We give a constructive proof of the general Nullstellensatz: a univariate polynomial ring over a commutative Jacobson ring is Jacobson. This theorem implies that every finitely generated algebra over a zero-dimensional ring or the ring of integers is Jacobson, which has been an open problem in constructive algebra. We also prove a variant of the general Nullstellensatz for finitely Jacobson rings.

Bayesian inference for survival regression modeling offers numerous advantages, especially for decision-making and external data borrowing, but demands the specification of the baseline hazard function, which may be a challenging task. We propose an alternative approach that does not need the specification of this function. Our approach combines pseudo-observations to convert censored data into longitudinal data with the Generalized Methods of Moments (GMM) to estimate the parameters of interest from the survival function directly. GMM may be viewed as an extension of the Generalized Estimating Equation (GEE) currently used for frequentist pseudo-observations analysis and can be extended to the Bayesian framework using a pseudo-likelihood function. We assessed the behavior of the frequentist and Bayesian GMM in the new context of analyzing pseudo-observations. We compared their performances to the Cox, GEE, and Bayesian piecewise exponential models through a simulation study of two-arm randomized clinical trials. Frequentist and Bayesian GMM gave valid inferences with similar performances compared to the three benchmark methods, except for small sample sizes and high censoring rates. For illustration, three post-hoc efficacy analyses were performed on randomized clinical trials involving patients with Ewing Sarcoma, producing results similar to those of the benchmark methods. Through a simple application of estimating hazard ratios, these findings confirm the effectiveness of this new Bayesian approach based on pseudo-observations and the generalized method of moments. This offers new insights on using pseudo-observations for Bayesian survival analysis.

This study proposes a modification to the yield condition that addresses the mathematical constraints inherent in the Directional Distortional Hardening models developed by Feigenbaum and Dafalias. The modified model resolves both the mathematical inconsistency found in the complete model and the limitations of the r-model. In the complete model, inconsistency arises between the distortional term in the yield surface and the plastic part of the free energy in the absence of kinematic hardening. Additionally, the r-model fails to capture the flattening of the yield surface in the reverse loading direction due to the absence of a fourth-order anisotropic tensor structure in the distortional term. To address these issues, the proposed model introduces a decoupled distortional hardening term in the yield function. This modification enables the simultaneous representation of both flattening and sharpening of the yield surface, and permits isotropic hardening with distortion even without kinematic hardening. A consistent mathematical formulation based on rational mechanics and a corresponding numerical algorithm are also developed, establishing a foundation for future experimental investigations and model validation.

Over a commutative Noetherian ring, we show that the Auslander-Reiten conjecture holds true for the class of (finitely generated) modules whose dual has finite complete intersection dimension. We provide another result that validates the conjecture for the class of modules whose self dual has finite complete intersection dimension and either the module or its dual has finite Gorenstein dimension. Thus we combine and strengthen a number of results in the literature, due to Auslander-Ding-Solberg, Dey-Ghosh and Rubio-Pérez.

This paper considers energy-efficient connectivity for Internet of Things (IoT) devices in a coexistence scenario between two distinctive communication models: pull- and push-based. In pull-based, the base station (BS) decides when to retrieve a specific type of data from the IoT devices, while in push-based, the IoT device decides when and which data to transmit. To this end, this paper advocates introducing the content-based wake-up (CoWu), which enables the BS to remotely activate only a subset of pull-based nodes equipped with wake-up receivers, observing the relevant data. In this setup, a BS pulls data with CoWu at a specific time instance to fulfill its tasks while collecting data from the nodes operating with a push-based communication model. The resource allocation plays an important role: longer data collection duration for pull-based nodes can lead to high retrieval accuracy while decreasing the probability of data transmission success for push-based nodes, and vice versa. Numerical results show that CoWu can manage communication requirements for both pull-based and push-based nodes while realizing the high energy efficiency (up to 38%) of IoT devices, compared to the baseline scheduling method.

We consider a setup with Internet of Things (IoT), where a base station (BS) collects data from nodes that use two different communication modes. The first is pull-based, where the BS retrieves the data from specific nodes through queries. In addition, the nodes that apply pull-based communication contain a wake-up receiver: upon a query, the BS sends wake-up signal (WuS) to activate the corresponding devices equipped with wake-up receiver (WuDs). The second one is push-based communication, in which the nodes decide when to send to the BS. Consider a time-slotted model, where the time slots in each frame are shared for both pull-based and push-based communications. Therein, this coexistence scenario gives rise to a new type of problem with fundamental trade-offs in sharing communication resources: the objective to serve a maximum number of queries, within a specified deadline, limits the transmission opportunities for push sensors, and vice versa. This work develops a mathematical model that characterizes these trade-offs, validates them through simulations, and optimizes the frame design to meet the objectives of both the pull- and push-based communications.

This paper investigates the role and the impact of control operations for dynamic mobile edge computing (MEC) empowered by Reconfigurable Intelligent Surfaces (RISs), in which multiple devices offload their computation tasks to an access point (AP) equipped with an edge server (ES), with the help of the RIS. While usually ignored, the control aspects related to channel estimation (CE), resource allocation (RA), and control signaling play a fundamental role in the user-perceived delay and energy consumption. In general, the higher the resources involved in the control operations, the higher their reliability; however, this introduces an overhead, which reduces the number of resources available for computation offloading, possibly increasing the overall latency experienced. Conversely, a lower control overhead translates to more resources available for computation offloading but impacts the CE accuracy and RA flexibility. This paper establishes a basic framework for integrating the impact of control operations in the performance evaluation of the RIS-aided MEC paradigm, clarifying their trade-offs through theoretical analysis and numerical simulations.

This paper explores the application of quantum non-locality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on a novel application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a new distributed task for mobile agents grounded in the graph domination problem. Through an investigation across various graph scenarios, we showcase the quantum advantage. Additionally, we scrutinize deterministic strategies, highlighting their comparatively lower efficiency compared to quantum strategies. The paper concludes with a numerical analysis, providing further insights into our findings.

Contemporary focus on selective inference has renewed interest in the theory of selection models. In this paper, we analyze the asymptotic properties of selection models built on independent and identically distributed observations. We show that, under suitable regularity conditions, they behave asymptotically like a sequence of Gaussian selection models. This provides a natural generalization of the Local Asymptotic Normality framework of Le Cam (1960), and indicates a notion of local asymptotic selective normality as the appropriate simplifying theoretical framework for analysis of selective inference. As a key application, we consider the methodological consequences of the asymptotic theory for Bayesian selective inference. Specifically, we prove that the posterior distribution constructed from a selection model under a fixed prior is asymptotically equivalent to the posterior derived in the corresponding asymptotic Gaussian selection model under a uniform prior. Notably, the latter is often mis-calibrated in a frequentist sense, particularly for one-sided selection mechanisms. This demonstrates that the familiar asymptotic equivalence between Bayesian and frequentist approaches does not hold under selection.

Estimating the probability of failure for expensive simulations is a central task in reliability analysis for structural design, power grid design, and safety certification, among other areas. This work derives credible intervals on the probability of failure by modeling the simulation as a realization of a Gaussian process surrogate. These intervals are governed by the pointwise binary classification error of the surrogate and are compatible with the broad class of adaptive sampling schemes proposed in the literature. We further propose a novel batch sampling scheme that suggests multiple evaluation points per iteration, enabling parallel simulation on HPC systems. The method is empirically validated using our scalable, open-source implementation on a variety of test problems including a Tsunami model where failure is quantified in terms of maximum wave height.

General relativity (GR) admits two alternative formulations with the same dynamics attributing the gravitational phenomena to torsion or nonmetricity of the manifold's connection. They lead, respectively, to the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we focus on STEGR and present its differences with the conventional, curvature-based GR. We exhibit the 3+1 decomposition of the STEGR Lagrangian in the coincident gauge and present the Hamiltonian, the Hamiltonian and momenta constraints, and Hamilton's equations. For a particular case of spherical symmetry, we explicitly show the differences in the Hamiltonian and the Hamiltonian constraint between GR and STEGR. We finally discuss the implications that these differences, which represent genuine different features between the two formulations of gravity, might encompass to numerical relativity.

For a strongly connected inhomogeneous graph-directed self-similar set $K^C$ satisfying the strong open set condition, we characterize the asymptotic behaviour of the $r$-covering number $N_r(K^C)$ as $r \downarrow 0$ in terms of the Minkowski dimension $s_0(G)$ of the attractor. If $\int_0^\infty e^{-s_0(G)t}N_{e^{-t}}(C_i)\,\mathrm{d} t<\infty$ for all vertices $i$, then $e^{-s_0(G)t}N_{e^{-t}}(K^C)$ has a limit as $t\to\infty$, which is a positive constant when the log-contraction group $G_M$ is $\mathbb{R}$ and a positive periodic function when $G_M$ is a lattice; if the integral diverges for some $i$, the limit is infinite.

The research on Reconfigurable Intelligent Surfaces (RISs) has dominantly been focused on physical-layer aspects and analyses of the achievable adaptation of the wireless propagation environment. Compared to that, questions related to system-level integration of RISs have received less attention. We address this research gap by analyzing the necessary control/signaling operations that are necessary to integrate RIS as a new type of wireless infrastructure element. We build a general model for evaluating the impact of control operations along two dimensions: i) the allocated bandwidth of the control channels (in-band and out-of-band), and ii) the rate selection for the data channel (multiplexing or diversity). Specifically, the second dimension results in two generic transmission schemes, one based on channel estimation and the subsequent optimization of the RIS, while the other is based on sweeping through predefined RIS phase configurations. We analyze the communication performance in multiple setups built along these two dimensions. While necessarily simplified, our analysis reveals the basic trade-offs in RIS-assisted communication and the associated control operations. The main contribution of the paper is a methodology for systematic evaluation of the control overhead in RIS-aided networks, regardless of the specific control schemes used.

Efficient integration of reconfigurable intelligent surfaces (RISs) into the current wireless network standard is not a trivial task due to the overhead generated by performing channel estimation (CE) and phase-shift optimization. In this paper, we propose a framework enabling the coexistence between orthogonal-frequency division multiplexing (OFDM) and RIS technologies. Instead of wasting communication symbols for the CE and optimization, the proposed framework exploits the localization information obtainable by RIS-aided communications to provide a robust allocation strategy for user multiplexing. The results demonstrate the effectiveness of the proposed approach with respect to CE-based transmission methods.

In this note, we prove two results regarding the variation of K-moduli. The first one reveals the relationship between the chamber decomposition for K-semistable domains and the variation of GIT. The second one presents the relationship between the K-moduli generically parametrizing K-semistable smooth Fano complete intersections of the form $S_1\cap...\cap S_k$ and the K-moduli generically parametrizing K-semistable log Fano manifolds of the form $(\mathbb{P}^n, \sum_{j=1}^kx_jS_j)$, where $x_j\in (0,1)\cap \mathbb{Q}$ and $S_j\subset \mathbb{P}^n$ is a hypersurface of degree $d_j$ for each $1\leq j\leq k$.

Questionnaires in the behavioral sciences tend to be lengthy. However, literature suggests that survey length is a contributing factor to careless responding, with longer questionnaires yielding higher probability that participants start responding carelessly. Consequently, in long surveys a large number of participants may engage in careless responding, posing a major threat to internal validity. We propose a novel method for identifying the onset of careless responding (or an absence thereof) that searches for a changepoint in combined measurements of multiple dimensions in which carelessness may manifest, such as inconsistency and invariability. It is highly flexible, based on machine learning, and provides statistical guarantees for controlling the false positive rate. In simulation experiments, the proposed method achieves high accuracy in identifying carelessness onset and discriminates well between attentive and various types of careless responding, even when a large number of careless respondents are present. An empirical application highlights how identifying partial carelessness uncovers novel insights on careless responding behavior. Furthermore, we provide the freely available open source software package "carelessonset" to facilitate adoption by empirical researchers.

The use of Reconfigurable Intelligent Surfaces (RIS) technology to extend coverage and allow for better control of the wireless environment has been proposed in several use cases, including Ultra-Reliable Low-Latency Communications (URLLC), communications. However, the extremely challenging latency constraint makes explicit channel estimation difficult, so positioning information is often used to configure the RIS and illuminate the receiver device. In this work, we analyze the effect of imperfections in the positioning information on the reliability, deriving an upper bound to the outage probability. We then use this bound to perform power control, efficiently finding the minimum power that respects the URLLC constraints under positioning uncertainty. The optimization is conservative, so that all points respect the URLLC constraints, and the bound is relatively tight, with an optimality gap between 1.5 and 4.5~dB.

In this note, we reduce various conjectures in birational geometry, including Shokurov conjecture on singularities of the base of log Calabi-Yau fibrations of Fano type and boundedness conjecture for rationally connected Calabi-Yau varieties, to a conjecture on multiplicities of fibers of Fano fibrations over curves.

Reconfigurable intelligent surfaces (RISs) are arrays of passive elements that can control the reflection of the incident electromagnetic waves. While RIS are particularly useful to avoid blockages, the protocol aspects for their implementation have been largely overlooked. In this paper, we devise a random access protocol for a RIS-assisted wireless communication setting. Rather than tailoring RIS reflections to meet the positions of users equipment (UEs), our protocol relies on a finite set of RIS configurations designed to cover the area of interest. The protocol is comprised of a downlink training phase followed by an uplink access phase. During these phases, a base station (BS) controls the RIS to sweep over its configurations. The UEs then receive training signals to measure the channel quality with the different RIS configurations and refine their access policies. Numerical results show that our protocol increases the average number of successful access attempts; however, at the expense of increased access delay due to the realization of a training period. Promising results are further observed in scenarios with a high access load.

5G technology allows heterogeneous services to share the wireless spectrum within the same radio access network. In this context, spectrum slicing of the shared radio resources is a critical task to guarantee the performance of each service. We analyze a downlink communication serving two types of traffic: enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC). Due to the nature of low-latency traffic, the base station knows the channel state information (CSI) of the eMBB users while having statistical CSI for the URLLC users. We study the power minimization problem employing orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes. Based on this analysis, we propose a lookup table-based approach and a block coordinated descent (BCD) algorithm. We show that the BCD is optimal for the URLLC power allocation. The numerical results show that NOMA leads to lower power consumption than OMA, except when the average channel gain of the URLLC user is very high. For the latter case, the optimal approach depends on the channel condition of the eMBB user. Even when OMA attains the best performance, the gap with NOMA is negligible, showing the capability of NOMA to reduce power consumption in practically every condition.

Spectrum slicing of the shared radio resources is a critical task in 5G networks with heterogeneous services, through which each service gets performance guarantees. In this paper, we consider a setup in which a Base Station (BS) should serve two types of traffic in the downlink, enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC), respectively. Two resource allocation strategies are compared: non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA). A framework for power minimization is presented, in which the BS knows the channel state information (CSI) of the eMBB users only. Nevertheless, due to the resource sharing, it is shown that this knowledge can be used also to the benefit of the URLLC users. The numerical results show that NOMA leads to a lower power consumption compared to OMA for every simulation parameter under test.

For each $n=0,1,2,\ldots$, the central trinomial coefficient $T_n$ is the coefficient of $x^n$ in the expansion of $(x^2+x+1)^n$. Let $p>3$ be a prime, and let $n$ be any positive integer. In 2016, the second author conjectured that the quotient $(T_{pn}-T_n)/(pn)^2$ is always a $p$-adic integer. In this paper, we confirm this conjecture, and further prove that $$\frac{T_{pn}-T_n}{(pn)^2}\equiv\frac{T_{n-1}}6\left(\frac p3\right)B_{p-2}\left(\frac13\right)\pmod p,$$ where $(\frac p3)$ is the Legendre symbol and $B_{p-2}(x)$ is the Bernoulli polynomial of degree $p-2$.

In this paper we formalize and prove the soundness of Tarsis, a new abstract domain based on the abstract interpretation theory that approximates string values through finite state automata. The main novelty of Tarsis is that it works over an alphabet of strings instead of single characters. On the one hand, such approach requires a more complex and refined definition of the widening operator, and the abstract semantics of string operators. On the other hand, it is in position to obtain strictly more precise results than than state-of-the-art approaches. We implemented a prototype of Tarsis, and we applied it on some case studies taken from some of the most popular Java libraries manipulating string values. The experimental results confirm that Tarsis is in position to obtain strictly more precise results than existing analyses.

We study the critical droplet for a close-to-equilibrium Widom-Rowlinson model of interacting particles, represented by disks of radius $1$, in the two-dimensional plane at low temperature. The critical droplet is the set of macroscopic states that correspond to saddle points for the passage from a low-density supersaturated vapour to a stable high-density liquid. We analyse the mesoscopic fluctuations of the surface of the critical droplet, which turns out to be the set of particle configurations that are close to a disk of a certain deterministic radius. Our results represent the first detailed rigorous analysis of the surface fluctuations of a continuum interacting particle system exhibiting condensation and, as such, constitute a fundamental step in the study of phase separation from the perspective of stochastic geometry. At the same time, our results serve as a basis for the study of a non-equilibrium version of the Widom-Rowlinson model, to be analysed elsewhere, where they lead to a correction term in the Arrhenius formula for the average vapour-liquid crossover time.

Power and channel allocation in interference-limited systems is a key enabler for beyond 5G (B5G) technologies, such as multi-carrier full duplex non-orthogonal multiple access (FD-NOMA). In FD-NOMA systems power allocation is a very computationally intense non-convex problem due to the presence of strong interference and the integrality condition on channel allocation. In this paper, we propose an iterative power allocation algorithm based on the minimization of the weighted mean square error, which converges to a feasible allocation of the original problem. Experimental results show that the proposed algorithm has by far the lowest complexity among other state-of-the-art solutions. Moreover, they assess the validity of our approach showing performance close to the theoretical optimum.

Network slicing is considered to be one of the key enablers to Fifth Generation (5G) communication system. Legacy telecommunication networks have been providing various services to all kinds of customers through a single network infrastructure. In contrast, with the deployment of network slicing, operators are now able to partition entire network into different slices, each with its own configuration and Quality of Service (QoS) requirements. There are many applications across industry, each needs an independent slice with its own functions and features. All these applications open new business opportunities, which require new business models and therefore every single slice needs an individual Service Level Agreement (SLA). In this paper, we proposed a comprehensive end-to-end structure of SLA between tenant and service provider of slice-based 5G network, which balances the interests of both sides. The proposed SLA is expected to define reliability, availability, and performance of delivered telecommunication services in order to ensure that right information gets to the right destination at right time, safely and securely. We also discussed the metrics of slice-based network SLA such as throughput, penalty, cost, revenue, profit, and QoS related metrics, which we think are very critical to be considered during the agreement.

Knowledge of the mechanical properties of materials is required for the design and analysis of engineering products, however, the characterisation of heterogeneous properties using traditional techniques is limited by spatial resolution or insufficient reliability. This paper presents a novel methodology for the characterisation of heterogeneous mechanical properties by extending the virtual fields method through the automated spatial parameterisation of constitutive parameters. Collaboration with the United Kingdom Atomic Energy Authority provided this project with an application focus on the characterisation of the spatially-varying, elastoplastic mechanical properties of welded joints. The developed methodology enables the novel characterisation of welds with assorted geometries, varied loading configurations and dissimilar materials. Numerical verification of the developed method was performed using synthetic data equivalent to that obtained experimentally using optical measurements, where the kinematic fields are known and controlled. The results confirm that the proposed approach converges towards the target parameter maps without any a priori information on the distribution of the properties, successfully demonstrating the established methodology as a proof of concept.

In this paper, the product of the Hausdorff metric on the product space is defined and the equivalency between the product Hausdorff metric and the Hausdorff metric on the product space is established. The finite product of the iterated function systems (IFS) on the product space is considered and the relation between the attractor of the product IFS and the attractors of the co-ordinate IFSs is studied. Dimension bounds of the homogeneous and inhomogeneous attractors on the product space is established. Also, the product fractal interpolation function on the higher dimensional space is constructed.

Photopolymerization enables the production of micro-optical elements, such as diffractive optical elements or GRIN optics. This process utilizes targeted spatial modulation of the refractive index, which is achieved through additive manufacturing. In this context, a thorough understanding of the dynamic processes during curing is essential in order to be able to accurately predict the optical function of the element. For this reason, this work investigates the kinetics and resulting optical properties of an acrylate-based photopolymer under UV irradiation using a DLP projection system. The experimental approach combines two measurement methods: On the one hand, the absolute change in the refractive index is determined in a time-resolved manner at the interface of a prism using a method based on total reflection. On the other hand, the formation of a phase grating in the volume of the polymer is monitored in real time by analyzing the diffraction orders of a coherent sample laser. The results show a characteristic S-shaped curve of the refractive index change, which reflects the phases of polymerization: oxygen inhibition, autoacceleration, and vitrification. Analysis of the diffraction patterns reveals complex intensity curves and substructures in the diffraction orders. These could be traced back experimentally and through simulations to the discrete pixel structure of the DLP projector and the existing dead zones. Furthermore, the simulation model developed on the basis of Fourier optics reproduces the experimental diffraction patterns and confirms the hypothesis that scattered light and radical diffusion lead to time-delayed polymerization in the theoretically unexposed areas. This results in a reduction of the refractive index contrast over time. This work thus provides parameters for the simulation and optimization of exposure strategies in 3D printing of micro-optics.

The LEGEND Experiment searches for the neutrinoless double beta (0$νββ$) decay of $^{76}$Ge employing active high purity germanium detectors enriched in $^{76}$Ge beyond 86%. LEGEND's experimental program is articulated in two phases: LEGEND-200, currently ongoing, and LEGEND-1000, the next generation development. LEGEND-200 started operating in 2023 at Laboratori Nazionali del Gran Sasso (LNGS) and ran in a stable physics data taking regime for about one year with 142.5 kg of detectors installed. With a target background index of $2 \cdot 10^{-4} $ counts/(keV kg yr) at Q$_{ββ} \sim$ 2039 keV and a final exposure of 1000 kg yr, LEGEND-200 aims to reach a 3$σ$ discovery sensitivity for a 0$νββ$ half-life of $10^{27}$ yr. In this contribution, the LEGEND-200 experiment will be presented, with a focus on its current status and on the results obtained with the first year of data. In particular, the employed analysis routines will be introduced, the signal identification and background suppression performance will be discussed, and the background appearing in the region of interest around $Q_{ββ}$ will be analyzed. The performed analysis of LEGEND-200 data finds no evidence for a 0$νββ$ signal: a lower limit to its half-life is set instead, $T_{1/2}^{0ν} > 0.5 \cdot 10^{26}$ yr, at 90% CL. A joint GERDA + MAJORANA Demonstrator + LEGEND-200 analysis provides a limit of $T_{1/2}^{0ν} > 1.9 \cdot 10^{26}$ yr, at 90% CL. This work is supported by the U.S. DOE and the NSF, the LANL, ORNL and LBNL LDRD programs; the European ERC and Horizon programs; the German DFG, BMBF, and MPG; the Italian INFN; the Polish NCN and MNiSW; the Czech MEYS; the Slovak RDA; the Swiss SNF; the UK STFC; the Canadian NSERC and CFI; the LNGS and SURF facilities.