Towards Noncommutative Linking Numbers via the Seiberg-Witten Map by H. García-Compeán, O. Obregón, R. Santos-Silva

“…In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. …”
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Cellular Stress Responses: Cell Survival and Cell Death by Simone Fulda, Adrienne M. Gorman, Osamu Hori, Afshin Samali

“…The implications of cellular stress responses to human physiology and diseases are manifold and will be discussed in this review in the context of some major world health issues such as diabetes, Parkinson's disease, myocardial infarction, and cancer.…”
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Non-invertible symmetry in Calabi-Yau conformal field theories by Clay Córdova, Giovanni Rizi

“…Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. …”
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Stability of a weighted L2 projection in a weighted Sobolev norm by Averseng, Martin

“…The result also holds when the disk $\mathbb{D}$ is replaced by a more general surface $\Gamma \subset \mathbb{R}^3$, replacing the weight $\omega $ by $\omega _\Gamma (x) := \sqrt{\mathrm{d}(x,\partial \Gamma )}$, the square root of the distance from $x$ to the manifold boundary of $\Gamma $.…”
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New Fuzzy Support Vector Machine for the Class Imbalance Problem in Medical Datasets Classification by Xiaoqing Gu, Tongguang Ni, Hongyuan Wang

“…In this paper, a fuzzy support machine (FSVM) for the class imbalance problem (called FSVM-CIP) is presented, which can be seen as a modified class of FSVM by extending manifold regularization and assigning two misclassification costs for two classes. …”
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Relativistic Localizing Processes Bespeak an Inevitable Projective Geometry of Spacetime by Jacques L. Rubin

“…As a result, the spacetime manifold can be seen as a generalized Cartan space modeled on a four-dimensional real projective space, that is, a spacetime with both a local four-dimensional projective structure and a compatible (pseudo-)Riemannian structure. …”
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Dynamics Analysis of a Class of Delayed Economic Model by Chuangxia Huang, Changlin Peng, Xiaohong Chen, Fenghua Wen

“…The main tools to obtain our results are the normal form method and the center manifold theory introduced by Hassard. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. …”
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Grassmannian Constellation Based on Antipodal Points and Orthogonal Design and Its Simplified Detecting Algorithm by Li Peng, Dacong Hu, Lin Zhang, Zhen Qin

“…This study presents a framework of the unitary space time modulation (USTM) constellation based on antipodal points over Grassmannian manifold. The antipodal constellation enables an intrinsic simplified ML detecting algorithm. …”
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Routes to Multiple Equilibria for Mass-Action Kinetic Systems by Antonio A. Alonso, Irene Otero-Muras, Manuel Pájaro

“…With this in hand, we prove that deficiency-one networks can only admit multiple equilibria via folding of the equilibrium manifold, whereas a bifurcation leading to multiple branches is only possible in networks with deficiencies larger than one. …”
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Multi-stage refinement network for point cloud completion based on geodesic attention by Yuchen Chang, Kaiping Wang

“…Thus, we propose a novel geodesic attention-based multi-stage refinement transformer network, which enables the alignment of feature dimensions among query, key, and value, and long-range geometric dependencies are captured on the manifold. Then, a novel Position Feature Extractor is designed to enhance geometric features and explicitly capture graph-based non-Euclidean properties of point cloud objects. …”
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Improving the accuracy of the information retrieval evaluation process by considering unjudged document lists from the relevant judgment sets by Minnu Helen Joseph, SriDevi Ravana

“…Documents that were relevant and not retrieved by the systems were found from the document corpus and assigned new scores based on the Manifold fusion techniques then moved into the relevant judgment sets. …”
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3G Long Term Evolution Baseband Processing with Application-Specific Processors by Perttu Salmela, Juho Antikainen, Teemu Pitkänen, Olli Silvén, Jarmo Takala

“…Data rates in the upcoming 3G long term evolution (LTE) standard will be manifold when compared to the current universal mobile telecommunications system. …”
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Robust Control of Aeronautical Electrical Generators for Energy Management Applications by Giacomo Canciello, Alberto Cavallo, Beniamino Guida

“…A new strategy for the control of aeronautical electrical generators via sliding manifold selection is proposed, with an associated innovative intelligent energy management strategy used for efficient power transfer between two sources providing energy to aeronautical loads, having different functionalities and priorities. …”
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Vibration Failure Analysis and Countermeasures of the Inlet Pipelines at a Gas Compressor Station by Shuangshuang Li, Liwen Zhang, Chunyan Kong

“…Three different modification models against vibration were proposed by shortening the length of the pipe to avoid acoustic resonance, enlarging the volume of the gathering manifold to buffer pressure pulsation, and adding supports to increase the stiffness. …”
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Identifying preseizure state in intracranial EEG data using diffusion kernels by Dominique Duncan, Ronen Talmon, Hitten P. Zaveri, Ronald R. Coifman

“…A novel approach based on the recently developed diffusion map framework, which is considered to be one of the leading manifold learning methods, is proposed. Diffusion mapping provides dimensionality reduction of the data as well as pattern recognition that can be used to distinguish different states of the patient, for example, interictal and preseizure. …”
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Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles by Yaoyao Wang, Jiawang Chen, Linyi Gu

“…Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. …”
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On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth by Urszula Ledzewicz, Omeiza Olumoye, Heinz Schättler

“…The corresponding regions of attraction are separated by thestable manifold of a saddle. The optimal control problem of movingan initial condition that lies in the malignant region into thebenign region is formulated and the structure of optimal singularcontrols is determined.…”
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Poetics of Friction by Nadja Ben Khelifa, Étienne Allaix, Jörg Sternagel

“…While the sources of such an inspiration are manifold, three of them come into movement and display during the rehearsal: (1) excavation, (2) meaning, and (3) sense. …”
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Zinc Therapy in Dermatology: A Review by Mrinal Gupta, Vikram K. Mahajan, Karaninder S. Mehta, Pushpinder S. Chauhan

“…Its use has expanded manifold over the years for a number of dermatological conditions including infections (leishmaniasis, warts), inflammatory dermatoses (acne vulgaris, rosacea), pigmentary disorders (melasma), and neoplasias (basal cell carcinoma). …”
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Spinoza’s Evanescent Self by Sanja Särman

“…Whereas for Descartes and Leibniz, there is a manifold of thinking substances, for Spinoza, there is, crucially only one: God (1p14; 2p1). …”
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