@article{10023, abstract = {We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms of an appropriate Hilbertian norm; and in the case of the relative entropy, in terms of a Dirichlet form which morphs into a version of the familiar Fisher information under conditions of detailed balance. Here we obtain trajectorial versions of these results, valid along almost every path of the random motion and most transparent in the backwards direction of time. Martingale arguments and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer and Tschiderer for conservative diffusions. Extensions are developed to general “convex divergences” and to countable state-spaces. The steepest descent and gradient flow properties for the variance, the relative entropy, and appropriate generalizations, are studied along with their respective geometries under conditions of detailed balance, leading to a very direct proof for the HWI inequality of Otto and Villani in the present context.}, author = {Karatzas, Ioannis and Maas, Jan and Schachermayer, Walter}, issn = {1526-7555}, journal = {Communications in Information and Systems}, keywords = {Markov Chain, relative entropy, time reversal, steepest descent, gradient flow}, number = {4}, pages = {481--536}, publisher = {International Press of Boston}, title = {{Trajectorial dissipation and gradient flow for the relative entropy in Markov chains}}, doi = {10.4310/CIS.2021.v21.n4.a1}, volume = {21}, year = {2021}, } @article{10204, abstract = {Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals.}, author = {Osang, Georg F and Edelsbrunner, Herbert and Saadatfar, Mohammad}, issn = {1744-6848}, journal = {Soft Matter}, number = {40}, pages = {9107--9115}, publisher = {Royal Society of Chemistry}, title = {{Topological signatures and stability of hexagonal close packing and Barlow stackings}}, doi = {10.1039/d1sm00774b}, volume = {17}, year = {2021}, } @phdthesis{9733, abstract = {This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.}, author = {Feliciangeli, Dario}, issn = {2663-337X}, pages = {180}, publisher = {Institute of Science and Technology Austria}, title = {{The polaron at strong coupling}}, doi = {10.15479/at:ista:9733}, year = {2021}, } @article{10222, abstract = {Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density.}, author = {Akopyan, Arseniy and Edelsbrunner, Herbert and Nikitenko, Anton}, issn = {1944-950X}, journal = {Experimental Mathematics}, pages = {1--15}, publisher = {Taylor & Francis}, title = {{The beauty of random polytopes inscribed in the 2-sphere}}, doi = {10.1080/10586458.2021.1980459}, year = {2021}, } @article{9241, abstract = {Volumetric light transport is a pervasive physical phenomenon, and therefore its accurate simulation is important for a broad array of disciplines. While suitable mathematical models for computing the transport are now available, obtaining the necessary material parameters needed to drive such simulations is a challenging task: direct measurements of these parameters from material samples are seldom possible. Building on the inverse scattering paradigm, we present a novel measurement approach which indirectly infers the transport parameters from extrinsic observations of multiple-scattered radiance. The novelty of the proposed approach lies in replacing structured illumination with a structured reflector bonded to the sample, and a robust fitting procedure that largely compensates for potential systematic errors in the calibration of the setup. We show the feasibility of our approach by validating simulations of complex 3D compositions of the measured materials against physical prints, using photo-polymer resins. As presented in this paper, our technique yields colorspace data suitable for accurate appearance reproduction in the area of 3D printing. Beyond that, and without fundamental changes to the basic measurement methodology, it could equally well be used to obtain spectral measurements that are useful for other application areas.}, author = {Elek, Oskar and Zhang, Ran and Sumin, Denis and Myszkowski, Karol and Bickel, Bernd and Wilkie, Alexander and Křivánek, Jaroslav and Weyrich, Tim}, issn = {1094-4087}, journal = {Optics Express}, number = {5}, pages = {7568--7588}, publisher = {Optica Publishing Group}, title = {{Robust and practical measurement of volume transport parameters in solid photo-polymer materials for 3D printing}}, doi = {10.1364/OE.406095}, volume = {29}, year = {2021}, } @inproceedings{10666, abstract = {Adversarial training is an effective method to train deep learning models that are resilient to norm-bounded perturbations, with the cost of nominal performance drop. While adversarial training appears to enhance the robustness and safety of a deep model deployed in open-world decision-critical applications, counterintuitively, it induces undesired behaviors in robot learning settings. In this paper, we show theoretically and experimentally that neural controllers obtained via adversarial training are subjected to three types of defects, namely transient, systematic, and conditional errors. We first generalize adversarial training to a safety-domain optimization scheme allowing for more generic specifications. We then prove that such a learning process tends to cause certain error profiles. We support our theoretical results by a thorough experimental safety analysis in a robot-learning task. Our results suggest that adversarial training is not yet ready for robot learning.}, author = {Lechner, Mathias and Hasani, Ramin and Grosu, Radu and Rus, Daniela and Henzinger, Thomas A}, booktitle = {2021 IEEE International Conference on Robotics and Automation}, isbn = {978-1-7281-9078-5}, issn = {2577-087X}, location = {Xi'an, China}, pages = {4140--4147}, publisher = {IEEE}, title = {{Adversarial training is not ready for robot learning}}, doi = {10.1109/ICRA48506.2021.9561036}, year = {2021}, } @inproceedings{9678, abstract = {We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and more generally for locally optimal semi-matchings. The prior work by Czygrinow et al. (DISC 2012) finds a stable orientation in O(Δ^5) rounds in graphs of maximum degree Δ, while we improve it to O(Δ^4) and also prove a lower bound of Ω(Δ). For the more general problem of locally optimal semi-matchings, the prior upper bound is O(S^5) and our new algorithm runs in O(C · S^4) rounds, which is an improvement for C = o(S); here C and S are the maximum degrees of customers and servers, respectively.}, author = {Brandt, Sebastian and Keller, Barbara and Rybicki, Joel and Suomela, Jukka and Uitto, Jara}, booktitle = {Annual ACM Symposium on Parallelism in Algorithms and Architectures}, isbn = {9781450380706}, location = { Virtual Event, United States}, pages = {129--139}, publisher = {Association for Computing Machinery}, title = {{Efficient load-balancing through distributed token dropping}}, doi = {10.1145/3409964.3461785}, year = {2021}, } @inproceedings{10667, abstract = {Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction. We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems. Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate. In particular, we show that the certificate network guarantees the safety of the system over a subset of the BNN weight posterior's support. Our method first computes a safe weight set and then alters the BNN's weight posterior to reject samples outside this set. Moreover, we show how to extend our approach to a safe-exploration reinforcement learning setting, in order to avoid unsafe trajectories during the training of the policy. We evaluate our approach on a series of reinforcement learning benchmarks, including non-Lyapunovian safety specifications.}, author = {Lechner, Mathias and Žikelić, Ðorđe and Chatterjee, Krishnendu and Henzinger, Thomas A}, booktitle = {35th Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {Virtual}, publisher = {Neural Information Processing Systems Foundation}, title = {{Infinite time horizon safety of Bayesian neural networks}}, doi = {10.48550/arXiv.2111.03165}, year = {2021}, } @inproceedings{10670, abstract = {Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.}, author = {Vorbach, Charles J and Hasani, Ramin and Amini, Alexander and Lechner, Mathias and Rus, Daniela}, booktitle = {35th Conference on Neural Information Processing Systems}, issn = {1049-5258}, location = {Virtual}, publisher = {Neural Information Processing Systems Foundation}, title = {{Causal navigation by continuous-time neural networks}}, year = {2021}, } @article{9293, abstract = {We consider planning problems for graphs, Markov Decision Processes (MDPs), and games on graphs in an explicit state space. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems with k different target sets: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in a given sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds, based on the boolean matrix multiplication (BMM) conjecture and strong exponential time hypothesis (SETH), establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs, and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) problem-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.}, author = {Chatterjee, Krishnendu and Dvořák, Wolfgang and Henzinger, Monika H and Svozil, Alexander}, issn = {0004-3702}, journal = {Artificial Intelligence}, number = {8}, publisher = {Elsevier}, title = {{Algorithms and conditional lower bounds for planning problems}}, doi = {10.1016/j.artint.2021.103499}, volume = {297}, year = {2021}, } @inproceedings{9441, abstract = {Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. }, author = {Boissonnat, Jean-Daniel and Kachanovich, Siargey and Wintraecken, Mathijs}, booktitle = {37th International Symposium on Computational Geometry}, isbn = {978-3-95977-184-9}, issn = {1868-8969}, location = {Virtual}, pages = {17:1--17:16}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations}}, doi = {10.4230/LIPIcs.SoCG.2021.17}, volume = {189}, year = {2021}, } @inproceedings{9345, abstract = {Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction.}, author = {Edelsbrunner, Herbert and Heiss, Teresa and Kurlin , Vitaliy and Smith, Philip and Wintraecken, Mathijs}, booktitle = {37th International Symposium on Computational Geometry}, issn = {1868-8969}, location = {Virtual}, pages = {32:1--32:16}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The density fingerprint of a periodic point set}}, doi = {10.4230/LIPIcs.SoCG.2021.32}, volume = {189}, year = {2021}, } @inproceedings{10041, abstract = {Yao’s garbling scheme is one of the most fundamental cryptographic constructions. Lindell and Pinkas (Journal of Cryptograhy 2009) gave a formal proof of security in the selective setting where the adversary chooses the challenge inputs before seeing the garbled circuit assuming secure symmetric-key encryption (and hence one-way functions). This was followed by results, both positive and negative, concerning its security in the, stronger, adaptive setting. Applebaum et al. (Crypto 2013) showed that it cannot satisfy adaptive security as is, due to a simple incompressibility argument. Jafargholi and Wichs (TCC 2017) considered a natural adaptation of Yao’s scheme (where the output mapping is sent in the online phase, together with the garbled input) that circumvents this negative result, and proved that it is adaptively secure, at least for shallow circuits. In particular, they showed that for the class of circuits of depth δ , the loss in security is at most exponential in δ . The above results all concern the simulation-based notion of security. In this work, we show that the upper bound of Jafargholi and Wichs is basically optimal in a strong sense. As our main result, we show that there exists a family of Boolean circuits, one for each depth δ∈N , such that any black-box reduction proving the adaptive indistinguishability of the natural adaptation of Yao’s scheme from any symmetric-key encryption has to lose a factor that is exponential in δ√ . Since indistinguishability is a weaker notion than simulation, our bound also applies to adaptive simulation. To establish our results, we build on the recent approach of Kamath et al. (Eprint 2021), which uses pebbling lower bounds in conjunction with oracle separations to prove fine-grained lower bounds on loss in cryptographic security.}, author = {Kamath Hosdurg, Chethan and Klein, Karen and Pietrzak, Krzysztof Z and Wichs, Daniel}, booktitle = {41st Annual International Cryptology Conference}, isbn = {978-3-030-84244-4}, issn = {1611-3349}, location = {Virtual}, pages = {486--515}, publisher = {Springer Nature}, title = {{Limits on the Adaptive Security of Yao’s Garbling}}, doi = {10.1007/978-3-030-84245-1_17}, volume = {12826}, year = {2021}, } @phdthesis{10035, abstract = {Many security definitions come in two flavors: a stronger “adaptive” flavor, where the adversary can arbitrarily make various choices during the course of the attack, and a weaker “selective” flavor where the adversary must commit to some or all of their choices a-priori. For example, in the context of identity-based encryption, selective security requires the adversary to decide on the identity of the attacked party at the very beginning of the game whereas adaptive security allows the attacker to first see the master public key and some secret keys before making this choice. Often, it appears to be much easier to achieve selective security than it is to achieve adaptive security. A series of several recent works shows how to cleverly achieve adaptive security in several such scenarios including generalized selective decryption [Pan07][FJP15], constrained PRFs [FKPR14], and Yao’s garbled circuits [JW16]. Although the above works expressed vague intuition that they share a common technique, the connection was never made precise. In this work we present a new framework (published at Crypto ’17 [JKK+17a]) that connects all of these works and allows us to present them in a unified and simplified fashion. Having the framework in place, we show how to achieve adaptive security for proxy re-encryption schemes (published at PKC ’19 [FKKP19]) and provide the first adaptive security proofs for continuous group key agreement protocols (published at S&P ’21 [KPW+21]). Questioning optimality of our framework, we then show that currently used proof techniques cannot lead to significantly better security guarantees for "graph-building" games (published at TCC ’21 [KKPW21a]). These games cover generalized selective decryption, as well as the security of prominent constructions for constrained PRFs, continuous group key agreement, and proxy re-encryption. Finally, we revisit the adaptive security of Yao’s garbled circuits and extend the analysis of Jafargholi and Wichs in two directions: While they prove adaptive security only for a modified construction with increased online complexity, we provide the first positive results for the original construction by Yao (published at TCC ’21 [KKP21a]). On the negative side, we prove that the results of Jafargholi and Wichs are essentially optimal by showing that no black-box reduction can provide a significantly better security bound (published at Crypto ’21 [KKPW21c]).}, author = {Klein, Karen}, issn = {2663-337X}, pages = {276}, publisher = {Institute of Science and Technology Austria}, title = {{On the adaptive security of graph-based games}}, doi = {10.15479/at:ista:10035}, year = {2021}, } @inproceedings{11453, abstract = {Neuronal computations depend on synaptic connectivity and intrinsic electrophysiological properties. Synaptic connectivity determines which inputs from presynaptic neurons are integrated, while cellular properties determine how inputs are filtered over time. Unlike their biological counterparts, most computational approaches to learning in simulated neural networks are limited to changes in synaptic connectivity. However, if intrinsic parameters change, neural computations are altered drastically. Here, we include the parameters that determine the intrinsic properties, e.g., time constants and reset potential, into the learning paradigm. Using sparse feedback signals that indicate target spike times, and gradient-based parameter updates, we show that the intrinsic parameters can be learned along with the synaptic weights to produce specific input-output functions. Specifically, we use a teacher-student paradigm in which a randomly initialised leaky integrate-and-fire or resonate-and-fire neuron must recover the parameters of a teacher neuron. We show that complex temporal functions can be learned online and without backpropagation through time, relying on event-based updates only. Our results are a step towards online learning of neural computations from ungraded and unsigned sparse feedback signals with a biologically inspired learning mechanism.}, author = {Braun, Lukas and Vogels, Tim P}, booktitle = {35th Conference on Neural Information Processing Systems}, isbn = {9781713845393}, issn = {1049-5258}, location = {Virtual, Online}, pages = {16437--16450}, publisher = {Neural Information Processing Systems Foundation}, title = {{Online learning of neural computations from sparse temporal feedback}}, volume = {20}, year = {2021}, } @inproceedings{11452, abstract = {We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a new quantized variant of Riemannian gradient descent to solve this problem, and prove that the algorithm converges with high probability under a set of necessary spherical-convexity properties. We give bounds on the number of bits transmitted by the algorithm under common initialization schemes, and investigate the dependency on the problem dimension in each case.}, author = {Alimisis, Foivos and Davies, Peter and Vandereycken, Bart and Alistarh, Dan-Adrian}, booktitle = {35th Conference on Neural Information Processing Systems}, isbn = {9781713845393}, issn = {1049-5258}, location = {Virtual, Online}, pages = {2823--2834}, publisher = {Neural Information Processing Systems Foundation}, title = {{Distributed principal component analysis with limited communication}}, volume = {4}, year = {2021}, } @article{22156, abstract = {Extending a recent breakthrough of Shitov, we prove that the chromatic number of the tensor product of two graphs can be a constant factor smaller than the minimum chromatic number of the two graphs. More precisely, we prove that there exists an absolute constant δ>0 such that for all c sufficiently large, there exist graphs G and H with chromatic number at least (1+δ)c for which χ(G×H)≤c.}, author = {He, Xiaoyu and Wigderson, Yuval}, issn = {0095-8956}, journal = {Journal of Combinatorial Theory, Series B}, keywords = {Graph coloring, Hedetniemi's conjecture}, pages = {485--494}, publisher = {Elsevier}, title = {{Hedetniemi's conjecture is asymptotically false}}, doi = {10.1016/j.jctb.2020.03.003}, volume = {146}, year = {2021}, } @article{9331, abstract = {Quantum entanglement has been generated and verified in cold-atom experiments and used to make atom-interferometric measurements below the shot-noise limit. However, current state-of-the-art cold-atom devices exploit separable (i.e., unentangled) atomic states. This perspective piece asks the question: can entanglement usefully improve cold-atom sensors, in the sense that it gives new sensing capabilities unachievable with current state-of-the-art devices? We briefly review the state-of-the-art in precision cold-atom sensing, focusing on clocks and inertial sensors, identifying the potential benefits entanglement could bring to these devices, and the challenges that need to be overcome to realize these benefits. We survey demonstrated methods of generating metrologically useful entanglement in cold-atom systems, note their relative strengths and weaknesses, and assess their prospects for near-to-medium term quantum-enhanced cold-atom sensing.}, author = {Szigeti, Stuart S. and Hosten, Onur and Haine, Simon A.}, issn = {0003-6951}, journal = {Applied Physics Letters}, number = {14}, publisher = {AIP Publishing}, title = {{Improving cold-atom sensors with quantum entanglement: Prospects and challenges}}, doi = {10.1063/5.0050235}, volume = {118}, year = {2021}, } @article{22161, abstract = {Recently, Souza introduced blowup Ramsey numbers as a gener- alization of bipartite Ramsey numbers. For graphs G and H, say G r −→ H if every r-edge-coloring of G contains a monochromatic copy of H. Let H[t] denote the t-blowup of H. Then the blowup Ramsey number of G, H, r, and t is defined as the minimum n such that G[n] r −→ H[t]. Souza proved upper and lower bounds on n that are exponential in t, and conjectured that the exponential constant does not depend on G. We prove that the dependence on G in the exponential constant is indeed unnecessary, but conjecture that some dependence on G is unavoidable. An important step in both Souza’s proof and ours is a theorem of Nikiforov, which says that if a graph contains a constant fraction of the possible copies of H, then it contains a blowup of H of logarithmic size. We also provide a new proof of this theorem with a better quantitative dependence.}, author = {Fox, Jacob and Luo, Sammy and Wigderson, Yuval}, issn = {2150-959X}, journal = {Journal of Combinatorics}, number = {1}, pages = {1--15}, publisher = {International Press of Boston}, title = {{Extremal and Ramsey results on graph blowups}}, doi = {10.4310/joc.2021.v12.n1.a1}, volume = {12}, year = {2021}, } @article{17132, abstract = {Extracellular recording is an accessible technique used in animals and humans to study the brain physiology and pathology. As the number of recording channels and their density grows it is natural to ask how much improvement the additional channels bring in and how we can optimally use the new capabilities for monitoring the brain. Here we show that for any given distribution of electrodes we can establish exactly what information about current sources in the brain can be recovered and what information is strictly unobservable. We demonstrate this in the general setting of previously proposed kernel Current Source Density method and illustrate it with simplified examples as well as using evoked potentials from the barrel cortex obtained with a Neuropixels probe and with compatible model data. We show that with conceptual separation of the estimation space from experimental setup one can recover sources not accessible to standard methods.}, author = {Chintaluri, Chaitanya and Bejtka, Marta and Średniawa, Władysław and Czerwiński, Michał and Dzik, Jakub M. and Jędrzejewska-Szmek, Joanna and Kondrakiewicz, Kacper and Kublik, Ewa and Wójcik, Daniel K.}, issn = {1553-7358}, journal = {PLOS Computational Biology}, number = {5}, publisher = {Public Library of Science}, title = {{What we can and what we cannot see with extracellular multielectrodes}}, doi = {10.1371/journal.pcbi.1008615}, volume = {17}, year = {2021}, }