Trump's Appearance in Ohio Underscores All the Reasons the GOP Is Unpopular Will the president's steadfast support of data centers cost Ohio Republicans a victory? President Donald Trump speaks during a midterm election rally, Saturday, Oct. 3, 2026, in Vandalia, Ohio. Get your news from a source that's not owned and controlled by oligarchs. On Saturday, President Donald Trump hosted a campaign rally for Ohio senatorial and gubernatorial candidates, John Husted and Vivek Ramaswamy. As part of his campaign to revive GOP turnout and avoid what is widely predicted to be a Democratic sweep, he appeared in Ohio following weekend visits to Texas, Oklahoma, and Alabama.

Cowboys legend Randy White endorses Ken Paxton, warns James Talarico'can't be trusted' Fever star Sophie Cunningham tells Aces' A'ja Wilson to'grow up' in response to her playoff meltdown Fever general manager Amber Cox calls out'attacks' on the fan base in season-ending press conference Hall of Famer praises Dan Lanning's'perfect' response after Dante Moore was carted off following vicious hit Former OpenAI safety chief warns AI industry's culture is'broken' Chris Hansen slams'Primetime' movie, calls it an insult Sen John Thune: The Democratic Party doesn't want to give the president any victories'Gangs' vs. 'Cliques': Seattle's crime language comes under fire Tomi Lahren says France protests are a'cautionary tale' for the US Rep Mike Lawler: These leaders don't want to hold people accountable for their actions Super Bowl winning football coach Jon Gruden had an NFL reputation for using his fire and enthusiasm, not to mention his offensive strategies, to great success and we saw some of that at the rally President Donald Trump held Saturday night in Ohio. First of all, who knew Gruden was a conservative? He watched the president deliver his message standing side-by-side with Ohio Sen. Jon Husted, who is running for re-election, and gubernatorial candidate Vivek Ramaswamy. A supporter holds a Trump Country flag as President Donald Trump speaks during a campaign rally in Vandalia, Ohio, on Oct. 3, 2026. And at one point during Trump's comments, a protester began to say something or other, and was escorted out while the crowd chanted, Na Na Hey Hey Kiss Him Goodbye.

Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data. Supervised machine learning methods have demonstrated promise in learning efficient surrogate models that can (partially) replace expensive high-fidelity models, making many-query analyses, such as optimization, uncertainty quantification, and inference, tractable. However, when training data must be obtained through the evaluation of an expensive model or experiment, the amount of training data that can be obtained is often limited, which can make learned surrogate models unreliable. However, in many engineering and scientific settings, cheaper \emph{low-fidelity} models may be available, for example arising from simplified physics modeling or coarse grids. These models may be used to generate additional low-fidelity training data. The goal of \emph{multifidelity} machine learning is to use both high- and low-fidelity training data to learn a surrogate model which is cheaper to evaluate than the high-fidelity model, but more accurate than any available low-fidelity model. This work proposes a new multifidelity training approach for Gaussian process regression which uses low-fidelity data to define additional features that augment the input space of the learned model. The approach unites desirable properties from two separate classes of existing multifidelity GPR approaches, cokriging and autoregressive estimators. Numerical experiments on several test problems demonstrate both increased predictive accuracy and reduced computational cost relative to the state of the art.

Recent studies suggest that asymmetric binary perceptron (ABP) likely exhibits the so-called statistical-computational gap characterized with the appearance of two phase transitioning constraint density thresholds: \textbf{\emph{(i)}} the \emph{satisfiability threshold} $α_c$, below/above which ABP succeeds/fails to operate as a storage memory; and \textbf{\emph{(ii)}} \emph{algorithmic threshold} $α_a$, below/above which one can/cannot efficiently determine ABP's weight so that it operates as a storage memory. We consider a particular parametric utilization of \emph{fully lifted random duality theory} (fl RDT) [85] and study its potential ABP's algorithmic implications. A remarkable structural parametric change is uncovered as one progresses through fl RDT lifting levels. On the first two levels, the so-called $\c$ sequence -- a key parametric fl RDT component -- is of the (natural) decreasing type. A change of such phenomenology on higher levels is then connected to the $α_c$ -- $α_a$ threshold change. Namely, on the second level concrete numerical values give for the critical constraint density $α=α_c\approx 0.8331$. While progressing through higher levels decreases this estimate, already on the fifth level we observe a satisfactory level of convergence and obtain $α\approx 0.7764$. This allows to draw two striking parallels: \textbf{\emph{(i)}} the obtained constraint density estimate is in a remarkable agrement with range $α\in (0.77,0.78)$ of clustering defragmentation (believed to be responsible for failure of locally improving algorithms) [17,88]; and \textbf{\emph{(ii)}} the observed change of $\c$ sequence phenomenology closely matches the one of the negative Hopfield model for which the existence of efficient algorithms that closely approach similar type of threshold has been demonstrated recently [87].

To create photorealistic avatars that users can embody, human modeling must be complete (encompass the full body), driveable (able to reproduce motion of the user from lightweight sensors), and generalizable ( i.e., easily adaptable to novel identities). Towards these goals, paired captures, that is, captures of the same subject obtained from systems of diverse quality and availability, are crucial. However, paired captures are rarely available to researchers outside of dedicated industrial labs: Codec Avatar Studio is our proposal to close this gap. Towards generalization and driveability, we introduce a dataset of 256 subjects captured in two modalities: high resolution multi-view scans of their heads, and video from the internal cameras of a headset.

In [104] a powerful fully lifted (fl) probabilistic blirp interpolating mechanism was introduced. It arrived as a strong upgrade on partially lifted concepts from [100, 101] and the basic ones from [49, 84] (see also, e.g., [31, 32, 60, 106] for early considerations as well as [5, 64, 67, 101, 107] for a brief history, relevance, and development overview). While the range of applicability in a variety of scientific fields is rather wide, applications in random optimizations are of our prevalent interest. They became particularly fruitful over the last two decades (some of the most prominent examples include, compressed sensing, machine learning, and neural network statistical studies; see, e.g., [50, 72-75, 86-91, 108]). Characterizing typical behavior of their various features ranging from standard optimization metrics (objective values, optimal solutions, relations between optimizing variables) to associated algorithmic ones (accuracy, speed, convergence) became possible in large part due to a strong progress made in understanding and developing powerful comparison mechanisms. For example, many of the above performance metrics often exhibit the so-calledphase-transition (PT) phenomenon where they undergo an abrupt change as one moves from one region of system parameters to another.

We consider \emph{bilinearly indexed random processes} (blirp) and study their interpolating comparative mechanisms. Generic introduction of the \emph{fully lifted} (fl) blirp interpolation in [105] was followed by a corresponding stationarization counterpart in [103]. A \emph{large deviation} upgrade of [105] introduced in companion paper [106] is complemented here with the corresponding one of [103]. Similarly to [106], the mechanism that we introduce extends the range of [103]'s applicability so that it encompasses random structures \emph{atypical} features. Among others these include the \emph{local entropies} (LE) which explain atypical solutions clusterings in hard random optimization problems believed to be directly responsible for the presumable existence of the so-called \emph{computational gaps}. Moreover (and similar to [105]), despite on occasion somewhat involved technical considerations, the final forms of the uncovered fundamental interpolating parameters relations are rather elegant and as such provide a valuable tool readily available for further use.