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Natural faults often contain a fluid-saturated, granular fault-gouge layer, whose failure and sliding processes play a central role in earthquake dynamics. Using a two-dimensional discrete element model coupled with fluid dynamics, we simulate a fluid-saturated granular layer, where fluid pressure is incrementally raised. At a critical fluid pressure level, the layer fails and begins to accelerate. When we gradually reduce fluid pressure, a distinct behavior emerges: slip-rate decreases linearly until the layer halts at a fluid pressure level below that required to initiate failure. During this pressure cycle the system exhibits (1) velocity-strengthening friction and (2) frictional hysteresis. These behaviors, well established in dry granular media, are shown to extend here to shear of dense fluid-saturated granular layers. Additionally, we observe a delay between fluid pressure increase and failure, associated with pre-failure dilative strain and "dilational-hardening". During the delay period, small, arrested slip events dilate the layer in preparation for full-scale failure. Our findings may explain (i) fault motion that continues even after fluid pressure returns to pre-injection levels, and (ii) delayed failure in fluid-injection experiments, and (iii) pre-failure arrested slip events observed prior to earthquakes.

In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/non-conservation in individual cases. Specifically, in the above paper an experiment was presented in which it can be proven that in some individual cases energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome, and that something must be wrong if there are individual instances in which conservation doesn't hold, even though this is not required by the standard conservation law. Here we revisit that experiment and show that although its results are correct, there is a way to circumvent them and ensure individual case conservation in that situation. The solution is however quite unusual, challenging one of the basic assumptions of quantum mechanics, namely that any quantum state can be prepared, and it involves a time-holistic, double non-conservation effect. Our results bring new light on the role of the preparation stage of the initial state of a particle and on the interplay of conservation laws and frames of reference. We also conjecture that when such a full analysis of any conservation experiment is performed, conservation is obeyed in every individual case.

The Quantum Cheshire Cat experiment showed that when weak measurements are performed on pre- and post-selected system, the counterintuitive result has been obtained that a neutron is measured to be in one place without its spin, and its spin is measured to be in another place without the neutron. A generalization of this effect is presented with a massive particle whose mass is measured to be in one place with no momentum, while the momentum is measured to be in another place without the mass. The new result applies to any massive particle, independent of its spin or charge. A gedanken experiment which illustrates this effect is presented using a nested pair of Mach-Zehnder interferometers, but with some of the mirrors and beam splitters moving relative to the laboratory frame. The titular interpretation of this experiment is extremely controversial, and rests on several assumptions, which are discussed in detail. An alternative interpretation using the counterparticle model of Aharonov et al. is also discussed., Comment: 13 pages, 4 figures

The weak value exhibits numerous intriguing characteristics, such as values outside the operator spectrum, leading to unexpected phenomena. The measurement protocol used for measuring the weak value has been the subject of an on-going controversy. In particular, the possibility of gaining a metrological advantage using weak measurements was questioned. A rigorous characterization of this advantage is still missing when the primary system is noisy. We thus consider here the challenge of learning an unknown operator under the influence of noise on the primary system. For unital noise channels, we prove that the weak value measurement protocol (WVMP) is quadratically more robust to noise than strong measurements. Since the WVMP makes use both of weak entanglement as well as postselection, one might suspect that the advantage is solely due to the postselection aspect of the WVMP. We refute this by showing that for the amplitude and phase damping noise channel, the WVMP achieves a quadratic advantage even over strong measurement protocols which are allowed to apply postselection. By this we rigorously prove that in certain cases, the WVMP possesses a strict, provable advantage in robustness to noise.

In this short paper, we show how a quantum nonlocal effect of far-apart wavepackets in the Schrodinger picture of wavefunctions is replaced by a local instability problem when considering the hydrodynamical formulation of quantum mechanics, known as the Madelung picture. As a second result, we show how the Madelung equations describe quantized energies without any external quantization conditions.

Transfer of conserved quantities between two remote regions is generally assumed to be a rather trivial process: a flux of particles carrying the conserved quantities propagates from one region to another. We however demonstrate a flow of angular momentum from one region to another across a region of space in which there is a vanishingly small probability of any particles (or fields) being present. This shows that the usual view of how conservation laws work needs to be revisited., Comment: V4: 8 Pages, 2 Figures, minor improvements

We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to produce the Born rule in its explicit form by improving the result given in [1]. While the proposed postulate is still not part of the quantum mechanics postulates, every experiment obeys it, and it can not be deduced using the standard postulates of quantum mechanics.

The Aharonov-Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to generate an observable effect. In this Letter, we study a variant of the AB effect that apparently challenges this concept. The significance of weak values and nonlocal equations of motion is discussed as part of the analysis, shedding light on and connecting all these fundamental concepts., Comment: 7 pages, 2 figures, comments are welcome

We give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. This gives strong evidence that, in the presence of a constant rate of noise per gate, random circuit sampling (RCS) cannot be the basis of a scalable experimental violation of the extended Church-Turing thesis. Our algorithm is not practical in its current form, and does not address finite-size RCS based quantum supremacy experiments., Comment: 27 pages, 2 figures

We study the complexity of classical constraint satisfaction problems on a 2D grid. Specifically, we consider the complexity of function versions of such problems, with the additional restriction that the constraints are translationally invariant, namely, the variables are located at the vertices of a 2D grid and the constraint between every pair of adjacent variables is the same in each dimension. The only input to the problem is thus the size of the grid. This problem is equivalent to one of the most interesting problems in classical physics, namely, computing the lowest energy of a classical system of particles on the grid. We provide a tight characterization of the complexity of this problem, and show that it is complete for the class $FP^{NEXP}$. Gottesman and Irani (FOCS 2009) also studied classical translationally-invariant constraint satisfaction problems; they show that the problem of deciding whether the cost of the optimal solution is below a given threshold is NEXP-complete. Our result is thus a strengthening of their result from the decision version to the function version of the problem. Our result can also be viewed as a generalization to the translationally invariant setting, of Krentel's famous result from 1988, showing that the function version of SAT is complete for the class $FP^{NP}$. An essential ingredient in the proof is a study of the complexity of a gapped variant of the problem. We show that it is NEXP-hard to approximate the cost of the optimal assignment to within an additive error of $\Omega(N^{1/4})$, for an $N \times N$ grid. To the best of our knowledge, no gapped result is known for CSPs on the grid, even in the non-translationally invariant case. As a byproduct of our results, we also show that a decision version of the optimization problem which asks whether the cost of the optimal assignment is odd or even is also complete for $P^{NEXP}$., Comment: 75 pages, 13 figures

Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehavior of this operator occurs whenever the operator's weak value exceeds its eigenvalue bound. We give illustrative examples of this effect for total angular momentum and energy. In the later case, we demonstrate a sequence of harmonic oscillator potentials where a finite energy state converges everywhere on the real line, using only bounded superpositions of states whose asymptotic energy vanishes - "energy out of nothing". This limit requires postselecting the particle in a region whose size diverges in the considered limit. We further show that superenergy behavior implies that the state superoscillates in time with a rate given by the superenergy divided by the reduced Planck's constant. This example demonstrates the possibility of mimicking a high-energy state with coherent superpositions of nearly zero-energy states for as wide a spatial region as desired. We provide numerical evidence of these features to further bolster and elucidate our claims., Comment: 9 pages, 5 figures, expanded treatment of time

Text classification can be useful in many real-world scenarios, saving a lot of time for end users. However, building a custom classifier typically requires coding skills and ML knowledge, which poses a significant barrier for many potential users. To lift this barrier, we introduce Label Sleuth, a free open source system for labeling and creating text classifiers. This system is unique for (a) being a no-code system, making NLP accessible to non-experts, (b) guiding users through the entire labeling process until they obtain a custom classifier, making the process efficient -- from cold start to classifier in a few hours, and (c) being open for configuration and extension by developers. By open sourcing Label Sleuth we hope to build a community of users and developers that will broaden the utilization of NLP models., Comment: 7 pages, 2 figures To be published at EMNLP 2022

The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle's internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As a particular consequence, we prove that the effective Hamiltonian of two gravitationally interacting particles is non-Hermitian from the perspective of the clock of either particle., Comment: 7+2 pages, 2 figures. Author's published version

Paraphrase generation has been widely used in various downstream tasks. Most tasks benefit mainly from high quality paraphrases, namely those that are semantically similar to, yet linguistically diverse from, the original sentence. Generating high-quality paraphrases is challenging as it becomes increasingly hard to preserve meaning as linguistic diversity increases. Recent works achieve nice results by controlling specific aspects of the paraphrase, such as its syntactic tree. However, they do not allow to directly control the quality of the generated paraphrase, and suffer from low flexibility and scalability. Here we propose $QCPG$, a quality-guided controlled paraphrase generation model, that allows directly controlling the quality dimensions. Furthermore, we suggest a method that given a sentence, identifies points in the quality control space that are expected to yield optimal generated paraphrases. We show that our method is able to generate paraphrases which maintain the original meaning while achieving higher diversity than the uncontrolled baseline. The models, the code, and the data can be found in https://github.com/IBM/quality-controlled-paraphrase-generation., Comment: Accepted as a long paper at ACL 2022

In real-world scenarios, a text classification task often begins with a cold start, when labeled data is scarce. In such cases, the common practice of fine-tuning pre-trained models, such as BERT, for a target classification task, is prone to produce poor performance. We suggest a method to boost the performance of such models by adding an intermediate unsupervised classification task, between the pre-training and fine-tuning phases. As such an intermediate task, we perform clustering and train the pre-trained model on predicting the cluster labels. We test this hypothesis on various data sets, and show that this additional classification phase can significantly improve performance, mainly for topical classification tasks, when the number of labeled instances available for fine-tuning is only a couple of dozen to a few hundred., Comment: 9 pages, 6 figures; To be published in ACL 2022

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top-down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to individual localized objects describe an emergent particle model, with unusual particles whose masses and energies may be negative or imaginary. This retrocausal top-down model leads to an intuitive particle-based ontological picture, wherein weak measurements directly probe the properties of these exotic particles, which exist whether or not they are actually measured, Comment: 15 pages, 5 figures (Supporting Information: 16 pages, 3 figures)

In recent years, pretrained language models have revolutionized the NLP world, while achieving state of the art performance in various downstream tasks. However, in many cases, these models do not perform well when labeled data is scarce and the model is expected to perform in the zero or few shot setting. Recently, several works have shown that continual pretraining or performing a second phase of pretraining (inter-training) which is better aligned with the downstream task, can lead to improved results, especially in the scarce data setting. Here, we propose to leverage sentiment-carrying discourse markers to generate large-scale weakly-labeled data, which in turn can be used to adapt language models for sentiment analysis. Extensive experimental results show the value of our approach on various benchmark datasets, including the finance domain. Code, models and data are available at https://github.com/ibm/tslm-discourse-markers., Comment: Published in AAAI 2022

In a typical customer service chat scenario, customers contact a support center to ask for help or raise complaints, and human agents try to solve the issues. In most cases, at the end of the conversation, agents are asked to write a short summary emphasizing the problem and the proposed solution, usually for the benefit of other agents that may have to deal with the same customer or issue. The goal of the present article is advancing the automation of this task. We introduce the first large scale, high quality, customer care dialog summarization dataset with close to 6500 human annotated summaries. The data is based on real-world customer support dialogs and includes both extractive and abstractive summaries. We also introduce a new unsupervised, extractive summarization method specific to dialogs.

Shear strain localization into shear bands is associated with velocity weakening instabilities and earthquakes. Here, we simulate steady-state plane-shear flow of numerical granular material (gouge), confined between parallel surfaces. Both constant shear stress and constant strain-rate boundary conditions are tested and the two types of boundary conditions are found to yield distinct velocity profiles and friction laws. The inertial number, $I$, exerts the largest control on the layers' behavior, but additional dependencies of friction on normal stress and thickness of the layer are observed under constant stress boundary condition. We find that shear-band localization, which is present in the quasistatic regime ($I<10^{-3}$) in rate-controlled shear, is absent under stress-controlled loading. In the latter case, flow ceases when macroscopic friction coefficient approaches the quasistatic friction value. The inertial regime that occurs at higher inertial numbers ($I>10^{-3}$) is associated with distributed shear, and friction and porosity that increase with shear rate (rate-strengthening regime). The finding that shear under constant stress boundary condition produces the inertial, distributed shear but never quasistatic, localized deformation is rationalized based on low fluctuations of shear forces in granular contacts for stress-controlled loading. By examining porosity within and outside a shear band, we also provide a mechanical reason why the transition between quasistatic and inertial shear coincides with the transition between localized and distributed strain., Comment: 19 pages, 9 figures, regular article

We describe the 2021 Key Point Analysis (KPA-2021) shared task on key point analysis that we organized as a part of the 8th Workshop on Argument Mining (ArgMining 2021) at EMNLP 2021. We outline various approaches and discuss the results of the shared task. We expect the task and the findings reported in this paper to be relevant for researchers working on text summarization and argument mining.

Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating the ground energy of a fixed, translationally invariant Hamiltonian in the thermodynamic limit, to within a given precision; the number of bits $n$ for the precision is the sole input to the problem. The complexity of this problem captures how difficult it is for the physicist to measure or compute another digit in the approximation of a physical quantity in the thermodynamic limit. We show that this problem is contained in $\mbox{FEXP}^{\mbox{QMA-EXP}}$ and is hard for $\mbox{FEXP}^{\mbox{NEXP}}$. This means that the problem is doubly exponentially hard in the size of the input. As an ingredient in our construction, we study the problem of computing the ground energy of translationally invariant finite 1D chains. A single Hamiltonian term, which is a fixed parameter of the problem, is applied to every pair of particles in a finite chain. The length of the chain is the sole input to the problem and the task is to compute an approximation of the ground energy. No thresholds are provided as in the standard formulation of the local Hamiltonian problem. We show that this problem is contained in $\mbox{FP}^{\mbox{QMA-EXP}}$ and is hard for $\mbox{FP}^{\mbox{NEXP}}$. Our techniques employ a circular clock in which the ground energy is calibrated by the length of the cycle. This requires more precise expressions for the ground states of the resulting matrices than was required for previous QMA-completeness constructions and even exact analytical bounds for the infinite case which we derive using techniques from spectral graph theory. To our knowledge, this is the first use of the circuit-to-Hamiltonian construction which shows hardness for a function class., Comment: 78 pages, 18 figures. After announcing these results we found that similar results were achieved independently by Watson and Cubitt; they are posted simultaneously on the arXiv

A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre- and postselection is clarified., Comment: to be published in Physics Letters A

Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time dependent Schr\"odinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper we give a unified approach to determine the supershift property for the solution of the time dependent Schr\"odinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green's function, but not its explicit form. With this efficient general technique we are able to treat various potentials.

A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY interaction on the 2D square lattice -- are known to be universal. However, the known encodings can be very inefficient, requiring interaction energy that scales exponentially with system size if the original Hamiltonian has higher-dimensional, long-range, or even all-to-all interactions. In this work, we provide an efficient construction by which these universal families are in fact "strongly" universal. This means that the required interaction energy and all other resources in the 2D simulator scale polynomially in the size of the target Hamiltonian and precision parameters, regardless of the target's connectivity. This exponential improvement over previous constructions is achieved by combining the tools of quantum phase estimation algorithm and circuit-to-Hamiltonian transformation in a non-perturbative way that only incurs polynomial overhead. The simulator Hamiltonian also possess certain translation-invariance. Furthermore, we show that even 1D Hamiltonians with nearest-neighbor interaction of 8-dimensional particles on a line are strongly universal Hamiltonian simulators, although without any translation-invariance. Our results establish that analog quantum simulations of general systems can be made efficient, greatly increasing their potential as applications for near-future quantum technologies., Comment: 8+13 pages, 2 figures, 1 table, presented at QIP 2021

The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is, generally, complex-valued. This leads to new experimental protocols to detect the Aharonov-Bohm phase before the source is fully encircled. While this does not necessarily change the nonlocal status of the Aharonov-Bohm effect, it brings new insights into it. Moreover, we discuss how these results might have consequences for the correspondence principle, making complex vector potentials relevant to the study of classical systems., Comment: 9 pages, 3 figures. Author's accepted version

Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.

We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problem and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments., Comment: 77+19 pages, 11 figures; v2: improved introduction, typos fixed, references added

Current TSA evaluation in a cross-domain setup is restricted to the small set of review domains available in existing datasets. Such an evaluation is limited, and may not reflect true performance on sites like Amazon or Yelp that host diverse reviews from many domains. To address this gap, we present YASO - a new TSA evaluation dataset of open-domain user reviews. YASO contains 2,215 English sentences from dozens of review domains, annotated with target terms and their sentiment. Our analysis verifies the reliability of these annotations, and explores the characteristics of the collected data. Benchmark results using five contemporary TSA systems show there is ample room for improvement on this challenging new dataset. YASO is available at https://github.com/IBM/yaso-tsa., Comment: Accepted to EMNLP 2021 (long paper). To download YASO, see https://github.com/IBM/yaso-tsa

We present a minimal one-dimensional model for the transition from crack-like to pulse-like propagation of frictional rupture. In its non-dimensional form, the model depends on only two free parameters: the non-dimensional pre-stress and an elasticity ratio that accounts for the finite height of the system. The model contains stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. Results demonstrate that the existence of pulse-like ruptures requires only elastic relaxation and redistribution of initial pre-stress. The novelty of our findings is that pulse-like propagation along frictional interfaces is a generic elastic feature, whose existence is not sensitive to particular rate- or slip-dependencies of dynamic friction.

Deep neural models achieve some of the best results for semantic role labeling. Inspired by instance-based learning that utilizes nearest neighbors to handle low-frequency context-specific training samples, we investigate the use of memory adaptation techniques in deep neural models. We propose a parameterized neighborhood memory adaptive (PNMA) method that uses a parameterized representation of the nearest neighbors of tokens in a memory of activations and makes predictions based on the most similar samples in the training data. We empirically show that PNMA consistently improves the SRL performance of the base model irrespective of types of word embeddings. Coupled with contextualized word embeddings derived from BERT, PNMA improves over existing models for both span and dependency semantic parsing datasets, especially on out-of-domain text, reaching F1 scores of 80.2, and 84.97 on CoNLL2005, and CoNLL2009 datasets, respectively.

We revisit the "counterfactual quantum communication" of Salih et al. [1], who claim that an observer "Bob" can send one bit of information to a second observer "Alice" without any physical particle traveling between them. We show that a locally conserved, massless current - specifically, a current of modular angular momentum, $L_z$ mod 2$\hbar$ - carries the one bit of information. We integrate the flux of $L_z$ mod 2$\hbar$ from Bob to Alice and show that it equals one of the two eigenvalues of $L_z$ mod 2$\hbar$, either 0 or $\hbar$, thus precisely accounting for the one bit of information he sends her. We previously [2] obtained this result using weak values of $L_z$ mod 2$\hbar$; here we do not use weak values., Comment: Physical Review Letters, in press

Approaching new data can be quite deterrent; you do not know how your categories of interest are realized in it, commonly, there is no labeled data at hand, and the performance of domain adaptation methods is unsatisfactory. Aiming to assist domain experts in their first steps into a new task over a new corpus, we present an unsupervised approach to reveal complex rules which cluster the unexplored corpus by its prominent categories (or facets). These rules are human-readable, thus providing an important ingredient which has become in short supply lately - explainability. Each rule provides an explanation for the commonality of all the texts it clusters together. We present an extensive evaluation of the usefulness of these rules in identifying target categories, as well as a user study which assesses their interpretability., Comment: Accepted to Findings of EMNLP

StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as BPP, BQP, MA, QMA, etc.,this property remains open for StoqMA since Bravyi, Bessen and Terhal defined this class in 2006. In this note, we show that error reduction forStoqMA will imply that StoqMA = MA., Comment: Version 2 has punctual minor improvements

Recent years have seen important advances in the quality of state-of-the-art models, but this has come at the expense of models becoming less interpretable. This survey presents an overview of the current state of Explainable AI (XAI), considered within the domain of Natural Language Processing (NLP). We discuss the main categorization of explanations, as well as the various ways explanations can be arrived at and visualized. We detail the operations and explainability techniques currently available for generating explanations for NLP model predictions, to serve as a resource for model developers in the community. Finally, we point out the current gaps and encourage directions for future work in this important research area., Comment: To appear in AACL-IJCNLP 2020

In this paper we study the time dependent Schr\"odinger equation with all possible self-adjoint singular interactions located at the origin, which include the $\delta$ and $\delta'$-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability and oscillatory properties of the solution of the Schr\"odinger equation subject to a generalized point interaction when the initial datum is a superoscillatory function.

An educated and informed consumption of media content has become a challenge in modern times. With the shift from traditional news outlets to social media and similar venues, a major concern is that readers are becoming encapsulated in "echo chambers" and may fall prey to fake news and disinformation, lacking easy access to dissenting views. We suggest a novel task aiming to alleviate some of these concerns -- that of detecting articles that most effectively counter the arguments -- and not just the stance -- made in a given text. We study this problem in the context of debate speeches. Given such a speech, we aim to identify, from among a set of speeches on the same topic and with an opposing stance, the ones that directly counter it. We provide a large dataset of 3,685 such speeches (in English), annotated for this relation, which hopefully would be of general interest to the NLP community. We explore several algorithms addressing this task, and while some are successful, all fall short of expert human performance, suggesting room for further research. All data collected during this work is freely available for research., Comment: Accepted to ACL 2020 as Long Paper. For the associated debate speeches corpus, see https://www.research.ibm.com/haifa/dept/vst/debating_data.shtml#Debate%20Speech%20Analysis

Despite the interest in the complexity class MA, the randomized analog of NP, just a few natural MA-complete problems are known. The first problem was found by (Bravyi and Terhal, SIAM Journal of Computing 2009); it was then followed by (Crosson, Bacon and Brown, PRE 2010) and (Bravyi, Quantum Information and Computation 2015). Surprisingly, two of these problems are defined using terminology from quantum computation, while the third is inspired by quantum computation and keeps a physical terminology. This prevents classical complexity theorists from studying these problems, delaying potential progress, e.g., on the NP vs. MA question. Here, we define two new combinatorial problems and prove their MA-completeness. The first problem, ACAC, gets as input a succinctly described graph, with some marked vertices. The problem is to decide whether there is a connected component with only unmarked vertices, or the graph is far from having this property. The second problem, SetCSP, generalizes standard constraint satisfaction problem (CSP) into constraints involving sets of strings. Technically, our proof that SetCSP is MA-complete is based on an observation by (Aharonov and Grilo, FOCS 2019), in which it was noted that a restricted case of Bravyi and Terhal's problem (namely, the uniform case) is already MA-complete; a simple trick allows to state this restricted case using combinatorial language. The fact that the first, more natural, problem of ACAC is MA-hard follows quite naturally from this proof, while the containment of ACAC in MA is based on the theory of random walks. We notice that the main result of Aharonov and Grilo carries over to the SetCSP problem in a straightforward way, implying that finding a gap-amplification procedure for SetCSP (as in Dinur's PCP proof) is equivalent to MA=NP. This provides an alternative new path towards the major problem of derandomizing MA., Comment: Minor changes; Published in the proceedings of ITCS 2021

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced., Comment: 7 pages, 5 figures