Amoeboid Transition Occurs in Mammilian Tumor Cells in Response to Changes in Spacial Confinement and Adhesion

In this dissertation, we review how plasticity in the modes of cell migration can occur in response to changes in the extracellular matrix. Different modes of migration exhibit varying characteristics, such as cell adhesion, membrane protrusion, and proteolysis, allowing tumor cells to adapt to their current extracellular environment, thus enhancing invasive behavior in response to different antitumorigenic therapies. The combination of various cell migration characteristics results in a distinct mode of single-cell migration, which, for single-cell migration, falls under two general modes, mesenchymal-traction-force motility or amoeboid-propulsion-squeeze motility. Mesenchymal-to-amoeboid transition is known to occur when tumor cells are in a softer matrix with low adhesion and in a high-confinement environment. Under these conditions the tumor cells exhibit higher levels of cortical myosin activity. Amoeboid migration is characterized by high cortical contractility, mediated by increased myosin activity along the cell cortex. Understanding how contractility is increased under changes in adhesion and confinement is important to uncover the possible mechanisms a tumor cell uses to optimize motility. Here, I will introduce a model that explores how the differential regulation of RhoGTPases (Rac1 and RhoA) is modulated with changes in cell-matrix adhesion and cell-matrix confinement to induce mesenchymal-to-amoeboid-transition. In the model, tumor cells in soft matrix are exposed to fewer ligands to which they can bind their integrins and activate Rac1. Loss of Rac1 activation in soft matrix inhibits lamellipodia formation, and the double-negative relationship between Rac1 and RhoA will shift towards RhoA to promote increase cortical myosin activity for amoeboid migration (Figure 1). Myosin activity is further enhanced under confinement through retrograde flow and recycling of transmembrane protein like integrin and syndecan, which results in increase of RhoA-mediated contractility for amoeboid migration

Stabilized reduced order models for low speed flows

This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis. Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs. To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.Esta tesis presenta un modelo de orden reducido estabilizado paran fluidos a baja velocidad utilizando un enfoque de multiescala variacional. Para desarrollar esta formulación utilizamos el método de elementos finitos para el modelo no reducido y una descomposición en autovalores del mismo para construir la base. Adicional a la formulación del modelo reducido, presentamos dos técnicas que podemos formular al utilizar este enfoque: una reducción adicional del dominio, basada en la reducción de la malla, donde usamos una técnica de refinamiento adaptativa y un esquema de descomposición de dominio para el modelo reducido. Para ilustrar y probar la formulación propuesta, utilizamos cuatro diferentes modelos fisicos: una ecuación de convección-difusión-reacción, la ecuación de Navier-Stokes para fluidos incompresibles, una aproximación de Boussinesq para la ecuación de Navier-Stokes, y una aproximación para números de Mach bajos de la ecuación de Navier-Stokes.Postprint (published version

Duality for Hermitean systems in R2n

In this paper, using the algebraic structure of the space of circulant (2 × 2) matrix, we characterize the dual of the (Frechet) space of germs of left Hermitean monogenic matrix functions in a compact set of Euclidean space with even di;ension. As an application we describe the dual space of the so-called h-monogenic functions satisfying simultaneously two Dirac type equations

Stabilized reduced order models for low speed flows

This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis. Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs. To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.Esta tesis presenta un modelo de orden reducido estabilizado paran fluidos a baja velocidad utilizando un enfoque de multiescala variacional. Para desarrollar esta formulación utilizamos el método de elementos finitos para el modelo no reducido y una descomposición en autovalores del mismo para construir la base. Adicional a la formulación del modelo reducido, presentamos dos técnicas que podemos formular al utilizar este enfoque: una reducción adicional del dominio, basada en la reducción de la malla, donde usamos una técnica de refinamiento adaptativa y un esquema de descomposición de dominio para el modelo reducido. Para ilustrar y probar la formulación propuesta, utilizamos cuatro diferentes modelos fisicos: una ecuación de convección-difusión-reacción, la ecuación de Navier-Stokes para fluidos incompresibles, una aproximación de Boussinesq para la ecuación de Navier-Stokes, y una aproximación para números de Mach bajos de la ecuación de Navier-Stokes

Clergy & Police a Semiotic Analysis of Clergy on Patrol

The Clergy On Patrol (COP) program is a collaboration between the Norfolk Police Department and community faith leaders of the Norfolk Urban Renewal Center. This study analyzed themes and patterns in the communicative relationship between police and clergy members, using a semiotic approach and the scholarship of intergroup communication. Additionally, an added secondary analysis of media coverage helped focus the results of the study using themes. This thesis merged the two semiotic analyses to examine a style of community policing that has lacked a closer eye. This thesis guided itself by the argument that clergy-police collaborative programs structure themselves around the assumption that faith-based organizations (FBOs) will provide community connection. Further, it is the assumption, by media and other agencies, that the presence of faith leaders taking part in police engagements is a positive method of rectifying issues of trust and miscommunication between community and law enforcement. A primary focus of this study serves to highlight this assumption in media texts, which contrasts with perceptions of participating members within the COP program in Norfolk. The study further argues the aspirational goals of the program outshine its current development, while still highlighting positive aspects of these programs. Guided by themes and principles in media communication studies, this thesis attempted to determine common communication problems hindering the collaborative efforts of clergy and police. Through the semiotic analyses, the result of this study found that COP and other programs framed a positive relationship between clergy and police. This relationship, like any, revealed to be less cohesive then speculated in the media. However, the accounts of clergy reaffirm a positive impact on the community despite a lack of empirical evidence. There is an even greater need to determine new ways of community engagement that may aid in reconnecting our men and women in uniform with their communities

Stabilized reduced order models for low speed flows

This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis. Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs. To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.Esta tesis presenta un modelo de orden reducido estabilizado paran fluidos a baja velocidad utilizando un enfoque de multiescala variacional. Para desarrollar esta formulación utilizamos el método de elementos finitos para el modelo no reducido y una descomposición en autovalores del mismo para construir la base. Adicional a la formulación del modelo reducido, presentamos dos técnicas que podemos formular al utilizar este enfoque: una reducción adicional del dominio, basada en la reducción de la malla, donde usamos una técnica de refinamiento adaptativa y un esquema de descomposición de dominio para el modelo reducido. Para ilustrar y probar la formulación propuesta, utilizamos cuatro diferentes modelos fisicos: una ecuación de convección-difusión-reacción, la ecuación de Navier-Stokes para fluidos incompresibles, una aproximación de Boussinesq para la ecuación de Navier-Stokes, y una aproximación para números de Mach bajos de la ecuación de Navier-Stokes

Generalized Moisil-Théodoresco systems and Cauchy integral decompositions

Let ℝ0,m+1(s) be the space of s-vectors (0≤s≤m+1) in the Clifford algebra ℝ0,m+1 constructed over the quadratic vector space ℝ0,m+1, let r,p,q∈ℕ with 0≤r≤m+1, 0≤p≤q, and r+2q≤m+1, and let ℝ0,m+1(r,p,q)=∑j=pq⨁ ℝ0,m+1(r+2j). Then, an ℝ0,m+1(r,p,q)-valued smooth function W defined in an open subset Ω⊂ℝm+1 is said to satisfy the generalized Moisil-Théodoresco system of type (r,p,q) if ∂xW=0 in Ω, where ∂x is the Dirac operator in ℝm+1. A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs. Furthermore, if Ω is bounded with boundary Γ, where Γ is an Ahlfors-David regular surface, and if W is a ℝ0,m+1(r,p,q)-valued Hölder continuous function on Γ, then necessary and sufficient conditions are given under which W admits on Γ a Cauchy integral decomposition W=W++W−