Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...

For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion ...

In this paper, we propose novel algorithmic models based on feature transformation in cross-modal subspace and their multimodal fusion for different types of residue features extracted from several intra-frame and inter-frame pixel sub-blocks in video sequences for detecting digital video tampering or forgery. An evaluation of proposed residue features – the noise residue features and the quant...

In this paper, we propose novel algorithmic models based on information fusion and feature transformation in crossmodal subspace for different types of residue features extracted from several intra-frame and inter-frame pixel sub-blocks in video sequences for detecting digital video tampering or forgery. An evaluation of proposed residue features – the noise residue features and the quantizatio...

Observational studies on couple interactions are often based on manual annotations of a set of behavior codes. Such annotations are expensive, time-consuming, and often suffer from low inter-annotator agreement. In previous studies it has been shown that the lexical channels contain sufficient information for capturing behavior and predicting the interaction labels, and various automated proces...

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g -frames. In this paper we introduce frames of submodules, fusion frames and g -frames in Hilbert C∗ -modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g -frames in Hilbert spaces.

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the classical notions of designs and cubature formulas in Grassmann spaces and are analyzed with methods from harmonic analysis in the Grassmannians. We define the p-f...

The present experiment investigates the frame of reference involved in Visual-Auditory (VA) fusion over space. This multisensory phenomenon refers to the perception of unity (Welch & Warren, 1986) resulting from visual and auditory stimuli despite their potential spatial disparity. The extent of this illusion depends on the eccentricity in azimuth of the bimodal stimulus (Godfroy, Roumes, & Dau...

Pyoderma gangrenosum is a rare autoinflammatory syndrome manifested by skin lesions eventually creating ulcers. Surgical management can lead to scarring and contracture at the site of the lesion due to the pathergy phenomenon. A 43-year-old woman presented with a 5-year history of severe equinovarus deformity due to chronic pyoderma gangrenosum on her posteromedial ankle. She underwent a staged...