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How likely is $G(n;p)$ to have a less-than-typical number of triangles? This is a foundational question in non-linear large deviation theory. When $p \ll 1/\sqrt{n}$ or $p \gg 1/\sqrt{n}$ the answer is fairly well-understood, with Janson's inequality applying in the former case and regularity- or container-based methods applying in the latter. We study the regime $p=c/\sqrt{n}$, with $c$ fixed, with the large deviation event having at most $\eta$ times the expected number of triangles, for a fixed $\eta \in [0,1)$.

We prove explicit formula for the log-asymptotics of the event in question, for a wide range of pairs $(c,\eta)$. In particular, we show that for sufficiently small $\eta$ (including the triangle-free case $\eta=0$) there is a phase transition as $c$ increases, in the sense of a non-analytic point in the rate function. On the other hand, if $\eta > 1/2$, then there is no phase transition.

As corollaries, we obtain analogous results for the $G(n;m)$ model, when $m = Cn^{3/2}$. In contrast to the $G(n;p)$ case, we show that a phase transition occurs as $C$ increases for \textit{all} $\eta$.

Finally, we show that the probability of $G(n;m)$ being triangle free, where $m=Cn^{3/2}$ for a sufficiently small constant $C$, conforms to a Poisson heuristic.

Joint with Matthew Jenssen, Will Perkins, and Aditya Potukuchi. Based on arXiv:2410.22951 and arXiv:2411.18563.

Amyotrophic lateral sclerosis (ALS) is a fatal motor neuron disease characterized by TDP-43 mislocalization, aggregation, and disruption of neuromuscular junctions (NMJs). We have identified a key pathological mechanism involving the accumulation of TDP-43 in axons, which impairs local protein synthesis and drives NMJ degeneration. This process is linked to dysregulated muscle-derived exosomes carrying miR-126a-5p, essential for maintaining proper nerve-muscle communication. In ALS, reduced levels of miR-126a-5p lead to abnormal TDP-43 synthesis in axons. Restoring miR-126 in vivo and in human co-culture systems provides neuroprotection. Our findings highlight a transcellular signaling axis between muscles and neurons, offering new insights into NMJ maintenance and a potential foundation for ALS therapeutic strategies.

The efficiency of a thermoelectric (TE) device depends on the extent to which, in response to a given temperature gradient, its electron/hole transport symmetry at the Fermi level is broken. This requirement makes molecular junctions highly promising for TE applications due to their non-linear transmission properties. Yet, in the absence of an efficient method to tune the position of the Fermi level within the transmission landscape of these junctions, the Seebeck values of metal-molecules-metal junctions are typically |S|≤50μV/K, while based on their electrical and thermal conductance, it should be |S|≥1mV/K to be relevant for applications. I will describe our effort to reach this goal, which recently has culminated in molecular junctions with the semimetal Bismuth (Bi) as one of their leads and with |S| in the required mV/K range. Unlike the conventional approach to tweak the transmission properties by modifying the structure of the molecules, here the high Seebeck is a result of molecularly induced deterministic changes in the density of states within the Bi lead in the form of quantized 2D interfacial states, that in turn result in highly non-linear transport properties. I will argue that this effect is just one glimpse into the very rich and complex terra incognita of molecular layers on semimetals.

Viral infections pose a major threat to human health. Vaccines protect from specificinfections, yet newly emerging or pandemic viral strains that exhibit genetic drift or reassortmentof genes preclude immediate responses using a vaccine strategy. Moreover, for SARS CoV-2,although current vaccines reduce severity of disease, they do not protect from re-infection,resulting in persistent community transmission and outbreaks. The emergence of drug resistancealso mitigates against pathogen-specific antiviral drugs. A complementary strategy focusing onthe host not the pathogen is the basis for development of broad-spectrum antivirals.Our immediate response to any and all virus infections is the immediate production of interferon(IFN). Data reveal that the robustness of an IFN response to respiratory infections, determinesthe outcome – an aggressive or mild infection. We provide evidence that an IFN response to viralinfection, and/or IFN treatment, induces an activated phenotype in target cells that results in anantiviral state and an optimized innate immune response, regardless of the virus. We extendedthese findings to examine the therapeutic potential of IFN treatment in hospitalized individualsinfected with SARS and showed that IFN treatment accelerated viral clearance and reduced lungabnormalities. Similarly, using human lung explants, IFN treatment cleared infection againstH5N1 avian and pandemic H1N1 influenza strains. During the Ebola virus outbreak in WestAfrica, we conducted a clinical study in Guinea and provided evidence of increased survivalassociated with IFN treatment. At the start of the COVID-19 pandemic we undertook a clinicalstudy in Wuhan, China, providing evidence that early treatment with an inhaled IFN acceleratedviral clearance, reduced inflammation and also reduced lung abnormalities. Given that limitingtransmission is the solution to shutting down any outbreak, we next conducted a clinical trial todetermine whether IFN treatment of SARS CoV-2 exposed, but uninfected individuals, wouldprotect from infection. We provide evidence that prophylactic treatment with IFN limitshousehold transmission, being most effective when the infected case in the household has a highviral burden.

During her conversation, Shira will share her personal journey and share what has led her to each decision and what are her key learnings.She will also share more about her position today as a Partner at Vintage, leading their investments in Healthcare and Climate.Join our ABC CHATS, Where CEOs share their ABC’s on scientific leadership, breakthroughs and failures throughout their personal stories