Explicit Description Research Articles

Isomorphism classes of Drinfeld modules over finite fields

We study isogeny classes of Drinfeld A-modules over finite fields k with commutative endomorphism algebra D, in order to describe the isomorphism classes in a fixed isogeny class. We study when the minimal order A[π] of D generated by the Frobenius π occurs as an endomorphism ring by proving when it is locally maximal at π, and show that this happens if and only if the isogeny class is ordinary or k is the prime field. We then describe how the monoid of fractional ideals of the endomorphism ring E of a Drinfeld module ϕ up to D-linear equivalence acts on the isomorphism classes in the isogeny class of ϕ, in the spirit of Hayes. We show that the action is free when restricted to kernel ideals, of which we give three equivalent definitions, and determine when the action is transitive. In particular, the action is free and transitive on the isomorphism classes in an isogeny class which is either ordinary or defined over the prime field, yielding a complete and explicit description in these cases, which can be implemented as a computer algorithm.

On an uncountable family of graphs whose spectrum is a Cantor set

For each p\geq 1 , the star automaton group \mathcal{G}_{S_p} is an automaton group which can be defined starting from a star graph on p+1 vertices. We study Schreier graphs associated with the action of the group \mathcal{G}_{S_p} on the regular rooted tree T_{p+1} of degree p+1 and on its boundary \partial T_{p+1} . With the transitive action on the n -th level of T_{p+1} is associated a finite Schreier graph \Gamma^{p}_{n} , whereas there exist uncountably many orbits of the action on the boundary, represented by infinite Schreier graphs which are obtained as the limits of the sequence \{\Gamma_{n}^{p}\}_{n\geq 1} in the Gromov–Hausdorff topology. We obtain an explicit description of the spectrum of the graphs \{\Gamma_{n}^{p}\}_{n\geq 1} . Then, by using amenability of \mathcal{G}_{S_p} , we prove that the spectrum of each infinite Schreier graph is the union of a Cantor set of zero Lebesgue measure, which is the Julia set of the quadratic map f_{p}(z) = z^{2}-2(p-1)z -2p , and a countable collection of isolated points supporting the Kesten–Neumann–Serre spectral measure. We also give a complete classification of the infinite Schreier graphs up to isomorphism of unrooted graphs, showing that they may have 1 , 2 or 2p ends, and that the case of 1 end is generic with respect to the uniform measure on \partial T_{p+1} .

Action of automorphisms on irreducible characters of finite reductive groups of type 𝖠

Abstract Let 𝐺 be a finite reductive group such that the derived subgroup of the underlying algebraic group is a product of quasi-simple groups of type 𝖠. In this paper, we give an explicit description of the action of automorphisms of 𝐺 on the set of its irreducible complex characters. This generalizes a recent result of M. Cabanes and B. Späth [Equivariant character correspondences and inductive McKay condition for type 𝖠, J. Reine Angew. Math. 728 (2017), 153–194] and provides a useful tool for investigating the local sides of the local-global conjectures as one usually needs to deal with Levi subgroups. As an application we obtain a generalization of the stabilizer condition in the so-called inductive McKay condition [B. Späth, Inductive McKay condition in defining characteristic, Bull. Lond. Math. Soc. 44 (2012), 3, 426–438; Theorem 2.12] for irreducible characters of 𝐺. Moreover, a criterion is given to explicitly determine whether an irreducible character is a constituent of a given generalized Gelfand–Graev character of 𝐺.

The 4-fold Pandharipande–Thomas vertex

We give a conjectural but full and explicit description of the (K-theoretic) equivariant vertex for Pandharipande–Thomas stable pairs on toric Calabi–Yau 4-folds, by identifying torus-fixed loci as certain quiver Grassmannians and prescribing a canonical half of the tangent-obstruction theory. For any number of non-trivial legs, the DT/PT vertex correspondence can then be verified by computer in low degrees.

Evaluating the clinical utility of artificial intelligence assistance and its explanation on the glioma grading task

Clinical evaluation evidence and model explainability are key gatekeepers to ensure the safe, accountable, and effective use of artificial intelligence (AI) in clinical settings. We conducted a clinical user-centered evaluation with 35 neurosurgeons to assess the utility of AI assistance and its explanation on the glioma grading task. Each participant read 25 brain MRI scans of patients with gliomas, and gave their judgment on the glioma grading without and with the assistance of AI prediction and explanation. The AI model was trained on the BraTS dataset with 88.0% accuracy. The AI explanation was generated using the explainable AI algorithm of SmoothGrad, which was selected from 16 algorithms based on the criterion of being truthful to the AI decision process. Results showed that compared to the average accuracy of 82.5±8.7% when physicians performed the task alone, physicians’ task performance increased to 87.7±7.3% with statistical significance (p-value = 0.002) when assisted by AI prediction, and remained at almost the same level of 88.5±7.0% (p-value = 0.35) with the additional assistance of AI explanation. Based on quantitative and qualitative results, the observed improvement in physicians’ task performance assisted by AI prediction was mainly because physicians’ decision patterns converged to be similar to AI, as physicians only switched their decisions when disagreeing with AI. The insignificant change in physicians’ performance with the additional assistance of AI explanation was because the AI explanations did not provide explicit reasons, contexts, or descriptions of clinical features to help doctors discern potentially incorrect AI predictions. The evaluation showed the clinical utility of AI to assist physicians on the glioma grading task, and identified the limitations and clinical usage gaps of existing explainable AI techniques for future improvement.

Data-driven control of input saturated systems: a LMI-based approach

This paper addresses three complex control challenges related to input-saturated systems from a data-driven perspective. Unlike the traditional two-stage process involving system identification and model-based control, the proposed approach eliminates the need for an explicit model description. The method combines data-based closed-loop representations, Lyapunov theory, instrumental variables, and a generalized sector condition to formulate data-driven linear matrix inequalities (LMIs). These LMIs are applied to maximize the origin’s basin of attraction, minimize the closed-loop reachable set with bounded disturbances, and introduce a new data-driven ℓ2-gain minimization problem. Demonstrations on benchmark examples highlight the advantages and limitations of the proposed approach compared to an explicit identification of the system, emphasizing notable benefits in handling nonlinear dynamics.

A Benchmark for Controllable Text -Image-to-Video Generation

Automatic video generation is a challenging research topic, attracting interests from different perspectives, including Image-to-Video generation (I2V), Video-to-Video generation (V2V), and Text-to-Video generation (T2V). To pursue more controllable and fine-grained video generation, a novel video generation task, named Text-Image-to-Video generation (TI2V), and a corresponding baseline solution, named Motion Anchor-based video Generator (MAGE), were proposed. However, two other factors, namely clean datasets and reliable evaluation metrics, also play important roles in the success of the TI2V task. In this paper, we present a complete benchmark for the TI2V task which includes synthetic video-text paired datasets, a baseline method, and two evaluation metrics. More specifically: (1) Two versions of synthetic datasets are built based on CATER containing rich combinations of objects and actions, as well as the resulting changes of brightness and shadow. We also provide both explicit and ambiguous text descriptions to support deterministic and diverse video generation, respectively. (2) A refined version of MAGE, dubbed MAGE+, is proposed with an innovative motion anchor structure to store appearance-motion aligned representation, which can be further injected with explicit condition and implicit randomness to model the uncertainty in data distribution. (3) To evaluate the quality of generated video especially given ambiguous description, we introduce action precision and referring expression precision to assess the quality of motion based on captioning-and-matching method. Experiments conducted on proposed datasets, as well as relevant datasets, verify the effectiveness of our baseline and show appealing potentials of TI2V task. Code and data are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/Youncy-Hu/MAGE</uri> .

Event-Triggered Distributed Hypothesis Testing for Multiagent Networks Based on Observations Cumulation.

This article is concerned with the distributed hypothesis testing problem for multiagent networks, where a group of agents aim to learn an optimal hypothesis set via informative observations and event-triggered communication. Within this framework, a new event-triggered distributed hypothesis testing algorithm based on cumulation of historical observations is proposed. Theoretically, it is proven that due to the introduction of cumulation of historical observations, the proposed algorithm can always ensure the convergence whatever the event-triggered parameters are selected. This convergence result is different from that of the existing algorithm without involving historical observations, where the event-triggered parameters should satisfy a specific design condition to ensure the convergence of the algorithm. In addition, an explicit description of the convergence rate of the proposed algorithm is provided. Finally, the effectiveness of the algorithm is demonstrated through simulation examples.

Towards Transparent Deep Image Aesthetics Assessment with Tag-based Content Descriptors.

Deep learning approaches for Image Aesthetics Assessment (IAA) have shown promising results in recent years, but the internal mechanisms of these models remain unclear. Previous studies have demonstrated that image aesthetics can be predicted using semantic features, such as pre-trained object classification features. However, these semantic features are learned implicitly, and therefore, previous works have not elucidated what the semantic features are representing. In this work, we aim to create a more transparent deep learning framework for IAA by introducing explainable semantic features. To achieve this, we propose Tag-based Content Descriptors (TCDs), where each value in a TCD describes the relevance of an image to a human-readable tag that refers to a specific type of image content. This allows us to build IAA models from explicit descriptions of image contents. We first propose the explicit matching process to produce TCDs that adopt predefined tags to describe image contents. We show that a simple MLP-based IAA model with TCDs only based on predefined tags can achieve an SRCC of 0.767, which is comparable to most state-of-the-art methods. However, predefined tags may not be sufficient to describe all possible image contents that the model may encounter. Therefore, we further propose the implicit matching process to describe image contents that cannot be described by predefined tags. By integrating components obtained from the implicit matching process into TCDs, the IAA model further achieves an SRCC of 0.817, which significantly outperforms existing IAA methods. Both the explicit matching process and the implicit matching process are realized by the proposed TCD generator. To evaluate the performance of the proposed TCD generator in matching images with predefined tags, we also labeled 5101 images with photography-related tags to form a validation set. And experimental results show that the proposed TCD generator can meaningfully assign photography-related tags to images.

AN OPEN LABELLED CLINICAL TRIAL TO EVALUATE THE EFFICACY OF MATRA BASTI WITH SUKUMARA GHRITA FOLLOWED BY THE ADMINISTRATION OF VAISHWANARA CHURNA IN THE MANGEMENT OF VIBANDHA VIS-A-VIS CONSTIPATION IN GERIATRIC AGE GROUP

Background: Constipation is a frequently reported bowel symptom in the elderly with considerable impact on quality of life and health expenses. Disease-related morbidity and even mortality have been reported in the affected frail elderly. Although constipation is not a physiologic consequence of normal aging, decreased mobility, medications, underlying diseases, and rectal sensory-motor dysfunction may all contribute to its increased prevalence in older adults. Direct and explicit description of Vibandha as a disease is not found in Ayurveda but different presentation of Purisha like Baddha Purisha, Ghana Purisha/Grathita Purisha, Sushka Purisha, Mala avabaddhata are found in different contexts of Ayurveda, these can be taken as various manifestations of Vibandha Objective Of The Study: To evaluate the effect of Matra basti with Sukumara ghrita, followed by the administration of Vaishwanara churna with ghrita in the management of Vibandha vis-a-vis constipation in geriatric population. Methods: A clinical study with pre-post design. Data was collected on before intervention ie 0 day,mid intervention ,after matrabasti ie 9th day and and after the complete course of intervention,after internal administration of vaishwanara churna ie on 31 st day.The data obtained were analysed statistically by applying descriptive statistics,Paired t test and Chi square test,using statistical presentation system software (SPSS) for windows. Intervention:Matra basti with sukumara ghrita for the first 8 consecutive days of intervention in the dose of 60 ml. After Matra basti, Vaishwanara churna with ghrita as anupana was administered internally in the dosage of 12 gms in two equally divided doses, before food, for 22 days. Total duration of the study was 30 days Bristol Stool form scale and Patient assessment of constipation-Quality of life were used to assess the pre and post data gathered through pre designed research proforma.The results having ‘p’ value of &lt;0.001 was considered to be statistically highly significant in this study. Results: Overall assessment showed significant improvement in all the 32 subjects in this study. Interpretation and Conclusion: It can be concluded that Matra basti with sukumara ghrita followed by internal administration of Vaishwanara churna showed better results in Bristol Stool form scale and Patient assessment of constipaion- Quality of life.

Finiteness of One-Valued Function Classes in Many-Valued Logic

This paper addresses the theoretical issues in k-valued logic, which are crucial for developing solutions in various fields of science and technology. One of the fundamental issues is a complete description of the closed classes of functions of three-valued logic. The explicit description of closed classes in multivalued logic is an open problem. In this study, we consider a special case of the finite generation of all closed classes of three-valued logic through the operation of superposition. Previously, we considered the issue of the finite generation of classes containing a subset of single-variable functions. We have also provided a description of superlattices (lattices of lattices) containing a precomplete class of unary functions. The finite generation of these superlattices is proved. On the basis of these results, in this paper, we have proven that any class containing any of the precomplete classes from the set of single-valued functions is also finitely generated. The main result of this paper consists of three theorems on the finite generation of classes containing precomplete classes of single-valued functions and classes including all monotone unary functions. Thus, the obtained theoretical result provides easily verifiable criteria for the finiteness of classes of multivalued logic functions. It allows you to use simple procedures instead of cumbersome explicit constructs. The finite generation of overlattices allows the development of digital computing circuits that are crucial for practical applications. The proofs are based on an explicit description of these classes by an induction in the number of variables and essentially use the properties of functionally closed (Burle) classes of functions.

Understanding Lithium-Ion Battery Degradation through P2D Model Parameters Evolution

Despite its commercial level, lithium-ion battery ageing is still a hot topic in the research community. Indeed, the relation between ageing and the operating conditions and loads in a real-life operation is under investigation and the corresponding residual life prediction is still a challenging task.In this work, a combined approach with experiments and modeling is applied. A wide driving cycle campaign is carried out, involving 12 different profiles to test different combinations of temperature, C-rate, SoC and DoD, whose values were defined after a literature review about the most common values in a real application, and highlight their effect on battery ageing. Two calendar ageing campaigns at the same temperatures are also conducted to quantify the acceleration of the degradation rate due to cycling and analyse if the degradation path is different.For the interpretation of the results, the P2D model is employed. No explicit description of the main degradation mechanisms is applied. Indeed, the degradation is described through the variation of the physical parameters of the usual model implementation, like a reduction of lithium inventory or active electrode material or a variation of reaction rates and diffusion constants. A specific sequence of tests has been developed as check-up procedure. As detailed in 1, it is a trade-off between testing time and the operating conditions that maximise the identifiability of the parameters of the model.Therefore, the parameter identification problem is performed periodically upon check-ups and parameters trend over time/cycles is derived. Since it is a physical model, every parameter has a physical meaning and its evolution can be associated to a certain range of degradation phenomena. In this way, the model can support the identification of the most likely phenomena that are ongoing in the battery and the value of the parameters constitutes a new concept of state of health, more comprehensive than the residual capacity value.Finally, the model interpretation is proved in two ways. First, a validation dataset is provided, to evaluate the capabilities of the calibrated model in reproducing the behaviour of an aged cell under different operating conditions with respect to the check-up procedure. Then, some cells undergo post-mortem analyses to verify the origin of degradation and measure the values of the physical parameters, like optical and chemical analyses, q-OCP discharges of harvested electrodes in coin cell setup for thermodynamic parameters or EIS for kinetic parameters.This approach, though not suitable on-board, provides a novel physics-based method for a reliable analysis of lithium-ion batteries degradation. 1 G. Sordi, C. Rabissi, A. Casalegno, Reliable thermal-physical modeling of lithium-ion batteries: consistency between high-frequency impedance and ion transport. Under Review

Grounding End-to-End Pre-trained architectures for Semantic Role Labeling in multiple languages

Situated natural language interactions between humans and robots are strictly necessary for complex applications: communication here implies the reference to the environment shared between a user and the robot. This paper proposes a transformer-based architecture that supports the integration of spatial information (as logical representation) about a semantic map of the environment and the input utterances. The generated interpretation is a logical form of the command that makes references to the state of the world through a single end-to-end process, stimulated at each interaction by an explicit linguistic description of the environment. In this specific work, the end-to-end capability of the targeted transformer is studied in light of its multilingual applications where the robot can be queried in different natural languages. The obtained experimental results confirm the applicability of transformers to grounded human-robotic interaction, with benefits in terms of both portability of the approach across domains and effectiveness in terms of reachable accuracy. Moreover, language-specific processing chains are shown to be preferable to large-scale multilingual models for their better trade-off between accuracy and complexity. Overall, the proposed architecture outperforms previous approaches and paves the way for sustainable multilingual architectures.

Corrigendum to “K-theoretic Characterization of C*-algebras with Approximately Inner Flip”

Abstract An error in the original paper is identified and corrected. The $\textrm {C}^{\ast }$-algebras with approximately inner flip, which satisfy the UCT, are identified (and turn out to be fewer than what is claimed in the original paper). The action of the flip map on K-theory turns out to be more subtle, involving a minus sign in certain components. To this end, we introduce new geometric resolutions for $\textrm {C}^{\ast }$-algebras, which do not involve index shifts in K-theory and thus allow for a more explicit description of the quotient map in the Künneth formula for tensor products.

Generic Hecke algebra and theta correspondence over finite fields

We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for type I dual pairs over finite fields. For the product of the pair of Hecke algebras under consideration, we show that there is a generic Hecke algebra module whose specializations at prime powers give the Hecke algebra modules and whose specialization at 1 can be explicitly described. As an application, we prove the conservation relation on the first occurrence indices for all irreducible representations. As another application, we recover the results of Aubert-Michel-Rouquier and Pan on the explicit description of theta correspondence between Harish-Chandra series.

Modeling strain-induced martensitic transformation in austenitic stainless steels subjected to cryogenic temperatures using incremental mean-field homogenization schemes

Austenitic stainless steels are commonly used as structural materials in high-field superconducting magnet systems because they retain high strength, ductility, and toughness at very low temperatures, and they are paramagnetic or antiferromagnetic under the Néel temperature in their fully austenitic state. However, they are susceptible to strain-induced martensitic transformation, especially at cryogenic temperatures, which modifies the material properties, induces volume changes and additional strain hardening, and leads to ferromagnetic behavior. Thus, accurate predictions of the structural performance of these materials at very low temperatures are of great interest for the conception and design of these cryo-magnetic systems. In this paper, we propose an adequate constitutive model for the evolving bi-phase material—austenite and martensite—based on a Hill-type incremental formulation. Two different versions of the model are proposed based on the linear mean-field homogenization scheme: Mori-Tanaka and Self-Consistent. Moreover, a rate-independent nonlinear mixed kinematic-isotropic hardening law is used for each phase, and the martensitic transformation is described by the nonlinear kinetic law proposed by Olson and Cohen (1975). The constitutive model is implemented in ABAQUS/Standard through a UMAT user subroutine, for which a return mapping algorithm based on the implicit backward Euler integration scheme is used and a closed-form expression of the consistent Jacobian tensor is provided. The Mori-Tanaka and Self-Consistent approaches are evaluated in terms of their ability to describe the mechanical behavior of the bi-phase aggregate by comparing the predictions of the homogenization schemes with unit-cell finite element calculations with an explicit description of the martensite inclusions and the austenite matrix. The comparison is carried out for different stress states with controlled triaxiality and Lode parameter under monotonic and cycling loading, paying special attention to the evolution of the mechanical fields in each phase. The unit-cell calculations are performed for both constant and evolving martensite volume fractions. In addition, numerical simulations of tensile tests on samples subjected to different initial temperatures are carried out for the transforming bi-phase material and the results are compared to experimental data for AISI 304L and AISI 316LN steels.

Explicit and implicit description of the factors impact on the NO 2 concentration in the traffic corridor

Explicit and implicit description of the factors impact on the NO 2 concentration in the traffic corridor

Community Engagement in Behavioral Medicine: A Scoping Review.

Behavioral medicine has made key contributions toward improving health outcomes. Engaging community partners in research is critical to addressing persistent health inequities. The aim of this scoping review was to explore how researchers engaged community partners within the field of behavioral medicine research from 2005 to 2023. Publication databases and gray literature were searched for research that engaged community partners to address questions relevant to behavioral medicine. Articles were screened by title and abstract, and then by full text. Articles meeting the inclusion criteria were coded using the framework provided by the Engagement Navigator to identify engagement approaches, methods, and tools and when they were used during the research. Of 1486 articles initially identified, 58 met the inclusion criteria. Most articles used well-known approaches (e.g., community-based participatory research; 67%), methods (e.g., advisory committees; 59%), and tools (e.g., interviews; 41%), and engaged with healthcare service providers (62%) and/or patients (53%). Community partners were most often included in research planning and design (79%), and less often in dissemination (45%). Community engagement has considerable potential to address health inequities. Our assessment of the approaches, methods, and tools used by behavioral medicine researchers to engage with a diverse range of community partners points toward promising strategies for enhancing the impact of community engagement. Researchers should incorporate explicit descriptions of community engagement strategies in publications, an outcome that could be facilitated by clear publishing guidelines, structured reporting tools, and clear messaging from funders about the value of community engagement in behavioral medicine research.

Geometry of Hermitian symmetric spaces under the action of a maximal unipotent group

Let [Formula: see text] be a non-compact irreducible Hermitian symmetric space of rank [Formula: see text] and let [Formula: see text] be an Iwasawa decomposition of [Formula: see text]. The group [Formula: see text] acts on [Formula: see text] by biholomorphisms and the real [Formula: see text]-dimensional submanifold [Formula: see text] intersects every [Formula: see text]-orbit transversally in a single point. Moreover [Formula: see text] is contained in a complex [Formula: see text]-dimensional submanifold of [Formula: see text] biholomorphic to [Formula: see text], the product of [Formula: see text] copies of the upper half-plane in [Formula: see text]. This fact leads to a one-to-one correspondence between [Formula: see text]-invariant domains in [Formula: see text] and tube domains in [Formula: see text]. In this setting we prove an analogue of Bochner’s tube theorem. Namely, an [Formula: see text]-invariant domain [Formula: see text] in [Formula: see text] is Stein if and only if the base [Formula: see text] of the associated tube domain is convex and “cone invariant”. We also prove the univalence of [Formula: see text]-invariant holomorphically separable Riemann domains over [Formula: see text]. This yields a precise description of the envelope of holomorphy of an arbitrary [Formula: see text]-invariant domain in [Formula: see text]. Finally, we obtain a characterization of several classes of [Formula: see text]-invariant plurisubharmonic functions on [Formula: see text] in terms of the corresponding classes of convex functions on [Formula: see text]. As an application we present an explicit Lie group theoretical description of all [Formula: see text]-invariant potentials of the Killing metric on [Formula: see text] and of the associated moment maps.

Decompositions of Schubert varieties and small resolutions

We construct new small resolutions of Schubert varieties Xw , provide an explicit description of Xw as a Bott–Samelson type variety when w has a (complete) BP decomposition, and simplify resolutions of Schubert varieties constructed quite generally to Gelfand–MacPherson resolutions. Our methods are applied to type A Weyl groups where we determine precisely which Schubert varieties admit small resolutions in low-rank, prove that pattern avoidance does not characterize Schubert varieties admitting small resolutions, and describe a new family of small resolutions via pattern avoidance.