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For an evolution of metrics (M, g t ) there is a t-smooth family of embeddings e t : M→ R N inducing g t , but in general there is no family of embeddings extending a given initial embedding e. We give an example of this phenomenon when g t is the evolution of g under the Ricci flow. We show that there are embeddings e inducing g which do not admit of t-smooth extensions to e t inducing g t for any t> 0. We also find hypersurfaces of dim > 2 that will not remain a hypersurface under Ricci flow for any positive time. © 2019, Springer Nature B.V  

We consider d-dimensional simplicial complexes which can be PL embedded in the 2d-dimensional Euclidean space. In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in the (Formula presented.)-dimensional Euclidean space. In addition, we use similar considerations on links of vertices to derive a new asymptotic upper bound on the total number of d-simplices in an (continuously) embeddable complex in 2d-space with n vertices, improving known upper bounds, for all (Formula presented.). Moreover, we show that the same asymptotic bound also applies to the size of d-complexes linklessly embeddable in the... 

We consider d-dimensional simplicial complexes which can be PL embedded in the 2d-dimensional Euclidean space. In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in the (2 d- 1 ) -dimensional Euclidean space. In addition, we use similar considerations on links of vertices to derive a new asymptotic upper bound on the total number of d-simplices in an (continuously) embeddable complex in 2d-space with n vertices, improving known upper bounds, for all d≥ 2. Moreover, we show that the same asymptotic bound also applies to the size of d-complexes linklessly embeddable in the (2 d+ 1 ) -dimensional... 

Let f : M {long rightwards arrow} over(M, -) be an isometric immersion between Riemannian manifolds. For certain conditions on M and over(M, -) in terms of curvatures and external diameter, we extend the non-embedding theorem of Chern and Kuiper to the isometric immersions of non-compact manifolds. Also, our results generalize and improve the main results of Jorge and Koutroufiotis [L. Jorge, D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (4) (1981) 711-725] and Veeravalli [A. R. Veeravalli, A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms, Bull. Austral. Math. Soc. 62 (1) (2000) 165-170]. © 2008 Elsevier B.V.... 

Low power consumption and high-reliability are often major objectives in the design of embedded systems. To reduce power consumption, embedded systems usually employ system-level power management techniques, e.g. Dynamic Voltage Scaling (DVS) and Dynamic Power Management (DPM). To achieve high reliability, embedded systems often exploit fault-tolerant techniques. Fault-tolerant techniques are in a trade-off with energy consumption, peak-power consumption, and temperature. Thus, different methods have been introduced that simultaneously consider reliability and power consumption as the system constraints. Several novel methods have been proposed in previous works to reduce the power... 

The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces. © 2021 Elsevier Inc  

A family of matrix embedding steganographic schemes for digital images is investigated. The target schemes are applied to blocks of n pixels in a cover image. In every block, at most m pixels are allowed to change with q-ary steps. We have derived some upper bounds on the embedding efficiency of these schemes for different values on m. It is also shown that these upper bounds approach the general upper bound on the embedding efficiency of q-ary steganography. For the case of q=3, we have shown that there is no feasible optimum member of the family for m=2, although for m=1, a well-known example exists. Instead, for m=2, a new close-to-bound scheme in the family is presented which exploits... 

Overlay networks have been an active area of research for the past few years. The control overhead and the recovery from failure are the two important issues in the topology aware embedded overlay networks. In this research, we have introduced an enhanced version of the NICE protocol, called resilient NICE (R-NICE) that reduces the control overhead significantly. Furthermore, by saving the join path for an end host, the time and overhead of rejoining for isolated nodes have also been reduced. This will cause the clusters and consequently the overall network to become more stable and the effect of a node failure become localized. Our experimental results have confirmed the superior... 

Scratchpad memories (SPMs) are widely employed inmulticore embedded processors. Reliability is one of the major constraints in the embedded processor design, which is threatened with the increasing susceptibility of memory cells to multiple-bit upsets (MBUs) due to continuous technology down-scaling. This article proposes a low-cost and efficient data replication mechanism, called In-Scratchpad Memory Replication (ISMR), to correct MBUs in SPMs of multicore embedded processors. The main feature of ISMR is a smart controller, called Replication Management Unit (RMU), which is responsible for dynamically analyzing the activity of the SPM blocks at runtime and efficiently replicating the... 

A family of matrix embedding steganographic schemes for digital images is investigated. The target schemes are applied to blocks of n pixels in a cover image. In every block, at most m pixels are allowed to change with q-ary steps. We have derived some upper bounds on the embedding efficiency of these schemes for different values on m. It is also shown that these upper bounds approach the general upper bound on the embedding efficiency of q-ary steganography. For the case of q=3, we have shown that there is no feasible optimum member of the family for m=2, although for m=1, a well-known example exists. Instead, for m=2, a new close-to-bound scheme in the family is presented which exploits... 

In real-world networks, nodes might have more than one type of relationship. Signed networks are an important class of such networks consisting of two types of relations: positive and negative. Recently, embedding signed networks has attracted increasing attention and is more challenging than classic networks since nodes are connected by paths with multi-types of links. Existing works capture the complex relationships by relying on social theories. However, this approach has major drawbacks, including the incompleteness/inaccurateness of such theories. Thus, we propose network transformation based embedding to address these shortcomings. The core idea is that rather than directly finding the... 

The Least Significant Bit (LSB) substitution is an old and simple data hiding method that could almost effortlessly be implemented in spatial or transform domain over any digital media. This method can be attacked by several steganalysis methods, because it detectably changes statistical and perceptual characteristics of the cover signal. A typical method for steganalysis of the LSB substitution is the histogram attack that attempts to diagnose anomalies in the cover image's histogram. A well-known method to stand the histogram attack is the LSB + steganography that intentionally embeds some extra bits to make the histogram look natural. However, the LSB + method still affects the perceptual... 

While performance and power consumption of processors present a classic trade-off in designing embedded hardware, software can be optimized in favor of both performance and energy. We evaluate the impact of optimizations at different stages of designing embedded software. We show that algorithm choice and compiler optimizations aimed at improving performance can also reduce energy consumption of an embedded processor. We also propose energy-aware compilation guidelines which can further reduce energy consumption without performance penalties. Our experimental results show that up to 85% energy reduction and 89% performance improvement can be achieved by these techniques  

In this paper, we propose a very fast and accurate analytical approach to estimate the overall SER and to identify the most vulnerable gates,flip-flops, and paths of a circuit. Using such information, designers can selectively protect the vulnerable parts resulting in lower power and area overheads that are the most important factors in embedded systems. Unlike previous approaches, the proposed approach firstly does not rely on fault injection or fault simulation; secondly it measures the SER for multi cycles of circuit operation; thirdly, the proposed approach accurately computes all three masking factors, namely, logical, electrical, and timing masking; fourthly, the effects of error... 

Multicore processors are widely used in today's real-time embedded systems to satisfy the performance and predictability requirements as well as reduce cost. A vast majority of multicore embedded systems are running several tasks with mixed-criticality, in which the non-functional requirements of the tasks are different or even conflicting. A major challenge in mixed-criticality systems is to maximise the efficiency of shared resources while satisfying the criticality requirements. Shared memory is a key component that should be well managed and memory controller plays the main role in this case. Several memory controllers have been introduced in the literature for multicore processors. In... 

Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information. Recent methods like Graph Convolutional Network (GCN) try to consider node attributes (if available) besides node relations and learn node embeddings for unsupervised and semi-supervised tasks on graphs. On the other hand, multi-layer graph analysis has been received attention recently. However, the existing methods for multi-layer graph embedding cannot incorporate all available information (like node attributes). Moreover, most of them consider either... 

In both public and private sectors, critical technology-based tasks, such as innovation, forecasting, and road-mapping, are faced with unmanageable complexity due to the ever-expanding web of technologies which can range into thousands. This context cannot be easily handled manually or with efficient speed. However, more precise and insightful answers are expected. These answers are the fundamental challenge addressed by tech-mining. For tech-mining, discovering the associations among them is a critical task. These associations are used to form a weighted directed graph of technologies called 'association tech-graph' which is used for technology development, trend analysis, policymaking,...