Abstract The asymptotic dependence structure between multivariate extreme values is fully characterized by their projections on the unit simplex. Under mild conditions, the only constraint on the resulting distributions is that their marginal means must be equal, which results in a nonparametric model that can be difficult to use in applications. Mixtures of Dirichlet distributions have been proposed for use as a semiparametric model, but fitting them is awkward. In this article, we propose a new approach to the use of Dirichlet mixtures, based on tilting, to ensure that the moment conditions are satisfied. We show that these tilted mixtures are dense in the full nonparametric family, are well defined in all dimensions, and allow the probabilistic clustering of extreme events. In order to fit them, we use a fast Markov chain Monte Carlo algorithm that does not require fine‐tuning. Its performance is assessed using simulations and an application to financial data.

The capillary tube is an expansion device in the vapor compression refrigeration cycle (VCRC) that functions to reduce refrigerant pressure from high to low levels. The tube’s diameter and length significantly affect the pressure and performance of the refrigeration system. Therefore, selecting the appropriate capillary tube size is essential to achieve optimal system operation. This study aims to determine the optimal capillary tube diameter to improve the performance of a 100 liter ice maker unit utilizing a 1 PK air conditioner outdoor unit as the condensing unit. The system is designed to support an efficient and simple ice freezing process for fish preservation. The main variable analyzed is the capillary tube diameter (0.028 inch, 0.031 inch, and 0.040 inch). Evaluation parameters include refrigeration effect (Qc), compressor work (Wk), condenser heat rejection (Qk), and coefficient of performance (COP). The results indicate that a 0.028-inch capillary tube yields a refrigeration effect of 345.35 kJ/kg, compressor work of 78.26 kJ/kg, and a COP of 3.41. The 0.031-inch and 0.040-inch diameters result in COP values of 3.31 and 3.29, respectively. Therefore, the 0.028-inch capillary tube provides the highest performance and is considered the most suitable for the 100 liter ice maker system.

This paper proposes a semi-analytical method based on the spectral geometry approach for the rapid prediction of underwater vibration and acoustic radiation of in-plane inhomogeneous plates under turbulent boundary layer excitation. Arbitrary elastic boundary conditions are modeled by introducing two sets of virtual springs (linear and torsional), and a grid-based modal superposition framework is developed to handle plates with arbitrary geometries and multi-material embedded sub-plates. The turbulent boundary layer pressure field is synthesized by superimposing uncorrelated wall plane waves, enabling efficient coupling between the statistical wall-pressure model and the deterministic vibro-acoustic model. A simple and reproducible singularity treatment is proposed by analytically averaging the Rayleigh integral kernel over an equivalent-area circular domain. Numerical validations demonstrate that the proposed method achieves high accuracy while significantly reducing computational cost. The influence of acoustic-structural coupling on convergence is systematically analyzed, together with the effects of sub-plate materials, geometrical configurations, and boundary conditions on structural vibration and sound radiation characteristics. The results confirm that the developed method provides an efficient and reliable computational tool for analyzing flow-induced vibration and acoustic radiation of complex in-plane structures with arbitrary multi-material configurations.

Background: Cryotherapy, ranging from simple ice packs to systemic cryogenic chambers, has evolved from an ancient practice to a scientifically grounded method used for acute injury management, chronic inflammatory conditions, and mental well-being. The recent popularity of systemic methods like Cold Water Immersion (CWI) and Whole-Body Cryotherapy (WBC) has broadened the focus beyond local analgesia to complex physiological systems. Aims and Objectives: This review aims to meticulously examine the fundamental physiological and biochemical mechanisms of cold therapy, comparatively evaluate the evidence-based clinical efficacy of local and systemic modalities across sports medicine, rehabilitation, and general health, and discuss the existing gaps and future research directions in the field. Methodology): This article utilized a comprehensive narrative review approach, synthesizing existing literature to cover the historical context, physiological mechanisms, clinical applications, risks, contraindications, and safety protocols of cryotherapy. Key Findings: The literature confirms cryotherapy's established role in pain reduction and edema control via local physiological changes, while systemic applications show compelling evidence for enhanced subjective recovery and powerful neuroendocrine activation. Conclusion: Cryotherapy is a versatile modality, though protocol standardization remains a key limitation. Future research must prioritize establishing definitive dose-response curves and clarifying long-term molecular and psychological effects.

Abstract We present the results of James Webb Space Telescope observations of the protostar ST6 in the Large Magellanic Cloud (LMC) with the Medium Resolution Spectrograph of the Mid-Infrared Instrument (4.9–27.9 μm). Characterized by one-third to half-solar metallicity and strong UV radiation fields, the environment of the LMC allows us to study the physics and chemistry of star-forming regions under conditions similar to those at earlier cosmological epochs. We detected five icy complex organic molecules (COMs): methanol (CH3OH), acetaldehyde (CH3CHO), ethanol (CH3CH2OH), methyl formate (HCOOCH3), and acetic acid (CH3COOH). This is the first conclusive detection of CH3COOH ice in an astrophysical context, and CH3CHO, CH3CH2OH, and HCOOCH3 ices are the first secure detections outside the Galaxy and in a low-metallicity environment. We address the presence of glycolaldehyde (HOCH2CHO, a precursor of biomolecules), an isomer of HCOOCH3 and CH3COOH, but its detection is inconclusive. ST6’s spectrum is also rich in simple ices: H2O, CO2, CH4, SO2, H2CO, HCOOH, OCN−, HCOO−, NH3, and NH4 +. We obtain the composition and molecular abundances in the icy dust mantles by fitting the spectrum in the 6.8–8.4 μm range with a large sample of laboratory ice spectra using the ENIIGMA fitting tool or the local continuum method. We found differences in the simple and COM ice abundances with respect to H2O ice between ST6 and Galactic protostars that likely reflect differences in metallicity and UV flux. More laboratory ice spectra of COMs are needed to better reconstruct the observed infrared spectra of protostars.

Given a finite admixture model whose components and weights are unknown, let the number of identifiable components be a function of the amount of data sampled from a known distribution on the unit simplex. We use techniques from stochastic convex geometry to find the growth rate of its expected value. In addition, when the components are known but the weights are not, we provide an application of the classic Glivenko-Cantelli's theorem that allows us to retrieve the Choquet measure supported on the identifiable admixture components. In turn, this gives us the identifiable admixture weights. Finally, we propose a novel algorithm that estimates the model capturing the complexity of the data using only the strictly necessary number of components.

Abstract The nonlinearities controlling sea ice thermodynamics integrate forcing from the ocean and atmosphere in surprising ways, rendering it difficult to understand the processes affecting sea ice response to climate change. In this study, a simple ice thickness model is forced by realistic stochastic atmospheric and oceanic heat fluxes. Ensemble experiments show that the nonlinearities in the system rectify the added zero-mean noise on weather time scales leading to a change in the mean sea ice state. Most notably, there is a thinning in summer when sea ice is already at its minimum. The sea ice system integrates high-frequency forcing to influence longer time scales, thus changing not only the mean state but also the interannual-to-decadal variability of sea ice. Adding a trend to the forcing variables yields estimates of the dominant drivers of the current and future ice loss in the Arctic, with a prevalent role of ice–ocean heat flux over surface heat fluxes. This study reveals sea ice as a fundamental climate component, absorbing the energy into its mean state and transforming weather fluctuations with time scales of days to weeks into internal variability on time scales of months to decades. Significance Statement Understanding how sea ice responds to changes in the Arctic climate is crucial to predict its future. Using a simple model, ice thickness is shown to react in unexpected ways to small changes in atmospheric and oceanic conditions. Sea ice absorbs parts of those changes to modify its average thickness and transforms short-term weather fluctuations (lasting days to weeks) into longer-term changes in ice thickness (lasting months to decades). When it comes to Arctic warming, trends in the atmosphere and ocean have different impacts on the ice melt. The ocean plays a bigger role in determining when a seasonally ice-free Arctic will occur. This study emphasizes that sea ice is a key part of the climate system.

This paper argues against the LF-Copy VP-ellipsis model in Oku (1998) and for a PF-deletion approach. Simplex (SE) anaphor data from Thai is used to show that long-distance person blocking patterns are incompatible with elided content being copied in at the interface, post-agreement. This analysis adopts Reuland’s (2011) φ-feature agreement approach to SE-anaphor valuation, with Giblin’s (2015) modifications for long-distance anaphors (LDAs). It is shown that positions where Reuland’s account predicts valuation via φ-feature agreement do not licence Vehicle Change (VC), the phenomenon where interpretations of elided elements would require different anaphora in overt counterparts. In LDA blocking contexts it can be seen that SE-anaphors must be valued independently of each other. This interaction in syntax between overt and elided material is only possible under a PF deletion analysis. This has consequences for analyses of ellipsis and reconstruction, as well as the more general division of labour between interfaces.

Abstract The joint alignment of multivariate functional data plays an important role in various fields such as signal processing, neuroscience and medicine, including the statistical analysis of data from wearable devices. Traditional methods often ignore the phase variability and instead focus on the variability in the observed amplitude. We present a novel method for joint alignment of multivariate quasi-periodic functions using deep neural networks, decomposing, but retaining all the information in the data by preserving both phase and amplitude variability. Our proposed neural network uses a special activation of the output that builds on the unit simplex transformation, and we utilize a loss function based on the Fisher-Rao metric to train our model. Furthermore, our method is unsupervised and can provide an optimal common template function as well as subject-specific templates. We demonstrate our method on two simulated datasets and one real example, comprising data from 12-lead 10s electrocardiogram recordings.

Abstract The aim of this article is the classification of simple 0-dimensional isolated complete intersection singularities (ICIS) in positive characteristic. As usual, a singularity is called simple or 0-modal if there are only finitely many isomorphism classes of singularities into which the given singularity can deform. The notion of simpleness was introduced by V. I. Arnold and the classification of low modality singularities has become a fundamental task in singularity theory. Simple complex analytic ICIS were classified by M. Giusti. However, the classification in positive characteristic requires different methods and is much more involved. The final result is nevertheless similar to the classification in characteristic 0 with some additional normal forms in low characteristic. The theoretical results in this paper mainly concern families of ICIS that are formal in the fiber and algebraic in the base (formal deformation theory is not sufficient). In particular, we give a definition of modality in this situation and prove its semicontinuity.

Abstract We consider Shimura varieties associated to a unitary group of signature $(n-1,1)$. For these varieties, we construct $p$-adic integral models over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$ given by the stabilizer of a vertex lattice in the hermitian space. Our models are given by a variation of the construction of the splitting models of Pappas–Rapoport and they have a simple moduli theoretic description. By an explicit calculation, we show that these splitting models are normal, flat, Cohen–Macaulay and with reduced special fiber. In fact, they have relatively simple singularities: we show that a single blow-up along a smooth codimension one subvariety of the special fiber produces a semi-stable model. This also implies the existence of semi-stable models of the corresponding Shimura varieties.

Abstract Our aim is to determine the regular homotopy classes of immersions related to Arnol'd's simple singularities. For every type of simple singularities, we determine the regular homotopy class of the inclusion map of the link into the 5‐sphere. We further show that the inclusion map is regularly homotopic to the immersion associated with the corresponding Dynkin diagram, which was constructed by Kinjo. We prove these by computing the complete invariants of the immersions given by Wu and Saeki–Szűcs–Takase. As an application, we also determine the Smale invariants of Kinjo's immersions.

In this paper, we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of such arrangements.

In this paper, we study the four-point celestial leaf amplitudes of massless scalar and MHV gluon scattering. These leaf amplitudes are non-distributional decompositions of the celestial amplitudes associated with a hyperbolic foliation of the Klein spacetime. Bulk scale invariance imposes constraints on the total conformal weights of the massless scalars or gluons. Using this constraint we show that the four-point leaf amplitudes have a simple pole singularity at z = z¯, where, z,z¯ are two real independent conformal cross ratios. The distributional nature of the four-point celestial amplitudes is recovered by adding the leaf amplitudes in the timelike and spacelike wedges of the spacetime. We also verify that the MHV gluon leaf amplitudes satisfy a set of differential equations previously obtained for celestial MHV gluon amplitudes by considering the soft gluon theorems and the subleading terms in the OPE expansion between two positive helicity gluons.

A new approach to the local and global explanation based on selecting a convex hull constructed for the finite number of points around an explained instance is proposed. The convex hull allows us to consider a dual representation of instances in the form of convex combinations of extreme points of a produced polytope. Instead of perturbing new instances in the Euclidean feature space, vectors of convex combination coefficients are uniformly generated from the unit simplex, and they form a new dual dataset. A dual linear surrogate model is trained on the dual dataset. The explanation feature importance values are computed by means of simple matrix calculations. The approach can be regarded as a modification of the well-known model LIME. The dual representation inherently allows us to get the example-based explanation. The neural additive model is also considered as a tool for implementing the example-based explanation approach. Many numerical experiments with real datasets are performed for studying the approach. A code of proposed algorithms is available. The proposed results are fundamental and can be used in various application areas. They do not involve specific human subjects and human data.

The purpose of this service is to improve children's reading literacy, writing literacy, and science literacy skills through the development of a reading corner. The object of service is the children of Jungkare village, Karanganom sub-district, Klaten district. Reading literacy and writing literacy activities are wall magazine making while science literacy is in the form of simple rotary ice cream making activities. The service methods used are presentation, discussion, and practice. The activity stages consisted of socialization of the implementation and project exhibition. The results showed that the children of Jungkare village were very enthusiastic in participating in reading literacy, writing literacy, and science literacy activities.

With the development of nanotechnology, nano-functional units of different dimensions, morphologies, and sizes exhibit the potential for efficient microwave absorption (MA) performance. However, the multi-unit coupling enhancement mechanism triggered by the alignment and orientation of nano-functional units has been neglected, hindering the further development of microwave absorbing materials (MAMs). In this paper, two typical ZIF-derived nanomaterials are self-assembled into two-dimensional ordered polyhedral superstructures by the simple ice template method. The nano-functional units exhibit distinctive dielectric-sensitive behaviors after self-assembling into two-dimensional ordered arrays. The modified 2D ordered polyhedral superstructures not only inherit the atomic-level doping and well-designed shell structure, but also further amplify the loss properties to realize the multi-scale modulated MA response. Satisfactory MA performance in C, X and Ku bands is finally achieved. In particular, the ultra-broadband microwave absorption bandwidth (EAB) of 6.41 GHz is realized at 1.82 mm thickness. Our work demonstrates the two-dimensional ordered array-induced multiscale polarization behavior, providing a direction to fully utilize the potential of wave-absorbing functional units.

Defect of irreducible plane curves with simple singularities

$J$-functions and Hodge moduli algebras of simple elliptic singularities

Jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper we introduce two local algebras associated to jet closure and jet support closure, respectively. We show that these two algebras are invariants of singularities. We compute and investigate these invariants for some interesting cases, such as the cases of monomial ideals and homogeneous ideals. For application, we can distinguish different simple curve singularities by a finite number of jet support closures, and this number is close to the Milnor number of the singularity. We also introduce a new filtration and a jet index for jet closures. The jet index describes which jet scheme recovers the information on the base scheme. Moreover, we obtain some properties of the jet index. Bibliography: 16 titles.