We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal, and runs in time $\sqrt{n} \cdot \mathrm{poly}(d,\log(n),\log(1/\varepsilon))$ which is sublinear for tall linear programs (i.e., $n \gg d$). Our algorithm speeds up the Newton step in the state-of-the-art interior point method of Lee and Sidford [FOCS~'14]. This requires us to efficiently approximate the Hessian and gradient of the barrier function, and these are our main contributions. To approximate the Hessian, we describe a quantum algorithm for the \emph{spectral approximation} of $A^T A$ for a tall matrix $A \in \mathbb R^{n \times d}$. The algorithm uses leverage score sampling in combination with Grover search, and returns a $\delta$-approximation by making $O(\sqrt{nd}/\delta)$ row queries to $A$. This generalizes an earlier quantum speedup for graph sparsification by Apers and de Wolf~[FOCS~'20]. To approximate the gradient, we use a recent quantum algorithm for multivariate mean estimation by Cornelissen, Hamoudi and Jerbi [STOC '22]. While a naive implementation introduces a dependence on the condition number of the Hessian, we avoid this by pre-conditioning our random variable using our quantum algorithm for spectral approximation.
This paper delivers the first evaluation of the 2005 French Disability Act, which was introduced to promote the employment of disabled people. The Act relies primarily on a legal employment quota for disabled people, with levies imposed in cases of non-compliance. We apply panel data methods equivalent to double and triple difference methods to the French Santé et Itinéraire Professionnel (SIP) survey (Survey on Health and Labour Market Histories). First, we estimate the effect of disability on the employment rate, finding a strong negative effect which is most pronounced among men and the oldest workers. However, since some observable characteristics of disabled workers, such as age, gender and education, vary over time, we extend our model to isolate the causal effect of the reform on the employment rate of disabled workers by taking into account the pre-reform (1991–2004) and post-reform (2005–2009) periods. Our findings suggest that the 2005 Act has met its initial objective, positively impacting the employment rate of disabled individuals, particularly in the private sector. The reform appears to have compensated for approximately half of the effect of disabilities on the employment rate. We also find that the reform's effect has been stronger for workers with secondary education.
El lector encontrará en este texto un primer esbozo de la historia de la noción de libertad. Sobre las relaciones entre determinismo y libertad, el autor adopta, tras analizar diversos casos, una opinión común que se remonta a Platón. Este análisis permite precisar nociones como la de azar local y extraer elementos que podrían conducir a una definición formal de la noción habitual de libertad.
This paper develops a record-based framework for detecting structural changes in climate time series, with a focus on daily air temperature. The approach combines three elements: a linear drift model (LDM) to represent progressive warming with approximately stationary daily variability; the concept of δ records, requiring each new record to exceed the previous maximum record level within a fixed threshold, and filtering out records that have become inflated in the presence of trend; a CUSUM-like statistic, calibrated on a Brownian empirical model, for testing changes in the probability of occurrence of records. Theoretically, the main properties of classical records are recalled, applied to the LDM framework, and a numerical integral for the likelihood of δ -record events is derived. Empirically, we analyzed a series of seasonally adjusted daily temperatures over the period 2000–2025. Removing the annual cycle, the data are well described by a linear warming of about 0.45 ^∘C per decade, with a residual daily variability of about 2 ^∘C . The observed numbers of both classical and δ records (with δ equal to one residual standard deviation) are consistent with Monte Carlo performance within the adjusted LDM framework, and the CUSUM bridge statistics remain below the Kolmogorov critical values, indicating that there is no statistically significant breakpoint in record-making. Overall, the results indicate a regime of gradual warming with no detectable structural break in the behavior of extremes and illustrate how record-based utilities may be used for monitoring the non-stationarity of weather extremes.
We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on Z(d) according to a contact process with parameter lambda > 0. With probability p is an element of [0,1] an offspring is fertile and can give birth, on neighboring sites, to other individuals at rate lambda. With probability 1 - p, an offspring is sterile and blocks the site it sits on until it dies. The goal is to prove that at fixed lambda, the system survives for large enough p and dies out for small enough p. The model is not attractive, since an increase of fertile individuals potentially causes that of sterile ones. However, thanks to a comparison argument with attractive models, we are able to answer our question.
