AI21 Labs, a startup formed by veterans from an elite tech unit in the IDF to build AI systems, announced on Thursday it raised $34.5 million in total equity capital to work on its AI-based writing solutions and offerings. The funding includes a seed round of $9.5 million in January 2019 and the latest round of $25 million led by Pitango First, the seed and early-stage fund of Pitango's investment platform. Pitango is Israel's largest venture capital fund and was co-founded by Chemi Peres, the son of former president Shimon Peres. The VC focuses on core technologies like deep tech, AI, and machine learning. Other investors in the latest funding round included TPY Capital, another VC headquartered in Tel Aviv.

The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed time $n$ may be observed. We consider here the problem of estimating $\gamma$ from this data. Let $\pi$ be the stationary distribution of $P$, and $\pi_\star = \min_x \pi(x)$. We show that if $n = \tilde{O}\bigl(\frac{1}{\gamma \pi_\star}\bigr)$, then $\gamma$ can be estimated to within multiplicative constants with high probability. When $\pi$ is uniform on $d$ states, this matches (up to logarithmic correction) a lower bound of $\tilde{\Omega}\bigl(\frac{d}{\gamma}\bigr)$ steps required for precise estimation of $\gamma$. Moreover, we provide the first procedure for computing a fully data-dependent interval, from a single finite-length trajectory of the chain, that traps the mixing time $t_{\text{mix}}$ of the chain at a prescribed confidence level. The interval does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time $t_{\text{relax}} = 1/\gamma$, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a $1/\sqrt{n}$ rate, where $n$ is the length of the sample path.

Former Israeli President Shimon Peres' condition was showing slight improvements after he suffered a major stroke, with his physicians saying Wednesday that he had regained consciousness and squeezed his doctor's hand, while the nation rallied in prayer and support for the 93-year-old elder statesman and Nobel Peace laureate. Dr. Yitzhak Kreiss, director of the Sheba Medical Center near Tel Aviv, said Peres' condition remained serious Wednesday afternoon, 24 hours after the stroke. But he said Peres' neurological signs were improving. He said that Peres, who had been placed in and out of a medically induced coma, was regaining consciousness from time to time and reacting to stimulation. Peres remained on mild sedatives and a respirator, Kreiss said.