Cancer is one of the greatest threats facing our society, being the second leading cause of death globally. Currents strategies for cancer diagnosis consist of the extraction of a solid tissue from ...the affected area. This sample enables the study of specific biomarkers and the genetic nature of the tumor. However, the tissue extraction is risky and painful for the patient and in some cases is unavailable in inaccessible tumors. Moreover, a solid biopsy is expensive and time consuming and cannot be applied repeatedly. New alternatives that overcome these drawbacks are rising up nowadays, such as liquid biopsy. A liquid biopsy is the analysis of biomarkers in a non-solid biological tissue, mainly blood, which has remarkable advantages over the traditional method; it has no risk, it is non-invasive and painless, it does not require surgery and reduces cost and diagnosis time. The most studied cancer non-invasive biomarkers are circulating tumor cells (CTCs), circulating tumor DNA (ctDNA), and exosomes. These circulating biomarkers play a key role in the understanding of metastasis and tumorigenesis, which could provide a better insight into the evolution of the tumor dynamics during treatment and disease progression. Improvements in isolation technologies, based on a higher grade of purification of CTCs, exosomes, and ctDNA, will provide a better characterization of biomarkers and give rise to a wide range of clinical applications, such as early detection of diseases, and the prediction of treatment responses due to the discovery of personalized tumor-related biomarkers.
Two new qubit stabilizer codes with parameters 〚77,0,19〛2 and 〚90,0,22〛2 are constructed for the first time by employing additive symplectic self-dual F4 codes from multidimensional circulant (MDC) ...graphs. We completely classify MDC graph codes for lengths 4≤n≤40 and show that many optimal 〚ℓ,0,d〛 qubit codes can be obtained from the MDC construction. Moreover, we prove that adjacency matrices of MDC graphs have nested block circulant structure and determine isomorphism properties of MDC graphs.
In Discrete Mathematics 306 (2005) 153-158, So proposed a conjecture saying that integral circulant graphs with different connection sets have different spectra. This conjecture is still open. We ...prove that this conjecture holds for integral circulant graphs whose orders have prime factorization of 4 types.
In this paper, we present a fast algorithm for solving the space-fractional Gross-Pitaevskii equation while preserving the law of mass conservation. First we discretize this equation by using a ...second-order weighted and shifted Grünward difference operator and obtain a system of semilinear differential equations with linear and nonlinear parts. Afterwards, we employ a Strang splitting method to solve this semi-discretization scheme. To further reduce computational time, we propose a two-level Strang splitting method from the linear part. This method significantly reduces computational complexity to O(nlogn) by implementing the fast Fourier transform. Importantly, our proposed method ensures the unconditional preservation of mass conservation and achieves second-order convergence. At last, we demonstrate the validity of our approach through numerical experiments and graphical results presented.
•A fast second-order method for high dimensional space-fractional Gross-Pitaevskii equations.•Split the Toeplitz matrix into the circulant and skew-circulant matrices.•Discrete mass conservation preserved unconditionally and global error estimated.
In recent years, many efficient key exchange protocols have been proposed based on matrices over the tropical semirings. The tropical addition of two elements is the minimum of the elements, while ...the tropical multiplication is the sum of the two elements. This paper proposes a novel key exchange protocol based on the min-plus semiring ($ \mathbb{Z}\cup\{\infty\}, \oplus, \otimes $) by introducing anti-$ s $-$ p $-circulant matrices, which forms a commutative subset of $ M_{n \times n}(\mathbb{Z}\cup \{\infty\}) $. We have given further analysis of the protocol in detail using upper or lower-$ s $-circulant matrices. Additionally, we prove that the set of all lower-$ s $-circulant matrices is a sub-semiring of the tropical semiring $ M_{n \times n}(\mathbb{Z}\cup \{\infty\}) $. We discuss the detailed security analysis of the protocol with upper or lower-$ s $-circulant matrices and provide cryptographic algorithms for both key exchange protocols with detailed explanations. We compare the protocol based on upper or lower-$ s $-circulant matrices and our proposed protocol in terms of time complexity and memory usage. Finally, we analyse the security and show that our protocol is safe against popular attacks of tropical key exchange protocols. The security of these protocols relies on the difficulty of solving tropical non-linear equations.
In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of λ-circulant and λ-reverse circulant matrices. By ...using the constructions on F2, we obtain new binary codes of lengths 64 and 68. We also apply the constructions to the ring R2 and considering the F2 and R1-extensions, we obtain new singly-even extremal binary self-dual codes of lengths 66 and 68. More precisely, we find 3 new codes of length 64, 13 new codes of length 66 and 21 new codes of length 68. These codes all have weight enumerators with parameters that were not known to exist in the literature.
High-Speed Tracking with Kernelized Correlation Filters Henriques, Joao F.; Caseiro, Rui; Martins, Pedro ...
IEEE transactions on pattern analysis and machine intelligence,
2015-March-1, 2015-Mar, 2015-3-1, 20150301, Volume:
37, Issue:
3
Journal Article
Peer reviewed
Open access
The core component of most modern trackers is a discriminative classifier, tasked with distinguishing between the target and the surrounding environment. To cope with natural image changes, this ...classifier is typically trained with translated and scaled sample patches. Such sets of samples are riddled with redundancies-any overlapping pixels are constrained to be the same. Based on this simple observation, we propose an analytic model for datasets of thousands of translated patches. By showing that the resulting data matrix is circulant, we can diagonalize it with the discrete Fourier transform, reducing both storage and computation by several orders of magnitude. Interestingly, for linear regression our formulation is equivalent to a correlation filter, used by some of the fastest competitive trackers. For kernel regression, however, we derive a new kernelized correlation filter (KCF), that unlike other kernel algorithms has the exact same complexity as its linear counterpart. Building on it, we also propose a fast multi-channel extension of linear correlation filters, via a linear kernel, which we call dual correlation filter (DCF). Both KCF and DCF outperform top-ranking trackers such as Struck or TLD on a 50 videos benchmark, despite running at hundreds of frames-per-second, and being implemented in a few lines of code (Algorithm 1). To encourage further developments, our tracking framework was made open-source.
In this paper, matrix order-reduction algorithms are realized to solve the CUPL-Toeplitz linear system. Firstly, we describe order-reduction algorithms for the multiplication of real skew-circulant ...matrix or complex circulant matrix and vector. Secondly, based on the two fast approaches 1 through splitting the CUPL-Toeplitz matrix into a Toeplitz matrix subtract a low-rank matrix, we propose new fast Toeplitz solvers to reduce the amount of calculation. Finally, numerical experiments are given to show the performance of the proposed algorithms.
The modularity of the modular multilevel dc-dc converters (MMDCs) makes them a competitive candidate in medium voltage applications but brings the submodule (SM) voltage balancing issue. This article ...proposes an optimal circulant modulation method for minimizing the SM voltage ripples with inherent balancing capability proven at the same time, which allows smaller SM capacitors and avoids the high-frequency communication for SM voltage balancing. First, the optimal switching pattern is strictly derived providing a general method to theoretically minimize the SM capacitor voltage ripple. Then the switching matrix of the optimal circulant modulation is formulated by introducing the generalized-circulant matrix. It verifies the circularity and full-rank feature of the optimal switching matrix, which promises the uniformity of SM actions and the inherent balancing of SM voltages. Finally, full-scale simulations and down-scaled experiments are both provided with the isolated LLC -based MMDC model and prototype. The results show that the proposed optimal circulant modulation can reduce the SM capacitor voltage ripple by 37% compared with the existed method, and it also promises the inherent SM voltage balancing and SM uniformity.
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