{A})_\mathbb{R},\mathbb{R})$, which are defined by semistable subcategories and semistable torsion pairs in $\mathcal{A}$ associated to elements $θ\in K_0(\mathcal{A})_\mathbb{R}^*$. In this paper, we introduce the $M$-TF equivalence for each object $M \in \mathcal{A}$ as a systematic way to coarsen the TF equivalence. We show that the set $Σ(M)$ of closures of $M$-TF equivalence classes is a rational generalized fan in $K_0(\mathcal{A})_\mathbb{R}^*$ which is finite and complete. More precisely, we show that $Σ(M)$ is the normal generalized fan of the Newton polytope $\mathrm{N}(M)$ in $K_0(\mathcal{A})_\mathbb{R}$. When $\mathcal{A}$ is the category of finitely generated modules over a finite dimensional algebra $A$, $Σ(M)$ can be regarded as a completion of a certain coarsening of the $g$-fan of $A$.

We re-analyze the data of the BU-FCRAO $^{13}{\rm CO}$ Galactic Ring Survey (GRS) to understand the dynamics of the turbulent molecular interstellar medium. We define molecular clouds by their spatial half-power contours of $^{13}{\rm CO}$ integrated intensity, independent of a boundary based on thresholding or tiling. We find properties of hydrostatic equilibrium (HE) and virial equilibrium (VE), the former independent and the latter dependent on time and spatial scales. We suggest that HE is a stationary property of the turbulence and that molecular clouds are high-density regions of a fluctuating component. The gravitational and turbulent kinetic energies within clouds are continuously evolving toward a time-dependent VE with the fluctuating, external, turbulent pressure energy (PE) that can be treated parametrically owing to the shorter time scale for virialization. The average PE is comparable to the pressure of the multiphase ISM at the Galactic mid-plane. Larson's scaling relations analyzed by different statistical methods are not significant. The non-dimensional variances of size, line width, and column density are of comparable magnitude, ruling out the inference of constant column density. Previously unrecognized autocorrelations may have contributed to the apparent validity of the inference.

The Rust programming language restricts aliasing to provide static safety guarantees. However, in certain situations, developers need to bypass these guarantees by using a set of unsafe features. If they are used incorrectly, these features can reintroduce the types of safety issues that Rust was designed to prevent. We seek to understand how current development tools can be improved to better assist developers who find it necessary to interact with unsafe code. To that end, we study how developers reason about foreign function calls, the limitations of the tools that they currently use, their motivations for using unsafe code, and how they reason about encapsulating it. We conducted a mixed-methods investigation consisting of semi-structured interviews with 19 developers, followed by a survey that reached an additional 160 developers. Our participants were motivated to use unsafe code when they perceived that there was no alternative, and most avoided using it. However, limited tooling support for foreign function calls made participants uncertain about their design choices, and certain foreign aliasing and concurrency patterns were difficult to encapsulate. To overcome these challenges, Rust developers need verification tools that can provide guarantees of soundness within multi-language applications.

The lack of diversity in physics remains a persistent worldwide problem. Despite being a quantitative discipline which relies on measurements to construct and validate hypotheses, there remains a paucity of data on both demographics and experiences of marginalized groups. In Canada, there has never been a nationwide assessment of those studying or working in physics. Here, we present findings from Canadian Physics Counts: the first national survey of equity, diversity, and inclusion (EDI) in the Canadian physics community. Our intersectional approach allowed us to gather a wealth of information on gender identity, sexual orientation, race, disability, and more. Analyses revealed key findings, including the first data on physicists who identify as non-binary or gender diverse, as well as the first data on Black and Indigenous scholars. Black physicists (1.2%) and Indigenous physicists (.3%) were found to be the most underrepresented, while White men were overrepresented across all sectors. Among respondents with a disability, 5% reported receiving full accommodations for their required needs at their place of work or study. One in four respondents from BIPOC gender diverse backgrounds identified as being disabled, and the proportion of sexually diverse students who reported having a disability was more than three times higher than the proportion of heterosexual students with a disability. The data also revealed that students represented more demographic diversity than working professionals, highlighting the importance of acting today in order to retain the diverse physicists of tomorrow. Our analysis identifies areas for intervention and offers recommendations for building a diverse and inclusive physics community in Canada that can be a global exemplar.

We study the online busy time scheduling model on heterogeneous machines. In our setting, jobs with uniform length arrive online with a deadline that becomes known to the algorithm at the job's arrival time. An algorithm has access to machines, each with different associated capacities and costs. The goal is to schedule jobs on machines by their deadline, so that the total cost incurred by the scheduling algorithm is minimized. While busy time scheduling has been well-studied, relatively little is known when machines are heterogeneous (i.e., have different costs and capacities), despite this natural theoretical generalization being the most practical model for clients using cloud computing services. We make significant progress in understanding this model by designing an 8-competitive algorithm for the problem on unit-length jobs and providing a lower bound of 2 on the competitive ratio. The lower bound is tight in the setting when jobs form non-nested intervals. Our 8-competitive algorithm generalizes to one with competitive ratio $8(2p-1)/p < 16$ when all jobs have uniform length $p$.

YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) has favorable macroscopic superconducting properties of $T_\mathrm{c}$ up to 93 K and $H_{c2}$ up to 150 T. However, its nanoscale electronic structure remains mysterious because bulk-like electronic properties are not preserved near the surface of cleaved samples for easy access by local or surface-sensitive probes. It has been hypothesized that Ca-doping at the Y site could induce an alternate cleavage plane that mitigates this issue. We use scanning tunneling microscopy (STM) to study both Ca-free and 10% Ca-doped YBCO, and find that the Ca-doped samples do indeed cleave on an alternate plane, yielding a spatially-disordered partial (Y,Ca) layer. Our density functional theory calculations support the increased likelihood of this new cleavage plane in Ca-doped YBCO. On this surface, we image a superconducting gap with average value 24 $\pm$ 3 meV and characteristic length scale 1-2 nm, similar to Bi-based high-$T_\mathrm{c}$ cuprates, but the first map of gap inhomogeneity in the YBCO family.

The classical Maass Spezialschar is a Hecke-stable subspace of the level one holomorphic Siegel modular forms of genus two cut out by certain linear relations between their Fourier coefficients. We define an analogous quaternionic Maass Spezialschar, which consists of level one quaternionic modular forms on split $\mathrm{SO}(8)$ whose Fourier coefficients satisfy certain linear relations. We characterize this space in terms of the theta lift from holomorphic Siegel modular forms on $\mathrm{Sp}(4)$ and in terms of periods. We also give a conjecture for the Dirichlet series of the standard $L$-function of quaternionic modular eigenforms on $\mathrm{SO}(8)$ and verify our conjecture on the quaternionic Maass Spezialschar.

We revisit the state of the light element abundances from big bang nucleosynthesis in early 2024 with particular focus on the derived baryon abundance. We find that the largest differences between the final baryon abundances are typically driven by the assumed Deuterium burning rates, characterized in this work by the underlying code. The rates from theoretical ab-initio calculations favor smaller baryon abundances, while experimentally-determined rates prefer higher abundances. Through robust marginalization over a wide range of nuclear rates, the recently released $\mathtt{PRyMordial}$ code allows for a conservative estimate of the baryon abundance at $Ω_b h^2 = 0.02218 \pm 0.00055$ (using PDG-recommended light element abundances) in $Λ$CDM and $Ω_b h^2 = 0.02196 \pm 0.00063$ when additional ultra-relativistic relics are considered ($Λ$CDM + $N_\mathrm{eff}$). These additional relics themselves are constrained to $ΔN_\mathrm{eff} = -0.14 \pm 0.21$ by light element abundances alone.

The streaming instability, a promising mechanism to drive planetesimal formation in dusty protoplanetary discs, relies on aerodynamic drag naturally induced by the background radial pressure gradient. This gradient should vary in disks, but its effect on the streaming instability has not been sufficiently explored. For this purpose, we use numerical simulations of an unstratified disc to study the non-linear saturation of the streaming instability with mono-disperse dust particles and survey a wide range of gradients for two distinct combinations of the particle stopping time and the dust-to-gas mass ratio. As the gradient increases, we find most kinematic and morphological properties increase but not always in linear proportion. The density distributions of tightly-coupled particles are insensitive to the gradient whereas marginally-coupled particles tend to concentrate by more than an order of magnitude as the gradient decreases. Moreover, dust-gas vortices for tightly-coupled particles shrink as the gradient decreases, and we note higher resolutions are required to trigger the instability in this case. In addition, we find various properties at saturation that depend on the gradient may be observable and may help reconstruct models of observed discs dominated by streaming turbulence. In general, increased dust diffusion from stronger gradients can lower the concentration of dust filaments and can explain the higher solid abundances needed to trigger strong particle clumping and the reduced planetesimal formation efficiency previously found in vertically-stratified simulations.

YbB$_6$ is a predicted topological insulator, with experimental evidence for conducting surface states of yet-unproven origin. However, its lack of a natural cleavage plane, and resultant surface-dependent polarity, has obscured its study. We use scanning tunneling microscopy to image the cleaved surface of YbB$_6$, exhibiting several coexisting terminations with distinct atomic structures. Our spectroscopic measurements show band-bending between the terminations, resulting in both conducting and fully-gapped regions. In the conductive regions, we observe spectral peaks that are suggestive of van Hove singularities arising from Rashba spin-split quantum well states. The insulating regions rule out the possibility that YbB$_6$ is a strong topological insulator, while the spin-polarized conducting regions suggest possible utility for spintronic devices.

Spiking Neural Networks (SNNs) have gained significant attention as a potentially energy-efficient alternative for standard neural networks with their sparse binary activation. However, SNNs suffer from memory and computation overhead due to spatio-temporal dynamics and multiple backpropagation computations across timesteps during training. To address this issue, we introduce Tensor Train Decomposition for Spiking Neural Networks (TT-SNN), a method that reduces model size through trainable weight decomposition, resulting in reduced storage, FLOPs, and latency. In addition, we propose a parallel computation pipeline as an alternative to the typical sequential tensor computation, which can be flexibly integrated into various existing SNN architectures. To the best of our knowledge, this is the first of its kind application of tensor decomposition in SNNs. We validate our method using both static and dynamic datasets, CIFAR10/100 and N-Caltech101, respectively. We also propose a TT-SNN-tailored training accelerator to fully harness the parallelism in TT-SNN. Our results demonstrate substantial reductions in parameter size (7.98X), FLOPs (9.25X), training time (17.7%), and training energy (28.3%) during training for the N-Caltech101 dataset, with negligible accuracy degradation.

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted locally, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, away from or towards fuel source and waste sink, depending on the product molecules' affinity towards fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

Let $G$ be a semisimple simply connected algebraic group over ${\mathbb C}$ of exceptional type. For each $G$-equivariant nilpotent cover of a nilpotent coadjoint $G$-orbit ${\mathbb O}$, we determine the unique birationally rigid induction datum from which it is birationally induced.

We define the notion of {\it strongly interlocked} for indecomposable generalized modules for a vertex operator algebra, and show that the notion of graded pseudo-trace is well defined for modules which satisfy this property in certain settings. We prove that in these settings the graded pseudo-trace is a symmetric linear operator that satisfies the logarithmic derivative property. As an application, we prove that all the indecomposable reducible generalized modules for the rank one Heisenberg (one free boson) vertex operator algebras are strongly interlocked, independent of the choice of conformal vector and have well-defined graded pseudo-traces. We also completely characterize which indecomposable reducible generalized modules for the universal Virasoro vertex operator algebras induced from the level zero Zhu algebra are strongly interlocked. In particular, we prove that the universal Virasoro vertex operator algebra with central charge $c$ has modules induced from the level zero Zhu algebra with conformal weight $h$ that are strongly interlocked if and only if either $(c,h)$ is outside the extended Kac table, or the central charge is either $c = 1$ or $25$, the conformal weight satisfies a certain property, and the level zero Zhu algebra module being induced is determined by a Jordan block of size less than a certain specified parameter. We prove that all these modules for the universal Virasoro vertex operator algebra that are strongly interlocked have well-defined graded pseudo-traces. We give several examples of graded pseudo-traces for these Heisenberg and Virasoro strongly interlocked modules.

Superposed orders of quantum channels have already been proved - both theoretically and experimentally - to enable unparalleled opportunities in the quantum communication domain. As a matter of fact, superposition of orders can be exploited within the quantum computing domain as well, by relaxing the (traditional) assumption underlying quantum computation about applying gates in a well-defined causal order. In this context, we address a fundamental question arising with quantum computing: whether superposed orders of single-qubit gates can enable universal quantum computation. As shown in this paper, the answer to this key question is a definitive "yes". Indeed, we prove that any two-qubit controlled quantum gate can be deterministically realized, including the so-called Barenco gate that alone enables universal quantum computation.

The aim of this paper is to give natural examples of $\mathbfΣ_1^1$-complete and $\mathbfΠ_1^1$-complete sets. In the first part, we consider ideals on $ω$. In particular, we show that the Hindman ideal $\mathcal{H}$ is $\mathbfΠ_1^1$-complete and consider a number of ideals generated in the similar fashion. Moreover, we show that the ideal $\mathcal{D}$ is also $\mathbfΠ_1^1$-complete. In the second part, we focus on families of trees (on $ω$ and $2$) containing a specific tree type. We show the connection between two topics and explore some classical tree types (like Sacks and Miller).

We consider the problem of finding a solution to the incompressible Euler equations $$ ω_t + v\cdot \nabla ω= 0 \quad \hbox{ in } \mathbb{R}^2 \times (0,\infty), \quad v(x,t) = \frac 1{2π} \int_{{\mathbb R}^2} \frac {(y-x)^\perp}{|y-x|^2} ω(y,t)\, dy $$ that is close to a superposition of traveling vortices as $t\to \infty$. We employ a constructive approach by gluing classical traveling waves: two vortex-antivortex pairs traveling at main order with constant speed in opposite directions. More precisely, we find an initial condition that leads to a 4-vortex solution of the form $$ ω(x,t) = ω_0(x-ct\, e ) - ω_0 ( x+ ct \, e) + o(1) \ \hbox{ as } t\to\infty $$ where $$ ω_0( x ) = \frac 1{\varepsilon^{2}} W \left ( \frac {x-q} \varepsilon \right ) - \frac 1{\varepsilon^{2}}W \left ( \frac {x+q} \varepsilon \right ) + o(1) \ \hbox{ as } \varepsilon \to 0 $$ and $W(y)$ is a certain fixed smooth profile, radially symmetric, positive in the unit disc zero outside.

We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "visibility" indicates the existence of John curves connecting the interior point to the points on the "visible boundary". In this paper, we provide an affirmative answer in the setting of a doubling metric measure space supporting a $p$-Poincaré inequality for $1<p<\infty$, thus extending the results of [20,2,9] to non-Ahlfors regular spaces. We show that $t$-codimensional thickness of the boundary for $0<t<p$ implies $p$-codimensional thickness of the visible boundary. For such domains we prove that traces of Sobolev functions on the domain belong to the Besov class of the visible boundary.

Given a non-singular action $Γ\curvearrowright (X,μ)$, we define the $*$-algebra $\mathbb C_{\rm fp}[Γ\curvearrowright X]$ of operators of finite dynamical propagation associated with this action. This assignment is completely canonical and only depends on the measure class of $μ$. We prove that the algebraic crossed product $L^{\infty}X \rtimes_{\rm alg} Γ$ surjects onto $\mathbb C_{\rm fp}[Γ\curvearrowright X]$ and that this surjection is a $\ast$-isomorphism whenever the action is essentially free. As a consequence, we canonically characterize ergodicity and strong ergodicity of the action in terms of structural properties of $\mathbb C_{\rm fp}[Γ\curvearrowright X]$ and its closure. We also use these techniques to describe the Roe algebra of a warped space in terms of the Roe algebra of the (non-warped) space and the group action. We apply this result to Roe algebras of warped cones.