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Articles 1 - 30 of 33
Full-Text Articles in Physical Sciences and Mathematics
On The Colorability Of The Sphere Complex, Bennett Haffner
On The Colorability Of The Sphere Complex, Bennett Haffner
Master's Theses
One of the most prominently studied groups in geometric group theory is the outer automorphism group of the free group Out(F). The sphere complex provides a topological model for Out(F). We demonstrate the chromatic number of the sphere complex is finite.
Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım
Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım
Faculty Publications
We show that for any positive integer n, there is some fixed A such that d(x) = d(x +n) = A infinitely often where d(x) denotes the number of divisors of x. In fact, we establish the stronger result that both x and x +n have the same fixed exponent pattern for infinitely many x. Here the exponent pattern of an integer x > 1is the multiset of nonzero exponents which appear in the prime factorization of x.
University Scholar Series: Tatiana Shubin, Tatiana Shubin
University Scholar Series: Tatiana Shubin, Tatiana Shubin
University Scholar Series
Moving in Circles: the Beauty and Joy of Mathematics for Everyone
Tatiana Shubin joined the faculty of San Jose State University in 1985 after earning her Ph.D. in Mathematics from University of California, Santa Barbara. In 1998, she founded San Jose Math Circle and the Bay Area Math Adventures. In 2006, Shubin became a co-founder of the first Math Teachers' Circle in the US. This circle proved to be a seed which germinated to produce the entire Math Teachers' Circle Network. She launched the Navajo Nation Math Circles project in 2012, became a co-founder and co-director of the Alliance of …
The Knill Graph Dimension From The Minimum Clique Cover, Kassahun Betre, Evatt Salinger
The Knill Graph Dimension From The Minimum Clique Cover, Kassahun Betre, Evatt Salinger
Faculty Publications
In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim(G1+G2)=1+dimG1+dimG2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order N will have dimension N−1. We finish by finding lower and upper bounds on the Knill dimension of a graph in terms of its clique number.
On The Strong Chromatic Index Of Sparse Graphs, Philip Deorsey, Jennifer Diemunsch, Michael Ferrara, Nathan Graber, Stephen Hartke, Sogol Jahanbekam, Bernard Lidicky, Luke Nelsen, Derrick Stolee, Eric Sullivan
On The Strong Chromatic Index Of Sparse Graphs, Philip Deorsey, Jennifer Diemunsch, Michael Ferrara, Nathan Graber, Stephen Hartke, Sogol Jahanbekam, Bernard Lidicky, Luke Nelsen, Derrick Stolee, Eric Sullivan
Faculty Publications
The strong chromatic index of a graph G, denoted χ′s(G), is the least number of colors needed to edge-color G so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted χ′s,ℓ(G), is the least integer k such that if arbitrary lists of size k are assigned to each edge then G can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if G is a subcubic planar graph with girth(G)≥41 then χ′s,ℓ(G)≤5, answering a question …
Additive List Coloring Of Planar Graphs With Given Girth, Axel Brandt, Sogol Jahanbekam, Jennifer Diemunsch
Additive List Coloring Of Planar Graphs With Given Girth, Axel Brandt, Sogol Jahanbekam, Jennifer Diemunsch
Faculty Publications
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two adjacent vertices have distinct sums of labels on their neighbors. The least integer k for which a graph G has an additive coloring is called the additive coloring number of G, denoted \luck(G). Additive coloring is also studied under the names lucky labeling and open distinguishing. In this paper, we improve the current bounds on the additive coloring number for particular classes of graphs by proving results for a list version of additive coloring. We apply the discharging method and …
A Survey On Network Security-Related Data Collection Technologies, Huaqing Lin, Zheng Yan, Yu Chen, Lifang Zhang
A Survey On Network Security-Related Data Collection Technologies, Huaqing Lin, Zheng Yan, Yu Chen, Lifang Zhang
Faculty Publications, Information Systems & Technology
Security threats and economic loss caused by network attacks, intrusions, and vulnerabilities have motivated intensive studies on network security. Normally, data collected in a network system can reflect or can be used to detect security threats. We define these data as network security-related data. Studying and analyzing security-related data can help detect network attacks and intrusions, thus making it possible to further measure the security level of the whole network system. Obviously, the first step in detecting network attacks and intrusions is to collect security-related data. However, in the context of big data and 5G, there exist a number of …
Weak Dynamic Coloring Of Planar Graphs, Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger
Weak Dynamic Coloring Of Planar Graphs, Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger
Faculty Publications
The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min{k, d(v)} colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.
List-Distinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger
List-Distinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger
Faculty Publications
The distinguishing number of a graph G, denoted D(G), is the minimum number of colors needed to produce a coloring of the vertices of G so that every nontrivial isomorphism interchanges vertices of different colors. A list assignment L on a graph G is a function that assigns each vertex of G a set of colors. An L-coloring of G is a coloring in which each vertex is colored with a color from L(v). The list distinguishing number of G, denoted Dℓ(G) is the minimum k such that every list assignment L that assigns a list of size at least …
The Chromatic Number Of The Square Of Subcubic Planar Graphs, Stephen Hartke, Sogol Jahanbekam, Brent Thomas
The Chromatic Number Of The Square Of Subcubic Planar Graphs, Stephen Hartke, Sogol Jahanbekam, Brent Thomas
Faculty Publications
Wegner conjectured in 1977 that the square of every planar graph with maximum degree at most 3 is 7-colorable. We prove this conjecture using the discharging method and computational techniques to verify reducible configurations.
Lucky Choice Number Of Planar Graphs With Given Girth, Axel Brandt, Jennifer Diemunsch, Sogol Jahanbekam
Lucky Choice Number Of Planar Graphs With Given Girth, Axel Brandt, Jennifer Diemunsch, Sogol Jahanbekam
Faculty Publications
No abstract provided.
Extremal Theorems For Degree Sequence Packing And The Two-Color Discrete Tomography Problem, Jennifer Diemunsch, Michael Ferrara, Sogol Jahanbekam, James Shook
Extremal Theorems For Degree Sequence Packing And The Two-Color Discrete Tomography Problem, Jennifer Diemunsch, Michael Ferrara, Sogol Jahanbekam, James Shook
Faculty Publications
No abstract provided.
Antimagic-Type Labelings, Sogol Jahanbekam
On The Dynamic Coloring Of Cartesian Product Graphs., Saieed Akbari, Maryam Ghanbari, S. Jahanbekam
On The Dynamic Coloring Of Cartesian Product Graphs., Saieed Akbari, Maryam Ghanbari, S. Jahanbekam
Faculty Publications
No abstract provided.
On The Dynamic Coloring Of Strongly Regular Graphs, Saieed Akbari, Maryam Ghanbari, Sogol Jahanbekam
On The Dynamic Coloring Of Strongly Regular Graphs, Saieed Akbari, Maryam Ghanbari, Sogol Jahanbekam
Faculty Publications
No abstract provided.
Variation Of Instructor-Student Interactions In An Introductory Interactive Physics Course, Emily West, Cassandra Paul, David Webb, Wendell Potter
Variation Of Instructor-Student Interactions In An Introductory Interactive Physics Course, Emily West, Cassandra Paul, David Webb, Wendell Potter
Faculty Publications
The physics instruction at UC Davis for life science majors takes place in a long-standing reformed large-enrollment physics course in which the discussion or laboratory instructors (primarily graduate student teaching assistants) implement the interactive-engagement (IE) elements of the course. Because so many different instructors participate in disseminating the IE course elements, we find it essential to the instructors’ professional development to observe and document the student-instructor interactions within the classroom. Out of this effort, we have developed a computerized real-time instructor observation tool (RIOT) to take data of student-instructor interactions. We use the RIOT to observe 29 different instructors for …
The 1, 2-Conjecture For Graphs With Relatively Small Chromatic Number, Sogol Jahanbekam, Douglas West
The 1, 2-Conjecture For Graphs With Relatively Small Chromatic Number, Sogol Jahanbekam, Douglas West
Faculty Publications
No abstract provided.
Unpredictable Binary Strings, Richard Low, Mark Stamp, R. Craigen, G. Faucher
Unpredictable Binary Strings, Richard Low, Mark Stamp, R. Craigen, G. Faucher
Faculty Publications, Computer Science
We examine a class of binary strings arising from considerations about stream cipher encryption: to what degree can one guarantee that the number of pairs of entries distance k apart that disagree is equal to the number that agree, for all small k? In a certain sense, a keystream with such a property achieves a degree of unpredictability. The problem is also restated combinatorially in terms of seating arrangements. We examine sequences s of length 2n in which this property holds for all k ≤ Mn, where Mn is the largest number for which this is possible among strings of …
Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka
Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka
Faculty Publications
No abstract provided.
Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka
Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka
Richard P. Kubelka
No abstract provided.
Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp
Pokémon® Cards And The Shortest Common Superstring, Mark Stamp, Austin Stamp
Faculty Publications, Computer Science
Evidence is presented that certain sequences of Pokémon cards are determined by selecting consecutive elements from a longer sequence. We then consider the problem of recovering the shortest common superstring (SCS), i.e., the shortest string that contains each of the Pokémon card sequences as a consecutive substring. The SCS problem arises in many applications, most notably in DNA sequencing.
Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka
Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka
Richard P. Kubelka
For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula to explain the global geometric patterns that occur in K(p,s). Indeed, if we consider the finite (truncated) versions of K(p,s), we find that they can be decomposed into superpositions of tensor products of certain primitive p x …
Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka
Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka
Faculty Publications
For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula …
Rush Hour® And Dijkstra’S Algorithm, Mark Stamp, Brad Engel, Mcintosh Ewell, Victor Morrow
Rush Hour® And Dijkstra’S Algorithm, Mark Stamp, Brad Engel, Mcintosh Ewell, Victor Morrow
Faculty Publications, Computer Science
The game of Rush Hour® includes a 6 × 6 grid and game pieces representing cars and trucks. The object of the puzzle is to move a special car out of a gridlocked “traffic jam.” In this note we apply Dijkstra’s algorithm and a breadth-first search to solve any Rush Hour configuration.
Random Walks On Wheels, Matthew Lee, Mark Stamp
Random Walks On Wheels, Matthew Lee, Mark Stamp
Faculty Publications, Computer Science
Suppose two particles occupy distinct vertices of a wheel graph and at each step the two particles move independently to adjacent vertices. In this paper we find the expected number of moves until the particles land on the same vertex.
How I Got Gnarly, Rudy Rucker
How I Got Gnarly, Rudy Rucker
SWITCH
The article describes how Rudy Rucker’s curious interest in celluar automata led to his career in mathematical computer science at San José State University. After conducting interviews on the theory of cellular automata as a freelance writer, he felt compelled to be involved in this great intellectual revolution in computer-aided experimental mathematics. Committed to reinventing himself, Rucker's interactions with mathematicians inspired him to write “Mind Tools”, a book that surveys mathematics from the standpoint that is information. After publishing his book, in 1987, he was eventually offered a position at SJSU in the Mathematics and Computer Science department. With assistance …
Gnarled Defined, Rudy Rucker
Gnarled Defined, Rudy Rucker
SWITCH
The article is a reflection of the author’s conception of the term ‘gnarly’, extending the term’s meaning from its origins in California surfer slang. 'Gnarly' is often used in a colloquial context, however, the author believes that the term is able to be used in an academic field as it pertains to outcomes and results of equations. Discussions towards the application of the term 'gnarly' showcase how it can be used in a scientific, mathematical, and artistic context through seemingly random patterns. In order to be gnarly, things must lie and exist between the realm of orderly and chaotic often …
Virtual Celluoid, Switch Staffs
Virtual Celluoid, Switch Staffs
SWITCH
The article is an analysis of the author’s research pertaining to films relating to or containing the concept of virtual reality. The author lists several films such as Johnny Mnemnonic, Virtuosity, The Net, and Disclosure and provides a brief synopsis and review of each movie. Each film explains the concept of virtual reality through differing plots and methods such as cyberspace, progressive software, and artificial intelligence. The author also gives their own insight into and ratings of the films, explaining what they think is the most relatable in terms of overall storyline as well as how realisticly the movie portrays …
Vr Products, P.D. Quick
Vr Products, P.D. Quick
SWITCH
The article is an analysis of the author’s experience testing several virtual reality items at Siggraph, an annual convention displaying computer machinery and interactive technology products. The author explains each device and how they work, the company behind the invention, as well as how it can help with future technological advancements. Several products are explained in more depth; the i-Glasses by Virtual I/O, Red Planet by Virtual World Entertainment Inc., Venturer S-2 by Thomson Entertainment Systems, and several more. Each item explores virtual reality in differing ways such as interactive video games, more user-friendly 3D modeling, and virtual movie theater …
Analysis Of The Convergence History Of Fluid Flow Through Nozzles With Shocks, Mohammad Saleem, A Cheer, M Hafez, T Pulliam
Analysis Of The Convergence History Of Fluid Flow Through Nozzles With Shocks, Mohammad Saleem, A Cheer, M Hafez, T Pulliam
Mohammad Saleem
"Convergence of iterative methods for the solution of the steady quasi-one-dimensional nozzle problem with shocks is considered. The finite-difference algorithms obtained from implicit schemes are used to approximate both the Euler and Navier-Stokes Equations. These algorithms are investigated for stability and convergence characteristics. The numerical methods are broken down into their matrix-vector components and then analyzed by examining a subset of the eigensystem using a method based on the Arnoldi process. The eigenvalues obtained by this method are accurate to within 5 digits for the largest ones and to within 2 digits for the ones smaller in magnitude compared the …