Diversity of graphs with highly variable connectivity

A popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large-scale connectivity. While it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent, the relationship between competing descriptions is not entirely understood. This paper lends perspective on this problem by showing how the degree sequence and other constraints (e.g., connectedness, no self-loops or parallel edges) on a particular graph play a primary role in dictating many features, including its correlation structure. Building on recent work, we show how a simple structural metric characterizes key differences between graphs having the same degree sequence. More broadly, we show how the (often implicit) choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions

Maximum Weight Spectrum Codes

In the recent work \cite{shi18}, a combinatorial problem concerning linear codes over a finite field \F_q was introduced. In that work the authors studied the weight set of an $[n,k]_q$ linear code, that is the set of non-zero distinct Hamming weights, showing that its cardinality is upper bounded by $\frac{q^k-1}{q-1}$. They showed that this bound was sharp in the case $q=2$, and in the case $k=2$. They conjectured that the bound is sharp for every prime power $q$ and every positive integer $k$. In this work quickly establish the truth of this conjecture. We provide two proofs, each employing different construction techniques. The first relies on the geometric view of linear codes as systems of projective points. The second approach is purely algebraic. We establish some lower bounds on the length of codes that satisfy the conjecture, and the length of the new codes constructed here are discussed.Comment: 19 page

Maximum Distance Separable Codes and Arcs in Projective Spaces

Given any linear code $C$ over a finite field $GF(q)$ we show how $C$ can be described in a transparent and geometrical way by using the associated Bruen-Silverman code. Then, specializing to the case of MDS codes we use our new approach to offer improvements to the main results currently available concerning MDS extensions of linear MDS codes. We also sharply limit the possibilities for constructing long non-linear MDS codes.Comment: 18 Pages; co-author added; some results updated; references adde

Contrasting Views of Complexity and Their Implications For Network-Centric Infrastructures

There exists a widely recognized need to better understand and manage complex “systems of systems,” ranging from biology, ecology, and medicine to network-centric technologies. This is motivating the search for universal laws of highly evolved systems and driving demand for new mathematics and methods that are consistent, integrative, and predictive. However, the theoretical frameworks available today are not merely fragmented but sometimes contradictory and incompatible. We argue that complexity arises in highly evolved biological and technological systems primarily to provide mechanisms to create robustness. However, this complexity itself can be a source of new fragility, leading to “robust yet fragile” tradeoffs in system design. We focus on the role of robustness and architecture in networked infrastructures, and we highlight recent advances in the theory of distributed control driven by network technologies. This view of complexity in highly organized technological and biological systems is fundamentally different from the dominant perspective in the mainstream sciences, which downplays function, constraints, and tradeoffs, and tends to minimize the role of organization and design

Piezomorphic materials

The development of stress-induced morphing materials which are described as piezomorphic materials is reported. The development of a piezomorphic material is achieved by introducing spatial dependency into the compliance matrix describing the elastic response of a material capable of undergoing large strain deformation. In other words, it is necessary to produce an elastically gradient material. This is achieved through modification of the microstructure of the compliant material to display gradient topology. Examples of polymeric (polyurethane) foam and microporous polymer (expanded polytetrafluoroethylene) piezomorphic materials are presented here. These materials open up new morphing applications where dramatic shape changes can be triggered by mechanical stress

Deleterious Changes To The T Cell Compartment Following Immunotherapy

Abstract: The combination of anti-CD40 and interleukin-2 is a potent immunotherapy regimen that results in synergistic anti-tumor responses. This has been demonstrated in multiple murine tumor models of metastatic disease with various tumor types. The primary anti-tumor responses elicited by this combination are capable of inducing tumor regression and prolonged survival. However, the generation of secondary T cell responses after irradiated tumor vaccine is abrogated after anti-CD40 and IL-2. This abrogation also occurs after other immunotherapeutic approaches that prompt the production of large amounts of interferon-gamma (IFNγ). These observations correlated with a significant skewing of the T cell compartment. First, we observed a selective decreased of conventional CD4+ T cells following immunotherapy. Second, we observed a more than five fold expansion of memory phenotype cells which were incapable of generating responses to new antigens. The data presented here suggest that despite initial tumor regression, potent systemic immunotherapy may impair responses to new immunological challenges.Selective CD4+ T cell death after immunotherapy results in an alteration in the ratio of CD4+ T cells to CD8+ T cells and impairs the generation of a secondary immune response. Our data suggest that this phenomenon after immunotherapy is the result of the selective upregulation of programmed death-1 (PD-1) and its IFNγ responsive ligand, B7-H1. We show that the expression of PD-1 is restricted to the surface of Foxp3neg CD4+ T cells and that CD8+ T cells and CD4+ Foxp3+ regulatory T cells remain PD-1 low after immunotherapy. Furthermore, the expression of PD-1 correlates with CD4+ T cell death after immunotherapy. In the absence of IFNγ either by the use of mice lacking IFNγ (IFNγ-/-) or the receptor for IFNγ (IFNγR-/-), B7-H1 remains low after immunotherapy. Subsequently, CD4+ T cells expand in response to immunotherapy in the absence of IFNγ responsive B7-H1. We observed a significant expansion of memory phenotype T cells after cytokine based immunotherapy which correlated with impairment of proliferative responses to new antigens. Memory T cells are more sensitive to cytokine stimulation than naïve T cells. Therefore, we used a young thymectomized mouse model to determine if pre-existing memory T cells were preferentially expanded by immunotherapy. The thymectomized mouse model allowed us to evaluate long term T cell responses to immunotherapy in the absence of de novo T cell generation. Using this model, we observed expansion of memory T cells, within both the CD4+ and CD8+ T cell compartments without a major sacrifice of the size of the naïve T cell compartment. Compared to memory T cell expansion, there was relatively small change in the naïve T cell compartment. Naïve CD8+ T cell numbers were unchanged by immunotherapy and naïve CD4+ T cells were decreased by less than half. Memory T cells were still significantly expanded after 30 days of rest. Furthermore, the persistent expansion of memory T cells correlated with a maintained decrease in proliferative function to new antigens. Taken together, these data demonstrate a long term consequence of immunotherapy to the phenotypic makeup and, importantly, the function of the T cell compartment

On the Weights of General MDS Codes

The weight spectra of MDS codes of length $n$ and dimension $k$ over the arbitrary alphabets are studied. For all $q$-ary MDS codes of dimension $k$ containing the zero codeword, it is shown that all $k$ weights from $n$ to $n-k+1$ are realized. The remaining case $n=q+k-1$ is also determined. Additionally, we prove that all binary MDS codes are equivalent to linear MDS codes. The proofs are combinatorial, and self contained

A note on full weight spectrum codes

A linear $[n,k]_q$ code $C$ is said to be a full weight spectrum (FWS) code if there exist codewords of each nonzero weight less than or equal to $n$. In this brief communication we determine necessary and sufficient conditions for the existence of linear $[n,k]_q$ full weight spectrum (FWS) codes. Central to our approach is the geometric view of linear codes, whereby columns of a generator matrix correspond to points in $PG(k-1,q)$