The Dynamic Time Warping (DTW) distance is a popular similarity measure for polygonal curves (i.e., sequences of points). It finds many theoretical and practical applications, especially for temporal data, and is known to be a robust, outlier-insensitive alternative to the \frechet distance. For static curves of at most $n$ points, the DTW distance can be computed in $O(n^2)$ time in constant dimension. This tightly matches a SETH-based lower bound, even for curves in $\mathbb{R}^1$. In this work, we study \emph{dynamic} algorithms for the DTW distance. Here, the goal is to design a data structure that can be efficiently updated to accommodate local changes to one or both curves, such as inserting or deleting vertices and, after each operation, reports the updated DTW distance. We give such a data structure with update and query time $O(n^{1.5} \log n)$, where $n$ is the maximum length of the curves. As our main result, we prove that our data structure is conditionally \emph{optimal}, up to subpolynomial factors. More precisely, we prove that, already for curves in $\mathbb{R}^1$, there is no dynamic algorithm to maintain the DTW distance with update and query time~\makebox{$O(n^{1.5 - \delta})$} for any constant $\delta > 0$, unless the Negative-$k$-Clique Hypothesis fails. In fact, we give matching upper and lower bounds for various trade-offs between update and query time, even in cases where the lengths of the curves differ.

Image-to-fMRI encoding is important for both neuroscience research and practical applications. However, such "Brain-Encoders" have been typically trained per-subject and per fMRI-dataset, thus restricted to very limited training data. In this paper we propose a Universal Brain-Encoder, which can be trained jointly on data from many different subjects/datasets/machines. What makes this possible is our new voxel-centric Encoder architecture, which learns a unique "voxel-embedding" per brain-voxel. Our Encoder trains to predict the response of each brain-voxel on every image, by directly computing the cross-attention between the brain-voxel embedding and multi-level deep image features. This voxel-centric architecture allows the functional role of each brain-voxel to naturally emerge from the voxel-image cross-attention. We show the power of this approach to (i) combine data from multiple different subjects (a "Crowd of Brains") to improve each individual brain-encoding, (ii) quick & effective Transfer-Learning across subjects, datasets, and machines (e.g., 3-Tesla, 7-Tesla), with few training examples, and (iii) use the learned voxel-embeddings as a powerful tool to explore brain functionality (e.g., what is encoded where in the brain).

Interaction-powered supernovae (SNe) explode within an optically-thick circumstellar medium (CSM) that could be ejected during eruptive events. To identify and characterize such pre-explosion outbursts we produce forced-photometry light curves for 196 interacting SNe, mostly of Type IIn, detected by the Zwicky Transient Facility between early 2018 and June 2020. Extensive tests demonstrate that we only expect a few false detections among the 70,000 analyzed pre-explosion images after applying quality cuts and bias corrections. We detect precursor eruptions prior to 18 Type IIn SNe and prior to the Type Ibn SN2019uo. Precursors become brighter and more frequent in the last months before the SN and month-long outbursts brighter than magnitude -13 occur prior to 25% (5 - 69%, 95% confidence range) of all Type IIn SNe within the final three months before the explosion. With radiative energies of up to $10^{49}\,\text{erg}$, precursors could eject $\sim1\,\text{M}_\odot$ of material. Nevertheless, SNe with detected precursors are not significantly more luminous than other SNe IIn and the characteristic narrow hydrogen lines in their spectra typically originate from earlier, undetected mass-loss events. The long precursor durations require ongoing energy injection and they could, for example, be powered by interaction or by a continuum-driven wind. Instabilities during the neon and oxygen burning phases are predicted to launch precursors in the final years to months before the explosion; however, the brightest precursor is 100 times more energetic than anticipated.

Reconstructing natural videos from fMRI brain recordings is very challenging, for two main reasons: (i) As fMRI data acquisition is difficult, we only have a limited amount of supervised samples, which is not enough to cover the huge space of natural videos; and (ii) The temporal resolution of fMRI recordings is much lower than the frame rate of natural videos. In this paper, we propose a self-supervised approach for natural-movie reconstruction. By employing cycle-consistency over Encoding-Decoding natural videos, we can: (i) exploit the full framerate of the training videos, and not be limited only to clips that correspond to fMRI recordings; (ii) exploit massive amounts of external natural videos which the subjects never saw inside the fMRI machine. These enable increasing the applicable training data by several orders of magnitude, introducing natural video priors to the decoding network, as well as temporal coherence. Our approach significantly outperforms competing methods, since those train only on the limited supervised data. We further introduce a new and simple temporal prior of natural videos, which - when folded into our fMRI decoder further - allows us to reconstruct videos at a higher frame-rate (HFR) of up to x8 of the original fMRI sample rate.

Single image generative models perform synthesis and manipulation tasks by capturing the distribution of patches within a single image. The classical (pre Deep Learning) prevailing approaches for these tasks are based on an optimization process that maximizes patch similarity between the input and generated output. Recently, however, Single Image GANs were introduced both as a superior solution for such manipulation tasks, but also for remarkable novel generative tasks. Despite their impressiveness, single image GANs require long training time (usually hours) for each image and each task. They often suffer from artifacts and are prone to optimization issues such as mode collapse. In this paper, we show that all of these tasks can be performed without any training, within several seconds, in a unified, surprisingly simple framework. We revisit and cast the "good-old" patch-based methods into a novel optimization-free framework. We start with an initial coarse guess, and then simply refine the details coarse-to-fine using patch-nearest-neighbor search. This allows generating random novel images better and much faster than GANs. We further demonstrate a wide range of applications, such as image editing and reshuffling, retargeting to different sizes, structural analogies, image collage and a newly introduced task of conditional inpainting. Not only is our method faster ($\times 10^3$-$\times 10^4$ than a GAN), it produces superior results (confirmed by quantitative and qualitative evaluation), less artifacts and more realistic global structure than any of the previous approaches (whether GAN-based or classical patch-based).

We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain $(\mathbb{F}_2^{m\times m})^V \quad \xrightarrow{\delta^0}\quad (\mathbb{F}_2^{m})^{E} \quad\xrightarrow{\delta^1} \quad \mathbb{F}_2^F$ where $V$ ($X$-checks) are the vertices, $E$ (qubits) are the edges, and $F$ ($Z$-checks) are the squares of a left-right Cayley complex, and where the maps are defined based on a pair of constant-size random codes $C_A,C_B:\mathbb{F}_2^m\to\mathbb{F}_2^\Delta$ where $\Delta$ is the regularity of the underlying Cayley graphs. One of the main ingredients in the analysis is a proof of an essentially-optimal robustness property for the tensor product of two random codes.

We present detailed optical photometry for 25 Type Ibc supernovae within d\approx150 Mpc obtained with the robotic Palomar 60-inch telescope in 2004-2007. This study represents the first uniform, systematic, and statistical sample of multi-band SNe Ibc light curves available to date. We correct the light curves for host galaxy extinction using a new technique based on the photometric color evolution, namely, we show that the (V-R) color of extinction-corrected SNe Ibc at t\approx10 days after V-band maximum is tightly distributed, (V-R)=0.26+-0.06 mag. Using this technique, we find that SNe Ibc typically suffer from significant host galaxy extinction, E(B-V)\approx0.4 mag. A comparison of the extinction-corrected light curves for SNe Ib and Ic reveals that they are statistically indistinguishable, both in luminosity and decline rate. We report peak absolute magnitudes of M_R=-17.9+-0.9 mag and M_R=-18.3+-0.6 mag for SNe Ib and Ic, respectively. Focusing on the broad-lined SNe Ic, we find that they are more luminous than the normal SNe Ibc sample, M_R=-19.0+-1.1 mag, with a probability of only 1.6% that they are drawn from the same population of explosions. By comparing the peak absolute magnitudes of SNe Ic-BL with those inferred for local engine-driven explosions (GRB-SN 1998bw, XRF-SN 2006aj, and SN2009bb) we find a 25% probability that they are drawn from the SNe Ic-BL population. Finally, we fit analytic models to the light-curves to derive typical Ni-56 masses of M_Ni \approx0.2 and 0.5 M_sun for SNe Ibc and SNe Ic-BL, respectively. With reasonable assumptions for the photospheric velocities, we extract kinetic energy and ejecta mass values of M_ej \approx 2 M_sun and E_K\approx1e+51 erg for SNe Ibc, while for SNe Ic-BL we find higher values, M_ej\approx5 M_sun and E_K\approx1e+52 erg. We discuss the implications for the progenitors of SNe Ibc and their relation to engine-driven explosions [ABRIDGED].

When a very fast dynamic event is recorded with a low-framerate camera, the resulting video suffers from severe motion blur (due to exposure time) and motion aliasing (due to low sampling rate in time). True Temporal Super-Resolution (TSR) is more than just Temporal-Interpolation (increasing framerate). It can also recover new high temporal frequencies beyond the temporal Nyquist limit of the input video, thus resolving both motion-blur and motion-aliasing effects that temporal frame interpolation (as sophisticated as it maybe) cannot undo. In this paper we propose a "Deep Internal Learning" approach for true TSR. We train a video-specific CNN on examples extracted directly from the low-framerate input video. Our method exploits the strong recurrence of small space-time patches inside a single video sequence, both within and across different spatio-temporal scales of the video. We further observe (for the first time) that small space-time patches recur also across-dimensions of the video sequence - i.e., by swapping the spatial and temporal dimensions. In particular, the higher spatial resolution of video frames provides strong examples as to how to increase the temporal resolution of that video. Such internal video-specific examples give rise to strong self-supervision, requiring no data but the input video itself. This results in Zero-Shot Temporal-SR of complex videos, which removes both motion blur and motion aliasing, outperforming previous supervised methods trained on external video datasets.

Combining Functional MRI (fMRI) data across different subjects and datasets is crucial for many neuroscience tasks. Relying solely on shared anatomy for brain-to-brain mapping is inadequate. Existing functional transformation methods thus depend on shared stimuli across subjects and fMRI datasets, which are often unavailable. In this paper, we propose an approach for computing functional brain-to-brain transformations without any shared data, a feat not previously achieved in functional transformations. This presents exciting research prospects for merging and enriching diverse datasets, even when they involve distinct stimuli that were collected using different fMRI machines of varying resolutions (e.g., 3-Tesla and 7-Tesla). Our approach combines brain-to-brain transformation with image-to-fMRI encoders, thus enabling to learn functional transformations on visual stimuli to which subjects were never exposed. Furthermore, we demonstrate the applicability of our method for improving image-to-fMRI encoding of subjects scanned on older low-resolution 3T fMRI datasets, by using a new high-resolution 7T fMRI dataset (scanned on different subjects and different stimuli).

Despite remarkable progress on visual recognition tasks, deep neural-nets still struggle to generalize well when training data is scarce or highly imbalanced, rendering them extremely vulnerable to real-world examples. In this paper, we present a surprisingly simple yet highly effective method to mitigate this limitation: using pure noise images as additional training data. Unlike the common use of additive noise or adversarial noise for data augmentation, we propose an entirely different perspective by directly training on pure random noise images. We present a new Distribution-Aware Routing Batch Normalization layer (DAR-BN), which enables training on pure noise images in addition to natural images within the same network. This encourages generalization and suppresses overfitting. Our proposed method significantly improves imbalanced classification performance, obtaining state-of-the-art results on a large variety of long-tailed image classification datasets (CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, Places-LT, and CelebA-5). Furthermore, our method is extremely simple and easy to use as a general new augmentation tool (on top of existing augmentations), and can be incorporated in any training scheme. It does not require any specialized data generation or training procedures, thus keeping training fast and efficient.

This note is based on the summary of our book entitled "Non-perturbative field theoryfrom two dimensional conformal field theory to QCD in four dimensions", published recently by Cambridge University Press. It includes 436 pages. The book provides a detailed description of the tool box of non-perturbative techniques, presents applications of them to simplified systems, mainly of gauge dynamics in two dimensions, and examines the lessons one can learn from those systems about four dimensional QCD and hadron physics. In particular the book deals with conformal invariance, integrability, bosonization, large N, solitons in two dimensions and monopoles and instantons in four dimensions, confinement versus screening and finally the hadronic spectrum and scattering. We also attach the table of contents and the list of references of the book. We would be grateful for any comments or suggestions related to the material in the book. These may be incorporated in a possible future edition. They may be sent via the e-mails below.

This paper considers an intelligent reflecting surface (IRS)-assisted bi-static localization architecture for the sixth-generation (6G) integrated sensing and communication (ISAC) network. The system consists of a transmit user, a receive base station (BS), an IRS, and multiple targets in either the far-field or near-field region of the IRS. In particular, we focus on the challenging scenario where the line-of-sight (LOS) paths between targets and the BS are blocked, such that the emitted orthogonal frequency division multiplexing (OFDM) signals from the user reach the BS merely via the user-target-IRS-BS path. Based on the signals received by the BS, our goal is to localize the targets by estimating their relative positions to the IRS, instead of to the BS. We show that subspace-based methods, such as the multiple signal classification (MUSIC) algorithm, can be applied onto the BS's received signals to estimate the relative states from the targets to the IRS. To this end, we create a virtual signal via combining user-target-IRS-BS channels over various time slots. By applying MUSIC on such a virtual signal, we are able to detect the far-field targets and the near-field targets, and estimate the angle-of-arrivals (AOAs) and/or ranges from the targets to the IRS. Furthermore, we theoretically verify that the proposed method can perfectly estimate the relative states from the targets to the IRS in the ideal case with infinite coherence blocks. Numerical results verify the effectiveness of our proposed IRS-assisted localization scheme. Our paper demonstrates the potential of employing passive anchors, i.e., IRSs, to improve the sensing coverage of the active anchors, i.e., BSs.

The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disordered medium. We consider the case when the matrix potential is Gaussian, and prove three results: localisation at strong disorder, a Wegner-type estimate on the mean density of eigenvalues, and a Minami-type estimate on the probability of having multiple eigenvalues in a short interval. The last two results are proved in the more general setting of deformed block-Gaussian matrices, which includes a class of Gaussian band matrices as a special case. Emphasis is placed on the dependence of the bounds on the number of orbitals. As an additional application, we improve the upper bound on the localisation length for one-dimensional Gaussian band matrices.

We introduce a high-dimensional cubical complex, for any dimension t>0, and apply it to the design of quantum locally testable codes. Our complex is a natural generalization of the constructions by Panteleev and Kalachev and by Dinur et. al of a square complex (case t=2), which have been applied to the design of classical locally testable codes (LTC) and quantum low-density parity check codes (qLDPC) respectively. We turn the geometric (cubical) complex into a chain complex by relying on constant-sized local codes $h_1,\ldots,h_t$ as gadgets. A recent result of Panteleev and Kalachev on existence of tuples of codes that are product expanding enables us to prove lower bounds on the cycle and co-cycle expansion of our chain complex. For t=4 our construction gives a new family of "almost-good" quantum LTCs -- with constant relative rate, inverse-polylogarithmic relative distance and soundness, and constant-size parity checks. Both the distance of the quantum code and its local testability are proven directly from the cycle and co-cycle expansion of our chain complex.

Edge connectivity of a graph is one of the most fundamental graph-theoretic concepts. The celebrated tree packing theorem of Tutte and Nash-Williams from 1961 states that every $k$-edge connected graph $G$ contains a collection $\cal{T}$ of $\lfloor k/2 \rfloor$ edge-disjoint spanning trees, that we refer to as a tree packing; the diameter of the tree packing $\cal{T}$ is the largest diameter of any tree in $\cal{T}$. A desirable property of a tree packing, that is both sufficient and necessary for leveraging the high connectivity of a graph in distributed communication, is that its diameter is low. Yet, despite extensive research in this area, it is still unclear how to compute a tree packing, whose diameter is sublinear in $|V(G)|$, in a low-diameter graph $G$, or alternatively how to show that such a packing does not exist. In this paper we provide first non-trivial upper and lower bounds on the diameter of tree packing. First, we show that, for every $k$-edge connected $n$-vertex graph $G$ of diameter $D$, there is a tree packing $\cal{T}$ of size $\Omega(k)$, diameter $O((101k\log n)^D)$, that causes edge-congestion at most $2$. Second, we show that for every $k$-edge connected $n$-vertex graph $G$ of diameter $D$, the diameter of $G[p]$ is $O(k^{D(D+1)/2})$ with high probability, where $G[p]$ is obtained by sampling each edge of $G$ independently with probability $p=\Theta(\log n/k)$. This provides a packing of $\Omega(k/\log n)$ edge-disjoint trees of diameter at most $O(k^{(D(D+1)/2)})$ each. We then prove that these two results are nearly tight. Lastly, we show that if every pair of vertices in a graph has $k$ edge-disjoint paths of length at most $D$ connecting them, then there is a tree packing of size $k$, diameter $O(D\log n)$, causing edge-congestion $O(\log n)$. We also provide several applications of low-diameter tree packing in distributed computation.

We report on the first experimental demonstration of enantioselective rotational control of chiral molecules with a laser field. In our experiments, two enantiomers of propylene oxide are brought to accelerated unidirectional rotation by means of an optical centrifuge. Using Coulomb explosion imaging, we show that the centrifuged molecules acquire preferential orientation perpendicular to the plane of rotation, and that the direction of this orientation depends on the relative handedness of the enantiomer and the rotating centrifuge field. The observed effect is in agreement with theoretical predictions and is reproduced in numerical simulations of the centrifuge excitation followed by Coulomb explosion of the centrifuged molecules. The demonstrated technique opens new avenues in optical enantioselective control of chiral molecules with a plethora of potential applications in differentiation, separation and purification of chiral mixtures.

The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph signal processing (GSP), sampling on graphs has various promising applications. In this article, we review current progress on sampling over graphs focusing on theory and potential applications. Although most methodologies used in graph signal sampling are designed to parallel those used in sampling for standard signals, sampling theory for graph signals significantly differs from the theory of Shannon--Nyquist and shift-invariant sampling. This is due in part to the fact that the definitions of several important properties, such as shift invariance and bandlimitedness, are different in GSP systems. Throughout this review, we discuss similarities and differences between standard and graph signal sampling and highlight open problems and challenges.

We consider the incompressible Euler equations in a bounded domain in three space dimensions. Recently, the first two authors proved Onsager's conjecture for bounded domains, i.e., that the energy of a solution to these equations is conserved provided the solution is Hölder continuous with exponent greater than 1/3, uniformly up to the boundary. In this contribution we relax this assumption, requiring only interior Hölder regularity and continuity of the normal component of the energy flux near the boundary. The significance of this improvement is given by the fact that our new condition is consistent with the possible formation of a Prandtl-type boundary layer in the vanishing viscosity limit.

This work is aimed at understanding the basic principles of adsorption process in great details as adsorptive separation process has broad applications in the industry. To this end, a simple mathematical model has been used to describe transient fixed bed physical adsorption process. Governing equations are solved numerically to obtain breakthrough curves for single component and multi-component monolayer adsorption. Desorption of a saturated bed by an inert fluid is also considered. A full parametric study is performed to analyze the effects of different parameters such as bed length, velocity, diffusivity, particle radius and isotherm properties on the nature of the breakthrough curve. Analysis of these results led to the development of the generic breakthrough curve for a single component monolayer adsorption which will enable us to tell the nature of breakthrough curve for different process parameters without recourse to the numerical simulation or experiment. Thus this study will be of great interest in the industrial separation process.