Surface plasmon polaritons (SPPs) are known to preserve quantum optical properties --such as squeezing-- over distances far exceeding those of classical field amplitudes. However, the surviving squeezing typically becomes so weak that its detection requires prohibitively large numbers of measurements. Here we introduce a fundamentally new paradigm for plasmonic communication in which nonclassicality itself carries the information. We (i) encode classical data (bits or dits) directly into the {\it degree of nonclassicality} (e.g., squeezing) of SPPs, thereby enabling information transfer over distances where classical amplitude encoding fails. We further (ii) show that this information can be retrieved from long-lived correlations generated at the readout stage via a beam splitter. Crucially, we demonstrate that (iii) encoding on initially noisy states leads to a counterintuitive enhancement: the encoded information remains accessible after long propagation distances using only a few measurements, outperforming both squeezed vacuum and amplitude-based schemes by orders of magnitude. Finally, (iv) in the THz regime --relevant for graphene and carbon-nanotube platforms at room temperature-- we \textit{exploit}, rather than suppress, the intrinsic thermal background, enabling robust, high-bandwidth nanoscale communication.

The power of adaptivity in algorithms has been intensively studied in diverse areas of theoretical computer science. In this paper, we obtain a number of sharp lower bound results which show that adaptivity provides a significant extra power in cryptanalytic time-space tradeoffs with (possibly unlimited) preprocessing time. Most notably, we consider the discrete logarithm (DLOG) problem in a generic group of $N$ elements. The classical `baby-step giant-step' algorithm for the problem has time complexity $T=O(\sqrt{N})$, uses $O(\sqrt{N})$ bits of space (up to logarithmic factors in $N$) and achieves constant success probability. We examine a generalized setting where an algorithm obtains an advice string of $S$ bits and is allowed to make $T$ arbitrary non-adaptive queries that depend on the advice string (but not on the challenge group element). We show that in this setting, the $T=O(\sqrt{N})$ online time complexity of the baby-step giant-step algorithm cannot be improved, unless the advice string is more than $Ω(\sqrt{N})$ bits long. This lies in stark contrast with the classical adaptive Pollard's rho algorithm for DLOG, which can exploit preprocessing to obtain the tradeoff curve $ST^2=O(N)$. We obtain similar sharp lower bounds for several other cryptanalytic problems. To obtain our results, we present a new model that allows analyzing non-adaptive preprocessing algorithms for a wide array of search and decision problems in a unified way. Since previous proof techniques inherently cannot distinguish between adaptive and non-adaptive algorithms for the problems in our model, they cannot be used to obtain our results. Consequently, our proof uses a variant of Shearer's lemma for this setting, due to Barthe, Cordero-Erausquin, Ledoux, and Maurey (2011). This seems to be the first time a variant of Shearer's lemma for permutations is used in an algorithmic context.

We introduce a measure for evaluating the efficiency of finite universal quantum gate sets $\mathcal{S}$, called the Quantum Circuit Overhead (QCO), and the related notion of $T$-Quantum Circuit Overhead ($T$-QCO). QCO compares the circuit length required by $\mathcal S$ with the best possible length among gate sets of the same size. The $T$-QCO adapts this idea to cost models in which only selected costly gates are counted, while cheap operations are absorbed into an effective gate set. We demonstrate the usefulness of the ($T$-)QCO by extensive numerical calculations of its upper bounds, providing insight into the efficiency of various choices of single-qubit $\mathcal{S}$, including Haar-random gate sets and the gate sets derived from finite subgroups, such as Clifford and Hurwitz groups. In particular, our results suggest that, in terms of the upper bounds on the $T$-QCO, the famous T gate is a highly non-optimal choice for the completion of the Clifford gate set, even among the gates of order 8. We identify the optimal choices of such completions for both finite subgroups.

We study the possibility of elementary energy quanta with vacuum propagation speed w < c, capable of interacting with each other to form massive bound states. The slow matter thus formed is shown to follow laws of Special Relativity mediated by velocity w rather than c, and to possess dynamical properties recalling some characteristics of Dark Matter.

Two-dimensional moiré Chern bands provide an exceptional platform for exploring a variety of many-body quantum phases at zero magnetic field within a lattice system. One particular intriguing possibility is that flat Chern bands can, in principle, support exotic superconducting phases together with fractional topological phases. Here, we report the observation of integer and fractional quantum anomalous Hall effects, the reentrant quantum anomalous Hall effect, and superconductivity within the first moiré Chern band of twisted bilayer MoTe2. The superconducting phase emerges from a normal state exhibiting anomalous Hall effects. Our results present the first example of superconductivity emerging within a flat Chern band that simultaneously hosts fractional quantum anomalous effects, a phenomenon never observed in any other systems. Our work expands the understanding of emergent quantum phenomena in moiré Chern bands, and offers a nearly ideal platform for engineering Majorana and parafermion zero modes in gate-controlled hybrid devices.

Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid model-specific formulations or stochastic black-box optimization routines. Tangent approximation is a principled class of structured variational methods that exploits the geometry of the underlying probability model. However, its utility has largely been confined to logistic regression and related modeling regimes. In this article, we propose a novel variational framework based on tangent transformation for a broad class of probability models characterized by strongly super-Gaussian likelihoods. Our method leverages convex duality to construct tangent minorants of the log-likelihood, thereby inducing conjugacy with Gaussian priors over model parameters in an otherwise intractable setup. Under mild assumptions on the data-generating mechanism, we establish algorithmic convergence guarantees, a contribution that stands in contrast to the limited theoretical assurances typically available for black-box variational methods. Additionally, we derive near-minimax optimal bounds for the variational risk. Superior performance of our proposed methodology is illustrated on simulated and real-data scenarios that challenge state-of-the-art variational algorithms in terms of scalability and their ability to consistently capture complex underlying data structure.

Existing financial sentiment analysis methods often fail to capture the multi-faceted nature of risk in bond markets due to their single-level approach and neglect of temporal dynamics. We propose Multi-level Financial Sentiment Analysis (MulFSA) based on pre-trained language models (PLMs) and large language models (LLMs), a novel framework that systematically integrates firm-specific micro-level sentiment, industry-specific meso-level sentiment, and duration-aware smoothing to model the latency and persistence of textual impact. Applying MulFSA to the comprehensive Chinese bond market corpus constructed by us (2013-2023, 1.35M texts), we extracted a daily composite sentiment index. Empirical results show statistically measurable improvements in credit spread forecasting when incorporating sentiment (10.25% MAE and 11.94% MAPE reduction), with sentiment shifts closely correlating with major social risk events and firm-specific crises. Project Page: https://mulfsa.github.io/.

Silicon (Si) is the primary donor dopant in gallium nitride (GaN), introduced through epitaxial growth or ion implantation. However, precise control over Si diffusion remains a critical challenge for high-performance device applications. This study investigates Si diffusion mechanisms in bulk GaN using first-principles density functional theory (DFT) calculations, supported by ultra-high-pressure annealing (UHPA) experiments. Vacancy-mediated diffusion pathways were analyzed using the SIESTA code, with minimum energy paths (MEPs) and activation barriers determined via the nudged elastic band (NEB) method. The results indicate that Si diffusion barriers vary with crystallographic direction, with the lowest barrier of 3.2 eV along [11-20] and the highest barrier of ~9.9 eV along [1-100], rendering diffusion in this direction highly improbable. Alternative diffusion mechanisms, including direct exchange and ring-like migration, exhibit prohibitively high barriers ($>$12 eV). Phonon calculations confirm that temperature-induced reductions in effective diffusion barriers are minimal. Experimental validation using SIMS analysis on Si-implanted GaN samples subjected to UHPA (1450°C, 1 GPa) confirms negligible Si diffusion under these extreme conditions. These findings resolve inconsistencies in prior reports and establish that Si-doped GaN remains highly stable, ensuring reliable doping profiles for advanced electronic and optoelectronic applications.

Quantum kernel methods are one of the most explored approaches to quantum machine learning. However, the structural properties and inductive bias of quantum kernels are not fully understood. In this work, we introduce the notion of entangled tensor kernels - a generalization of product kernels from classical kernel theory - and show that all embedding quantum kernels can be understood as an entangled tensor kernel. We discuss how this perspective allows one to gain novel insights into both the unique inductive bias of quantum kernels, and potential methods for their dequantization.

Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped Langevin dynamics. There are many variants of Langevin dynamics that often show superior performance in practice. In this paper, we provide a unified approach to study the acceleration of the variants of the overdamped Langevin dynamics through the lens of large deviations theory. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of these variants.

Removal strategies for atmospheric pollutants are increasingly being considered to mitigate global warming and improve public health. However, the global potential of surface-based removal techniques has not yet been quantified based on limits of pollutant transport and removal rates. We evaluate the atmospheric pollutant transport to surfaces and assess the potential of surface-based removal technologies for global-scale deployment across a variety of configurations, including air interaction with the built environment, mechanical ventilation and convection systems, and over the global transportation fleet. Cities provide the highest transport-limited removal potential, with median annual atmospheric flow rates of 30 GtCO$_2$, 0.06 GtCH$_4$, 0.007 GtNO$_\text{x}$ and 0.0001 GtPM$_{2.5}$ to their total surface area. Cities, solar farms and HVAC systems have flow rates large enough to potentially remove more than 1 GtCO$_2$/y (1 GtCO$_2$e/y for CH$_4$, 20-year GWP), if laboratory-scale removal efficiencies from the literature are applied to their total surface area, however, achieving this would require technological advances. Based on their transport-limited upper bounds, HVAC filters have the potential to achieve costs as low as \$600 per tCO$_2$ removed (\$2000 per tCO$_2$e) if CO$_2$-sorption (CH$_4$-catalyst) technologies are incorporated into their surfaces and performance is maintained through routine replacement, compared with \$3000 per tCO$_2$ (\$10000 per tCO$_2$e) for city surfaces, using literature values for these technologies' material and application costs. These findings demonstrate that integrating surface-based pollutant removal technologies into infrastructure may offer a pathway to advance climate objectives, though further studies are needed to assess their feasibility in application, and application-implementation rates and cost.

In the classical NP-hard metric $k$-median problem, we are given a set of $n$ clients and centers with metric distances between them, along with an integer parameter $k\geq 1$. The objective is to select a subset of $k$ open centers that minimizes the total distance from each client to its closest open center. In their seminal work, Jain, Mahdian, Markakis, Saberi, and Vazirani presented the Greedy algorithm for facility location, which implies a $2$-approximation algorithm for $k$-median that opens $k$ centers in expectation. Since then, substantial research has aimed at narrowing the gap between their algorithm and the best achievable approximation by an algorithm guaranteed to open exactly $k$ centers. During the last decade, all improvements have been achieved by leveraging their algorithm or a small improvement thereof, followed by a second step called bi-point rounding, which inherently increases the approximation guarantee. Our main result closes this gap: for any $ε>0$, we present a $(2+ε)$-approximation algorithm for $k$-median, improving the previous best-known approximation factor of $2.613$. Our approach builds on a combination of two algorithms. First, we present a non-trivial modification of the Greedy algorithm that operates with $O(\log n/ε^2)$ adaptive phases. Through a novel walk-between-solutions approach, this enables us to construct a $(2+ε)$-approximation algorithm for $k$-median that consistently opens at most $k + O(\log n{/ε^2})$ centers. Second, we develop a novel $(2+ε)$-approximation algorithm tailored for stable instances, where removing any center from an optimal solution increases the cost by at least an $Ω(ε^3/\log n)$ fraction. Achieving this involves a sampling approach inspired by the $k$-means++ algorithm and a reduction to submodular optimization subject to a partition matroid.

Linear relations, defined as submodules of the direct sum of two modules, can be viewed as objects that carry dynamical information and reflect the inherent uncertainty of sampled dynamics. These objects also provide an algebraic structure that enables the definition of subtle invariants for dynamical systems. In this paper, we prove that linear relations defined on modules of finite length are shift equivalent to bijective mappings.

A functional analog of the Klain-Schneider theorem for vector-valued valuations on convex functions is established, providing a classification of continuous, translation covariant, simple valuations. Under additional rotation equivariance assumptions, an analytic counterpart of the moment vector is characterized alongside a new epi-translation invariant valuation. The former arises as the top-degree operator in a family of functional intrinsic moments, which are linked to functional intrinsic volumes through translations. The latter represents the top-degree operator in a class of Minkowski vectors, which are introduced in this article and which lack classical counterparts on convex bodies, as they vanish due to the Minkowski relations. Additional classification results are obtained for homogeneous valuations of extremal degrees.

A search for exotic decays of the Higgs boson into a pair of low-mass scalars that subsequently decay into $τ$-leptons, $H\rightarrow aa\rightarrow τ^+τ^-τ^+τ^-$, is presented. In models with Yukawa-like couplings, the decay to $τ$-leptons is favoured for light $a$-bosons, with mass in the range of $2m_τ < m_a < 2m_{b}$. Results are presented in the range of $4 \, \mathrm{GeV} < m_a < 15 \, \mathrm{GeV} $ using the $140\,\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider. This search focuses on the scenario where, for both di-$τ$ pairs, one of the $τ$-leptons decays to hadrons and neutrinos, while the other decays to a muon and neutrinos. In this mass range, the $a\rightarrow τ^+τ^-$ is Lorentz-boosted and a dedicated muon removal technique is used to reconstruct the di-$τ$ pairs. No significant excess above the Standard Model background prediction is observed. Upper limits on $(σ(H)/σ_{\mathrm{SM}}(H))\times \mathcal{B}(H\rightarrow aa\rightarrow 4τ)$ at $95\%$ confidence level are provided, ranging from $0.03$ to $0.10$ depending on the $a$-boson mass.

We present a quantum token scheme in which the token is a quantum state that ensures secure authentication or payment. In our approach, rooted in Wiesner's quantum money concept, a token is encoded in a multi-qubit state generated by a single-photon source and transmitted to a user who holds a quantum memory register. By leveraging state-dependent reflection from a highly efficient sawfish nanophotonic crystal cavity and implementing high-fidelity fractional quantum gates through a pulse train of optical pi/8 pulses, our design achieves gate fidelities exceeding 99% under realistic operating conditions. We also analyze microwave control, which extends the viability to longer storage times, albeit at reduced operational rates. We rigorously examine the impact of finite photon bandwidth, cavity design parameters, spectral diffusion, and control imperfections on overall performance. Our comprehensive model indicates that, with near-term improvements in device efficiency and conversion rates, the token acceptance rate can approach the MHz regime for short-distance communication links while remaining robust against optimal cloning attacks. These findings pave the way for integrating unforgeable quantum tokens into larger-scale quantum networks, thereby significantly enhancing the security of future quantum network applications.

Linux is increasingly deployed in Low Earth Orbit on commercial off the shelf systems on chip that were not designed for space radiation. Ionizing particles can trigger single event functional interrupts that crash the kernel without warning. Prior work mainly measured board level cross sections, leaving unclear which Linux subsystems fail and how a single upset propagates into an operating system wide failure across architectures, stress conditions, and irradiation conditions. We address this gap by subjecting three Linux platforms to proton irradiation in the 20 to 58 MeV range: a Raspberry Pi Zero 2W with a 40 nm planar ARM Cortex A53, an NXP i MX 8M Plus with a 14 nm FinFET ARM Cortex A53, and an OrangeCrab ECP5 FPGA hosting a VexRiscV RV32I soft core at 40 nm. Through kernel log forensics, we trace all 133 observed Linux failures, most of which have not been previously reported, to their originating kernel handlers. Failure profiles differ sharply across nodes. On the two 40 nm platforms, memory management and driver handlers account for 67 to 78% of events, while on the 14 nm SoC approximately 90% of failures funnel through a single eMMC storage path, comprising 56% filesystem failures and 34% driver failures. This shows that a SEFI susceptible peripheral can strongly dictate system reliability. The 14 nm SoC also shows roughly an order of magnitude lower Linux SEFI cross section, although irradiation geometry and DRAM exposure differences preclude isolating the contribution of process scaling. Reconstructed propagation chains show that faults can cascade through up to six kernel subsystems before terminal failure in severe events. Rather than motivating blanket redundancy, these results identify the kernel subsystem boundaries where radiation induced faults originate, enabling targeted mitigations for hardening COTS Linux systems for orbit.

In this paper, we compute the cohomology sheaves of the $\ell$-adic nearby cycles on the local model of the PEL $\mathrm{GU}(n-1,1)$ Shimura variety over a ramified prime, with level given by the stabilizer of a self-dual lattice. This local model is known to have isolated singularities. If $n=2$ it has semi-stable reduction, and if $n\geq 3$ the blow-up at the singular point has semi-stable reduction. We compute the nearby cycles on the blow-up, then use proper base change to describe them on the original local model. As a result, we prove that the nearby cycles are trivial when $n$ is odd, and that only a single higher cohomology sheaf does not vanish when $n$ is even. In this case, we also describe the Galois action by computing the associated Frobenius eigenvalue.

We consider the motion of a two-layer thin film that consists of two immiscible viscous fluids and is endowed with an anti-surfactant solute. The presence of such solute particles induces variations of the surface tension and interfacial stress driving a Marangoni-type flow. We first analyze a lubrication limit and derive one-dimensional evolution equations for film heights and solute concentrations. Then, under the assumption that the capillarity and diffusion effects are negligible and the solute is perfectly soluble, we obtain a conservative first-order system in terms of film heights and concentration gradients. This reduced system is found to be strictly hyperbolic for a certain set of states and to admit an entire class of entropy/entropy-flux pairs. We also provide a strictly convex entropy for the hyperbolic system. Thus, the well-posedness for the Cauchy problem is given. Moreover, the system is almost a Temple-class system, which allows to compute explicit solutions of the Riemann problem. The paper concludes with numerical experiments using a Godunov-type finite volume method, which relies on the exact Riemann solver.

Let (x_n; n\in Z) be a bisequence of elements x_n in the 1-dimensional torus R/Z, which is called a stream over R/Z. Let P(z)=a_k z^k+...+a_1 z+a_0 be a polynomial with integer coefficients. Define the set of streams over R/Z such that the convolution product P(z)\times(x_n; n\in Z)=(\sum_{i=0}^k a_i x_{n-i}; n\in Z)=(0; n\in Z), which is called the stream 0 of P. We study similarities between stream 0 of P and the roots of P(z)=0.

We prove that the Fourier dimension of the graph of fractional Brownian motion with Hurst index greater than $1/2$ is almost surely 1. This extends the result of Fraser and Sahlsten (2018) for the Brownian motion and confirms part of the conjecture of Fraser, Orponen and Sahlsten (2014). We introduce a combinatorial integration by parts formula to compute the moments of the Fourier transform of the graph measure. The proof of our main result is based on this integration by parts formula together with Faà di Bruno's formula and strong local nondeterminism of fractional Brownian motion. We also show that the graph of a symmetric $α$-stable process has Fourier dimension 1 almost surely when $α\in [1,2]$ and is a Salem set when $α= 1$.

Senders of messages prefer to communicate uncertainty verbally (e.g., something is likely to happen) rather than numerically (such as 75%), leaving receivers with imprecise information. While it is well established that receivers translate verbal probabilities into numerical values that systematically deviate from the intended numerical meaning, it is less clear how this discrepancy influences subsequent behavioral actions. Thus, the role of verbal versus numerical communication of uncertainty warrants additional attention, to investigate two critical questions: 1) whether differences in decision-making under uncertainty arise between these communication forms, and 2) whether such differences persist even when verbal phrases are translated accurately into the intended numerical meaning. By implementing a laboratory experiment, we show that individuals place significantly lower values on uncertain options with medium to high likelihoods when uncertainty is communicated verbally rather than numerically. This effect may lead to less rational decisions under verbal communication, particularly at high likelihoods. Those results remain consistent even if individuals translate verbal uncertainty correctly into the intended numerical uncertainty, implying that a biased behavioral response is not only induced by miscommunication. Instead, ambiguity about the exact meaning of a verbal phrase interferes with decision-making even beyond potential mistranslations. These findings tie in with previous research on ambiguity aversion, which has predominantly operationalized ambiguity through numerical ranges rather than verbal phrases. Based on our findings we conclude that managers should communicate uncertainty numerically, as verbal communication can unintentionally influence the decision-making process of employees.

We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state $|Ψ\rangle_{ABC}$ by local unitaries or local operations when each subsystem $A$, $B$, or $C$ has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance, showing a doubly-exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $ε$-net argument and concentration of measure. Viewing $|Ψ\rangle_{ABC}$ as a bipartite quantum error-correcting code $C\to AB$, this implies that neither output subsystem $A$ nor $B$ supports any non-trivial logical operator. We also establish general constraints on the structure of tripartite entanglement in Haar random states, showing that W- or GHZ-like entanglement cannot be distilled and that nontrivial global symmetries are absent. Finally, we discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief.

Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and processes. We construct an affine calculus for $1$-bounded complete metric spaces and the monad for probability measures equipped with the Kantorovich distance. The calculus includes a form of guarded recursion interpreted via Banach's fixed point theorem, useful, e.g., for recursive programming with processes. We then define an affine higher-order quantitative logic for reasoning about terms of our calculus. The logic includes novel principles for guarded recursion, and induction over probability measures and natural numbers. We illustrate the expressivity of the logic by a sequence of case studies: Proving upper limits on bisimilarity distances of Markov processes, showing convergence of a temporal learning algorithm and of a random walk using a coupling argument.

Given a closed symplectic $4$-manifold $(X,ω)$, a collection $D$ of embedded symplectic submanifolds satisfying certain normal crossing conditions is called a symplectic divisor. In this paper, we consider the pair $(X,ω,D)$ with symplectic log Kodaira dimension $-\infty$ in the spirit of Li-Zhang. We introduce the notion of symplectic affine-ruledness, which characterizes the divisor complement $X\setminus D$ as being foliated by symplectic punctured spheres. We establish a symplectic analogue of a theorem by Fujita-Miyanishi-Sugie-Russell in the algebraic settings which describes smooth open algebraic surfaces with $\overlineκ=-\infty$ as containing a Zariski open subset isomorphic to the product between a curve and the affine line. When $X$ is a rational manifold, the foliation is given by certain unicuspidal rational curves of index one with cusp singularities located at the intersection point in $D$. We utilize the correspondence between such singular curves and embedded curves in its normal crossing resolution recently highlighted by McDuff-Siegel, and also a criterion for the existence of embedded curves in the relative settings by McDuff-Opshtein. Another main technical input is Zhang's curve cone theorem for tamed almost complex $4$-manifolds, which is crucial in reducing the complexity of divisors. We also investigate the symplectic deformation properties of divisors and show that such pairs are deformation equivalent to Kähler pairs. As a corollary, the restriction of the symplectic structure $ω$ on an open dense subset in the divisor complement $X\setminus D$ is deformation equivalent to the standard product symplectic structure.

Self-consistent mean-field methods with Skyrme-type effective interactions and semiclassical approximations, such as the Thomas-Fermi approach and its extensions are particularly well-suited for describing in a thermodynamically consistent way the various phases of the dense matter present in the interior of neutron stars. These methods have been applied to predict the composition of the different regions, including the inner crust constituted by nuclear clusters coexisting with free neutrons and electrons. Because of the computational cost, the energy is typically calculated for a few selected average baryon number densities, and the results are interpolated to obtain the pressure numerically. However, this may introduce systematic errors in the calculations of the global structure of a neutron star and its dynamical evolution. In this paper, we show how the full equation of state can be consistently calculated within the same framework by deriving exact formulas for the chemical potentials and for the pressure that can be easily implemented in existing computer codes. These formulas are applicable to both catalyzed and accreted crusts. We discuss in each case the suitable conditions to impose to determine the composition. Numerical examples are also presented and discussed. Results from refined calculations of the BSk24 equation of state for the inner crust of nonaccreted neutron stars and the corresponding adiabatic index are provided.

Let $d \geq 0$ be an integer and let $P \subset \mathbb R^d$ be a $d$-dimensional lattice polytope. We call a polytope $M \subset \mathbb R^d$ such that $M \subset P$ and $M \sim P$ a {\itshape miniature} of $P,$ and it is said to be {\itshape horizontal} if $M$ is transformed into $P$ by translating and rescaling. A miniature $M$ of $P$ is said to be {\itshape average-sized} (resp.~{\itshape normal-sized}) if the volume of $M$ is equal to the limit of the sequence whose $n$-th term is the average of the volumes of all miniarures (resp.~all horizontal miniatures) whose vertices belong to $(n^{-1}\mathbb Z)^d.$ We prove that, for any lattice square $P \subset \mathbb R^2,$ the ratio of the areas of an average-sized miniature of $P$ and $P$ is $2:15.$ We also prove that, for any lattice simplex $P \subset \mathbb R^d,$ the ratio of the volume of a normal-sized miniature of $P$ to that of $P$ is $1:\binom{2d+1}{d}.$ This ratio is same as the known result for the hypercube $[0,1]^d$ provided by the author.

Cryptographic libraries, an essential part of cybersecurity, are shown to be susceptible to different types of attacks, including side-channel and memory-corruption attacks. In this article, we examine popular cryptographic libraries in terms of the security measures they implement, pinpoint security vulnerabilities, and suggest security improvements in their development process.

In this work, we provide a combinatorial formalism for dealing with the cancellations that have appeared recently in the context of dispersive PDEs with random initial data. The main idea is to transform iterated integrals encoded by decorated trees into words via an arborification map. This provides a formalism alternative to the one of molecules introduced by Deng and Hani (2023). It allows us to compute the cancellations coming from Wave turbulence and the proof of the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation.

This paper presents Flutter, the first Byzantine Total Order Broadcast implementation with a broadcast-to-delivery latency of $2Δ+ ε$ time units, $Δ$ being the message delay and $ε$ an arbitrarily small constant margin, when all processes are correct, the network is synchronous, hence local clocks are well-synchronized. Under the same conditions, state-of-the-art protocols require at least $3Δ$ time units in practical deployments where clients differ from servers. We prove Flutter's good-case latency is quasi-optimal, meaning it cannot be improved upon by any finite amount. Flutter is deterministic, leaderless, and signature-free hence quantum-resilient; it assumes partial synchrony and at least $5f + 1$ servers, where $f$ bounds the number of faults. Under the hood, Flutter builds upon Blink, a novel Binary Consensus implementation with Representative Validity, whose fast path enables decisions in $Δ$ time units when all correct servers propose the same value.