Multicolor Ramsey Number for Double Stars

For a graph $H$ and integer $k\ge1$, let $r(H;k)$ and $r_\ell(H;k)$ denote the $k$-color Ramsey number and list Ramsey number of $H$, respectively. Motivated by the work of Alon, Buci\'c, Kalvari, Kuperwasser and Szab\'o, who initiated the systematic study of list Ramsey numbers of graphs and hypergraphs, and conjectured that $r(K_{1,n};k)$ and $r_\ell(K_{1,n};k)$ are always equal, we study the $k$-color Ramsey number for double stars $S(n,m)$, where $n\ge m\ge1$. To the best of our knowledge, little is known on the exact value of $r(S(n,m);k)$ when $k\ge3$. A classic result of Erd\H{o}s and Graham from 1975 asserts that $r(T;k)>k(n-1)+1$ for every tree $T$ with $n\ge 1$ edges and $k$ sufficiently large such that $n$ divides $k-1$. Using a folklore double counting argument in set system and the edge chromatic number of complete graphs, we prove that if $k$ is odd and $n$ is sufficiently large compared with $m$ and $k$, then $$r(S(n,m);k)=kn+m+2.$$ This is a step in our effort to determine whether $r(S(n,m);k)$ and $r_\ell(S(n,m);k)$ are always equal, which remains wide open. We also prove that $r(S^m_n;k)=k(n-1)+m+2$ if $k$ is odd and $n$ is sufficiently large compared with $m$ and $k$, where $1\le m\le n$ and $S^m_n$ is obtained from $K_{1, n}$ by subdividing $m$ edges each exactly once. We end the paper with some observations towards the list Ramsey number for $S(n,m)$ and $S^m_n$

Strain stiffening universality in composite hydrogels and tissues

Soft biological tissues exhibit a remarkable resilience to large mechanical loads, a property which is associated with the strain stiffening capability of the biopolymer networks that structurally support the tissues. Yet, recent studies have shown that composite systems such as tissues and blood clots exhibit mechanical properties that contradict those of the polymer matrix - demonstrating stiffening in compression, but softening in shear and tension. The microscopic basis of this apparent paradox remains poorly understood. We show that composite hydrogels and tissues do indeed exhibit non-linear elastic stiffening in shear - which is governed by the stretching of the polymer chains in the matrix - and that it is driven by the same mechanism that drives compression stiffening. However, we show that the non-linear elastic stiffening in composite hydrogels and tissues is masked by mechanical dissipation arising from filler-polymer interactions known as the Mullins effect, and we introduce a method to characterize the non-linear elasticity of the composites in isolation from this overall strain softening response through large-amplitude oscillatory shear experiments. We present a comprehensive characterization of the non-linear elastic strain stiffening of composite hydrogels and soft tissues, and show that the strain stiffening in shear and compression are both governed by universal strain amplification factors that depend on essential properties of the composite system, such as the filler concentration and the filler-polymer interaction strength. These results elucidate the microscopic mechanisms governing the non-linear mechanics of tissues, which provides design principles for engineering tissue-mimetic soft materials, and have broad implications for cell-matrix mechanotransduction in living tissues

Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Gels made of telechelic polymers connected by reversible crosslinkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low valence crosslinkers, while larger supramolecular crosslinkers bring about much slower dynamics involving a wide distribution of time scales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring crosslinkers all disconnect. Larger crosslinkers allow for a greater average number of bonds connecting them, but also generate more heterogeneity. We characterize the resulting distribution of relaxation time scales analytically, and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of crosslinker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any crosslinker size and could thus be harnessed for the rational design of complex viscoelastic materials.Comment: 6 pages 5 figures 1 table for the main text and 9 pages 7 figures for the supplemen

DRINET –an Online Drought Research and Collaboration Environment

DRINET is a research environment for collecting and disseminating local to regional scale drought information while interoperating with other resources and tools. The disseminated information via the DRINET will be based on a comprehensive evaluation of causal factors for short and long term droughts, as well as on a standardization of data formats and collection practices. It thus lays the foundation for investigating and providing improved drought risk and trigger indicators

Therapeutic rAAVrh10 Mediated SOD1 Silencing in Adult SOD1(G93A) Mice and Nonhuman Primates

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease; survival in ALS is typically 3-5 years. No treatment extends patient survival by more than three months. Approximately 20% of familial ALS and 1-3% of sporadic ALS patients carry a mutation in the gene encoding superoxide dismutase 1 (SOD1). In a transgenic ALS mouse model expressing the mutant SOD1(G93A) protein, silencing the SOD1 gene prolongs survival. One study reports a therapeutic effect of silencing the SOD1 gene in systemically treated adult ALS mice; this was achieved with a short hairpin RNA, a silencing molecule that has raised multiple safety concerns, and recombinant adeno-associated virus (rAAV) 9. We report here a silencing method based on an artificial microRNA termed miR-SOD1 systemically delivered using adeno-associated virus rAAVrh10, a serotype with a demonstrated safety profile in CNS clinical trials. Silencing of SOD1 in adult SOD1(G93A) transgenic mice with this construct profoundly delayed both disease onset and death in the SOD1(G93A) mice, and significantly preserved muscle strength and motor and respiratory functions. We also document that intrathecal delivery of the same rAAVrh10-miR-SOD1 in nonhuman primates significantly and safely silences SOD1 in lower motor neurons. This study supports the view that rAAVrh10-miR-SOD1 merits further development for the treatment of SOD1-linked ALS in humans

Associations between differential aging and lifestyle, environment, current, and future health conditions : Findings from Canadian Longitudinal Study on Aging

Acknowledgement This research was made possible using the data/biospecimens collected by the Canadian Longitudinal Study on Aging (CLSA). Funding for the Canadian Longitudinal Study on Aging (CLSA) is provided by the Government of Canada through the Canadian Institutes of Health Research (CIHR) under grant reference: LSA 94473 and the Canada Foundation for Innovation, as well as the following provinces, Newfoundland, Nova Scotia, Quebec, Ontario, Manitoba, Alberta, and British Columbia. This research has been conducted using the CLSA dataset (Comprehensive Cohort), under Application Number 1906013. The CLSA is led by Drs. Parminder Raina, Christina Wolfson and Susan Kirkland.Peer reviewedPostprin