2019-20 MATRIX Annals (MATRIX Book Series, 4)

Preface
Contents
I Refereed Articles
	Part 1 Topology of Manifolds: Interactions Between High and Low Dimensions
		1
Connected sum decompositions of high-dimensional manifolds
			1 Introduction
			2 The connected sum operation
			3 Wall’s work on highly connected manifolds
			4 Thickenings of finite CW-complexes
				4.1 Thickenings of finite CW-complexes
				4.2 Boundaries of thickenings of finite complexes
				4.3 5-dimensional thickenings
			5 Finite 2-complexes, group presentations and the D2-problem
				5.1 Proof of Theorem 9
				5.2 Proof of Theorem 10
				5.3 The D2 problem
			6 Simply-connected complexes
			7 Prime manifolds
			8 Questions and problems
			References
		2
The Levine-Tristram signature: a survey
			1 Introduction
			2 Definition and properties
				2.1 The definition via Seifert surfaces
				2.2 Properties of the signature and nullity
				2.3 Lower bounds on the unlinking number
				2.4 Concordance invariance and the Murasugi-Tristram
inequalities
			3 4-dimensional definitions of the signature
				3.1 Signatures via exteriors of surfaces in the 4-ball
				3.2 Signatures as invariants of the 0-framed surgery
			4 Signatures via pairings on infinite cyclic covers
				4.1 Milnor signatures
				4.2 Signatures via the Blanchfield pairing
			5 Two additional constructions
				5.1 The Casson-Lin invariant
				5.2 The Gambaudo-Ghys formula
			References
		3 PD_4-complexes and 2-dimensional duality groups
			1 Introduction
			2 Modules and group rings
			3 The Whitehead functor and hermitian pairings
			4 Postnikov stages
			5 PD_4-complexes and intersection pairings
			6 Minimal models
			7 Existence of strongly minimal models
			8 Reduction
			9 Realization of pairings
			10 Strongly minimal models with p2 = 0
			11 Strongly minimal models with p virtually free
			12 Strongly minimal models with p one-ended
			13 Semidirect products and mapping tori
			14 Groups of cohomological dimension 2
			15 Realizing k-invariants
			16 PD_2-groups
			17 Cup products
			18 Orbits of the k-invariant
			19 Verifying the torsion condition for Z*_m
			20 4-manifolds and 2-knots
			21 Some questions
			References
		4 Topologically flat embedded 2-spheres in specific
simply connected 4-manifolds
			Introduction
			References
		5
Trisections of 5-Manifolds
			1 Introduction
			2 Trisecting Closed 5-Manifolds
				2.1 Trisections of Closed 4-Manifolds
				2.2 Trisections of Closed 5-Manifolds
			3 Trisecting 5-Manifolds with Boundary
				3.1 Gluing Cobordisms
				3.2 Standard Trisections
				3.3 Trisection Stabilization
				3.4 Morse Theory for Manifolds with Boundary
				3.5 Index-1
				3.6 Index-2
				3.7 Index-3
				3.8 Index-4
			References
		6
The octonionic projective plane
			1 Introduction
			2 Construction of O
			3 Construction of OP^2
				3.1 Manifold structure
				3.2 The projective line OP^1
				3.3 CW structure
			4 Cohomology of OP^2
				4.1 Connection with the Hopf invariant 1 problem
				4.2 Non-existence of higher octonionic projective spaces
				4.3 The story continues
			References
		7
Null-homologous twisting and the algebraic genus
			1 Introduction
			2 Properties of the algebraic genus
			3 Decreasing the algebraic genus
			4 Satellite knots
			5 Torus knots
			6 Anisotropic Seifert forms
			References
		8
A slicing obstruction from the 10/8+4 theorem
			1 Introduction
			2 The slicing obstruction
			References
	Part 2
Ergodic Theory, Diophantine Approximation and Related Topics
		9 A generalised multidimensional Jarník-Besicovitch theorem
			1 Localised Jarník-Besicovitch theorem
			2 Proof
				2.1 The upper bound
				2.2 The lower bound
			References
	Part 3
Influencing Public Health Policy with Data-informed Mathematical Models Of Infectious Diseases
		10 Model structures and structural identifiability: What? Why? How?
			1 Introduction
				1.1 Notation
			2 Preliminaries
				2.1 State-space structures
				2.2 Continuous-time linear, time-invariant structures
				2.3 Features of the states and outputs of a controlled LTI structure
			3 Testing an uncontrolled structure for structural global identifiability
				3.1 The Transfer Function Approach
				3.2 A demonstration of the testing of an uncontrolled LTI structure for SGI
			4 Testing controlled structures for structural global identifiability
				4.1 A demonstration of the testing of a controlled LTI structure for SGI when invariants are accessible from outputs
				4.2 A demonstration of the testing of a controlled LTI structure for SGI when invariants are not accessible from outputs
			5 Concluding remarks
			References
	Part 4
International Workshop on Spatial Statistics
		11
Spatial modelling of linear regression coefficients for gauge measurements against satellite estimates
			1 Introduction
			2 Methodology
			3 Results
			4 Conclusion
			References
	Part 5
Mathematics of Physiological Rhythms
		12 The new frontier of network physiology: Emerging physiologic states in health and disease from integrated organ network interactions
			1 Introduction
			2 Method
				2.1 Data
				2.2 Time Delay Stability (TDS) Method
				2.3 Averaging procedure for assessing links strength in physiological networks
			3 Results
				3.1 Networks of brain rhythms interactions across cortical locations
				3.2 Network interactions among brain rhythms within cortical areas
				3.3 Coexisting networks of brain rhythm interactions represent different types of physiologic coupling
				3.4 Dynamics of brain-organs interactions
				3.5 Network integration of interactions between the brain and peripheral organ systems
			4 Summary
			References
		13 Modelling oscillating living systems: Cell energy metabolism as weighted networks of nonautonomous oscillators
			1 Introduction
			2 Principles of an alternative approach
			3 Modelling a cell’s energy metabolism
			4 Outlook
			References
		14 A time-series approach to assess physiological and biomechanical regulatory mechanisms
			1 Introduction
			2 Selected physiological and biomechanical regulatory mechanisms
				2.1 Physiological regulation of body temperature
				2.2 Physiological regulation of blood oxygen saturation
				2.3 Physiological regulation of blood pressure
				2.4 Biomechanical regulation of gait
			3 Discussion
			4 Conclusions
			References
		15 InterCriteria Analysis Approach as a Tool for Promising Decision Making in Physiological Rhythms
			1 Introduction
			2 Brief description of ICrA
			3 ICrAData software package description
			4 ICrA applications in biomedical research and physiologicalrhythms
			5 Conclusions
			References
		16 “Ome” sweet “ome”: From the Genome to the Conductome
			1 The Micro-omes
			2 Disease-omes: relating the micro to the macro
			3 Omes from an Ecological perspective
			4 The Conductome
			References
		17 Delay-differential equations for glucose-insulin regulation
			1 Introduction
			2 The Model
			3 Periodic and asymptotically stable behaviour in glucose-insulin regulation system
			4 Conclusions
			References
	Part 6
Conservation Laws, Interfaces and Mixing
		18 Effect of adiabatic index on Richtmyer-Meshkov flows induced by strong shocks
			1 Introduction
				1.1 Motivation
				1.2 Approach
				1.3 RMI Dynamics
				1.4 Parameters of the System
				1.5 Parameter Regime
			2 Methods
				2.1 Theoretical Approaches
				2.2 Smoothed Particle Hydrodynamics Simulations
			3 Results
				3.1 Background Motion for Planar Interface Case
				3.2 Initial Amplitude Growth Rate for Perturbed Interface
				3.3 Discussion and Conclusion
			References
		19 Compressibility Effect on Markstein Number for a Flame front in Long-Wavelength Approximation
			1 Introduction
			2 Non-Dimensional Governing Equations
				2.1 Perturbations in Hydrodynamic Zone
				2.2 Long-Wavelength Approximation
			3 Equations in Preheat Zone
				3.1 Steady Planar Flow
				3.2 Perturbations with Translational Symmetry
			4 Boundary Condition of Mass Flux
				4.1 Matching Condition
				4.2 Low-Mach-Number Limit
				4.3 Compressibility Effect
			5 Effect of Compressible Markstein Number on DLI
			6 Conclusions
			References
		20 Computational fluid dynamics modelling of a transient solids concentration in a lagoon
			1 Introduction
			2 Governing equations
			3 Results and Discussion
			4 Conclusion
			References
		21 Regular and Singular Behaviours and New
Morphologies in the Rayleigh Taylor Instability
			1 Introduction
				1.1 Rayleigh Taylor Instability
			2 Theoretical Approach
				2.1 Governing Equations
				2.2 Interface Conditions
				2.3 Large Scale Dynamics
				2.4 Group Theory
				2.5 The Moments Expansion
				2.6 The Dynamical System
				2.7 Early Time Solutions
				2.8 Nonlinear Dynamics
			3 Bubble Dynamics
			4 Spike Dynamics
			5 Conclusion
			References
		22
The extended Prandtl closure model applied to the two-dimensional turbulent classical far wake
			1 Introduction
			2 Mathematical model for the two-dimensional turbulent classical far wake
			3 Similarity solutions
			4 Numerical results
			5 Further work and conclusions
			References
		23 Mixing, tunnelling and the direction of time in the context of Reichenbach's principles
			1 Introduction
			2 The direction of time and the second law
				2.1 Why don’t we remember the future?
				2.2 Parallelism of entropy increase
				2.3 The principle of the common cause
				2.4 Chemical kinetics and causality
			3 Why mixing is time-directional?
				3.1 Importance of the initial conditions
				3.2 Why is the principle of parallelism of entropy increase essential?
				3.3 The time primer
			4 Discussion
				4.1 Environmental time priming
				4.2 Intrinsic mechanisms of time priming
				4.3 Testing the symmetry of time priming.
			5 Conclusions
			References
			Appendix. Quantum tunnelling and decoherence
		24 Controlling stability of longwave oscillatory Marangoni patterns
			1 Introduction
			2 Amplitude Equations
			3 Weakly Nonlinear Analysis
				3.1 Basic Expansions
				3.2 Interaction of Waves
				3.3 Nonlinear Feedback Control
			4 Conclusions and Discussion
			References
		25 Rigorous modelling of nonlocal interactions determines a macroscale advection-diffusion PDE
			1 Introduction
			2 Zappa shear dispersion
			3 Many kernels generate local models
				3.1 Rewrite the equations for local dynamics
				3.2 Local-to-global system modelling theory
				3.3 Account for the coupling remainder
			4 Compact analysis, and connect to well-known methodology
			5 Conclusion
			6 Appendix: Computer algebra derives macroscale PDE
			References
		26 Influence of an oblique magnetic field on planar flame front instability
			1 introduction
			2 Basic equations and jump conditions
			3 Magnetic DLI subject to tangential magnetic field
				3.1 Hydromagnetic waves
				3.2 Linear perturbations in unburned and burned regions
				3.3 Jump conditions and dispersion relation
				3.4 Markstein effect
			4 Magnetic DLI subject to oblique magnetic field
				4.1 Jump of basic state
				4.2 Hydromagnetic waves
				4.3 Linear perturbations in unburned and burned regions
				4.4 Jump of perturbation fields
				4.5 Growth rate
			5 Conclusion
			References
		27 Numerical Study of Crystal Growth in
Reaction-Diffusion Systems using Front
Tracking
			1 Introduction
			2 Front Tracking
			3 Numerical Method
			4 Numerical Results
				4.1 Effects of k_AB and k
				4.2 Effect of the diffusivities
				4.3 Effect of the Damkohler Number
				4.4 Effect of the equilibrium concentration
			5 Summary and Conclusions
			References
		28 Numerical Study of Center of Reaction Front for Reaction-Diffusion System nA + mB → C with Arbitrary Diffusivities
			1 Introduction
			2 Numerical Method
			3 Results
				3.1 Numerical Results for DbDa= 1
				3.2 Numerical Results for DbDa 6= 1
			4 Summary and Conclusion
			References
	Part 7
Structural Graph Theory Downunder
		29 Subdivided Claws and the Clique-Stable Set Separation Property
			1 Introduction
			2 The Proof
			References
		30 Notes on tree- and path-chromatic number
			1 Introduction
			2 Separating χ, path-χ and tree-χ
			3 Hadwiger’s Conjecture for tree-χ and path-χ
			4 K_5-minor-free graphs
			5 Computing tree-χ and path-χ
			References
		31 Note on Hedetniemi's conjecture and the Poljak-Rödl function
			1 Introduction
			2 Exponential graph
			3 Shitov’s Theorem
			4 The Poljak-Rödl function
			5 Lower bound for f (n)
			References
		32 Notes on Graph Product Structure Theory
			1 Introduction
			2 Minor-Closed Classes
			3 Non-Minor Closed Classes
			4 Polynomial Growth
			5 Polynomial Expansion
			6 Bounded Expansion
			7 Geometric Graph Classes
			8 Open Problems
				8.1 Algorithmic Questions
			References
	Part 8
Harmonic Analysis and Dispersive PDEs: Problems and Progress
		33 A note on bilinear wave-Schrödinger interactions
			1 Introduction
			2 Proof of Theorem 2
			3 Counter Examples
				3.1 Proof of Theorem 3
				3.2 Proof of Theorem 4
			References
		34 A note on the scattering for 3D quantum Zakharov system with non-radial data in L^2
			1 Introduction
				1.1 Notation
				1.2 Normal form transform
			2 Angular Strichartz estimates and nonlinear estimates
			3 Nonlinear Estimates
			4 Scattering in L^2
			References
	Part 9
Tropical Geometry and Mirror Symmetry
		35 Algebraic and symplectic view point on compactifications of two-dimensional cluster varieties of finite type
			1 Introduction
			2 Mutations in algebraic geometry
				2.1 Cluster varieties
				2.2 Positive polytopes
				2.3 Canonical scattering diagrams
				2.4 Type B_2 and G_2
			3 Mutations in symplectic geometry
				3.1 Cluster varieties and Mirror Symmetry
				3.2 Compactifications of Cluster varieties
			References
		36 Observations on disks with tropical Lagrangian boundary
			1 Tropical Lagrangians and Holomorphic Disks
			2 Disks via sections of Lagrangian fibrations
			3 Towards computing Floer Support
			References
		37 Compactifying torus fibrations over integral affine manifolds with singularities
			1 Introduction
			2 Integral affine manifolds with singularities
			3 Local models
			4 Gluing the torus fibration with parameters
			5 Canonical Calabi-Yau families and their Kato-Nakayama spaces
			References
II Other Contributed Articles
	Part 10
Topology of Manifolds: Interactions Between High And Low Dimensions
		38 Graphical neighborhoods of spatial graphs
			1 Introduction
			2 Tubular neighborhoods
			3 Definition and existence of graphical neighborhoods
			4 Properties of Graphical Neighborhoods
			5 Uniqueness of graphical neighborhoods
				5.1 Proof of Theorem 3
			References
		39
Open Problems in the Topology of Manifolds
			Introduction
			References
	Part 11
Aperiodic Order meets Number Theory
		40 Aperiodic order meets number theory: Origin and structure of the field
			References
		41
Delone sets on spirals
			References
		42
Topological methods for symbolic discrepancy
			References
		43
Extended symmetry groups of multidimensional subshifts with hierarchical structure
			References
		44
Algebraic invariants for group actions on the Cantor set
			1 Minimal Cantor systems
			2 Algebraic properties of the topological full group of Toeplitz subshifts
				2.1 Toeplitz G-subshifts
			3 Algebraic properties of the group of automorphisms of a group action on the Cantor set
			References
		45 Lyapunov exponents: recent applications of Fürstenberg’s theorem in spectral theory
			1 The Anderson model
			2 Main results
			3 Lyapunov exponents: positivity and large deviation estimates
			4 Transfer matrices, Dirichlet determinants, and Green’s functions
			References
		46
Extended symmetries of Markov subgroups
			References
		47
Renormalisation for inflation tilings I: General theory
			References
		48 Problems in number theory related to aperiodic order
			References
		49 Pure point spectrum and regular model sets in substitution tilings on R^d
			References
		50 Automatic sequences are orthogonal to aperiodic
multiplicative functions
			References
		51
Similarity isometries of shifted lattices and point packings
			1 Some preliminaries
			2 Symmetry groups of point packings
			3 Similarity isometries of shifted lattices and point packings
			References
		52
Renormalisation for inflation tilings II: Connections to number theory
			References
		53
The Penrose and the Taylor–Socolar tilings, and first steps to beyond
			References
		54 Scaling properties of the Thue–Morse measure:
A summary
			References
		55
Weak model sets
			1 Square-free integers
			2 Weak model sets of maximal density
			References
		56
Doubly sparse measures on locally compact Abelian groups
			References
		57
The mean-median map
			References
		58
Similar sublattices and submodules
			References
	Part 12
Ergodic Theory, Diophantine Approximation and Related Topics
		59
A diffraction abstraction
			1 Introduction
			2 Three examples: diffraction measures of pure type
			3 An extended diffraction example: the Thue–Morse sequence
			4 A non-diffractive example: the Stern sequence
			5 Concluding remark
			References
	Part 13
Early Career Researchers Workshop on Geometric Analysis and PDEs
		60
Extrinsic curvature flows and applications
			1 Introduction
			2 Curvature functions
			3 Some hypersurface geometry
				3.1 Conventions on Riemannian geometry
			4 Classical inverse curvature flows
			5 Alexandrov-Fenchel inequalities
			References
		61
Short time existence for higher order curvature flows with and without boundary conditions
			1 Introduction
				1.1 The curvature flows of open curves with Neumann boundary condition
				1.2 The length-constrained curve diffusion flow of closed curves
			2 Short time existence for higher order curvature flows with Neumann boundary condition
				2.1 A sixth order flow of plane curves with boundary condition
				2.2 Higher order flows of plane curves with boundary conditions
			3 Short time existence for flow of closed planar curves without boundary
			References
	Part 14 Harmonic Analysis and Dispersive PDEs: Problems and Progress
		62
Hankel transforms and weak dispersion
			1 Introduction
			2 Fractional Schr¨odinger in Aharonov-Bohm field
				2.1 The massless Dirac-Coulomb equation
				2.2 The massless Dirac equation in Aharonov-Bohm field
			References
		63
A priori bounds for the kinetic DNLS
			1 Introduction
			2 Energy conservation
			References
64 Correction to: A priori bounds
for the kinetic DNLS
65
Correction to: Connected sum decompositions of high-dimensional manifolds