Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this work, we rigorously prove through information-theoretic analysis that one-dimensional logarithmic-depth random Clifford encoding circuits can achieve high quantum error correction performance. We demonstrate that these random codes typically exhibit good approximate quantum error correction capability by proving that their encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors. We show that the error correction inaccuracy decays once a threshold of logarithmic depth is exceeded, resulting in negligible recovery errors. This threshold is shown to be lower than that of the simple separate block encoding, and the decay rate is higher. We further establish that these codes are optimal by proving that logarithmic depth is necessary to maintain a constant encoding rate and high error correction performance. To prove our results, we propose decoupling theorems tailored for one-dimensional low-depth circuits. These results also imply strong decoupling and rapid thermalization properties in low-depth random circuits and have potential applications in quantum information science and physics.

We revisit the results of Kim, and of Katsoulis and Ramsey concerning hyperrigidity for non-degenerate C*-correspondences. We show that the tensor algebra is hyperrigid, if and only if Katsura's ideal acts non-degenerately, if and only if Katsura's ideal acts non-degenerately under any representation. This gives a positive answer to the question of Katsoulis and Ramsey, showing that their necessary condition and their sufficient condition for hyperrigidity of the tensor algebra are equivalent. Non-degeneracy of the left action of Katsura's ideal was also shown by Kim to be equivalent to hyperrigidity for the selfadjoint operator space associated with the C*-correspondence, and our approach provides a simplified proof of this result as well. In the process we study unitisations of selfadjoint operator spaces in the sense of Werner, and revisit Arveson's criterion connecting maximality with the unique extension property and hyperrigidity, in conjunction with the work of Salomon on generating sets.

The search for spin liquids, magnetic phases which lie outside the Landau paradigm, remains one of the central challenges for modern condensed matter physics. For a long time, the prime candidates were thought to be spin-1/2 magnets, but recently examples have been identified in many spin-1 materials, including the pyrochlore NaCaNi$_2$F$_7$. Here we use numerical simulation to explore the spin liquid phases which arise in a minimal model of a spin-1 magnet on the pyrochlore lattice. We find this model supports seven distinct spin liquid phases, including one with nematic correlations. Through quantitative comparison with inelastic neutron scattering, we show that this nematic spin liquid provides a compelling scenario for NaCaNi$_2$F$_7$. These results suggest that the behaviour of spin liquids found in spin-1 pyrochlore magnets may be even richer than in materials with spin-1/2 moments.

We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schrödinger equations with a real drift.

A large body of simulation research suggests that model predictive control (MPC) and reinforcement learning (RL) for heating, ventilation, and air-conditioning (HVAC) in residential and commercial buildings could reduce energy costs, pollutant emissions, and strain on power grids. Despite this potential, neither MPC nor RL has seen widespread industry adoption. Field demonstrations could accelerate MPC and RL adoption by providing real-world data that support the business case for deployment. Here we review 24 papers that document field demonstrations of MPC and RL in residential buildings and 80 in commercial buildings. After presenting demographic information -- such as experiment scopes, locations, and durations -- this paper analyzes experiment protocols and their influence on performance estimates. We find that 71% of the reviewed field demonstrations use experiment protocols that may lead to unreliable performance estimates. Over the remaining 29% that we view as reliable, the weighted-average cost savings, weighted by experiment duration, are 16% in residential buildings and 13% in commercial buildings. While these savings are potentially attractive, making the business case for MPC and RL also requires characterizing the costs of deployment, operation, and maintenance. Only 13 of the 104 reviewed papers report these costs or discuss related challenges. Based on these observations, we recommend directions for future field research, including: Improving experiment protocols; reporting deployment, operation, and maintenance costs; designing algorithms and instrumentation to reduce these costs; controlling HVAC equipment alongside other distributed energy resources; and pursuing emerging objectives such as peak shaving, arbitraging wholesale energy prices, and providing power grid reliability services.

We present a unified framework for representing commutative rings through affine algebraic theories and Boolean rings through hyperaffine algebraic theories. This yields categorical equivalences between these theories and, respectively, commutative rings and Boolean rings. We then analyse models of affine theories over a Boolean ring $B$, comparing them with the models of hyperaffine theories, the well-known $B$-sets. Two novel characterisations are presented: the first defines these models as Boolean vector spaces equipped with an action of the Boolean ring; the second provides a representation in terms of sheaves, in analogy with $B$-sets. Finally, we establish a connection between hyperaffine theories and multidimensional Boolean algebras, a recently introduced generalisation of Boolean algebras.

Two different Sinc-collocation methods for Volterra integral equations of the second kind have been independently proposed by Stenger and Rashidinia--Zarebnia. However, their relation remains unexplored. This study theoretically examines the solutions of these two methods, and reveals that they are not generally equivalent, despite coinciding at the collocation points. Strictly speaking, Stenger's method assumes that the kernel of the integral is a function of a single variable, but this study theoretically justifies the use of his method in general cases, i.e., the kernel is a function of two variables. Then, this study rigorously proves that both methods can attain the same, root-exponential convergence. In addition to the contribution, this study improves Stenger's method to attain significantly higher, almost exponential convergence. Numerical examples supporting the theoretical results are also provided.

Messaging Layer Security (MLS) and its underlying Continuous Group Key Agreement (CGKA) protocol allows a group of users to share a cryptographic secret in a dynamic manner, such that the secret is modified in member insertions and deletions. One of the most relevant contributions of MLS is its efficiency, as its communication cost scales logarithmically with the number of members. However, this claim has only been analysed in theoretical models and thus it is unclear how efficient MLS is in real-world scenarios. Furthermore, practical considerations such as the chosen paradigm and the evolution of the group can also influence the performance of an MLS group. In this work we analyse MLS from an empirical viewpoint: we provide real-world measurements for metrics such as commit generation and processing times and message sizes under different conditions. In order to obtain these results we have developed a highly configurable environment for empirical evaluations of MLS through the emulation of MLS clients. Among other findings, our results show that computation costs scale linearly in practical settings even in the best-case scenario.

The Helfrich model is a fundamental tool for determining the morphology of biological membranes. We relate the geometry of an important class of its equilibria to the geometry of sessile and pendant drops in the hyperbolic space ${\bf H}^3$. When the membrane surface meets the ideal boundary of hyperbolic space, a modification of the regularized area functional is related to the construction of closed equilibria for the Helfrich functional in ${\bf R}^3$.

We study $λ$-biased branching random walks on Bienaymé--Galton--Watson trees in discrete time. We consider the maximal displacement at time $n$, $\max_{\vert u \vert =n} \vert X(u) \vert$, and show that it almost surely grows at a deterministic, linear speed. We characterize this speed with the help of the large deviation rate function of the $λ$-biased random walk of a single particle. A similar result is given for the minimal displacement at time $n$, $\min_{\vert u \vert =n} \vert X(u) \vert$.

Let $J$ be a unital Jordan algebra, and let $\widehat{\mathfrak{sl}}_2(J)$ be the universal central extension of its Tits-Kantor-Koecher Lie algebra. In Part A, we study the category of $(\widehat{\mathfrak{sl}}_2(J), SL_2(K))$-modules. We characterize the dominant $J$-spaces, which are analogous to the dominant highest weights appearing in classical settings. A family of universal envelopes $\mathcal{U}_n(J)$ associated to such modules is introduced and studied. We also prove some finiteness theorems. In Part C, we define the notion of smooth $\widehat{\mathfrak{sl}}_2(J)$-modules for augmented Jordan algebras $J$, and investigate the category of smooth modules in the spirit of Cline-Parshall-Scott highest weight categories. We show that the standard modules of this category are finite dimensional when $J$ is finitely generated. The free unital Jordan algebra $J(D)$ over $D$ variables is an elusive object, but finiteness and Ext-vanishing properties suggest that the smooth $\widehat{\mathfrak{sl}}_2(J(D))$-modules with even eigenvalues might form a generalized highest weight category. However, we prove that such an assertion would contradict recently obtained information about the growth of free Jordan algebras. See [24] and [13] for more details. It then follows that the category of smooth $\widehat{\mathfrak{sl}}_2(J(D))$-modules with even eigenvalues is not a generalized highest weight category when $D\geq 2$. Surprisingly, the proofs of most of these results make use of deep theorems of E. Zelmanov.

Proper analysis of electron collisions in two spatial dimensions leads to the conclusion, that the odd harmonics of the electron distribution function decay much slower than the even ones at finite temperatures. The number of long-lived odd harmonics quickly shrinks with increasing temperature. Focusing on a channel geometry with boundary scattering, we show that such behavior of the odd decay rates leads to a characteristic behaviour of the conductance that we dub anomalous Knudsen effect: it initially grows with temperature but then starts to decrease, forming a peak. Further increase of the temperature forces the conductance to grow again due to the Gurzhi effect, associated with the crossover from ballistic to hydrodynamic transport. The simultaneous observation of the Gurzhi dip preceded by the anomalous Knudsen peak constitutes a particular signature of the long-lived modes in 2D electron transport at low temperatures.

According to the classical laws of magnetism, the shape of magnetically soft objects limits the effective susceptibility. For example, spherical soft magnets cannot display an effective susceptibility larger than 3. Although this is true for macroscopic multi-domain magnetic materials, we explain why magnetic nanoparticles in a single-domain state do not suffer from this limitation. For single-domain particles, the differences between demagnetization factors along principal axes are relevant and can influence susceptibility but do not limit the susceptibility to an upper value as in the case for multi-domain particles. We experimentally validated this result on spherical nanoparticles with varying diameter (9 to 150 nm) and varying volume fraction (0.1 to 47 vol%). In agreement with our predictions, we measure single-domain particle susceptibilities largely above 3, in fact up to more than 250. Moreover, contrary to an existing model for assemblies of particles, we find that the susceptibility of materials composed of non-interacting single-domain particles in a non-magnetic matrix scales linearly with the volume fraction of particles. This implies that high susceptibilities (>100) are achievable for nanoparticle-based composites and is relevant for the design of magnetically soft materials that are operational at MHz-GHz frequencies with negligible power losses.

The advent of Artificial Intelligence (AI) tools, such as Large Language Models, has introduced new possibilities for Qualitative Data Analysis (QDA), offering both opportunities and challenges. To help navigate the responsible integration of AI into QDA, we conducted semi-structured interviews with 15 Human-Computer Interaction (HCI) researchers experienced in QDA. While our participants were open to AI support in their QDA workflows, they expressed concerns about data privacy, autonomy, and the quality of AI outputs. In response, we developed a framework that spans from minimal to high AI involvement, providing tangible scenarios for integrating AI into QDA practices while addressing researchers' needs and concerns. Aligned with real-life QDA workflows, we identify potential for AI tools in areas such as data pre-processing, researcher onboarding, or conflict mediation. Our framework aims to provoke further discussion on the development of AI-supported QDA and to help establish community standards for responsible Human-AI collaboration.

When testing many hypotheses, often we do not have strong expectations about the directions of the effects. In some situations however, the alternative hypotheses are that the parameters lie in a certain direction or interval, and it is in fact expected that most hypotheses are false. This is often the case when researchers perform multiple noninferiority or equivalence tests, e.g. when testing food safety with metabolite data. The goal is then to use data to corroborate the expectation that most hypotheses are false. We propose a nonparametric multiple testing approach that is powerful in such situations. If the user's expectations are wrong, our approach will still be valid but have low power. Of course all multiple testing methods become more powerful when appropriate one-sided instead of two-sided tests are used, but our approach often has superior power then. The proposed methods are not at all limited to safety testing and can be used for testing hypotheses about various kinds of parameters, such as coefficients of a model. The methods in this paper control the median of the false discovery proportion (FDP), which is the fraction of false discoveries among the rejected hypotheses. This approach is comparable to false discovery rate control, where one ensures that the mean rather than the median of the FDP is small. Our procedures make use of a symmetry property of the test statistics, do not require independence and have finite-sample properties.

In this paper, we first characterize which generalized lexicographic products are divisor graphs. As applications, we show that power graphs, reduced power graphs and order graphs are all divisor graphs, which also implies the main result in [Power graph of a finite group is always divisor graph, Asian-European Journal of Mathematics 16 (2023)]. We then show that, the coprime graph of a group is a generalized lexicographic product, and characterize which coprime graphs are divisor graphs. Finally, we classify the finite groups $G$ having at most four prime divisors, whose coprime graphs are divisor graphs, and we also classify the finite groups $G$ whose coprime graphs are divisor graphs, if $G$ is a nilpotent group, a dihedral group, a generalized quaternion group, a symmetric group, an alternating group, a direct product of two non-trivial groups, and a sporadic simple group.

We report the emergence of a two-dimensional (2D) polar metal phase in van der Waals compound FePSe$_3$ under moderate pressures. This layered material is a Mott insulator with antiferromagnetic order under ambient conditions. We show that FePSe$_3$ uniquely allows tuning a 2D correlated insulator into an exotic metal state where a loss of inversion symmetry leads to periodic polar displacements of ions, within a conducting phase - a polar metal. Our combined synchrotron and neutron diffraction data allow us to present a long-sought, unambiguous high-pressure structural model and show the polar displacements of this new phase. We also observe the suppression of magnetic ordering at the insulator-to-metal transition correspondent with this structural change. Our work outlines a comprehensive temperature-pressure phase diagram of FePSe$_3$, combining detailed structural, magnetic and transport data. The high-pressure phase exhibits activated semiconductor behavior at high temperatures, a $T^2$-dependence in its resistivity at lower temperatures - despite the conditions required for a `good metal' Fermi-Liquid description not being met in this case - and a low-temperature resistivity upturn which is suppressed as the system is tuned away from the concomitant transitions. The realisation of a tunable 2D polar metal state in FePSe$_3$ due to the loss of its inversion symmetry combined with pressure-induced metallicity offers a promising new platform to investigate this exotic phase at accessible pressures.

We study the periodic homogenization for convex Hamilton-Jacobi equations on perforated domains under the Neumann type boundary conditions. We consider two types of conditions, the oblique derivative boundary condition and the prescribed contact angle boundary condition, which is important in the front propagation. We first establish a new representation formula for the solution by using the Skorokhod problem and modified Lagrangians. By using this formula essentially, we prove the sub and superadditivity properties of the extended metric functions, which will be applied to obtain the optimal convergence rate $O(\varepsilon)$ for homogenization of Neumann type problems.

The recently upgraded DMC diffractometer at SINQ, equipped with a state-of-the-art 2D He detector, enables high-resolution neutron diffraction experiments optimized for both powder and single-crystal studies. To address the increased complexity and volume of data produced by this instrument, we developed DMCPy, a Python-based software package tailored specifically for DMC data analysis. DMCPy facilitates seamless data reduction and visualization, supporting conversion to reciprocal space, normalization, and masking of detector artifacts. Its modular architecture integrates tools for analyzing both powder diffraction patterns and single-crystal datasets, including advanced visualization features like 3D reciprocal space mapping and interactive scan inspection. By streamlining workflows and enhancing data interpretation, DMCPy empowers researchers to unlock the full potential of the DMC instrument for probing nuclear and magnetic structures in condensed matter systems.

We consider the problem of computing the optimal solution and objective of a linear program under linearly changing linear constraints. The problem studied is given by $\min c^t x \text{ s.t } Ax + λDx \leq b$ where $λ$ belongs to a set of predefined values $Λ$. Based on the information given by a precomputed basis, we present three efficient LP warm-starting algorithms. Each algorithm is either based on the eigenvalue decomposition, the Schur decomposition, or a tweaked eigenvalue decomposition to evaluate the optimal solution and optimal objective of these problems. The three algorithms have an overall complexity $O(pm^2+pmn)$ where $m$ (resp. $n$) is the number of constraints (resp. variables) of the original problem and $p$ the number of values in $Λ$ after an initial preprocessing step. We also provide theorems related to the optimality conditions to verify when a basis is still optimal and a local bound on the objective.

We provide a general structural criterion implying that a group has infinite $m$-almost palindromic width. In particular, we prove that both HNN extensions and free products exhibit infinite $m$-almost palindromic width, with the unique exception of the infinite dihedral group among free products. This framework extends and strengthens the results of \cite{MS} and \cite{GK}.

Silicon carbide (SiC) hosts a number of point defects that are being explored as single-photon emitters for quantum applications. Unfortunately, these quantum emitters lose their photostability when placed in proximity to the surface of the host semiconductor. In principle, a uniform passivation of the surface's dangling bonds by simple adsorbates, such as hydrogen or mixed hydrogen/hydroxyl groups, should remove detrimental surface effects. However, the usefulness of atomic and molecular passivation schemes is limited by their lack of long-term chemical and/or thermal stability. In this first principles work, we use aluminum nitride (AlN) to passivate SiC surfaces in a core-shell nanowire model. By using a negatively charged silicon vacancy in SiC as the proof-of-principle quantum emitter, we show that AlN-passivation is effective in removing SiC surface states from the band gap and in restoring the defect's optical properties. We also report the existence of a silicon vacancy-based defect at the SiC-AlN interface, which displays distinct spin and optical properties as compared to the other well-studied defects in SiC.

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results for linear and branched polymers, multi-component spin systems, and percolation. Both short-range and long-range interactions are included. The universal finite-size scaling is inherited from the scaling of the system unwrapped to the infinite lattice. We also present conjectures for universal scaling profiles for the susceptibility and two-point function plateau in a critical window. For free boundary conditions, the universal scaling has been proven to apply at a pseudocritical point for hierarchical spins, and we conjecture that this holds generally.

We establish the bounds on Wilson coefficients of the Higgs effective field theory (HEFT) mandated by unitarity and analyticity. These positivity constraints can be projected into the space of the standard model effective field theory (SMEFT) as HEFT$\,\supset\,$SMEFT. Doing so reveals a subspace allowed by the HEFT but forbidden by SMEFT positivity, thereby identifying a region that could herald the use of the wrong EFT rather than a pathological UV. Restricting to custodial symmetric dimension-eight Higgs operators, there is a unique pair within the SMEFT where this concept can be sharply realized and is already being probed at colliders.

Spin qubits in quantum dots are a promising technology for quantum computing due to their fast response time and long coherence times. An electromagnetic pulse is applied to the system for a specific duration to perform a desired rotation. To avoid decoherence, the amplitude and gate time must be highly accurate. In this work, we aim to study the impact of leakage during the gate time evolution of a spin qubit encoded in a double quantum dot device. We prove that, in the weak interaction regime, leakage introduces a shift in the phase of the time evolution operator, causing over- or under-rotations. Indeed, controlling the leakage terms is useful for adjusting the time needed to perform a quantum computation and increasing the coherence time of the readout process. This is crucial for running fault-tolerant algorithms and is beneficial for Quantum Error Mitigation techniques.

Building from the work of von Bell et al.~(2022), we study the Ehrhart theory of order polytopes arising from a special class of distributive lattices, known as generalized snake posets. We present arithmetic properties satisfied by the Ehrhart polynomials of order polytopes of generalized snake posets along with a computation of their Gorenstein index. Then we give a combinatorial description of the chain polynomial of generalized snake posets as a direction to obtain the $h^*$-polynomial of their associated order polytopes. Additionally, we present explicit formulae for the $h^*$-polynomial of the order polytopes of the two extremal examples of generalized snake posets, namely the ladder and regular snake poset. We then provide a recursive formula for the $h^*$-polynomial of any generalized snake posets and show that the $h^*$-vectors are entry-wise bounded by the $h^*$-vectors of the two extremal cases.

For a polynomial $f$ from a class $\mathcal{C}$ of polynomials, we show that the problem to compute all the constant degree irreducible factors of $f$ reduces in polynomial time to polynomial identity tests (PIT) for class $\mathcal{C}$ and divisibility tests of $f$ by constant degree polynomials. We apply the result to several classes $\mathcal{C}$ and obtain the constant degree factors in 1. polynomial time, for $\mathcal{C}$ being polynomials that have only constant degree factors, 2. quasipolynomial time, for $\mathcal{C}$ being sparse polynomials, 3. subexponential time, for $\mathcal{C}$ being polynomials that have constant-depth circuits. Result 2 and 3 were already shown by Kumar, Ramanathan, and Saptharishi with a different proof and their time complexities necessarily depend on black-box PITs for a related bigger class $\mathcal{C}'$. Our complexities vary on whether the input is given as a blackbox or whitebox. We also show that the problem to compute the sparse factors of polynomial from a class $\mathcal{C}$ reduces in polynomial time to PIT for class $\mathcal{C}$, divisibility tests of $f$ by sparse polynomials, and irreducibility preserving bivariate projections for sparse polynomials. For $\mathcal{C}$ being sparse polynomials, it follows that it suffices to derandomize irreducibility preserving bivariate projections for sparse polynomials in order to compute all the sparse irreducible factors efficiently. When we consider factors of sparse polynomials that are sums of univariate polynomials, a subclass of sparse polynomials, we obtain a polynomial time algorithm. This was already shown by Volkovich with a different proof.

In this paper, we study nonmaximal representations of surface groups in PU(2,1). In genus large enough, we show the existence of convex-cocompact representations of non-maximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and almost totally geodesic. These examples can be obtained for any Toledo invariant of the form 2-2g +2/3 d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in PU(2,1) which do not lift to SU(2,1)

This paper analyzes the dynamics of higher education dropouts through an innovative approach that integrates recurrent events modeling and point process theory with functional data analysis. We propose a novel methodology that extends existing frameworks to accommodate hierarchical data structures, demonstrating its potential through a simulation study. Using administrative data from student careers at Politecnico di Milano, we explore dropout patterns during the first year across different bachelor's degree programs and schools. Specifically, we employ Cox-based recurrent event models, treating dropouts as repeated occurrences within both programs and schools. Additionally, we apply functional modeling of recurrent events and multilevel principal component analysis to disentangle latent effects associated with degree programs and schools, identifying critical periods of dropout risk and providing valuable insights for institutions seeking to implement strategies aimed at reducing dropout rates.

We consider a population spreading across a finite number of sites. Individuals can move from one site to the other according to a network (oriented links between the sites) that vary periodically over time. On each site, the population experiences a growth rate which is also periodically time varying. Recently, this kind of models have been extensively studied, using various technical tools to derive precise necessary and sufficient conditions on the parameters of the system (ie the local growth rate on each site, the time period and the strength of migration between the sites) for the population to grow. In the present paper, we take a completely different approach: using elementary comparison results between linear systems, we give sufficient condition for the growth of the population This condition is easy to check and can be applied in a broad class of examples. In particular, in the case when all sites are sinks (ie, in the absence of migration, the population become extinct in each site), we prove that when our condition of growth if satisfied, the population grows when the time period is large and for values of the migration strength that are exponentially small with respect to the time period, which answers positively to a conjecture stated by Katriel.