Recent Developments in Instantons in Noncommutative ℝ𝟒 by Akifumi Sako

“…These smooth deformations are the latest developments in noncommutative gauge theories, and we can extend the procedure to other types of solitons. As an example, vortex deformations are studied.…”
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Partially Coherent, Radially Polarized Beam with Annular Apodization by C. Mariyal, P. Suresh, K. B. Rajesh, T. V. S. Pillai

“…Based on the vectorial Debye theory, the tight focusing properties of partially coherent, radially polarized vortex beams are investigated in detail. In this paper, we propose to use an amplitude modulated filter in combination with a high NA lens to generate long focal depth in the focal region. …”
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Algorithmic Complexity and Bounds for Domination Subdivision Numbers of Graphs by Fu-Tao Hu, Chang-Xu Zhang, Shu-Cheng Yang

“…A subset D⊆V is a dominating set if every vertex not in D is adjacent to a vertex in D. The domination number of G, denoted by γG, is the smallest cardinality of a dominating set of G. …”
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Computation of Polynomial Degree-Based Topological Descriptors of Indu-Bala Product of Two Paths by Ghazanfar Abbas, Muhammad Ibrahim

“…As we all know, vertices and edges form a network whereas vertex and its degrees contribute to joining edges. …”
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THE STRUCTURE OF GRAPHS ON \(n\) VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO \(n-2\) by Do Nhu An

“…Let \(G\) be an undirected simple graph on n vertices and \(\sigma^2(G)=n-2\) (degree sum of any two non-adjacent vertices in \(G\) is equal to \(n-2\)) and \(\alpha(G)\) be the cardinality of an maximum independent set of \(G\). In \(G\), a vertex of degree \((n-1)\) is called total vertex. …”
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Reconciling Homeostatic and Use-Dependent Plasticity in the Context of Somatosensory Deprivation by John J. Orczyk, Preston E. Garraghty

“…Both a reduction of GABAergic inhibition and increase in glutamatergic excitatory transmission are observed in input-deprived cortex. Topographic reorganization of the adult somatosensory cortex is likely driven by both homeostatic and use-dependent mechanisms. …”
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Worldline Path-Integral Representations for Standard Model Propagators and Effective Actions by Somdatta Bhattacharya

“…Then we extend the formalism to the massive and dressed cases for the fermions and compute the QED vertex. We then go over fermionic one-loop effective actions and anomalies. …”
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On Roman balanced domination of graphs by Mingyu Zhang, Junxia Zhang

“…Let $ G $ be a graph with vertex set $ V $. A function $ f $ : $ V\to \{-1, 0, 2\} $ is called a Roman balanced dominating function (RBDF) of $ G $ if $ \sum_{u\in N_G[v]}f(u) = 0 $ for each vertex $ v\in V $. …”
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Fifteen Minutes of Left Prefrontal Repetitive Transcranial Magnetic Stimulation Acutely Increases Thermal Pain Thresholds in Healthy Adults by Jeffrey J Borckardt, Arthur R Smith, Scott T Reeves, Mitchell Weinstein, F Andrew Kozel, Ziad Nahas, Neal Shelley, R Kyle Branham, K Jackson Thomas, Mark S George

“…BACKGROUND: Transcranial magnetic stimulation (TMS) of the motor cortex appears to alter pain perception in healthy adults and in patients with chronic neuropathic pain. …”
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3-Total Edge Product Cordial Labeling for Stellation of Square Grid Graph by Rizwan Ullah, Gul Rahmat, Muhammad Numan, Kraidi Anoh Yannick, Adnan Aslam

“…Let G be a simple graph with vertex set VG and edge set EG. An edge labeling δ:EG⟶0,1,…,p−1, where p is an integer, 1≤p≤EG, induces a vertex labeling δ∗:VH⟶0,1,…,p−1 defined by δ∗v=δe1δe2⋅δenmodp, where e1,e2,…,en are edges incident to v. …”
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Migraine with Prolonged Aura: Correlation of Clinical and EEG Features by A. O. Ogunyemi

“…The aura symptoms evolved in a manner consistent with posterior-to-anterior dysfunction of the cerebral cortex. The EEG abnormalities were non-epileptiform and consisted of focal delta slow waves or theta slow waves. …”
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Novel intervention of high-frequency repetitive transcranial magnetic stimulation in patients with somatic symptom disorder and its safety and outcome by Nand Kumar, Prakamya Singal, Abhishek Chakladar

“…Double cone coil TMS at medial Prefrontal Cortex appears to be a safe therapeutic intervention with potentially good outcomes in SSDs.…”
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Mechanisms underlying CSD initiation implicated by genetic mouse models of migraine by Daniela Pietrobon, K.C. Brennan

“…In this review, after describing the available genetic mouse models of migraine, which all share increased susceptibility to experimentally induced CSD, we will discuss the functional alterations in their cerebral cortex and the mechanisms underlying the facilitation of CSD initiation in their cortex, as well as the insights that these mechanisms may give into the mechanisms of initiation of spontaneous CSDs in migraine.…”
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A New Type-2 Soft Set: Type-2 Soft Graphs and Their Applications by Khizar Hayat, Muhammad Irfan Ali, Bing-Yuan Cao, Xiao-Peng Yang

“…The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. …”
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Novel Walking Robot based on the Design of Origami Mechanism by Xinyang Jiang, Yong Xu, Yan Wang, Jiali Liu, Chuansen Zhao, Lü Yeping, Yu Wang

“…The theory of single-vertex origami is extended to the multi-vertex origami configuration， and the definite relationship between the crease corners of different units is obtained. …”
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On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities by Miroslav Rapčák

“…Abstract We discuss a class of vertex operator algebras W m n × ∞ $$ {\mathcal{W}}_{\left.m\right|n\kern0.33em \times \kern0.33em \infty } $$ generated by a super- matrix of fields for each integral spin 1, 2, 3, . . . . …”
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Bounds of the Spectral Radius and the Nordhaus-Gaddum Type of the Graphs by Tianfei Wang, Liping Jia, Feng Sun

“…The Laplacian spectra are the eigenvalues of Laplacian matrix L(G)=D(G)-A(G), where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of a graph G, respectively, and the spectral radius of a graph G is the largest eigenvalue of A(G). …”
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Error-driven upregulation of memory representations by Alexander Weuthen, Hans Kirschner, Markus Ullsperger

“…Previous studies associated increased error signals in posterior medial frontal cortex with improved memory formation. However, the neurophysiological mechanisms that facilitate post-error learning remain poorly understood. …”
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Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs by Wei Gao, Muhammad Kamran Jamil, Aisha Javed, Mohammad Reza Farahani, Shaohui Wang, Jia-Bao Liu

“…Using these nice mathematical properties, the extremal graphs among n-vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. …”
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Cerebellar-driven cortical dynamics can enable task acquisition, switching and consolidation by Joseph Pemberton, Paul Chadderton, Rui Ponte Costa

“…Next, we demonstrate that, when trained in working memory tasks, the cerebellum can also underlie the maintenance of cognitive-specific dynamics in the cortex, explaining a range of optogenetic and behavioural observations. …”
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