1,721,113 research outputs found
Lifespan of solutions for a class of fourth order parabolic equations involving the Hessian
Full text linkThis paper deals with blow-up solutions of a class of initial-boundary value problems for a fourth order parabolic equation involving the Hessian. A lower bound for the lifespan of such solutions is derived
La frequenza alle lezioni e l’esito di un esame. Un applicazione all’esame di Statistica nella Facoltà di Scienze Politiche
No full textQualitative Behavior of Solutions of a Chemotaxis System with Flux Limitation and Nonlinear Signal Production
No full textIn this paper we consider radially symmetric solutions of the following parabolic-elliptic cross-diffusion system {u(t)=Delta u-del(uf(|del v|(2))del v), 0=Delta v-mu(t)+g(u), mu(t)=1/|Omega|integral(Omega)g(u(& sdot;,t))dx u(x,0)=u(0)(x), in Omega x(0,infinity), with Omega a ball in R-N, N >= 1 under homogeneous Neumann boundary conditions, g(u) a regular function with the prototype g(u)=u(k), u >= 0, k>0. The function f(xi)=k(f) (1+xi)(-alpha), k (f )>0, describes gradient-dependent limitation of cross diffusion fluxes. Under suitable conditions on the data, we prove that the solution is global in time. If N >= 3, under conditions on f, g and initial data, we prove that if the solution u(x,t)blows up in L-infinity-norm at finite time T-max then for some p>1 it blows up also in L-p-norm. Moreover a lower bound of blow-up time is derived
Demographic Fairness in Multimodal Biometrics: A Comparative Analysis on Audio-Visual Speaker Recognition Systems
Full text linkIn urban scenarios, biometric recognition technologies are being increasingly adopted to empower citizens with a secure and usable access to personalized services. Given the challenging environmental scenarios, combining evidence from multiple biometrics at a certain step of the recognition pipeline has been often proved to increase the performance of the biometric-enabled recognition system. Despite the increasing accuracy achieved so far, it still remains under-explored how the adopted biometric fusion policy impacts on the quality of the decisions made by the biometric system, depending on the demographic characteristics of the citizen under consideration. In this paper, we investigate the extent to which state-of-the-art multimodal recognition systems based on facial and vocal biometrics are susceptible to unfairness towards legally-protected groups of individuals, characterized by a common sensitive attribute. Specifically, we present a comparative analysis of the performance across groups for two deep learning architectures tailored for facial and vocal recognition, under seven fusion policies that cover different pipeline steps (feature, model, score and decision). Experiments show that, compared to the unimodal systems alone and the other fusion policies, the multimodal system obtained via a fusion at the model step leads to the highest overall accuracy and the lowest disparity across groups
Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients
No full textWe study blow-up solutions of a nonlinear hyperbolic system of fourth order with time dependent coefficients under Dirichlet or Navier boundary conditions. We prove that under some restrictions on the data there exists a safe interval of existence of the solution and a lower bound of the lifespan is derived. The results are extended to a more general class of systems, where powers of the gradient of the solution are introduced. The proofs are based on some inequalities and coupled estimates techniques
A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term
Full text linkIn this paper we study a initial-boundary value problem for 4th order hyperbolic equations with weak and strong damping terms and superlinear source term. For blow-up solutions a lower bound of the blow-up time is derived. Then we extend the results to a class of equations where a positive power of gradient term is introduced
Behavior in time of solutions to a degenerate chemotaxis system with flux limitation
No full textWe study a new class of Keller-Segel models, which presents a limited flux and an optimal transport of cells density according to chemical signal density. As a prototype of this class we study radially symmetric solutions to the parabolic-elliptic system { = del center dot(del/root(2)+|del|(2)) -del center dot(del(1+|del|(2))), is an element of, >0, 0 =-+, is an element of, >0 under no flux boundary conditions in a ball = subset of and initial condition(,0) =(0)()>0, >0, >0, >0 and =1/|| integral(0).Under suitable conditions onand0it is shownthat the solution blows up in infinity-norm at a finite time and for some >1it blows up also in-norm. The proofs are mainly based on an helpful change of variables, on comparison arguments and some suitable estimates
Connecting user and item perspectives in popularity debiasing for collaborative recommendation
Full text linkRecommender systems learn from historical users’ feedback that is often non-uniformly distributed across items. As a consequence, these systems may end up suggesting popular items more than niche items progressively, even when the latter would be of interest for users. This can hamper several core qualities of the recommended lists (e.g., novelty, coverage, diversity), impacting on the future success of the underlying platform itself. In this paper, we formalize two novel metrics that quantify how much a recommender system equally treats items along the popularity tail. The first one encourages equal probability of being recommended across items, while the second one encourages true positive rates for items to be equal. We characterize the recommendations of representative algorithms by means of the proposed metrics, and we show that the item probability of being recommended and the item true positive rate are biased against the item popularity. To promote a more equal treatment of items along the popularity tail, we propose an in-processing approach aimed at minimizing the biased correlation between user-item relevance and item popularity. Extensive experiments show that, with small losses in accuracy, our popularity-mitigation approach leads to important gains in beyond-accuracy recommendation quality
Robust reputation independence in ranking systems for multiple sensitive attributes
Full text linkRanking systems have an unprecedented influence on how and what information people access, and their impact on our society is being analyzed from different perspectives, such as users’ discrimination. A notable example is represented by reputation-based ranking systems, a class of systems that rely on users’ reputation to generate a non-personalized item-ranking, proved to be biased against certain demographic classes. To safeguard that a given sensitive user’s attribute does not systematically affect the reputation of that user, prior work has operationalized a reputation independence constraint on this class of systems. In this paper, we uncover that guaranteeing reputation independence for a single sensitive attribute is not enough. When mitigating biases based on one sensitive attribute (e.g., gender), the final ranking might still be biased against certain demographic groups formed based on another attribute (e.g., age). Hence, we propose a novel approach to introduce reputation independence for multiple sensitive attributes simultaneously. We then analyze the extent to which our approach impacts on discrimination and other important properties of the ranking system, such as its quality and robustness against attacks. Experiments on two real-world datasets show that our approach leads to less biased rankings with respect to multiple users’ sensitive attributes, without affecting the system’s quality and robustness
Data-Efficient Student Profiling in Online Courses
No full textOnline courses in higher education have gained popularity, but students struggle with self-regulation in online learning. The absence of traditional classroom guidance due to limited educator oversight highlights the need for effective student profiling. Existing profiling methods focus on non-university contexts with data-rich platforms, leaving platforms like Moodle at a disadvantage. In this paper, we explore the creation of useful student profiles with limited data, often found in Moodle and similar platforms. We propose to adopt a clustering method based on eight key self-regulation variables: revision, progress, consistency, dedication, regularity, focus, and practicality. Across diverse online university courses, our experiments show that our approach effectively identifies meaningful profiles, even with limited data. These profiles also reveal unique demographics, providing insights into online learning behavior
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