Entropic Dynamics Of Networks,
2021
Department of Physics, University at Albany, State University of New York
Entropic Dynamics Of Networks, Felipe Xavier Costa, Pedro Pessoa
Northeast Journal of Complex Systems (NEJCS)
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.
Knots And Links In Overtwisted Contact Manifolds,
2021
Louisiana State University and Agricultural and Mechanical College
Knots And Links In Overtwisted Contact Manifolds, Rima Chatterjee
LSU Doctoral Dissertations
Suppose $(\M,\xi)$ be an overtwisted contact 3-manifold. We prove that any Legendrian and transverse link in $(\M,\xi)$ having overtwisted complement can be coarsely classified by their classical invariants. Next, we defined an invariant called the support genus for transverse links and extended the definition of support genus of Legendrian knots to Legendrian links and prove that any coarse equivalence class of Legendrian and transverse loose links has support genus zero. Further, we show that the converse is not true by explicitly constructing an example. We also find a relationship between the support genus of the transverse link and its Legendrian …
Designing Efficient Algorithms For Sensor Placement,
2021
Georgia Southern University
Designing Efficient Algorithms For Sensor Placement, Gabriel Loos
Honors College Theses
Sensor placement has many applications and uses that can be seen everywhere you go.These include, but not limited to, monitoring the structural health of buildings and bridgesand navigating Unmanned Aerial Vehicles(UAV).We study ways that leads to efficient algorithms that will place as few as possible sen-sors to cover an entire area. We will tackle the problem from both 2-dimensional and3-dimensional points of view. Two famous related problems are discussed: the art galleryproblem and the terrain guarding problem. From the top view an area presents a 2-D im-age which will enable us to partition polygonal shapes and use graph theoretical results …
On The Surface Area Of Scalene Cones And Other Conical Bodies,
2021
Northern Kentucky University
On The Surface Area Of Scalene Cones And Other Conical Bodies, Daniel J. Curtin
Euleriana
This paper first appeared in the Novi Commentarii academiae scientiarum Petropolitanae vol. 1, 1750, pp. 3-19 and is reprinted in the Opera Omnia: Series 1, Volume 27, pp. 181–199. Its Eneström number is E133. This translation and the Latin original are available from the Euler Archive.
Calculating The Virtual Cohomological Dimension Of The Automorphism Group Of A Raag,
2021
University of Arkansas, Fayetteville
Calculating The Virtual Cohomological Dimension Of The Automorphism Group Of A Raag, Matthew B. Day, Andrew W. Sale, Richard D. Wade
Mathematical Sciences Faculty Publications and Presentations
We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right-angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis-conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe–Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups.
One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane,
2021
McGill University
One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef
Journal of Humanistic Mathematics
No abstract provided.
Boxes, Extended Boxes And Sets Of Positive Upper Density In The Euclidean Space,
2021
Chapman University
Boxes, Extended Boxes And Sets Of Positive Upper Density In The Euclidean Space, Polona Durcik, Vjekoslav Kovač
Mathematics, Physics, and Computer Science Faculty Articles and Research
We prove that sets with positive upper Banach density in sufficiently large dimensions contain congruent copies of all sufficiently large dilates of three specific higher-dimensional patterns. These patterns are: 2n vertices of a fixed n-dimensional rectangular box, the same vertices extended with n points completing three-term arithmetic progressions, and the same vertices extended with n points completing three-point corners. Our results provide common generalizations of several Euclidean density theorems from the literature.
Gordian Adjacency For Positive Braid Knots,
2021
Georgia Institute of Technology
Gordian Adjacency For Positive Braid Knots, Tolson H. Bell, David C. Luo, Luke Seaton, Samuel P. Serra
Rose-Hulman Undergraduate Mathematics Journal
A knot $K_1$ is said to be Gordian adjacent to a knot $K_2$ if $K_1$ is an intermediate knot on an unknotting sequence of $K_2$. We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In addition, we explore unknotting sequences of positive braid knots and give a proof that there are only finitely many positive braid knots for a given unknotting number.
The Adams Spectral Sequence For Topological Modular Forms,
2021
Wayne State University
The Adams Spectral Sequence For Topological Modular Forms, Robert Bruner, John Rognes
Mathematics Faculty Research Publications
The connective topological modular forms spectrum, 𝑡𝑚𝑓, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of 𝑡𝑚𝑓 and several 𝑡𝑚𝑓-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account …
Cayley Map Embeddings Of Complete Graphs,
2021
Rollins College
Cayley Map Embeddings Of Complete Graphs, Miriam Scheinblum
Honors Program Theses
This paper looks at Cayley map embeddings of complete graphs on orientable surfaces. Cayley maps constrain graph embeddings to those with cyclical edge rotations, so optimal embeddings on surfaces with the minimum genus may not always be possible. We explore instances when Cayley maps succeed at optimally embedding complete graphs, and when optimal embeddings are not possible, we determine how close to optimal they can get by finding vertex rotations that result in the smallest possible genus. Many of the complete graphs we consider have prime numbers of vertices, so for each complete graph Kn we focus on mappings with …
Elementary College Geometry (2021 Ed.),
2021
CUNY New York City College of Technology
Elementary College Geometry (2021 Ed.), Henry Africk
Open Educational Resources
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem proving or formal methods of reasoning. However the topics …
Diagrams In Intra-Configurational Analysis,
2021
Chapman University
Diagrams In Intra-Configurational Analysis, Marco Panza, Gianluca Longa
MPP Published Research
In this paper we would like to attempt to shed some light on the way in which diagrams enter into the practice of ancient Greek geometrical analysis. To this end, we will first distinguish two main forms of this practice, i.e., trans-configurational and intra-configurational. We will then argue that, while in the former diagrams enter in the proof essentially in the same way (mutatis mutandis) they enter in canonical synthetic demonstrations, in the latter, they take part in the analytic argument in a specific way, which has no correlation in other aspects of classical geometry. In intra-configurational analysis, diagrams represent …
Analysis, Constructions And Diagrams In Classical Geometry,
2021
Chapman University
Analysis, Constructions And Diagrams In Classical Geometry, Marco Panza
MPP Published Research
Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback,
2021
Old Dominion University
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output …
Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces,
2021
Eastern Illinois University
Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces, Ronald E. Hoagland
Masters Theses
This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U2/Γ(4), where U2 is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U2 . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the …
Geometric Morphometric Analyses Define Riverine And Lacustrine Species Flocks Of Himalayan Snowtrout (Cyprinidae: Schizothorax) In Nepal,
2021
University of Arkansas, Fayetteville
Geometric Morphometric Analyses Define Riverine And Lacustrine Species Flocks Of Himalayan Snowtrout (Cyprinidae: Schizothorax) In Nepal, Binod Regmi, Marlis R. Douglas, David R. Edds, Michael E. Douglas
Biological Sciences Faculty Publications and Presentations
Freshwater fishes in the river and lake systems in the Himalayas and Tibetan Plateau are morphologically diverged but the evolutionary relationship of putative subspecies separated in these freshwater systems has not been explored. Snowtrout (Schizothorax spp.) are minnows (Cyprinidae) broadly distributed in Asia. Body shapes of 3 Lake Rara (northwest Nepal) endemics (S. macrophthalmus, S. nepalensis, S. raraensis) and 2 widely distributed riverine species (S. progastus, S. richardsonii) across 3 drainages in Nepal (i.e. Karnali, Gandaki, and Koshi Rivers) were studied using geometric morphometry. Data were derived from museum voucher specimens/tissues collected …
Calabi-Yau Products: Graded Quivers For General Toric Calabi-Yaus,
2021
CUNY City College
Calabi-Yau Products: Graded Quivers For General Toric Calabi-Yaus, Sebastián Franco, Azeem Hasan
Publications and Research
The open string sector of the topological B-model on CY (m + 2)-folds is described by m-graded quivers with superpotentials. This correspondence generalizes the connection between CY (m + 2)-folds and gauge theories on the worldvolume of D(5 − 2m)-branes for m = 0, . . . , 3 to arbitrary m. In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CYm+2 and CYn+2 produces the quiver theory for a related CYm+n+3 …
Dimers, Orientifolds And Anomalies,
2021
Université Libre de Bruxelles
Dimers, Orientifolds And Anomalies, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo Garcia-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
Publications and Research
We study 4d N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.
Dimers, Orientifolds And Stability Of Supersymmetry Breaking Vacua,
2021
Université Libre de Bruxelles
Dimers, Orientifolds And Stability Of Supersymmetry Breaking Vacua, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff
Publications and Research
We study (orientifolded) toric Calabi-Yau singularities in search for D-brane configurations which lead to dynamical supersymmetry breaking at low energy. By exploiting dimer techniques we are able to determine that while most realizations lead to a Coulomb branch instability, a rather specific construction admits a fully stable supersymmetry breaking vacuum. We describe the geometric structure that a singularity should have in order to host such a construction, and present its simplest example, the Octagon.
Light-Ray Moments As Endpoint Contributions To Modular Hamiltonians,
2021
CUNY Lehman College
Light-Ray Moments As Endpoint Contributions To Modular Hamiltonians, Daniel Kabat, Gilad Lifschytz, Phuc Nguyen, Debajyoti Sarkar
Publications and Research
We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J(n) of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator …
