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A convex cone is said to be projectionally exposed (p-exposed) if every face arises as a projection of the original cone. It is known that, in dimension at most four, the intersection of two p-exposed cones is again p-exposed. In this paper we construct two p-exposed cones in dimension $5$ whose intersection is not p-exposed. This construction also leads to the first example of an amenable cone that is not projectionally exposed, showing that these properties, which coincide in dimension at most $4$, are distinct in dimension $5$. In order to achieve these goals, we develop a new technique for constructing arbitrarily tight inner convex approximations of compact convex sets with desired facial structure. These inner approximations have the property that all proper faces are extreme points, with the exception of a specific exposed face of the original set.
The emergence of a hantavirus variant aboard a commercial cruise ship presents a significant public health concern. This study develops a discrete-time stochastic Susceptible-Exposed-Infectious-Recovered-Dead model to estimate transmission dynamics, hidden exposed infections, and outbreak risk among passengers and crew. Epidemiological parameters and latent disease states were inferred using an Ensemble Adjustment Kalman Filter calibrated to reported case data from WHO and ECDC situation reports. The estimated basic reproduction number was 2.76, with a 95\% confidence interval of 2.52-2.99, indicating substantial potential for sustained onboard transmission before strict quarantine measures. Simulations further suggest that several exposed individuals may remain unidentified during the early outbreak phase, creating a hidden reservoir that symptom-based surveillance alone may fail to detect. These findings highlight the importance of rapid surveillance, widespread testing, targeted quarantine, and active monitoring of exposed individuals in confined travel settings. The proposed modeling framework can support timely outbreak assessment and intervention planning for infectious-disea
Application programming interfaces (APIs) have become a central part of the modern IT environment, allowing developers to enrich the functionality of applications and interact with third parties such as cloud and payment providers. This interaction often occurs through authentication mechanisms that rely on sensitive credentials such as API keys and tokens that require secure handling. Exposure of these credentials can pose significant consequences to organizations, as malicious attackers can gain access to related services. Previous studies have shown exposure of these sensitive credentials in different environments such as cloud platforms and GitHub. However, the web remains unexplored. In this paper, we study exposure of credentials on the web by analyzing 10M webpages. Our findings reveal that API credentials are widely and publicly exposed on the web, including highly popular and critical webpages such as those of global banks and firmware developers. We identify 1,748 distinct credentials from 14 service providers (e.g., cloud and payment providers) across nearly 10,000 webpages. Moreover, our analysis of archived data suggest credentials to remain exposed for periods ranging
Building on the task-based approach to labour markets, we develop the Generative AI Susceptibility Index (GAISI), a job-level measure of UK exposure to large language models (LLMs). Drawing on Eloundou et al. (2024), we use LLMs as probabilistic raters to classify task exposure, linking ratings to worker-reported task data from the British Skills and Employment Surveys. GAISI measures the share of job activities where LLMs can reduce task completion time by at least 25% beyond existing tools. Systematic validations demonstrate high reliability, strong validity, and predictive power over existing exposure measures. By 2023/24, nearly all UK jobs (94%) exhibited some LLM exposure, yet only 13% were heavily exposed (GAISI > 0.5), with the highest concentration in scientific and technical professions. Aggregate exposure rose 16% of one standard deviation since 2017, driven by occupational shifts rather than within-occupation task changes. The wage premium for AI-exposed tasks declined 12% between 2017 and 2023/24, and the period since ChatGPT's release has coincided with a relative contraction of job postings in more AI-exposed occupations. These findings are consistent with generat
We characterize the extreme and exposed points of the unit ball (with respect to the $L^1$-norm) in the shift-invariant space generated by the Gaussian function, as well as in the quasi shift-invariant space generated by the hyperbolic secant.
The criterion for a point in the unit ball to be a strongly exposed point is given. The necessity and sufficiency conditions for Orlicz-Lorentz spaces to possess strongly exposed property are given. Besides, some useful methods are obtained to handle issues related to decreasing rearrangement.
The Number needed to treat (NNT) is an efficacy index defined as the average number of patients needed to treat to attain one additional treatment benefit. In observational studies, specifically in epidemiology, the adequacy of the populationwise NNT is questionable since the exposed group characteristics may substantially differ from the unexposed. To address this issue, groupwise efficacy indices were defined: the Exposure Impact Number (EIN) for the exposed group and the Number Needed to be Exposed (NNE) for the unexposed. Each defined index answers a unique research question since it targets a unique sub-population. In observational studies, the group allocation is typically affected by confounders that might be unmeasured. The available estimation methods that rely either on randomization or the sufficiency of the measured covariates for confounding control will result in inconsistent estimators of the true NNT (EIN, NNE) in such settings. Using Rubin's potential outcomes framework, we explicitly define the NNT and its derived indices as causal contrasts. Next, we introduce a novel method that uses instrumental variables to estimate the three aforementioned indices in observat
The elementary processes during the fixation of nitrogen by plasma catalysis are studied in a low-pressure plasma experiment using N$_2$ and O$_2$ as source gases. The formation of surface groups on an iron oxide foil are monitored with infrared reflection spectroscopy. Surface nitrates (NO$_3$) are formed when the samples are exposed to a 1:1 N$_2$:O$_2$ plasma, as well as O$_3$, NO$_2$, NO, and N$_2$O in the gas phase. During plasma exposure, bidentate nitrates are formed. The structure of this surface group changes after plasma exposure. It is postulated that adsorption plasma created NO$_x$(g) yields the formation of these NO$_3$ species. This constitutes an intermediate step for NO$_x$ formation by plasma catalysis.
We provide a complete and explicit characterization of the exposed extreme rays of the cone of sums of nonnegative circuit (SONC) polynomials. The criterion we derive is purely combinatorial and depends only on the existence of certain circuits within the ground set and on the nature of the corresponding extreme ray. Our constructive proofs also yield explicit exposing functionals, offering a basis for algorithmic detection of exposed rays in SONC-based optimization.
For $σ>0$, the Bernstein space \ $B^1_σ$ consists of those $L^1(R)$\ functions whose Fourier transforms are supported by $[-σ,σ]$. Since $B^1_σ$ is separable and dual to some Banach space, the closed unit ball $D(B^1_σ)$ of $B^1_σ$\ has sufficiently large sets of both exposed and strongly exposed points. Moreover, $D(B^1_σ)$ coincides with the closed convex hull of its strongly exposed points. We investigate some properties of exposed points, construct several examples and obtain as corollaries the relations between the sets of exposed, strongly exposed, weak$^{\ast}$ exposed, and weak$^{\ast}$ strongly exposed points of $D(B^1_σ)$.
Electronic structure calculations are performed to obtain the As-exposed Si(211) and the Te adsorbed As-exposed Si(211) surface. Arsenic-exposed Si(211) may be obtained by adsorbing As on Si(211) or by replacing surface Si atoms by As. First, we carry out systematic investigations to obtain stable As-exposed Si(211) due to As adsorption at various coverages. We find that at 1/2 monolayer (ML) coverage of As, the highly terraced Si(211) surface becomes flat decorated with parallel As chains extending along the [$01\bar{1}$] direction. At 1 ML coverage the Si surface essentially retains its ideal structure with an added layer of As. Motivated by the adsorption sequence in the HgCdTe (MCT) growth on Si, Te adsorption on such an As-exposed Si(211) is studied and 1/2 ML of Te coverage is found to be energetically feasible. Next, we explore a stable As-exposed Si(211) upon replacement of surface Si atoms by As. An energetic comparison reveals that the As-exposed Si(211) obtained by replacing surface Si atoms with As is more favorable compared to that obtained by adsorbing As on Si(211). In line with the adsorption sequence in the MCT growth on Si, Te is then adsorbed on the most favorabl
Backdoor attacks covertly implant triggers into deep neural networks (DNNs) by poisoning a small portion of the training data with pre-designed backdoor triggers. This vulnerability is exacerbated in the era of large models, where extensive (pre-)training on web-crawled datasets is susceptible to compromise. In this paper, we introduce a novel two-step defense framework named Expose Before You Defend (EBYD). EBYD unifies existing backdoor defense methods into a comprehensive defense system with enhanced performance. Specifically, EBYD first exposes the backdoor functionality in the backdoored model through a model preprocessing step called backdoor exposure, and then applies detection and removal methods to the exposed model to identify and eliminate the backdoor features. In the first step of backdoor exposure, we propose a novel technique called Clean Unlearning (CUL), which proactively unlearns clean features from the backdoored model to reveal the hidden backdoor features. We also explore various model editing/modification techniques for backdoor exposure, including fine-tuning, model sparsification, and weight perturbation. Using EBYD, we conduct extensive experiments on 10 im
Extending the temperature limits of quantum coherence in the system representing a chain of coupled two-level systems (TLS) exposed to an electromagnetic field is complicated due to the adverse influence of noise. Such a system frequently serves as a basic element of various quantum devices. In the steady state, the quantum coherence in TLS is merely destroyed by noise, which intensifies as the temperature increases. The behavior is complicated when the external field is applied modulating also the noise. In this work, using the computerized model, we study the temperature limits of the transitional quantum dynamics in the all-electrically controlled graphene single-TLS and three-TLS devices exposed to the electromagnetic field. We analyze how the external ac field changes the state of the system and observe that it not only influences the coherent transport there but modifies the effect of noise. The conducted numerical experiments determine the conditions provided the quantum coherence in QC may be much prolonged even above the ambient room temperature which can improve the performance of various quantum devices.
Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and magnetic field. This fan looks identical irrespective of the electron dispersion details that determines the field dependence of the Landau level energy. This is no surprise, since the position of conductance minima solely depends on the level degeneracy which is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they too create just linear fans for the same reason. Here, we report on conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule of flux linearity and attribute the anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown.
Low Density Polyethylene (LDPE) films were exposed at an altitude of 40 km over a 3 day NASA stratospheric balloon mission from Alice Springs, Australia. The radiation damage, oxidation and nitration in the LDPE films exposed in stratosphere were measured using ESR, FTIR and XPS spectroscopy. The results were compared with those from samples stored on the ground and exposed in a laboratory plasma. The types of free radicals, unsaturated hydrocarbon groups, oxygen-containing and nitrogen-containing groups in LDPE film exposed in the stratosphere and at the Earth's surface are different. The radiation damage in films exposed in the stratosphere are observed in the entire film due to the penetration of high energy cosmic rays through their thickness, while the radiation damage in films exposed on the ground is caused by sunlight penetrating into only a thin surface layer. A similarly thin layer of the film is damaged by exposure to plasma due to the low energy of the plasma particles. The intensity of oxidation and nitration of LDPE films reflects the difference of atmospheric pressure on the ground and in the stratosphere. The high-density radiation damage of the LDPE films above the
In situations with non-manipulable exposures, interventions can be targeted to shift the distribution of intermediate variables between exposure groups to define interventional disparity indirect effects. In this work, we present a theoretical study of identification and nonparametric estimation of the interventional disparity indirect effect among the exposed. The targeted estimand is intended for applications examining the outcome risk among an exposed population for which the risk is expected to be reduced if the distribution of a mediating variable was changed by a (hypothetical) policy or health intervention that targets the exposed population specifically. We derive the nonparametric efficient influence function, study its double robustness properties and present a targeted minimum loss-based estimation (TMLE) procedure. All theoretical results and algorithms are provided for both uncensored and right-censored survival outcomes. With offset in the ongoing discussion of the interpretation of non-manipulable exposures, we discuss relevant interpretations of the estimand under different sets of assumptions of no unmeasured confounding and provide a comparison of our estimand to
The attributable fraction among the exposed (\textbf{AF}$_e$), also known as the attributable risk or excess fraction among the exposed, is the proportion of disease cases among the exposed that could be avoided by eliminating the exposure. Understanding the \textbf{AF}$_e$ for different exposures helps guide public health interventions. The conventional approach to inference for the \textbf{AF}$_e$ assumes no unmeasured confounding and could be sensitive to hidden bias from unobserved covariates. In this paper, we propose a new approach to reduce sensitivity to hidden bias for conducting statistical inference on the \textbf{AF}$_e$ by leveraging case description information. Case description information is information that describes the case, e.g., the subtype of cancer. The exposure may have more of an effect on some types of cases than other types. We explore how leveraging case description information can reduce sensitivity to bias from unmeasured confounding through an asymptotic tool, design sensitivity, and simulation studies. We allow for the possibility that leveraging case definition information may introduce additional selection bias through an additional sensitivity par
We study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. We assume that infections occur both locally with a rate that depends on the patch as well as "from distance" from all the other patches. The exposed and infectious periods have general distributions, and are not affected by the possible migrations of the individuals. The migration processes in either of the three states are assumed to be Markovian, and independent of the exposed and infectious periods. We establish a functional law of large number (FLLN) and a function central limit theorem (FCLT) for the susceptible, exposed/latent, infectious and recovered processes. In the FLLN, the limit is determined by a set of Volterra integral equations. In the special case of deterministic exposed and infectious periods, the limit becomes a system of ODEs with delays. In the FCLT, the limit is given by a set of stochastic Volterra integral equations driven by a sum of independent Brownian motions and continuous Gaussian processes with an explicit covariance structure.
A closed convex cone K is called nice, if the set K^* + F^\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\perp is the orthogonal complement of the linear span of F. The niceness property is important for two reasons: it plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer. We prove several characterizations of nice cones and show a strong connection with facial exposedness. We prove that a nice cone must be facially exposed; in reverse, facial exposedness with an added condition implies niceness. We conjecture that nice, and facially exposed cones are actually the same, and give supporting evidence.
Due to their antimicrobial properties, silver nanoparticles (AgNPs) are being used in non-edible and edible consumer products. It is not clear though if exposure to these chemicals can exert toxic effects on the host and gut microbiome. Conflicting studies have been reported on whether AgNPs result in gut dysbiosis and other changes within the host. We sought to examine whether exposure of Sprague-Dawley male rats for two weeks to different shapes of AgNPs, cube (AgNC) and sphere (AgNS) affects gut microbiota, select behaviors, and induces histopathological changes in the gastrointestinal system and brain. In the elevated plus maze (EPM), AgNS-exposed rats showed greater number of entries into closed arms and center compared to controls and those exposed to AgNC. AgNS and AgNC treated groups had select reductions in gut microbiota relative to controls. Clostridium spp., Bacteroides uniformis, Christensenellaceae, and Coprococcus eutactus were decreased in AgNC exposed group, whereas, Oscillospira spp., Dehalobacterium spp., Peptococcaeceae, Corynebacterium spp., Aggregatibacter pneumotropica were reduced in AgNS exposed group. Bacterial reductions correlated with select behavioral