# E. Cohen - The Rockefeller University, USA

## Contact Details

NameE. Cohen |
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AffiliationThe Rockefeller University, USA |
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CityNew York |
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CountryUnited States |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesQuantum Physics (21) Physics - Statistical Mechanics (6) Physics - Physics Education (6) Mathematics - Combinatorics (5) Computer Science - Data Structures and Algorithms (3) High Energy Physics - Theory (3) High Energy Physics - Experiment (3) Physics - Instrumentation and Detectors (3) Computer Science - Learning (2) Computer Science - Databases (1) Computer Science - Robotics (1) Mathematics - Mathematical Physics (1) Statistics - Methodology (1) Statistics - Theory (1) Mathematical Physics (1) Physics - Other (1) Computer Science - Information Retrieval (1) Computer Science - Networking and Internet Architecture (1) Computer Science - Cryptography and Security (1) General Relativity and Quantum Cosmology (1) Cosmology and Nongalactic Astrophysics (1) Mathematics - Group Theory (1) Mathematics - Probability (1) Mathematics - Statistics (1) |

## Publications Authored By E. Cohen

**Authors:**MicroBooNE collaboration, R. Acciarri, C. Adams, R. An, J. Anthony, J. Asaadi, M. Auger, L. Bagby, S. Balasubramanian, B. Baller, C. Barnes, G. Barr, M. Bass, F. Bay, M. Bishai, A. Blake, T. Bolton, B. Bullard, L. Camilleri, D. Caratelli, B. Carls, R. Castillo Fernandez, F. Cavanna, H. Chen, E. Church, D. Cianci, E. Cohen, G. H. Collin, J. M. Conrad, M. Convery, J. I. Crespo-Anadon, G. De Geronimo, M. Del Tutto, D. Devitt, S. Dytman, B. Eberly, A. Ereditato, L. Escudero Sanchez, J. Esquivel, A. A. Fadeeva, B. T. Fleming, W. Foreman, A. P. Furmanski, D. Garcia-Gamez, G. T. Garvey, V. Genty, D. Goeldi, S. Gollapinni, N. Graf, E. Gramellini, H. Greenlee, R. Grosso, R. Guenette, A. Hackenburg, P. Hamilton, O. Hen, J. Hewes, C. Hill, J. Ho, G. Horton-Smith, A. Hourlier, E. -C. Huang, C. James, J. Jan de Vries, C. -M. Jen, L. Jiang, R. A. Johnson, J. Joshi, H. Jostlein, D. Kaleko, G. Karagiorgi, W. Ketchum, B. Kirby, M. Kirby, T. Kobilarcik, I. Kreslo, A. Laube, S. Li, Y. Li, A. Lister, B. R. Littlejohn, S. Lockwitz, D. Lorca, W. C. Louis, M. Luethi, B. Lundberg, X. Luo, A. Marchionni, C. Mariani, J. Marshall, D. A. Martinez Caicedo, V. Meddage, T. Miceli, G. B. Mills, J. Moon, M. Mooney, C. D. Moore, J. Mousseau, R. Murrells, D. Naples, P. Nienaber, J. Nowak, O. Palamara, V. Paolone, V. Papavassiliou, S. F. Pate, Z. Pavlovic, E. Piasetzky, D. Porzio, G. Pulliam, X. Qian, J. L. Raaf, V. Radeka, A. Rafique, S. Rescia, L. Rochester, C. Rudolf von Rohr, B. Russell, D. W. Schmitz, A. Schukraft, W. Seligman, M. H. Shaevitz, J. Sinclair, A. Smith, E. L. Snider, M. Soderberg, S. Soldner-Rembold, S. R. Soleti, P. Spentzouris, J. Spitz, J. St. John, T. Strauss, A. M. Szelc, N. Tagg, K. Terao, M. Thomson, C. Thorn, M. Toups, Y. -T. Tsai, S. Tufanli, T. Usher, W. Van De Pontseele, R. G. Van de Water, B. Viren, M. Weber, D. A. Wickremasinghe, S. Wolbers, T. Wongjirad, K. Woodruff, T. Yang, L. Yates, B. Yu, G. P. Zeller, J. Zennamo, C. Zhang

The low-noise operation of readout electronics in a liquid argon time projection chamber (LArTPC) is critical to properly extract the distribution of ionization charge deposited on the wire planes of the TPC, especially for the induction planes. This paper describes the characteristics and mitigation of the observed noise in the MicroBooNE detector. The MicroBooNE's single-phase LArTPC comprises two induction planes and one collection sense wire plane with a total of 8256 wires. Read More

The final state proposal [G.T. Horowitz and J. Read More

The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic Molecular Dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which is then numerically simulated and directly compared with the original physical system. Read More

**Authors:**MicroBooNE collaboration, R. Acciarri, C. Adams, R. An, J. Anthony, J. Asaadi, M. Auger, L. Bagby, S. Balasubramanian, B. Baller, C. Barnes, G. Barr, M. Bass, F. Bay, M. Bishai, A. Blake, T. Bolton, L. Bugel, L. Camilleri, D. Caratelli, B. Carls, R. Castillo Fernandez, F. Cavanna, H. Chen, E. Church, D. Cianci, E. Cohen, G. H. Collin, J. M. Conrad, M. Convery, J. I. Crespo-Anadon, M. Del Tutto, D. Devitt, S. Dytman, B. Eberly, A. Ereditato, L. Escudero Sanchez, J. Esquivel, B. T. Fleming, W. Foreman, A. P. Furmanski, D. Garcia-Gamez, G. T. Garvey, V. Genty, D. Goeldi, S. Gollapinni, N. Graf, E. Gramellini, H. Greenlee, R. Grosso, R. Guenette, A. Hackenburg, P. Hamilton, O. Hen, J. Hewes, C. Hill, J. Ho, G. Horton-Smith, E. -C. Huang, C. James, J. Jan de Vries, C. -M. Jen, L. Jiang, R. A. Johnson, J. Joshi, H. Jostlein, D. Kaleko, G. Karagiorgi, W. Ketchum, B. Kirby, M. Kirby, T. Kobilarcik, I. Kreslo, A. Laube, Y. Li, A. Lister, B. R. Littlejohn, S. Lockwitz, D. Lorca, W. C. Louis, M. Luethi, B. Lundberg, X. Luo, A. Marchionni, C. Mariani, J. Marshall, D. A. Martinez Caicedo, V. Meddage, T. Miceli, G. B. Mills, J. Moon, M. Mooney, C. D. Moore, J. Mousseau, R. Murrells, D. Naples, P. Nienaber, J. Nowak, O. Palamara, V. Paolone, V. Papavassiliou, S. F. Pate, Z. Pavlovic, E. Piasetzky, D. Porzio, G. Pulliam, X. Qian, J. L. Raaf, A. Rafique, L. Rochester, C. Rudolf von Rohr, B. Russell, D. W. Schmitz, A. Schukraft, W. Seligman, M. H. Shaevitz, J. Sinclair, E. L. Snider, M. Soderberg, S. Soldner-Rembold, S. R. Soleti, P. Spentzouris, J. Spitz, J. St. John, T. Strauss, K. A. Sutton, A. M. Szelc, N. Tagg, K. Terao, M. Thomson, M. Toups, Y. -T. Tsai, S. Tufanli, T. Usher, R. G. Van de Water, B. Viren, M. Weber, D. A. Wickremasinghe, S. Wolbers, T. Wongjirad, K. Woodruff, T. Yang, L. Yates, G. P. Zeller, J. Zennamo, C. Zhang

The MicroBooNE liquid argon time projection chamber (LArTPC) has been taking data at Fermilab since 2015 collecting, in addition to neutrino beam, cosmic-ray muons. Results are presented on the reconstruction of Michel electrons produced by the decay at rest of cosmic-ray muons. Michel electrons are abundantly produced in the TPC, and given their well known energy spectrum can be used to study MicroBooNE's detector response to low-energy electrons (electrons with energies up to ~50 MeV). Read More

Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in arXiv:1702. Read More

**Authors:**MicroBooNE collaboration, P. Abratenko, R. Acciarri, C. Adams, R. An, J. Asaadi, M. Auger, L. Bagby, S. Balasubramanian, B. Baller, C. Barnes, G. Barr, M. Bass, F. Bay, M. Bishai, A. Blake, T. Bolton, L. Bugel, L. Camilleri, D. Caratelli, B. Carls, R. Castillo Fernandez, F. Cavanna, H. Chen, E. Church, D. Cianci, E. Cohen, G. H. Collin, J. M. Conrad, M. Convery, J. I. Crespo-Anadon, M. Del Tutto, D. Devitt, S. Dytman, B. Eberly, A. Ereditato, L. Escudero Sanchez, J. Esquivel, B. T. Fleming, W. Foreman, A. P. Furmanski, D. Garcia-Gamez, G. T. Garvey, V. Genty, D. Goeldi, S. Gollapinni, N. Graf, E. Gramellini, H. Greenlee, R. Grosso, R. Guenette, A. Hackenburg, P. Hamilton, O. Hen, J. Hewes, C. Hill, J. Ho, G. Horton-Smith, E. -C. Huang, C. James, J. Jan de Vries, C. -M. Jen, L. Jiang, R. A. Johnson, B. J. P. Jones, J. Joshi, H. Jostlein, D. Kaleko, L. N. Kalousis, G. Karagiorgi, W. Ketchum, B. Kirby, M. Kirby, T. Kobilarcik, I. Kreslo, A. Laube, Y. Li, A. Lister, B. R. Littlejohn, S. Lockwitz, D. Lorca, W. C. Louis, M. Luethi, B. Lundberg, X. Luo, A. Marchionni, C. Mariani, J. Marshall, D. A. Martinez Caicedo, V. Meddage, T. Miceli, G. B. Mills, J. Moon, M. Mooney, C. D. Moore, J. Mousseau, R. Murrells, D. Naples, P. Nienaber, J. Nowak, O. Palamara, V. Paolone, V. Papavassiliou, S. F. Pate, Z. Pavlovic, E. Piasetzky, D. Porzio, G. Pulliam, X. Qian, J. L. Raaf, A. Rafique, L. Rochester, C. Rudolf von Rohr, B. Russell, D. W. Schmitz, A. Schukraft, W. Seligman, M. H. Shaevitz, J. Sinclair, E. L. Snider, M. Soderberg, S. Soldner-Rembold, S. R. Soleti, P. Spentzouris, J. Spitz, J. St. John, T. Strauss, A. M. Szelc, N. Tagg, K. Terao, M. Thomson, M. Toups, Y. -T. Tsai, S. Tufanli, T. Usher, R. G. Van de Water, B. Viren, M. Weber, J. Weston, D. A. Wickremasinghe, S. Wolbers, T. Wongjirad, K. Woodruff, T. Yang, L. Yates, G. P. Zeller, J. Zennamo, C. Zhang

We discuss a technique for measuring a charged particle's momentum by means of multiple Coulomb scattering (MCS) in the MicroBooNE liquid argon time projection chamber (LArTPC). This method does not require the full particle ionization track to be contained inside of the detector volume as other track momentum reconstruction methods do (range-based momentum reconstruction and calorimetric momentum reconstruction). We motivate use of this technique, describe a tuning of the underlying phenomenological formula, quantify its performance on fully contained beam-neutrino-induced muon tracks both in simulation and in data, and quantify its performance on exiting muon tracks in simulation. Read More

Graph-based semi-supervised learning (SSL) algorithms predict labels for all nodes based on provided labels of a small set of seed nodes. Classic methods capture the graph structure through some underlying diffusion process that propagates through the graph edges. Spectral diffusion, which includes personalized page rank and label propagation, propagates through random walks. Read More

Motivated by a recent new type of randomized Distributed Denial of Service (DDoS) attacks on the Domain Name Service (DNS), we develop novel and efficient distinct heavy hitters algorithms and build an attack identification system that uses our algorithms. Heavy hitter detection in streams is a fundamental problem with many applications, including detecting certain DDoS attacks and anomalies. A (classic) heavy hitter (HH) in a stream of elements is a key (e. Read More

A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and postselections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. Read More

A gedankenexperiment is presented where an excited and a ground-state atom are positioned such that, within the former's half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms become entangled. Read More

By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an analytical expression for the time autocorrelation function of a general fluctuating quantity. Read More

Theoretical achievements, as well as much controversy, surround multiverse theory. Various types of multiverses, with an increasing amount of complexity, were suggested and thoroughly discussed by now. While these types are very different, they all share the same basic idea -- our physical reality consists of more than just one universe. Read More

The study of graph-based submodular maximization problems was initiated in a seminal work of Kempe, Kleinberg, and Tardos (2003): An {\em influence} function of subsets of nodes is defined by the graph structure and the aim is to find subsets of seed nodes with (approximately) optimal tradeoff of size and influence. Applications include viral marketing, monitoring, and active learning of node labels. This powerful formulation was studied for (generalized) {\em coverage} functions, where the influence of a seed set on a node is the maximum utility of a seed item to the node, and for pairwise {\em utility} based on reachability, distances, or reverse ranks. Read More

One of the most common statistics computed over data elements is the number of distinct keys. A thread of research pioneered by Flajolet and Martin three decades ago culminated in the design of optimal approximate counting sketches, which have size that is double logarithmic in the number of distinct keys and provide estimates with a small relative error. Moreover, the sketches are composable, and thus suitable for streamed, parallel, or distributed computation. Read More

The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. Read More

Let $H_{\mathrm{WR}}$ be the path on $3$ vertices with a loop at each vertex. D. Galvin conjectured, and E. Read More

Quantum computation strongly relies on the realisation, manipulation and control of qubits. A central method for realizing qubits is by creating a double-well potential system with a significant gap between the first two eigenvalues and the rest. In this work we first revisit the theoretical grounds underlying the double-well qubit dynamics, then proceed to suggest novel extensions of these principles to a triple-well qutrit with periodic boundary conditions, followed by a general d-well analysis of qudits. Read More

In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by the external force and alters the Gaussian structure of the system's fluctuations. By solving this extended equation, we demonstrate that the statistical properties of the fluctuations in these systems can be predicted from physical observables, such as the temperature and the hydrodynamic gradients. Read More

Are the electromagnetic scalar and vector potentials dispensable? Lev Vaidman has suggested that local interactions of gauge-invariant quantities, e.g. magnetic torques, suffice for the description of all quantum electromagnetic phenomena. Read More

Semi-supervised learning (SSL) is an indispensable tool when there are few labeled entities and many unlabeled entities for which we want to predict labels. With graph-based methods, entities correspond to nodes in a graph and edges represent strong relations. At the heart of SSL algorithms is the specification of a dense {\em kernel} of pairwise affinity values from the graph structure. Read More

"Self-diagnosis tasks" aim at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. The recitation classes in an introductory physics class (~200 students) were split into a control group and three experimental groups in which different levels of guidance was provided for performing the self-diagnosis activities. We have been a) investigating how students in each group performed on subsequent near and far transfer questions given as part of the exams; and b) comparing student's initial scores on their quizzes with their performance on the exams, as well as comparing student's self-diagnosis scores with their performance on the exams. Read More

Previously we discussed how well students in an introductory physics course diagnosed their mistakes on a quiz problem with different levels of scaffolding support. In that case, the problem they self-diagnosed was unusually difficult. We also discussed issues related to transfer, particularly the fact that the transfer problem in the midterm that corresponded to the self-diagnosed problem was a far transfer problem. Read More

Helping students learn from their own mistakes can help them develop habits of mind while learning physics content. Based upon cognitive apprenticeship model, we asked students to self-diagnose their mistakes and learn from reflecting on their problem solution. Varying levels of scaffolding support were provided to students in different groups to diagnose their errors on two context-rich problems that students originally solved in recitation quizzes. Read More

Expert problem solvers are characterized by continuous evaluation of their progress towards a solution. One characteristic of expertise is self-diagnosis directed towards elaboration of the solvers' conceptual understanding, knowledge organization or strategic approach. "Self-diagnosis tasks" aim at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. Read More

"Self-diagnosis tasks" aim at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. We have been investigating the extent to which introductory physics students can diagnose their own mistakes when explicitly asked to do so with different levels of scaffolding support provided to them. In our study in an introductory physics class with more than 200 students, the recitation classes were split into three different experimental groups in which different levels of guidance were provided for performing the self-diagnosis activities. Read More

Helping students learn to think like a physicist is an important goal of many introductory physics courses. One characteristic distinguishing more experienced physicists from novice students is that they make better use of problem solving as a learning opportunity. Experts were found to spend more time than novices in monitoring their work, reflecting upon their possibly deficient approach to solving a problem, reconsidering their choices as necessary, and extending and refining their knowledge structure. Read More

This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based on a very weak von Neumann coupling, is a unique kind of quantum measurement with numerous theoretical and practical applications. In contrast to other measurement techniques, it allows to gather a small amount of information regarding the quantum system, with only a negligible probability of collapsing it. Read More

In the EPR experiment, each measurement addresses the question "What spin value has this particle along this orientation?" The outcome then proves that the spin value has been affected by the distant experimenter's choice of spin orientation. We propose a new setting where the question is reversed: "What is the orientation along which this particle has this spin value?" It turns out that the orientation is similarly subject to nonlocal effects. To enable the reversal, each particle's interaction with a beam-splitter at t1 leaves its spin orientation superposed. Read More

We discuss in this chapter the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong relations between the three. We conclude with a brief presentation of the D-Wave computer and some future challenges. Read More

Retrocausal models of QM add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time arrows, such that each system can forecast future events for the other. The loop is avoided by the fact that the choice to abort an event thus forecasted leads to the destruction of the forecaster's past. Read More

We consider the Widom-Rowlinson model of two types of interacting particles on d-regular graphs. We prove a tight upper bound on the occupancy fraction, the expected fraction of vertices occupied by a particle under a random configuration from the model. The upper bound is achieved uniquely by unions of complete graphs on d+1 vertices, $K_{d+1}$'s. Read More

The problem of entanglement detection for arbitrary spin systems is analyzed. We demonstrate how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states. For achieving this goal, we construct a tripartite analogy between the degeneracy of entanglement witness eigenstates, tensor products of $SO(3)$ representations and classical lattice walks with special constraints. Read More

This paper consists of a few results, discovered and proved during the 2012-2013 research group at Eastern Oregon University. Inertia tables are a visual representation of the possible inertias of a given graph. The inertia of a graph counts the number of real positive and negative eigenvalues of its corresponding adjacency matrix. Read More

The multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional least squares approach to estimating the model parameters is biased and inconsistent. The generalized least squares, ordinary least squares and maximum likelihood estimators (under the assumption of Gaussian errors) were derived in the seminal paper of Gleser (1981). Read More

We maintain that the wavefunction is an ensemble property rather than an individual particle property. For individual particles, we propose an ontology underwritten by the Heisenberg representation. It consists of properties represented by deterministic operators, which may have nonlocal dynamics. Read More

Recently it was demonstrated, both theoretically and experimentally, how to separate a particle from its spin, or any other property, a phenomenon known as the "Quantum Cheshire Cat". We present two novel gedanken experiments, based on the quantum Zeno effect, suggesting a dynamical process thorough which this curious phenomenon occurs. We analyze, for the first time, a quantum current consisting of spin without mass. Read More

{\em Multi-objective sampling} is a powerful, versatile, but not well understood technique for mining large data sets. Consider a set of keys $x\in X$ and associated values $f_x \geq 0$. A weighted sample $S^{(f)}$ of this data taken with respect to weight $f$ allows us to estimate {\em segment-sum statistics} Sum$(f;H) = \sum_{x\in H} f_x$, where $H$ is a segment of the keys, with statistically-guaranteed quality that depends on sample size and the relative weight of the segment $H$. Read More

We investigate the motion of a single particle moving on a two-dimensional square lattice whose sites are occupied by right and left rotators. These left and right rotators deterministically rotate the particle's velocity to the right or left, respectively and \emph{flip} orientation from right to left or from left to right after scattering the particle. We study three types of configurations of left and right rotators, which we think of as types of media, through with the particle moves. Read More

Robots built from soft materials can alter their shape and size in a particular profile. This shape-changing ability could be extremely helpful for rescue robots and those operating in unknown terrains and environments. In changing shape, soft materials also store and release elastic energy, a feature that can be exploited for effective robot movement. Read More

The Madelung equations map the non-relativistic time-dependent Schrodinger equation into hydrodynamic equations of a virtual fluid. Here we show that an increase of the Boltzmann entropy of this Madelung fluid is proportional to the expectation value of its velocity divergence. Hence, entropy growth is accompanied by expansion resulting from the ability of the Madelung fluid to be compressible. Read More

For systems in nonequilibrium steady states, a novel modulated Gaussian probability distribution is derived to incorporate a new phenomenon of biased current fluctuations, discovered by recent laboratory experiments and confirmed by molecular dynamics simulations. Our results consistently extend Onsager-Machlup fluctuation theory for systems in thermal equilibrium. Connections with the principles of Statistical Mechanics due to Boltzmann and Gibbs are discussed. Read More

One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or sequential weak values evaluation. Indeed, weak measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. Read More

We study the motion of a particle moving on a two-dimensional honeycomb lattice, whose sites are randomly occupied by either right or left rotators, which rotate the particle's velocity to its right or left, according to deterministic rules. In the model we consider, the scatterers are each initially oriented to the right with probability $p\in[0,1]$. This is done independently, so that the initial configuration of scatterers, which forms the medium through which the particle moves, are both independent and identically distributed. Read More

In this paper we perform a novel analysis of quantum Gaussian channels in the context of weak measurements. Suppose Alice sends classical information to Bob using a quantum channel. Suppose Bob is allowed to use only weak measurements, what would be the channel capacity? We formulate weak measurement theory in these terms and discuss the above question. Read More

Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the distance, but by the number of nodes that are closer to $v$ than $u$. That is, by the {\em rank} of $u$ in an ordering of nodes by increasing distance from $v$. Read More

Catalan numbers arise in many enumerative contexts as the counting sequence of combinatorial structures. In this work, we consider natural Markov chains on some of the realizations of the Catalan sequence. While our main result is in deriving an $O(n^2 \log n)$ bound on the mixing time in $L_2$ (and hence total variation) distance for the random transposition chain on Dyck paths, we raise several open questions, including the optimality of the above bound. Read More

Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system's dynamics. We present a gedanken experiment where a single system apparently follows mutually exclusive paths simultaneously, each with probability one, depending on which measurement was performed. Read More

Among the (in)famous differences between classical and quantum mechanics, quantum counterfactuals seem to be the most intriguing. At the same time, they seem to underlie many quantum oddities. In this article, we propose a simple explanation for counterfactuals, on two levels. Read More

The Cramer-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramer-Rao lower bound for the estimation of a feature's position (e. Read More

Entanglement and nonlocality are studied in the framework of pre-/post-selected ensembles with the aid of weak measurements and the Two-State-Vector Formalism. In addition to the EPR-Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose pre- or post-selected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting "emerging correlations" between independent pre- and post-selected ensembles of particles. Read More